JP7655695B2 - Pressure loss estimation method, reaction method for controlling pressure loss, pressure loss estimation derivation device, and pressure loss estimation program - Google Patents

Description

Application of Article 30, Paragraph 2 of the Patent Law, Abstract of the 48th Petroleum and Petrochemical Symposium (Tokyo Symposium Commemorating the 60th Anniversary of the Founding), p. 129, Published on October 17, 2018

Application of Article 30, Paragraph 2 of the Patent Act 48th Petroleum and Petrochemical Symposium (Tokyo Symposium Commemorating 60th Anniversary of the Founding), held on October 17, 2018

Application of Article 30, Paragraph 2 of the Patent Act 44th Refining Panel Discussion, held on February 22, 2019

The present invention relates to a method for estimating pressure loss in a fixed-bed flow reaction in which a gas and/or liquid fluid is circulated through a reactor packed with a solid catalyst, a reaction method for controlling pressure loss, a pressure loss estimation device, and a pressure loss estimation program.

Conventionally, a reaction method in which gaseous and/or liquid reactants are circulated through a reactor packed with a solid catalyst is known as a fixed-bed flow reaction. In a fixed-bed flow reaction reactor, the flow of the fluid containing the reactants is lost due to resistance from the solid catalyst layer. This loss is expressed in terms of pressure and is called pressure loss.

Normally, reactors used in fixed-bed flow reactions have an upper limit on the pressure resistance determined by the material, structure, etc., and the pressure inside the reactor must be constantly monitored to prevent this upper limit from being reached. In other words, the reaction must be stopped before the pressure inside the reactor reaches the upper limit of the reactor's pressure resistance. In particular, if pressure loss increases suddenly, the reaction may have to be stopped urgently, which can have a significant negative impact on operation plans, etc. Therefore, from the perspective of stable operation, there is a high demand for a method to estimate the change in pressure loss over time.

If impurities are present in the fluid, the impurities may accumulate on the solid catalyst layer. Also, if the fluid contains compounds that contain carbon, coke may form in the reactor and accumulate on the solid catalyst layer. When impurities, coke, etc. accumulate on the solid catalyst layer, the voids in the solid catalyst layer gradually become clogged. This is thought to be one of the factors that cause an increase in pressure loss in fixed-bed flow-type reactions.

The Ergun equation is one of the well-known equations for calculating pressure loss when the fluid is a single phase gas or liquid. The Ergun equation has a wide range of application, from laminar to turbulent flow, and has been widely used for a long time (Non-Patent Document 1). In addition, many equations have been proposed for calculating pressure loss when the Ergun equation is expanded to a two-phase system of gas and liquid, and the Ergun-Larkins equation is one such known equation (Non-Patent Document 2).

Ergun, S., Chem. Eng. Prog., 48-2 (1952), 89-94. R. P. LARKINS et al., “Two-Phase Concurrent Flow in Packed Beds”, A. I. Ch. E. Journal, (1961) Vol. 7, No. 2, 231-239.

The Ergun formula, Ergun-Larkins formula, etc. are both formulas that derive an estimated value of pressure loss by substituting necessary parameters such as the void fraction of the solid catalyst layer in the reactor, the fluid density, the fluid viscosity, and the fluid linear velocity into the formula.

However, it is difficult to obtain all of the parameters required to derive an estimated value of pressure loss from the Ergun equation, the Ergun-Larkins equation, etc., over time while the reaction is taking place. Therefore, it is practically impossible to accurately estimate the change in pressure loss over time.

The present invention has been made in consideration of the above circumstances, and aims to provide a method for accurately estimating the change over time in pressure loss in a reactor in a fixed-bed flow reaction in which a one-phase fluid of gas or liquid, or a two-phase fluid of gas and liquid, is circulated through the reactor, a reaction method for controlling the pressure loss in the reactor, a pressure loss estimation device, and a pressure loss estimation program.

In order to solve the above problems, the present invention has the following aspects.
[1] A method for estimating a pressure drop in a reactor at any reaction time _tx in a fixed bed flow reaction in which a single-phase fluid of gas or liquid, or a two-phase fluid of gas and liquid, is circulated through a reactor packed with a solid catalyst, comprising the steps of:
Acquiring the viscosity μ of the fluid, the linear velocity u of the fluid, and the density ρ of the fluid at the reaction time t _x ;
A step of acquiring a total amount of impurities S IN in the fluid flowing into the reactor during a period (t _x -t _x-1 ) between another arbitrary reaction time t _x-1 before the reaction time t _x and the reaction time t _x , and a total amount of impurities S _OUT in the fluid flowing out of the _reactor ;
and substituting the obtained S _IN and S _OUT into the following formula (1) to derive the porosity ε _x of the solid catalyst layer in the reactor at the reaction time t _x ,
The obtained μ, u, ρ, and ε _x are substituted into an equation for calculating a pressure drop based on the viscosity of the fluid, the linear velocity of the fluid, the density of the fluid, and the porosity of the solid catalyst layer in the reactor, to derive a calculated value of the pressure drop, ΔP _cal ;
A method for estimating a pressure drop in a reactor, comprising: substituting the obtained ΔP _cal into the following formula (2) to obtain an estimated value ΔP _sim of the pressure drop in the reactor at the reaction time t _x :

（式（１）中、ε_ｘ－１は、前記反応経過時ｔ_ｘ－１における反応器内の固体触媒層の空隙率、αはチューニングファクターである。）

(In formula (1), ε _x-1 is the void fraction of the solid catalyst layer in the reactor at the reaction time t _x-1 , and α is a tuning factor.)

（式（２）中、σはチューニングファクターである。）
［２］ さらに前記反応経過時ｔ_ｘにおける反応温度Ｔ_ｔ（ｘ）を取得するステップを有し、
前記Ｔ_ｔ（ｘ）とコーキングの閾値Ｔ_Ｂの関係が、Ｔ_ｔ（ｘ）＞Ｔ_Ｂを満たすときには、前記反応器内の固体触媒層の空隙率ε_ｘを導出するステップにおいて、前記式（１）に代えて、下記式（１－１）に前記Ｓ_ＩＮ、前記Ｓ_ＯＵＴ、前記Ｔ_Ｂ、及び前記Ｔ_ｔ（ｘ）を代入して、前記反応経過時ｔ_ｘにおける前記反応器内の固体触媒層の空隙率ε_ｘを導出する［１］に記載の反応器内の圧力損失の推定方法。

(In formula (2), σ is a tuning factor.)
[2] Further, the method includes a step of acquiring a reaction temperature T _t(x) at a reaction time t _x ,
The method for estimating a pressure drop in a reactor according to [1], wherein, when a relationship between the Tt _(x) and a threshold value T _B for coking satisfies T _t(x) > T _B , in the step of deriving a porosity ε _x of the solid catalyst layer in the reactor, the S _IN , the S _OUT , the T _B , and the Tt _(x) are substituted into the following formula (1-1) instead of the formula (1) to derive a porosity ε _x of the solid catalyst layer in the reactor at the reaction time t _x .

（式（１－１）中、Ｒは気体定数、β、γはチューニングファクターである。）
［３］ 固体触媒を充填した反応器に気体若しくは液体の１相の流体、又は気体及び液体の２相の流体を流通させる固定床流通式反応における任意の反応経過時ｔ_ｘの前記反応器内の圧力損失を制御するための反応方法であって、
前記反応経過時ｔ_ｘより前の別の任意の反応経過時ｔ_ｘ－１から前記反応経過時ｔ_ｘの間（ｔ_ｘ－ｔ_ｘ－１）に前記反応器に流入した流体中の不純物総量Ｓ_ＩＮ、及び前記反応器から流出した流体中の不純物総量Ｓ_ＯＵＴを取得するステップと、
取得したＳ_ＩＮ及びＳ_ＯＵＴを下記式（３）に代入して、前記反応経過時ｔ_ｘにおける前記反応器内の固体触媒層の空隙率ε_ｘを導出するステップと、を有し、
所期の前記反応器内の圧力損失ΔＰ_ｘを下記式（４）に代入し、ΔＰ_ｃａｌを導出し、
得られたΔＰ_ｃａｌ及び前記ε_ｘを流体の粘度、流体の線速度、流体の密度、及び反応器内の固体触媒層の空隙率により圧力損失を計算する式に代入し、
前記圧力損失を計算する式が成立するように流体の粘度μ、流体の線速度ｕ、及び流体の密度ρを調整して反応を行うことを特徴とする反応器内の圧力損失を制御するための反応方法。

(In formula (1-1), R is a gas constant, and β and γ are tuning factors.)
[3] A reaction method for controlling a pressure drop in a reactor at any reaction time t _x in a fixed bed flow reaction in which a one-phase fluid of gas or liquid, or a two-phase fluid of gas and liquid is flowed through a reactor packed with a solid catalyst, comprising:
A step of acquiring a total amount of impurities S IN in the fluid flowing into the reactor during a period (t _x -t _x-1 ) between another arbitrary reaction time t _x-1 before the reaction time t _x and the reaction time t _x , and a total amount of impurities S _OUT in the fluid flowing out of the _reactor ;
and substituting the obtained S _IN and S _OUT into the following formula (3) to derive the porosity ε _x of the solid catalyst layer in the reactor at the reaction time t _x ,
The desired pressure drop ΔP _x in the reactor is substituted into the following formula (4) to derive ΔP _cal ,
The obtained ΔP _cal and the ε _x are substituted into an equation for calculating the pressure drop based on the viscosity of the fluid, the linear velocity of the fluid, the density of the fluid, and the void fraction of the solid catalyst layer in the reactor,
A reaction method for controlling pressure drop in a reactor, comprising: carrying out a reaction by adjusting the viscosity μ of a fluid, the linear velocity u of the fluid, and the density ρ of the fluid so that the equation for calculating the pressure drop is satisfied.

（式（３）中、ε_ｘ－１は、前記反応経過時ｔ_ｘ－１における反応器内の固体触媒層の空隙率、αはチューニングファクターである。）

(In formula (3), ε _x-1 is the void fraction of the solid catalyst layer in the reactor at the reaction time t _x-1 , and α is a tuning factor.)

（式（４）中、σはチューニングファクターである。）
［４］ さらに前記反応経過時ｔ_ｘにおける反応温度Ｔ_ｔ（ｘ）を取得するステップを有し、
前記Ｔ_ｔ（ｘ）とコーキングの閾値Ｔ_Ｂの関係が、Ｔ_ｔ（ｘ）＞Ｔ_Ｂを満たすときには、前記反応器内の固体触媒層の空隙率ε_ｘを導出するステップにおいて、前記式（３）に代えて、下記式（３－１）に前記Ｓ_ＩＮ、前記Ｓ_ＯＵＴ、前記Ｔ_Ｂ、及び前記Ｔ_ｔ（ｘ）を代入して、前記反応経過時ｔ_ｘにおける前記反応器内の固体触媒層の空隙率ε_ｘを導出する［３］に記載の反応器内の圧力損失を制御するための反応方法。

(In equation (4), σ is a tuning factor.)
[4] Further, the method includes a step of acquiring a reaction temperature T _t(x) at a reaction time t _x ,
When the relationship between the Tt _(x) and the threshold value T _B for coking satisfies T _t(x) > T _B , in the step of deriving the porosity ε _x of the solid catalyst layer in the reactor, the S _IN , the S _OUT , the T _B , and the Tt _(x) are substituted into the following formula (3-1) instead of the formula (3) to derive the porosity ε _x of the solid catalyst layer in the reactor at the reaction time t _x .

［５］ 固体触媒を充填した反応器に気体若しくは液体の１相の流体、又は気体及び液体の２相の流体を流通させる固定床流通式反応における任意の反応経過時ｔ_ｘの前記反応器内の圧力損失推定導出装置であって、
前記反応経過時ｔ_ｘにおける流体の粘度μ、流体の線速度ｕ、及び流体の密度ρを取得する流体情報取得部と、
前記反応経過時ｔ_ｘより前の別の任意の反応経過時ｔ_ｘ－１から前記反応経過時ｔ_ｘの間（ｔ_ｘ－ｔ_ｘ－１）に前記反応器に流入した流体中の不純物総量Ｓ_ＩＮ、及び前記反応器から流出した流体中の不純物総量Ｓ_ＯＵＴを取得する不純物情報取得部と、
取得したＳ_ＩＮ及びＳ_ＯＵＴを下記式（５）に代入して、前記反応経過時ｔ_ｘにおける前記反応器内の固体触媒層の空隙率ε_ｘを導出する空隙率導出部と、
取得した前記μ、前記ｕ、前記ρ、及び前記ε_ｘを流体の粘度、流体の線速度、流体の密度、及び反応器内の固体触媒層の空隙率により圧力損失を計算する式に代入し、圧力損失の計算値であるΔＰ_ｃａｌを導出するΔＰ_ｃａｌ導出部と、
得られたΔＰ_ｃａｌを下記式（６）に代入し、前記反応経過時ｔ_ｘにおける前記反応器内の圧力損失の推定値ΔＰ_ｓｉｍを導出する圧力損失の推定値導出部と、
前記圧力損失の推定値ΔＰ_ｓｉｍを出力する出力部と、
を有することを特徴とする圧力損失推定導出装置。

[5] A device for estimating a pressure drop in a reactor at any reaction time _tx in a fixed bed flow reaction in which a one-phase fluid of gas or liquid, or a two-phase fluid of gas and liquid, is circulated through a reactor packed with a solid catalyst, comprising:
A fluid information acquisition unit that acquires the viscosity μ of the fluid, the linear velocity u of the fluid, and the density ρ of the fluid at the reaction time t _x ;
an impurity information acquisition unit that acquires a total amount S IN of impurities in the fluid flowing into the reactor during a period (t _x -t _x-1 ) between another arbitrary reaction time t _{x -1} before the reaction time t _x and the reaction time t _x and a total amount S _OUT of impurities in the fluid flowing out of the reactor;
a porosity deriving unit that derives the porosity ε _x of the solid catalyst layer in the reactor at the reaction time t _x by substituting the obtained S _IN and S _OUT into the following formula (5);
a ΔP cal derivation unit that substitutes the obtained μ, u, ρ, and ε _x into an equation for calculating a pressure drop based on a viscosity of a fluid, a linear velocity of the fluid, a density of the fluid, and a porosity of a solid catalyst layer in a reactor, and derives a calculated value of the pressure drop, ΔP _{cal ;}
a pressure loss estimated value deriving unit that substitutes the obtained ΔP _cal into the following formula (6) to derive an estimated value ΔP _sim of the pressure loss in the reactor at the reaction time t _x ;
an output unit that outputs the estimated pressure loss value ΔP _sim ;
A pressure loss estimation deriving device comprising:

（式（５）中、ε_ｘ－１は、前記反応経過時ｔ_ｘ－１における反応器内の固体触媒層の空隙率、αはチューニングファクターである。）

(In formula (5), ε _x-1 is the void fraction of the solid catalyst layer in the reactor at the reaction time t _x-1 , and α is a tuning factor.)

（式（６）中、σはチューニングファクターである。）
［６］ さらに前記反応経過時ｔ_ｘにおける反応温度Ｔ_ｔ（ｘ）を取得する温度情報取得部を有し、
前記Ｔ_ｔ（ｘ）とコーキングの閾値Ｔ_Ｂの関係が、Ｔ_ｔ（ｘ）＞Ｔ_Ｂを満たすときには、前記反応器内の固体触媒層の空隙率ε_ｘを導出する空隙率導出部において、前記式（５）に代えて、下記式（５－１）に前記Ｓ_ＩＮ、前記Ｓ_ＯＵＴ、前記Ｔ_Ｂ、及びＴ_ｔ（ｘ）を代入して、前記反応経過時ｔ_ｘにおける前記反応器内の固体触媒層の空隙率ε_ｘを導出する［５］に記載の圧力損失推定導出装置。

(In equation (6), σ is a tuning factor.)
[6] Further, a temperature information acquisition unit is provided for acquiring a reaction temperature T _t(x) at a reaction time t _x ,
When the relationship between the Tt _(x) and a threshold value T _B for coking satisfies T _t(x) > T _B , a porosity deriving unit for deriving the porosity ε _x of the solid catalyst layer in the reactor is configured to substitute the S _IN , the S _OUT , the T _B , and Tt _(x) into the following formula (5-1) instead of the formula (5) to derive the porosity ε _x of the solid catalyst layer in the reactor at the reaction time t _x .

（式（５－１）中、Ｒは気体定数、β、γはチューニングファクターである。）
［７］ コンピュータを、［５］又は［６］に記載の圧力損失推定導出装置の各部として機能させるための圧力損失推定プログラム。

(In formula (5-1), R is a gas constant, and β and γ are tuning factors.)
[7] A pressure loss estimation program for causing a computer to function as each part of the pressure loss estimation derivation device according to [5] or [6].

The pressure loss estimation method according to the present invention can provide a method for accurately estimating the change in pressure loss over time in a reactor in a fixed-bed flow reaction in which a one-phase fluid of gas or liquid, or a two-phase fluid of gas and liquid, is circulated through the reactor, a reaction method for controlling the pressure loss in the reactor, a pressure loss estimation device, and a pressure loss estimation program.

FIG. 4 is a diagram showing a flow for obtaining an estimated value of pressure loss in a reactor according to one embodiment. FIG. 4 is a diagram showing a flow for obtaining an estimated value of pressure loss in a reactor according to one embodiment. 1 is a configuration block diagram of a pressure loss estimation derivation device according to an embodiment. FIG. FIG. 2 is a diagram showing the change over time of the actual measured value of pressure drop in the hydrotreating reaction of heavy hydrocarbons and the change over time of the estimated value obtained by the pressure drop estimation method of one embodiment. FIG. 2 is a diagram showing the change over time of the actual measured value of pressure drop in the hydrotreating reaction of heavy hydrocarbons and the change over time of the estimated value obtained by the pressure drop estimation method of one embodiment.

The following describes in detail the embodiments of the present invention. However, the following description is merely an example of the embodiments of the present invention, and the present invention is not limited to these contents, and can be modified and implemented within the scope of the gist of the invention.

<Pressure loss estimation method>
The pressure drop estimation method of the present embodiment is a method for estimating a pressure drop in an arbitrary reaction time t _x in a fixed bed flow reaction in which a one-phase fluid of gas or liquid, or a two-phase fluid of gas and liquid is circulated through a reactor packed with a solid catalyst, the method including the steps of: acquiring a viscosity μ of the _fluid , a linear velocity u of the fluid, and a density ρ of the fluid at the reaction time t _x ( _S1A in FIG _{. 1); acquiring a total amount S IN of impurities in the fluid flowing into the reactor and a total amount S OUT of impurities in the fluid flowing out of the reactor during the period (t x -t x-1 ) from another} arbitrary reaction time t _{x-1 before the reaction time t x} to the reaction time t x; and substituting the acquired S _IN and S _OUT into the following formula (1) to obtain a porosity ε of the solid catalyst layer in the reactor at the reaction time t _x: and a step of deriving _{ΔP cal} , which is a calculated value of the pressure drop (S2 in FIG. 1), by substituting the acquired μ, u, ρ, and ε _x into an equation for calculating a pressure drop based on a viscosity of a fluid, a linear velocity of a fluid, a density of a fluid, and a porosity of a solid catalyst layer in a reactor (S1B-1 in FIG. 1). The method is characterized in that the method includes a step _of deriving ΔP _cal , which is a calculated value of the pressure drop, into the following equation (2) to obtain an estimated value ΔP _sim of the pressure drop in the reactor at the reaction time t _x (S3 in FIG. 1).

In the above formula (1), ε _x-1 is the void fraction of the solid catalyst layer in the reactor at the reaction time t _x-1 , and α is a tuning factor. The method for setting α will be described later.

In the above formula (2), σ is a tuning factor. The method for setting σ will be described later.

In a fixed bed flow reaction, scale accumulates in the solid catalyst layer in the reactor over the reaction time, and the porosity of the solid catalyst layer decreases. The main cause of scale formation is the deposition of impurities, typically metal compounds, contained in the fluid containing the reactants on the solid catalyst layer. In the formula (1), the difference (S _IN -S OUT ) between the total amount of impurities S IN in the fluid flowing into the reactor between the reaction time t _x-1 and the reaction time t _x (t _x -t _x-1 ) and the total amount of impurities S _OUT in the fluid flowing out of the reactor is calculated, and it is considered that the amount of impurities (S _{IN -S OUT} ) is deposited on the solid catalyst layer, reducing the porosity of the solid catalyst layer in _the reactor.

The S _IN can be obtained by measuring the impurity concentration (for example, ppm) in the fluid before flowing into the reactor during the reaction time t _x-1 to the reaction time t _x (t _{x -t x-1 ) and calculating the product with the total amount of fluid flowing into the reactor during that time (for example, kg). The S OUT can be obtained by measuring the impurity concentration (for example, ppm) in the fluid after flowing out of the reactor during the reaction time t x-1 to the} reaction time t _x (t _x -t _x-1 ) and calculating the product with the total amount of fluid flowing out of the reactor during that time (for example, kg). The impurity concentration in the fluid flowing into the reactor and the fluid flowing out of the reactor may be obtained at least once during the reaction time t _x-1 to t _x (t _x -t _x-1 ), and if obtained twice or more times, the average value thereof can be used.

When a plurality of different solid catalyst layers are formed in a reactor, the porosity ε _x(n) of each solid catalyst layer at the reaction time t _x can be calculated, for example, by the following formula (1-A) (method (1 _{) of deriving ε x(n)} ).

In the formula (1-A), n is an integer of 2 or more and represents the number of different solid catalyst layers. ε _x(n) is the porosity of the n-th solid catalyst layer from the reactor inlet side at the reaction time t _x , ε _x-1(n) is the porosity of the n-th solid catalyst layer from the reactor inlet side at the reaction time t _x-1 , α _(n) is the tuning factor of the n-th solid catalyst layer from the reactor inlet side, R _(n) is the solid catalyst layer ratio of the n-th solid catalyst layer from the reactor inlet side, and the sum of R ₍₁₎ to R _(n) is 1. _{S IN} and S _OUT are the same as above.

In the present invention, the solid catalyst layer ratio R _(n) is a coefficient for apportioning how much of the difference (S _{IN -S OUT} ) between the total amount of impurities S IN in the fluid flowing into the reactor between the reaction time t _{x-1 and the reaction time t x} (t _{x -t} x- ₁ ) and the total amount of impurities S _OUT in the fluid flowing out of the reactor is deposited in each of the plurality of different solid catalyst layers.

When a plurality of different solid catalyst layers are formed in a reactor, the porosity ε _x(n) of each solid catalyst layer at the reaction time t _x can also be calculated, for example, by the following formula (1-B) (method (2) of deriving ε _x(n) ).

In the formula (1-B), n is an integer of 2 or more and represents the number of different solid catalyst layers. ε _x(n) is the porosity of the n-th solid catalyst layer from the reactor inlet side at the reaction time t _x , ε _x-1(n) is the porosity of the n-th solid catalyst layer from the reactor inlet side at the reaction time t _x-1 , α _const is a tuning factor, and S _IN and S _OUT are the same as above. In the _{ε x(n)} derivation method (2), the same α _const is used to derive the porosities of the n solid catalyst layers, and the solid catalyst layer ratio is not used, so that the pressure loss can be estimated more simply than in the ε _x(n) derivation method (1).

In the present invention, when a plurality of different solid catalyst layers are formed in a reactor, it is preferable to employ the above-mentioned ε _x(n) deriving method (2) from the viewpoint of being able to estimate the pressure drop more simply.

In this specification, "impurities" means substances other than the reactants of the target chemical reaction at the reactor inlet, and substances originating from the "impurities" at the reactor inlet at the reactor outlet. In addition, there is no need to measure substances that are generally inactive in chemical reactions, such as nitrogen gas. It is sufficient to appropriately select impurities that accumulate on the solid catalyst layer according to the target chemical reaction, and measure only the above substances.
The method for measuring the concentration of impurities in a fluid can be a method known in the art depending on the type of impurity and fluid. Examples of the method include an inductively coupled plasma mass spectrometer ICP-MS, ICP-OES, ICP-AES, various types of chromatography such as liquid chromatography and gas chromatography, and fluorescent X-ray analysis.
The total amount of fluid flowing into the reactor during the reaction time t _x-1 to the reaction time t _x (t _x -t _x-1 ) and the total amount of fluid flowing out of the reactor can be obtained from a flow meter, changes in the liquid levels of the raw material tank and the product tank, etc. The total amount of fluid flowing into the reactor during the reaction time t _x-1 to the reaction time t _x (t _x -t _x-1 ) and the total amount of fluid flowing out of the reactor can also be controlled to a desired amount by a mass flow controller, a control valve, a pump, a compressor, etc.

The porosity ε _x-1 of the solid catalyst layer in the reactor at the reaction time t _x-1 in the formula (1) can be derived by measuring, for example, the porosity ε _x- 2 of the solid catalyst layer in the reactor at another arbitrary reaction time t _x-2 before the reaction time t _x-1 , the total amount of impurities S _IN in the fluid flowing into the reactor between the reaction time t _x- 2 and the reaction time t _x-1 , and the total amount of impurities S _OUT in the fluid flowing out of the reactor by the above-mentioned method and substituting them into the formula (1). That is, if the porosity ε ₀ of the solid catalyst layer in the reactor at the start of the reaction is known, the change over time in the porosity ε of the solid catalyst layer in the reactor can be obtained by repeatedly applying the above formula (1) thereafter.

The porosity ε ₀ of the solid catalyst layer in the reactor at the start of the reaction can be obtained, for example, by measuring the packing density BD (unit: kg/m ³ , for example) of the solid catalyst layer, the true density ρ _cat (unit: kg/m ³ , for example) of the packed solid catalyst, and the pore volume PV (unit: m ³ /kg, for example) of the packed solid catalyst, and calculating ε ₀ = 1 - (BD × (1/ρ _cat + PV)).
The packing density BD of the solid catalyst layer can be obtained by calculating BD=W _cat /V cat from the packing volume V _cat (unit: m ³ , for example) of the solid catalyst layer and the packing weight _{W cat (} unit: kg, for example) of the solid catalyst.
The packed volume V _cat of the solid catalyst layer can be obtained by multiplying the layer height (unit: m, for example) of the solid catalyst layer by the cross-sectional area (unit: m ² , for example) of the reactor (for example, a cylindrical tubular reactor). The method for measuring the layer height of the solid catalyst layer will be described later.
The true density ρ _cat of the solid catalyst can be measured by a method known in the art, for example, by measurement using a pycnometer method. The pycnometer method is a measurement method based on Archimedes' principle, and includes a liquid phase method and a gas phase method as a measurement means.
The pore volume PV of the solid catalyst can be obtained by mercury porosimetry or gas (nitrogen gas, etc.) adsorption method.

(Method 1 for setting tuning factors α (α _const ) and σ)
When a single solid catalyst layer is formed in the reactor, the tuning factor α in the formula (1) and the tuning factor σ in the formula (2) can be set, for example, by the following method (method 1 for setting α and σ).
The estimated value ΔP _sim of the pressure drop in the reactor at any reaction time t _x is derived from the above formula (1), a formula for calculating the pressure drop from the viscosity of the fluid, the linear velocity of the fluid, the density of the fluid, and the void fraction of the solid catalyst layer in the reactor, and the above formula (2). At this time, since α and σ are not determined, ΔP _sim is a function of α and σ.
The values of α and σ can be set so that the relationship between the actual measured value ΔP of the pressure loss at the reaction time t _x and the ΔP _sim satisfies ΔP=ΔP _sim .

When a plurality of different solid catalyst layers are formed in a reactor and the porosity ε _x(n) of each solid catalyst layer is derived by the above-mentioned ε _x(n) derivation method (2), the tuning factor α _const in the above-mentioned formula (1-B) and the tuning factor σ in the above-mentioned formula (2) can be set, for example, by the following method (method 1 for setting α _const and σ).
The calculated pressure loss ΔP _cal(n) of each solid catalyst layer in the reactor at any reaction time t _x is derived from the above formula (1-B), a formula for calculating pressure loss from the viscosity of the fluid, the linear velocity of the fluid, the density of the fluid, and the porosity of the solid catalyst layer in the reactor (n is an integer of 2 or more and represents the number of different solid catalyst layers. The same applies below). At this time, ΔP _cal(n) is a function of α _const . Next, the calculated pressure loss ΔP cal of all solid catalyst layers is obtained as a function of α _const by summing the calculated pressure loss ΔP _{cal (n)} of each solid catalyst layer. The calculated pressure loss ΔP _cal of all solid catalyst layers obtained is substituted into the above formula (2) to derive the estimated pressure loss ΔP _sim of all solid catalyst layers. At this time, since α _const and σ are not determined, ΔP _sim is a function of α _const and σ.
The values of α _const and σ can be set so that the relationship between the actual measured value ΔP of the pressure loss at the reaction time t _x and the ΔP _sim satisfies ΔP=ΔP _sim .

It is preferable to compare the estimated pressure loss ΔP _sim with the actual pressure loss ΔP at a plurality of reaction time points and determine tuning factors α (α _const ) and σ. For example, ΔP _sim and ΔP are obtained at any 15 or more reaction time points, _{and α (α const )} and σ can be set so that the ratio ΔP _(ave ) /ΔP _{sim ( ave)} of the respective average values ΔP _sim (ave) and ΔP (ave) approaches 1.

(Method 2 of Setting Tuning Factors α (α _const ), σ)
When a single solid catalyst layer is formed in the reactor, the tuning factors α and σ may be set by the following method (method 2 for setting α and σ).
The estimated value ΔP _sim of the pressure drop in the reactor at the initial stage t _int of the reaction is derived from the equation for calculating the pressure drop from the viscosity of the fluid, the linear velocity of the fluid, the density of the fluid, and the porosity of the solid catalyst layer in the reactor, and from the above-mentioned equation (2). At this time, the porosity of the solid catalyst layer in the reactor at the start of the reaction, ε _0, is used as the porosity of the solid catalyst layer in the reactor. In this case, ΔP _sim is a function of σ.
The value of σ can be set so that the relationship between the actual measured value ΔP of the pressure loss at the initial reaction start time t _int and the ΔP _sim satisfies ΔP=ΔP _sim .

The void ratio of the solid catalyst layer in the reactor at the initial time t _int of the reaction is set as ε ₀ , and the estimated value ΔP _sim of the pressure drop in the reactor at any time t _x of the reaction after the initial time t _int of the reaction is derived from the above formula (1), the formula for calculating the pressure drop from the viscosity of the fluid, the linear velocity of the fluid, the density of the fluid, and the void ratio of the solid catalyst layer in the reactor, and the above formula (2). At this time, σ is already determined, so ΔP _sim is a function of α.
The value of α can be set so that the relationship between the actual measured value ΔP of the pressure loss at the reaction time t _x and the ΔP _sim satisfies ΔP=ΔP _sim .

When a plurality of different solid catalyst layers are formed in a reactor and the porosity ε _x(n) of each solid catalyst layer is derived by the above-mentioned ε _x(n) deriving method (2), the tuning factor α _const in the above-mentioned formula (1-B) and the tuning factor σ in the above-mentioned formula (2) may be set by the following method (method 2 for setting α _const and σ).
The calculated pressure loss ΔP _{cal (n)} of each solid catalyst layer in the reactor at the beginning of the reaction t _int is derived from a formula for calculating pressure loss based on the viscosity of the fluid, the linear velocity of the fluid, the density of the fluid, and the porosity of the solid catalyst layer in the reactor. At this time, the porosity ε _{0 (n)} of each solid catalyst layer in the reactor at the start of the reaction is used as the porosity of each solid catalyst layer in the reactor. Then, the calculated pressure loss ΔP cal of all solid catalyst layers is obtained by summing the calculated pressure loss ΔP _{cal (n)} of each solid catalyst layer. The calculated pressure loss ΔP _cal of all solid catalyst layers obtained is substituted into the above formula (2) to derive the estimated pressure loss ΔP _sim of all solid catalyst layers. In this case, ΔP _sim is a function of σ.
The value of σ can be set so that the relationship between the actual measured value ΔP of the pressure loss at the initial reaction start time t _int and the ΔP _sim satisfies ΔP=ΔP _sim .

The porosity of each solid catalyst layer in the reactor at the initial time t _int of the reaction is set as ε _0(n) , and the calculated pressure loss ΔP _cal(n) of each solid catalyst layer in the reactor at any reaction time t _x after the initial time t _int of the reaction is derived from the above formula (1-B), the equation for calculating the pressure loss from the viscosity of the fluid, the linear velocity of the fluid, the density of the fluid, and the porosity of the solid catalyst layer in the reactor. At this time, ΔP _cal(n) is a function of α _const . Next, the calculated pressure loss ΔP _cal of all solid catalyst layers is obtained as a function of α _const by summing the calculated pressure loss ΔP _cal (n) of each solid catalyst layer. The calculated pressure loss ΔP _cal of all solid catalyst layers obtained is substituted into the above formula (2) to derive the estimated pressure loss ΔP _sim of all solid catalyst layers. At this time, since σ is already determined, ΔP _sim is a function of α _const .
The value of α _const can be set so that the relationship between the actual measured value ΔP of the pressure loss at the reaction time t _x and the ΔP _sim is ΔP=ΔP _sim .

In this specification, the early stage of the reaction in the second method for setting α (α _const ) and σ means the time when the reaction progresses at which V _flow /V _{cat , which is the ratio of the total volume (V flow ) of the fluid flowing into the reactor between the start of the reaction and the early stage of the reaction to the packed volume (V cat ) of} the solid catalyst layer, becomes 100 or less. Since almost no impurities are deposited in the solid catalyst layer at the early stage of the reaction when the above-mentioned relationship holds, σ and α (α _const ) can be determined stepwise and uniquely by approximately using ε ₀ as the void fraction of the solid catalyst layer in the reactor.

When the reaction is carried out in a multi-tubular reactor having a plurality of reactors, it is preferable to set the tuning factors α (α _const ) and σ for each reactor.

<Formula for calculating pressure drop based on fluid viscosity, fluid linear velocity, fluid density, and void fraction of solid catalyst layer in reactor>
As a formula for calculating the pressure drop based on the viscosity of the fluid, the linear velocity of the fluid, the density of the fluid, and the porosity of the solid catalyst layer in the reactor, a formula known in the art can be used. When the fluid is a single phase of gas or liquid, examples of the formula for calculating the pressure drop in the reactor include the Ergun formula, the Blake-Kozeny formula, the Burke-Plummer formula, the Kozeny-Carman formula, and the Fanning formula. When the fluid is a two-phase of gas and liquid, examples of the formula for calculating the pressure drop in the reactor include the Ergun-Larkins formula, the Lockhart-Martinelli formula, and the like, but are not limited thereto.
Hereinafter, the Ergun formula will be described as a formula for calculating the pressure drop in a reactor when the fluid is a single phase of gas or liquid, and the Ergun-Larkins formula will be described as a formula for calculating the pressure drop in a reactor when the fluid is a two-phase of gas and liquid, but the present invention is not limited to these formulas.

<Ergun method>
In a fixed bed flow reaction, the calculated value of the pressure drop in the reactor when the fluid is one phase of gas or liquid can be derived by the Ergun equation represented by the following formula (7). In this embodiment, the calculated value of the pressure drop in the reactor obtained by the Ergun equation is defined as ΔP1 _cal .

In the above formula (7), a, b, and m are constants in the Ergun formula, ε is the porosity of the solid catalyst layer in the reactor, μ is the viscosity of the fluid [kg/ms], u is the linear velocity of the fluid [m/s], ρ is the density of the fluid [kg/ ^m3 ], dp is the spherical diameter [m] when the solid catalyst is assumed to be a sphere, and H is the layer height of the solid catalyst [m].

In the above formula (7), a, b, and m are constants and are empirically determined values. For example, if the solid catalyst is spherical, a = 150, b = 1.75, and m = 3.0 can be used. For example, if the solid catalyst is not spherical, a = 180, b = 1.80, and m = 3.6 can be used.

In this embodiment, ε in the formula (7) is ε _x derived from the formula (1) or the formula (1-1) described later. μ is the viscosity of the fluid at the reaction temperature [kg/ms]. When the fluid is a gas, for example, the composition analysis results obtained by gas chromatography are introduced into a process simulator and calculated from the results. When the fluid is a liquid, for example, the results obtained from JIS K 2283 "Crude oil and petroleum products - Kinematic viscosity test method and viscosity index calculation method" are multiplied by the density converted to 15 ° C. obtained from JIS K2249 "Crude oil and petroleum products - Density test method and density, mass, and volume conversion table" to obtain the temperature conversion. Note that, at the reaction temperature of a general fixed bed flow reaction, the viscosity of the fluid, both gas and liquid, does not change so much as to affect the pressure loss in the reactor, so the value once obtained can be used continuously as a fixed value. ρ is the density of the fluid at the reaction temperature [kg/m ³ ]. When the fluid is a gas, for example, the composition analysis results obtained by gas chromatography are introduced into a process simulator, and the calculated results are considered to be constant. The density corresponding to the composition is corrected for temperature and pressure. When the fluid is a liquid, for example, the density converted to 15°C obtained by JIS K2249 "Crude oil and petroleum products - Density test method and density, mass, and volume conversion table" is corrected by temperature. u is the linear velocity of the fluid at the reaction temperature [m/s], and can be obtained by dividing the flow rate of the fluid [m ³ /s] by the cross-sectional area [m ² ] of the reactor (for example, a cylindrical tubular reactor). The flow rate of the fluid can be obtained by the same method as that described in the step of obtaining S _IN and S _OUT .

dp is the spherical diameter [m] when the solid catalyst is assumed to be a sphere. The shape of the solid catalyst used in the fixed bed flow reaction is selected according to the application, but ring-shaped, cylindrical, tablet-shaped, honeycomb-shaped, three-leaf-shaped, four-leaf-shaped, and even spherical catalyst shapes are often used.
In this embodiment, if the filled solid catalyst is spherical, its spherical diameter can be taken as dp. On the other hand, if the solid catalyst is not spherical, the spherical diameter can be calculated assuming that the solid catalyst is a sphere, and this diameter can be taken as dp. As described in a known document (Ind. Eng. Chem. Des. Dev. 1986, 25, 1034-1036), for example, if it is a cylinder, it can be calculated by formula (8-1), if it is a three-leaf clover, it can be calculated by formula (8-2), and if it is a four-leaf clover, it can be calculated by formula (8-3).

In the formulas (8-1) to (8-3), L is the average major axis [m] of the solid catalyst, and D is the average minor axis [m] of the solid catalyst. The average major axis and the average minor axis of the solid catalyst can be determined by measuring the major axis and the minor axis of, for example, 50 or more solid catalysts, and averaging the results.
In the present invention, the dp of the solid catalyst is measured before the start of the reaction, and the value of dp does not change during the reaction.

H is the bed height of the solid catalyst [m]. The bed height of the solid catalyst can be measured by a method known in the art when the solid catalyst is packed before the start of the reaction. The bed height of the solid catalyst can be measured, for example, by measuring the bed height of the catalyst when it is packed.
In the present invention, the bed height of the solid catalyst does not change during the reaction.

The above parameters are substituted into the formula (7) to derive ΔP1 _cal . Then, the obtained ΔP1 _cal is substituted into ΔP _cal in the formula (2) to obtain an estimated value ΔP _sim of the pressure loss in the reactor at the reaction time t _x (hereinafter, the estimated value of the pressure loss in the reactor when the fluid is one phase of gas or liquid may be referred to as ΔP1 _sim ).

<Ergun-Larkins style>
In a fixed bed flow reaction, the calculated value of the pressure drop in the reactor when the fluid is two-phase, that is, gas and liquid, can be derived by the Ergun-Larkins equation composed of the following equations (9) to (14). In this embodiment, the calculated value of the pressure drop in the reactor obtained by the Ergun-Larkins equation is defined as ΔP2 _cal .

In the formula (9), _δL is ΔP _cal /H of the liquid, _δG is ΔP _cal /H of the gas, _δLG is ΔP _cal /H of the gas-liquid, χ=( _δL / _δG ) ^1/2 , and 0.05<χ<30.

In the formula (10), R _L is the liquid holdup.

In the formula (11), ρ _m is the gas-liquid average density, ρ _L is the liquid density, ρ _G is the gas density, and R _L is the same as above.

The derivation of the calculated value ΔP2 _cal of the pressure drop in the reactor by the Ergun-Larkins equation will be described below.
First, δ _L and δ _G are derived by the Ergun equation as follows (Equation (13) and Equation (14) below).

In the above formula (13), a, b, and m are constants in the Ergun formula, ε is the porosity of the solid catalyst layer in the reactor, _μL is the viscosity of the liquid [kg/ms], _uL is the linear velocity of the liquid [m/s], _ρL is the density of the liquid [kg/ ^m3 ], dp is the spherical diameter [m] when the solid catalyst is assumed to be a sphere, and H is the height of the catalyst layer [m]. The method of determining these values is as explained in the Ergun formula.
In this embodiment, ε in the above formula (13) is ε _x derived from the above formula (1) or the formula (1-1) described below.

In the above formula (14), a, b, and m are constants in the Ergun formula, ε is the void fraction of the solid catalyst layer in the reactor, μ _G is the gas viscosity [kg/ms], u _G is the gas linear velocity [m/s], ρ _G is the gas density [kg/m ³ ], dp is the spherical diameter [m] when the solid catalyst is assumed to be a sphere, and H is the catalyst layer height [m]. The method of determining these values is as explained in the Ergun formula.
In this embodiment, ε in the above formula (14) is ε _x derived from the above formula (1) or the formula (1-1) described below.

From the obtained δ _L and δ _G , χ = (δ _L / δ _G ) ^1/2 is derived. Next, δ _LG is derived from the above formula (9) using δ _L , δ _G , and χ, and R _L is derived from the above formula (10). Next, ρ _m is derived from the above formula (11) using the obtained R _L. Then, ΔP2 _cal is derived from the above formula (12) using the obtained δ _LG and ρ _m . Then, by substituting the obtained ΔP2 _cal into ΔP _cal in the above formula (2), an estimated value ΔP _sim of the pressure loss in the reactor at the reaction time t _x (hereinafter, the estimated value of the pressure loss in the reactor when the fluid is two-phase, that is, gas and liquid, may be denoted as ΔP2 _sim ) can be obtained.

In the method for estimating pressure drop according to the present invention, when a plurality of different solid catalyst layers are formed in a reactor, the calculated value ΔP _{cal (n)} of the pressure drop in each solid catalyst layer is derived by the above-mentioned method, and these are integrated to obtain the calculated value ΔP _cal of the pressure drop of all the solid catalyst layers. Then, by substituting the obtained ΔP _cal into the above formula (2), the estimated value ΔP _sim of the pressure drop in the reactor when a plurality of different solid catalyst layers are formed in the reactor can be obtained.

The ΔP _sim obtained by the method for estimating pressure drop in a reactor of the present invention is preferably ΔP/ΔP _sim on average from 0.50 to 1.50, more preferably from 0.80 to 1.20, where ΔP is the actual measured value of pressure drop in the reactor. The average ΔP/ΔP _sim can be obtained, for example, by measuring ΔP/ΔP _sim at 15 or more points.

When the average value of ΔP/ _ΔPsim in a predetermined period falls outside the range, it is preferable to reset the tuning factor α. When the average value of ΔP/ _ΔPsim in a predetermined period falls outside the range, it suggests that the increase in pressure loss is caused not only by the accumulation of impurities in the fluid on the solid catalyst layer but also by other factors.

In the case where a single solid catalyst layer is formed in the reactor, when the average value of ΔP/ΔP _sim in a predetermined period falls outside the above range, it is preferable to reset the tuning factor α as follows.
The estimated value ΔP _sim of the pressure drop in the reactor at any reaction time t _x after the average value of ΔP/ΔP _sim in a predetermined period falls outside the range is derived from the above formula (1), a formula for calculating the pressure drop from the viscosity of the fluid, the linear velocity of the fluid, the density of the fluid, and the porosity of the solid catalyst layer in the reactor, and the above formula (2). At this time, the value of α may be reset so that the relationship between the actual pressure drop value ΔP at the reaction time t _x and the above ΔP _sim is ΔP = ΔP _sim .

In the case where a plurality of different solid catalyst layers are formed in a reactor and the porosity ε _x(n) of each solid catalyst layer is derived by the above-mentioned ε _x(n) deriving method (2), when the average value of ΔP/ΔP _sim in a predetermined period falls outside the above-mentioned range, it is preferable to reset the tuning factor α _const as follows.
The calculated pressure loss ΔP _cal(n) of each solid catalyst layer in the reactor at any reaction time t _x after the average value of ΔP/ΔP _sim in a predetermined period falls outside the range is derived from the above formula (1-B), the equation for calculating pressure loss from the viscosity of the fluid, the linear velocity of the fluid, the density of the fluid, and the porosity of the solid catalyst layer in the reactor. Then, the calculated pressure loss ΔP cal of all solid catalyst layers is obtained by summing the calculated pressure loss ΔP _{cal (n)} of each solid catalyst layer. The calculated pressure loss ΔP _cal of all solid catalyst layers obtained is substituted into the above formula (2) to derive the estimated pressure loss ΔP _sim of all solid catalyst layers. At this time, the value of α _const may be reset so that the relationship between the measured pressure loss value ΔP at the reaction time t _x and the ΔP _sim is ΔP=ΔP _sim .

It is preferable to compare the estimated pressure loss value ΔP _{sim with the actual pressure loss value ΔP after the average value of ΔP/ΔP sim in} a predetermined period falls outside the range at a plurality of reaction times, and to re-determine the tuning factor α (α _const ). For example, the ΔP _sim and the ΔP after the average value of ΔP/ΔP _sim in a predetermined period falls outside the range can be obtained at any 15 or more reaction times, and α (α _const ) can be re-set so that the ratio ΔP _(ave) /ΔP _{sim ( ave)} of the respective average values ΔP sim _(ave) and ΔP (ave) approaches 1 as close as possible.

The fact that the average value of ΔP/ _ΔPsim in the above-mentioned predetermined period is outside the above-mentioned range suggests that the porosity of the solid catalyst layer is reduced due to other factors in addition to the deposition of impurities contained in the fluid containing reactants such as metal compounds on the solid catalyst layer. For example, when the fluid contains a compound containing carbon element, coke is generated in the reactor and the coke is deposited on the solid catalyst layer, which may reduce the porosity of the solid catalyst layer.

The inventors of the present application have newly found a method for estimating a pressure drop in a reactor based on the above-mentioned method for estimating a pressure drop in a reactor, which further includes a step of acquiring a reaction temperature T _t(x) at the reaction time t _x (S1C in FIG. 2), and when the relationship between the T _{t(x) and} a threshold value T _B for coking satisfies T t(x) > T _B , in a step of deriving a porosity ε _x of the solid catalyst layer in the reactor, the S _IN , S _OUT , T _B , and T _t(x) are substituted into the following formula (1-1) instead of the formula (1) to derive a porosity ε _x of the solid catalyst layer in the reactor at the reaction time t _x (S1BC in FIG. 2), thereby estimating a change in the porosity of the solid catalyst layer over time and a pressure drop in a reactor due to the change in the porosity over time, taking into account not only the deposition of impurities in the solid catalyst layer but also the deposition of coke in the solid catalyst layer.

（式（１－１）中、Ｒは気体定数、β、γはチューニングファクターである。）

(In formula (1-1), R is a gas constant, and β and γ are tuning factors.)

As the reaction temperature Tt _(x) at the reaction time _tx , for example, the maximum temperature of the solid catalyst layer (hot spot temperature), the weight average temperature (WABT) of the solid catalyst layer, the inlet temperature of the reactor, the outlet temperature of the reactor, the average temperature of the inlet temperature of the reactor and the outlet temperature of the reactor, etc. can be used, among which it is preferable to use the maximum temperature of the solid catalyst layer. The above-mentioned temperature can be obtained, for example, by a thermometer in the reactor.

In the formula (1-1), the coking threshold T _B is the temperature at which coke is generated and begins to accumulate on the solid catalyst layer. The coking threshold is uniquely determined when a combination of the type of solid catalyst, the type of fluid containing reactants, and the liquid hourly space velocity (LHSV) and/or gas hourly space velocity (GHSV) of the fluid relative to the solid catalyst is determined. In other words, once the above combination is determined, T _B becomes a constant value. A method for acquiring the coking threshold T _B will be described below, but this method is merely an example, and the method for acquiring T _B is not limited thereto.

(Method 1 for obtaining the coking threshold T _B )
As described above, the threshold value of coking, T _B , is the temperature at which coke is generated and begins to accumulate on the solid catalyst layer. Therefore, in the case of a reaction in which the solid catalyst can be extracted over time, the extracted solid catalyst can be analyzed by elemental analysis or the like, and the reaction temperature at which the carbon concentration in the solid catalyst reaches a certain value or more can be taken as T _B. The certain value can be, for example, 0.05 mass% or more. The extraction and elemental analysis of the solid catalyst are preferably performed at reaction temperature intervals of 5 to 20°C, more preferably 5 to 10°C. The reaction temperature is as described above, and it is preferable to adopt the maximum temperature of the solid catalyst layer.
In this method, the coking threshold value T _B may be obtained while performing a reaction in an actual reaction system, or may be obtained in advance in a laboratory or bench scale that is smaller than the actual reaction system. When the coking threshold value T _B is obtained in advance in a laboratory or bench scale, as described above, the type of solid catalyst, the type of fluid containing reactants, and the LHSV and/or GHSV of the fluid relative to the solid catalyst may be set to be the same as the reaction conditions in the actual reaction system.
In an actual machine, it is often difficult to extract the catalyst over time, so in the method 1 for obtaining the coking threshold value T _B , it is preferable to obtain the coking threshold value T _B in advance on a laboratory or bench scale.

(Method 2 for obtaining the coking threshold T _B )
As described above, when coke begins to form, the coke starts to accumulate on the solid catalyst layer, gradually blocking the voids in the solid catalyst layer and increasing the pressure drop. In addition, in a fixed-bed flow reaction, the activity of the solid catalyst decreases over time due to various factors, so the reaction is carried out while increasing the reaction temperature over time in order to keep the activity of the entire reactor constant.
The inventors of the present application have studied the relationship between the reaction temperature and the measured value of the pressure drop in the reactor using a model of a hydrotreating reaction of heavy hydrocarbon oil, and have found that when the measured value of the pressure drop in the reactor is plotted against the reaction temperature in the early stage of the reaction when no coke has accumulated on the solid catalyst layer, a linear relationship (line 1) expressed by y = _a1x + _b1 is obtained. In line 1, y is the measured value of the pressure drop in the reactor, x is the reaction temperature, _a1 is the slope, and _b1 is the intercept. The reaction temperature is as explained above, and it is preferable to adopt the maximum temperature of the solid catalyst layer, and the same applies below.

As a result of further investigation, the inventors of the present application found that when the actual measured value of the pressure drop in the reactor after coke started to deposit on the solid catalyst layer was plotted against the reaction temperature, the plot significantly deviated upward from the straight line 1.
It was also found that when the measured value of the pressure drop in the reactor was plotted against the reaction temperature after the coke started to deposit on the solid catalyst layer, a new linear relationship (line 2) expressed by y = _a2x + _b2 was obtained. In line 2, y is the measured value of the pressure drop in the reactor, x is the reaction temperature, _a2 is the slope and satisfies _a2 > _a1 , and _b2 is the intercept and satisfies _b2 < _b1 .
That is, the inventors of the present application have found that when the measured value of the pressure drop in the reactor is plotted against the reaction temperature, the plot shifts from the line 1 to the line 2 before and after the start of deposition of coke on the solid catalyst layer, and T _B can be obtained as the reaction temperature at the intersection of the line 1 and the line 2 (the inflection point from the line 1 to the line 2).

The method for measuring the inflection point will be specifically described. From the start of the reaction, the actual pressure loss in the reactor and the reaction temperature are obtained over time, plotted, and line 1 is obtained using Excel or the like. For example, the above plot is performed at M points from the start of the reaction, and line 1 expressed by y = a ₁ x + b ₁ is obtained. M is a positive integer, for example, 5 to 350. Next, the reaction temperature at the M+1th point is substituted for x in the equation for line 1 to obtain y _(M+1) . ΔP _(M+1) / y _(M+1), which is the ratio of the obtained y ( _M+1) to the actual pressure loss value ΔP _(M+1) in the reactor at the M+1th point, is calculated.
When the ΔP _(M+1) /y _(M+1) is between 0.8 and 1.2, it is judged as a plot on the line 1, and this plot is also included to recalculate _a1 and _b1 of line 1. At the M+2 point and thereafter, the ratio between the calculated value and the pressure loss in the reactor is calculated in the same manner, and when the ratio is within the range of 0.8 to 1.2, the same process as for the M+1 point described above is carried out.

When the ratio exceeds 1.2, it can be determined that coke is generated, the coke starts to accumulate on the solid catalyst layer, and the plot of the actual pressure drop in the reactor against the reaction temperature shifts from the line 1 to the line 2. At N points after the point at which the ratio exceeds 1.2, the actual pressure drop in the reactor and the reaction temperature are obtained over time and plotted, and line 2 expressed by y = a ₂ x + b ₂ is obtained using Excel or the like. N is a positive integer, for example, 5 to 350.
Then, the intersection point of the straight line 1 and the straight line 2 is found, and the coking threshold value T _B can be obtained as x at the intersection point.
In this method, the coking threshold value T _B may be obtained while performing a reaction in an actual reaction system, or may be obtained in advance in a laboratory or bench scale that is smaller than the actual reaction system. When the coking threshold value T _B is obtained in advance in a laboratory or bench scale, as described above, the type of solid catalyst, the type of fluid containing reactants, and the LHSV and/or GHSV of the fluid relative to the solid catalyst may be set to be the same as the reaction conditions in the actual reaction system.

The method 2 for obtaining the coking threshold value T _B is preferable to the method 1 for obtaining the coking threshold value T _B in that it is not necessary to extract the solid catalyst and therefore is not necessary to stop the reaction.

The tuning factor α can continue to use the value set when T _t(x) ≦T _B by the above-mentioned method even after T _t(x) >T _B.
The tuning factors β and γ can be set, for example, by the following method.

(Method 1 for setting tuning factors β and γ)
The estimated pressure drop ΔP _sim in the reactor at any reaction time t _x when the relationship between the reaction temperature T _t(x) and the coking threshold T _B first satisfies T _t(x) > T _B is derived from the above formula (1-1), the formula for calculating the pressure drop from the viscosity of the fluid, the linear velocity of the fluid, the density of the fluid, and the void fraction of the solid catalyst layer in the reactor, and the above formula (2). At this time, since β and γ are not determined, ΔP _sim is a function of β and γ.
The values of β and γ can be set so that the relationship between the actual measured value ΔP of the pressure loss at the reaction time t _x and the ΔP _sim satisfies ΔP=ΔP _sim .

It is preferable to compare the estimated pressure loss ΔP _sim with the measured pressure loss ΔP at a plurality of reaction times subsequent to an arbitrary reaction time t _x at which the relationship between the reaction temperature T t _(x) and the coking threshold value T _B first satisfies T _t(x) > T _B , and determine the tuning factors β and γ. For example, the ΔP _sim and the ΔP are obtained at any 15 or more reaction times, and β and γ can be set so that the ratio ΔP _(ave) /ΔP _{sim (ave)} of the respective average values ΔP sim _(ave) and ΔP (ave) approaches 1.

(Method 2 for setting tuning factors β and γ)
The estimated pressure drop ΔP _sim in the reactor at any reaction time t _x when the relationship between the reaction temperature T _t(x) and the coking threshold T _B first satisfies T _t(x) >T _B is derived from the above formula (1-1), the formula for calculating the pressure drop from the viscosity of the fluid, the linear velocity of the fluid, the density of the fluid, and the porosity of the solid catalyst layer in the reactor, and the above formula (2). At this time, a provisional value is set as β. The provisional value of β may be, for example, greater than 0 and less than or equal to 10, or may be 1.
Due to the use of a tentative value for β, ΔP _sim derived by the above method is a function of γ.
The value of γ can be set so that the relationship between the actual measured value ΔP of the pressure loss at the reaction time t _x and the ΔP _sim satisfies ΔP=ΔP _sim .

Using β and γ thus obtained, an estimated value ΔP _sim of the pressure drop in the reactor at another arbitrary reaction time t _x+1 after the reaction time t _x is derived from the above formula (1-1), a formula for calculating the pressure drop from the viscosity of the fluid, the linear velocity of the fluid, the density of the fluid, and the porosity of the solid catalyst layer in the reactor, and the above formula (2).

When the ratio ΔP/ΔP _sim between the actual pressure loss value ΔP at the reaction time t _x+1 and the ΔP _sim falls outside the range of 0.5 to 1.5, the tentative value of β is changed, and the value of γ is set again by the above-mentioned method (so that the relationship between the actual pressure loss value ΔP at the reaction time t _x and the ΔP _sim becomes ΔP=ΔP _sim ).
On the other hand, when ΔP/ΔP _sim is within the range of 0.5 to 1.5, the estimated value ΔP _sim of the pressure drop in the reactor at another arbitrary reaction time t _x+2 after the reaction time t _x+1 is derived in the same manner as described above using the β and γ.
When ΔP/ΔP _sim , which is the ratio of the actual pressure loss value ΔP at the reaction time t _x+2 to the ΔP _sim , falls outside the range of 0.5 to 1.5, the tentative value of β is changed in the same manner as described above, and the value of γ is set again by the above-mentioned method.
On the other hand, when ΔP/ΔP _sim is within the range of 0.5 to 1.5, the estimated value ΔP _sim of the pressure drop in the reactor at another arbitrary reaction time t _x+ 3 after the reaction time t _x+2 is derived in the same manner as above using the β and γ, and the above-mentioned operation is repeated.

The above-mentioned operation is repeated, and when ΔP/ΔP _sim is within the range of 0.5 to 1.5 at all 15 points after the reaction time t _x , β and γ can be determined.

<Application example of the pressure loss estimation method of the present invention>
A suitable example of application of the method for estimating pressure drop in the case where the fluid is a two-phase gas and liquid fluid of the present invention is the hydrotreating reaction of heavy hydrocarbon oil. The method for estimating pressure drop in the hydrotreating reaction of heavy hydrocarbon oil will be described below.

(Hydrotreatment reaction of heavy hydrocarbon oil)
The hydrotreating reaction of heavy hydrocarbon oil is a two-phase fixed bed flow reaction in which liquid heavy hydrocarbon oil and gaseous hydrogen are circulated through a reactor to carry out the reaction. Heavy hydrocarbon oil contains metal impurities, and these metal impurities accumulate on the solid catalyst layer, causing the pressure loss to increase over time. Representative examples of metal elements contained in the metal impurities contained in heavy hydrocarbon oil include Ni, V, Fe, Na, Zn, Al, Ba, Ca, Mg, P, Pb, Mo, Cr, Cd, As, Se, and Si. In addition, in the hydrotreating reaction of heavy hydrocarbon oil, it is necessary to increase the reaction temperature over time as the activity of the solid catalyst decreases, and it is known that when the reaction temperature exceeds a certain value, coke is generated, and the coke begins to accumulate on the solid catalyst layer and blocks the voids in the fixed catalyst layer.

First, the total amount S IN of metal impurities in the heavy hydrocarbon oil flowing into the reactor during the period (t _x -t _x-1 ) between any other arbitrary reaction time t _{x-1 before} any arbitrary reaction time t _x and the reaction time t _x , and the total amount S _OUT of metal impurities in the heavy hydrocarbon oil flowing _out of the reactor are obtained. The S _IN can be obtained by measuring the metal impurity concentration (unit: ppm, for example) in the heavy hydrocarbon oil before flowing into the reactor during the period (t _x -t _x-1 ) between the reaction time t _x -1 and the reaction time t x, and calculating the product of this and the amount (unit: kg, for example) of heavy hydrocarbon oil flowing into the reactor during that period. In addition, the S _OUT can be obtained by measuring the metal impurity concentration (unit: ppm, for example) in the heavy hydrocarbon oil after flowing out from the reactor during the period from the reaction time t _x-1 to the reaction time _t x (t _x -t _x-1 ) and calculating the product by the amount (unit: kg, for example) of the heavy hydrocarbon oil flowing out from the reactor during that period.

Methods for measuring metal impurity concentrations include, for example, ICP-MS. The amount of heavy hydrocarbon oil flowing into the reactor and the amount of heavy hydrocarbon oil flowing out of the reactor can be obtained, for example, by a flow meter.

In addition, since the hydrogen used in the hydrotreating reaction of heavy hydrocarbon oil does not usually contain impurities that accumulate on the solid catalyst layer, there is no need to measure the impurity concentration in the hydrogen to derive the S _IN and S _OUT .

The obtained S _IN and S _OUT can be substituted into the above formula (1) to obtain the porosity ε _x of the solid catalyst layer in the reactor at the reaction time t _x . Note that the porosity ε ₀ of the solid catalyst layer in the reactor at the start of the reaction can be obtained by the above-mentioned method, and ε _x-1 can be obtained by repeatedly applying the above formula (1) starting from ε ₀ .

In this embodiment, the method further includes a step of acquiring a reaction temperature T _t(x) at the reaction time t _x . When the relationship between the T _t(x) and the threshold value T _B of coking satisfies T _t(x) > T _B , in the step of deriving the porosity ε _x of the solid catalyst layer in the reactor, it is preferable to obtain the porosity ε x of the solid catalyst layer in the reactor at the reaction time t _x by substituting the S _IN , S _OUT , T _B , and T _t(x) into the following formula (1-1 ₎ instead of the formula (1).
In this embodiment, the reaction temperature T _t(x) at the reaction time t _x is as described above, and it is preferable to adopt the maximum temperature of the catalyst layer. The reaction temperature can be obtained, for example, by a thermometer in the reactor.

The δ _L of the heavy hydrocarbon oil is derived by the above formula (13). At this time, the ε _x derived by the above formula (1) or the above formula (1-1) is used as the void fraction ε of the solid catalyst layer in the reactor. The viscosity μ _L [kg/ms] of the heavy hydrocarbon oil at the reaction temperature can be obtained by, for example, multiplying the result obtained by JIS K 2283 "Crude oil and petroleum products-Kinematic viscosity test method and viscosity index calculation method" by the density converted at 15°C obtained by JIS K2249 "Crude oil and petroleum products-Density test method and density, mass, and volume conversion table" and converting the result into a temperature value. The density ρ _L [kg/m ³ ] of the heavy hydrocarbon oil at the reaction temperature can be obtained by, for example, correcting the density converted at 15°C obtained by JIS K2249 "Crude oil and petroleum products-Density test method and density, mass, and volume conversion table" by temperature. The linear velocity u _L [m/s] of the heavy hydrocarbon oil can be obtained by dividing the flow rate [m ³ /s] of the heavy hydrocarbon oil by the cross-sectional area [m ² ] of the reactor (e.g., a cylindrical tubular reactor). The flow rate of the heavy hydrocarbon oil can be obtained, for example, by a flow meter.

The δ _G of hydrogen is derived by the above formula (14). In this case, the ε _x derived by the above formula (1) or the above formula (1-1) is used as the solid catalyst void ratio ε in the reactor. The viscosity μ _G [kg/ms] of hydrogen at the reaction temperature can be obtained by, for example, introducing the composition analysis results obtained by gas chromatography into a process simulator and calculating the results. The density ρ _G [kg/m ³ ] of hydrogen at the reaction temperature can be obtained by, for example, correcting the density corresponding to the composition of the composition analysis results obtained by gas chromatography with temperature. The linear velocity u _G [m/s] of hydrogen can be obtained by dividing the flow rate [m ³ /s] of hydrogen by the cross-sectional area [m ² ] of the reactor (for example, a cylindrical tubular reactor). The flow rate of hydrogen can be obtained, for example, by a gas meter.

From the obtained _δL and _δG , χ = ( _δL / _δG ) ^1/2 is derived. Next, _δLG is derived from the above formula (9) using _δL , _δG , and χ, and _RL is derived from the above formula (10). Next, _ρm is derived from the above formula (11) using the obtained _RL . Then, _ΔP2cal is derived from the above formula (12) using the obtained _δLG and _ρm . Then, by substituting the obtained _ΔP2cal for _ΔPcal in the above formula (2), an estimated value _ΔPsim ( _ΔP2sim ) of the pressure loss in the reactor at the reaction time _tx in the hydrotreating method of heavy hydrocarbon oil can be obtained.

The conditions for the hydrotreating reaction of heavy hydrocarbon oil are generally as follows: reaction temperature is 300 to 450° C., preferably 350 to 410° C.; hydrogen partial pressure is 4 to 20 MPa, preferably 8 to 15 MPa; liquid hourly space velocity in the reactor is 0.05 to 5 hr ⁻¹ , preferably 0.1 to 2 hr ⁻¹ ; and hydrogen/oil ratio is 400 to 3,000 (L/L), preferably 500 to 1,400 (L/L).

The catalyst used in the hydrotreating reaction of heavy hydrocarbon oil is not particularly limited, and any hydrotreating catalyst known in the art can be used. Various catalyst supports can be used, such as silica, alumina, boria, magnesia, titania, silica-alumina, silica-magnesia, silica-zirconia, silica-thoria, silica-beryllia, silica-titania, silica-boria, alumina-zirconia, alumina-titania, alumina-boria, alumina-chromia, titania-zirconia, silica-alumina-thoria, silica-alumina-zirconia, silica-alumina-magnesia, silica-magnesia-zirconia, and the like, or mixtures of two or more of these. Among these inorganic oxides, preferred ones include alumina, silica-alumina, alumina-titania, alumina-boria, and alumina-zirconia, and particularly preferred is alumina, and among aluminas, gamma alumina is particularly preferred. These inorganic oxides may be used alone or in combination of two or more.

The metal contained in the carrier as an active component includes at least one metal selected from the group 6 metals and the group 8 to 10 metals of the periodic table, and is preferably molybdenum, tungsten, cobalt, and nickel metals and compounds containing them. These metal components are effective in the form of metal, metal oxide, or metal sulfide, and may also be present in a form in which the metal component is bonded to the catalyst carrier by ion exchange or the like. The content of this metal component is usually within the range of about 10 to 25 mass% on a catalyst basis and oxide conversion basis. If the metal content is less than 10 mass%, the absolute amount of metal acting as an active site is small, so that hydrotreating activity including desulfurization activity (hereinafter simply referred to as hydrotreating activity) is not expressed, and conversely, if the content of the supported metal is too much than 25 mass%, the metal will aggregate and the number of active sites will decrease, resulting in a decrease in hydrotreating activity. Furthermore, if necessary, in addition to the active metals consisting of metals in Groups 6 and 8 of the Periodic Table, phosphorus, boron, zinc, zirconia, etc. can be contained.

As an example of a fixed-bed flow reaction in which a two-phase fluid of gas and liquid flows through a reactor packed with a solid catalyst, a hydrotreating reaction of heavy hydrocarbon oil has been given, but the present invention is not limited to this. In other words, the pressure loss estimation method of the present invention can be applied to any reaction in which impurities in the fluid can be measured and coke is produced. An example of such a reaction is the hydrotreating method of light hydrocarbons.

<How to use the pressure loss estimation method of the present invention>
Examples of applications of the pressure loss estimation method of the present invention include: (1) confirmation of an abnormal increase in pressure loss during a reaction operation; (2) estimation of the time to terminate a reaction; (3) estimation of the progress of pressure loss until the end of an operation period based on an operation plan; (4) estimation of operating conditions that result in an allowable pressure loss or less for the operation period; and (5) selection of a crude oil type that has an impurity content below an upper limit.

(Confirmation of abnormal increase in pressure loss during reaction operation)
When the estimated value ΔP _sim of the pressure loss obtained by the method for estimating the pressure loss using the porosity ε _x of the solid catalyst layer derived by the formula (1) of the present invention is significantly different from the actual measured value ΔP (particularly when ΔP/ΔP _sim >1.5), it is suggested that the increase in pressure loss is caused not only by the deposition of impurities in the fluid on the solid catalyst layer, but also by other factors. For example, the pressure loss may increase due to the formation of coke, the deposition of the coke on the solid catalyst layer, and the pores of the solid catalyst layer being gradually blocked. In this case, the time-dependent change in the pressure loss can be estimated again by resetting the tuning factor α. The method for resetting the tuning factor α is as described above. The estimated value ΔP _sim of the pressure loss may be obtained by the method described above using the porosity ε _x of the solid catalyst layer derived by the formula (1-1). The method using the formula (1-1) does not require the tuning factor α to be changed, and is therefore preferable to the method for resetting the tuning factor α described above.

(Estimation of when the reaction should be completed)
The estimated pressure loss values obtained by the method for estimating pressure loss of the present invention are plotted against the reaction time, and an estimated pressure loss curve is created by connecting these plots, thereby estimating the reaction time at which the allowable pressure loss set in the reactor is reached, and the time at which the reaction should be terminated can be determined with reference to the estimated time. In addition, the reaction time at which the allowable pressure loss set in the reactor is reached can also be estimated by plotting the estimated future pressure loss values against the reaction time by substituting the predicted values of the expected future operating conditions, the amount of impurities deposited, etc. into the above formula, and the time at which the reaction should be terminated can also be estimated with reference to the estimated time.

(Estimation of the change in pressure loss until the end of the operation period based on the operation plan)
The pressure loss until the end of operation can be estimated from the estimated pressure loss value obtained by the pressure loss estimation method of the present invention and future operating conditions, and it can be confirmed that the pressure loss will be below the allowable pressure loss under these operating conditions.

(Estimation of operating conditions that will keep pressure loss below allowable level for the operating period)
The estimated pressure loss obtained by the method for estimating pressure loss of the present invention can be used to estimate operating conditions (mainly flow rate) that will keep the pressure loss below the allowable pressure loss until the end of the operating period. Details will be described later.

(Selection of crude oil type with impurity content below the upper limit)
From the estimated pressure drop value obtained by the pressure drop estimation method of the present invention, it is possible to estimate the impurity content that will keep the pressure drop below the allowable pressure drop until the end of the operating period, and to select crude oil containing impurities at or below the estimated value.

<Reaction method for controlling pressure loss>
Another embodiment of the present invention is a reaction method for controlling a pressure drop in a reactor at any reaction time t _x in a fixed bed flow reaction in which a one-phase fluid of gas or liquid, or a two-phase fluid of gas and liquid is flowed through a reactor packed with a solid catalyst, the method comprising the steps of: acquiring a total amount S _IN of impurities in a fluid flowing into the reactor and a total amount S _OUT of impurities in a fluid flowing out of the reactor during a period (t _{x -t x-1} ) _between another arbitrary reaction time t x _- 1 before the reaction time t x and the reaction time t x; and substituting the acquired S _IN and S _OUT into the following formula (3) to derive a porosity ε _x of the solid catalyst layer in the reactor at the reaction time t _x . The desired pressure drop ΔP _x in the reactor is substituted into the following formula (4) to derive ΔP _cal , and the obtained ΔP _cal and the ε The reaction is characterized in that _x is substituted into an equation for calculating the pressure drop based on the viscosity of the fluid, the linear velocity of the fluid, the density of the fluid, and the porosity of the solid catalyst layer in the reactor, and the viscosity μ of the fluid, the linear velocity u of the fluid, and the density ρ of the fluid are adjusted so that the equation for calculating the pressure drop is valid.

式（３）中、ε_ｘ－１は、前記反応経過時ｔ_ｘ－１における反応器内の固体触媒層の空隙率、αはチューニングファクターであり、前記式（１）と同様である。

In formula (3), ε _x-1 is the void fraction of the solid catalyst layer in the reactor at the reaction time t _x-1 , and α is the tuning factor, which are the same as those in formula (1).

式（４）中、σはチューニングファクターであり、前記式（２）と同様である。

In formula (4), σ is a tuning factor, which is the same as in formula (2) above.

In the pressure loss estimation method already described, parameters such as the fluid viscosity μ, the fluid linear velocity u, and the fluid density ρ are substituted into a predetermined formula to derive an estimated pressure loss ΔP _sim , but in this embodiment, on the contrary, a desired pressure loss ΔP _x is set, ΔP _x is substituted into a predetermined formula, and the fluid viscosity μ, the fluid linear velocity u, and the fluid density ρ are adjusted so that the predetermined formula holds true, and a reaction is performed. The conditions of the fluid viscosity μ, the fluid linear velocity u, and the fluid density ρ necessary for control to achieve the desired pressure loss are obtained, and a reaction is performed under those conditions.

ε _{x at any reaction time t x and} the void fraction ε ₀ of the solid catalyst layer in the reactor at the start of the reaction can be calculated by the above formula (3) in the same manner as described in the above-mentioned method for estimating pressure drop. The tuning factors α and σ can be calculated in the same manner as described in the above-mentioned method for estimating pressure drop.

In this embodiment, the method further includes a step of acquiring the reaction temperature T _t(x) at the reaction time t _x , and when the relationship between the T _t(x) and the coking threshold T _B satisfies T _t(x) > T _B , it is preferable to obtain ε _x by the following formula (3-1) in the same manner as described in the above-mentioned pressure loss estimation method. The coking threshold T _B and the tuning factors β and γ can be obtained in the same manner as described in the above-mentioned pressure loss estimation method.

(When the fluid is one phase of gas or liquid)
A reaction method for controlling pressure loss when the fluid is a single phase of gas or liquid will be described using the Ergun formula to calculate pressure loss based on the viscosity of the fluid, the linear velocity of the fluid, the density of the fluid, and the porosity of the solid catalyst layer in the reactor. First, a desired pressure loss ΔP1 _x is set, and the ΔP1 _x is substituted for ΔP _x in the formula (4) to derive ΔP _cal (hereinafter, the calculated value of the pressure loss in the reactor when the fluid is a single phase of gas or liquid may be referred to as ΔP1 _cal ). Next, the ΔP1 _cal , ε _x derived from the formula (3) or the formula (3-1), the bed height H of the solid catalyst, and the spherical diameter dp when the solid catalyst is assumed to be a sphere are substituted into the Ergun formula represented by the formula (7).
The bed height H of the solid catalyst and the spherical diameter dp when the solid catalyst is assumed to be a sphere are as explained in the above-mentioned method for estimating pressure loss.

When the above parameters are substituted, the variables in the Ergun equation are the viscosity μ of the fluid, the linear velocity u of the fluid, and the density ρ of the fluid. By selecting a combination of μ, u, and ρ that satisfies the Ergun equation and performing a reaction under those conditions, a desired pressure loss ΔP1 _x can be achieved.

In chemical reactions, it is often difficult to significantly change the viscosity μ and density ρ of the fluid containing the reactants. In such cases, the desired pressure loss ΔP1 _x can be achieved by selecting u such that the Ergun equation holds true and carrying out the reaction.

(When the fluid is two-phase, gas and liquid)
A reaction method for controlling pressure loss when the fluid is in two phases of gas and liquid will be described using the Ergun-Larkins formula as a formula for calculating pressure loss based on the viscosity of the fluid, the linear velocity of the fluid, the density of the fluid, and the porosity of the solid catalyst layer in the reactor. First, a desired pressure loss ΔP2 _x is set, and the ΔP2 _x is substituted for ΔP _x in the formula (4) to derive ΔP _cal (hereinafter, the calculated value of the pressure loss in the reactor when the fluid is in two phases of gas and liquid may be referred to as ΔP2 _cal ). Next, the ΔP2 _cal , ε _x derived from the formula (3) or the formula (3-1), the bed height H of the solid catalyst, and the spherical diameter dp when the solid catalyst is assumed to be a sphere are substituted into the Ergun-Larkins formula composed of the formulas (9) to (14).
The bed height H of the solid catalyst and the spherical diameter dp when the solid catalyst is assumed to be a sphere are as explained in the above-mentioned method for estimating pressure loss.

Specifically, ΔP2 _cal and H are substituted into the formula (12), and ε _x and dp are substituted into the formulas (13) and (14). From the formulas (9), (13), and (14), δ _LG is defined as an equation expressed by liquid viscosity μ _L , liquid linear velocity u _L , liquid density ρ _L , gas viscosity μ _G , gas linear velocity u _G , and gas density ρ _G. From the formulas (10), (11), (13), and (14), ρ _m is defined as an equation expressed by μ _L , u _L , ρ _L , μ _G , u _G , and ρ _G. From these equations and the above equation (12), ΔP2 _cal can be expressed by μ _L , u _L , ρ _L , μ _G , u _G , and ρ _G , and by selecting a combination of μ _L , u _L , ρ _L , μ _G , u _G , and ρ _G such that this equation holds, and carrying out the reaction under these conditions, the desired pressure loss ΔP2 _x can be achieved.

As described above, in chemical reactions, it is often difficult to significantly change the viscosity μ and density ρ of the fluid containing the reactants. In such cases, the desired pressure loss ΔP2 _x can be achieved by selecting the linear velocity u _L of the liquid and the linear velocity u _G of the gas so that the above formula is satisfied.

<Pressure loss estimation device, pressure loss estimation program>
Another embodiment of the present invention is a pressure drop estimation deriving device in an arbitrary reaction time t x in a fixed _bed flow reaction in which a one-phase fluid of gas or liquid, or a two-phase fluid of gas and liquid is circulated through a reactor filled with a solid catalyst, the pressure drop estimation deriving device including a fluid information acquisition unit that acquires a viscosity μ of the _fluid , a linear velocity u of the fluid, and a density ρ of the fluid at the reaction time t _{x ,} an impurity information acquisition unit that acquires a total amount of impurities S _IN in the fluid that flowed into the reactor and a total amount of impurities S _OUT in the fluid that flowed out of the reactor between another arbitrary reaction time t _{x -1} before the reaction time t _x and the reaction time t x (t x -t x-1 ), and a porosity derivation unit that derives a porosity ε _x of the solid catalyst layer in the reactor at the reaction time t _x by substituting the acquired S _IN and S _OUT into the formula (5), and the acquired μ, u, ρ, and ε a ΔP _cal derivation unit that substitutes _x into an equation for calculating the pressure drop from the viscosity of the fluid, the linear velocity of the fluid, the density of the fluid, and the porosity of the solid catalyst layer in the reactor, and derives ΔP _cal , which is a calculated value of the pressure drop; a pressure loss estimate derivation unit that substitutes the obtained ΔP _cal into the equation (6) to derive an estimate value ΔP _sim of the pressure drop in the reactor at the reaction elapsed time _{t x} ; and an output unit that outputs the estimate value ΔP _sim of the pressure drop.

The pressure drop estimation deriving device of the present embodiment further includes a temperature information acquisition unit that acquires a reaction temperature T _t(x) at the reaction time t _x , and when the relationship between the T t _(x) and a coking threshold value T _B satisfies T _t(x) > T _B , in a porosity derivation unit that derives the porosity ε _x of the solid catalyst layer in the reactor, it is preferable to substitute the S _IN , the S _OUT , the T _B , and T _t(x) into the formula (5-1) instead of the formula (5) to derive the porosity ε _x of the solid catalyst layer in the reactor at the reaction time t _x .

Specifically, as shown in FIG. 3, the pressure loss estimation derivation device 10 of this embodiment has an acquisition unit 11, a computer main body 14 that processes information from the acquisition unit 11, and an output unit 20 that outputs information processed by the computer main body 14 (estimated value of pressure loss in the reactor) to the outside.

The acquisition unit 11 receives predetermined information input by a reaction operator and transmits the information acquired by this input to the computer 14. The acquisition unit 11 of this embodiment includes a fluid information acquisition unit 12 that acquires the viscosity μ of the fluid, the linear velocity u of the fluid, and the density ρ of the fluid at any reaction time t _{x ,} and an impurity information acquisition unit 13 that acquires the total amount of impurities S IN in the fluid that flowed into the reactor during the period (t _x -t _x-1 ) between another arbitrary reaction time t _x - ₁ before the reaction time t _x and the reaction time t x, and the total amount of impurities S _OUT in the fluid that flowed out of the reactor. In addition, the acquisition unit 11 of this embodiment preferably further includes a temperature information acquisition unit 19 that acquires the reaction temperature T _t(x) at the reaction time t _x .

Specifically, the fluid information acquisition unit 12 acquires the fluid viscosity μ (μ _L and μ _G if the fluid is in two phases of gas and liquid), the _fluid linear velocity u (u L and u G if the fluid is in two phases of gas and liquid), and the fluid density ρ (ρ _L and ρ _G if the fluid is in two phases of gas and liquid) at the reaction time _{t x} obtained by the above-mentioned measurement method by the reaction operator, and transmits this to the computer main body 14.
Specifically, the impurity information acquisition unit 13 acquires the total amount of impurities S IN in the fluid that flowed into the reactor during the period (t _x -t x -1) between another arbitrary reaction time t _x-1 before the reaction time t _{x and the reaction time t x} (t _x -t _{x -1} ) obtained by the above-mentioned measurement method, and transmits this to the computer main body 14 by the reaction operator inputting the total amount of impurities S _IN in the fluid _that flowed out of the reactor.
Specifically, the temperature information acquisition unit 19 acquires the reaction temperature T _t(x) at the reaction time t _x obtained by the above-mentioned measurement method by an operator of the reaction, and transmits this to the computer main body 14.

In this embodiment, the fluid information acquisition unit 12, the impurity information acquisition unit 13, and the temperature information acquisition unit 19 are configured with a common keyboard. The specific configurations of the fluid information acquisition unit 12, the impurity information acquisition unit 13, and the temperature information acquisition unit 19 are not limited, and although they are keyboards in this embodiment, they may be touch panels or the like. The fluid information acquisition unit 12, the impurity information acquisition unit 13, and the temperature information acquisition unit 19 may be configured separately and each may be independently connected to the computer main body 14. In addition, the fluid information acquisition unit 12, the impurity information acquisition unit 13, and the temperature information acquisition unit 19 may be configured to directly acquire the above-mentioned information from a computer, an analysis device, or the like used for controlling the reactor, by wire or wirelessly.

The computer main body 14 is a so-called computer capable of processing various information. A predetermined program is installed in the computer main body 14, and the execution of this program functionally constitutes a calculation unit 15. Specifically, the calculation unit 15 functionally constitutes a voidage derivation unit 16, a ΔP _cal derivation unit 17, and a pressure loss estimated value derivation unit 18 by executing the program.

When the above information is input from the acquisition unit 11 to the computer main body 14, the porosity derivation unit 16 calculates the porosity ε _x of the solid catalyst layer in the reactor from the above formula (5) when the relationship between the T _{t (x)} and the coking threshold T _B satisfies T t ₍ x) ≦ T _B , and from the above formula (5-1) when the relationship between the T _t(x) and the coking threshold T _B satisfies T t(x) > T _B. When the above information is input from the acquisition unit 11 to the computer main body 14, the ΔP _cal derivation unit 17 derives ΔP _cal from a formula for calculating pressure loss from the viscosity of the fluid, the linear velocity of the fluid, the density of the fluid, and the porosity of the solid catalyst layer in the reactor. When the fluid is a single phase gas or liquid, the ΔP _cal derivation unit 17 can derive ΔP _cal (ΔP1 _cal ) from the above Ergun formula, for example. In addition, when the fluid is two-phase, that is, gas and liquid, ΔP _cal (ΔP2 _cal ) can be derived, for example, from the above-mentioned Ergun-Larkins equation in ΔP _cal derivation unit 17. A pressure loss estimated value derivation unit 18 derives an estimated value ΔP _sim of the pressure loss at the reaction time t _x from ΔP _cal derived by the ΔP _cal derivation unit 17 using the equation (6).

In addition, it is preferable that the porosity derivation unit 16, the ΔP _cal derivation unit 17, and the pressure loss estimated value derivation unit 18 cooperate to have a function of deriving the tuning parameter α in the formula (5), the tuning factors β and γ in the formula (5-1), and the tuning factor σ in the formula (6) by the method already explained in the section on the pressure loss estimation method.

The calculation unit 15 outputs the calculation result obtained as described above based on the information input by the reaction operator to the output unit 20 as an estimated value of pressure loss.

The output unit 20 receives the calculation results (estimated values of pressure loss in the reactor) output by the computer main body 14 (more specifically, the calculation unit 15) and outputs them to the outside. The output unit 20 in this embodiment is configured with a display unit such as a CRT display, liquid crystal display, or PDP, but is not limited to this and may be configured to output to a printing unit such as a printer, or other devices (for example, a computer used for controlling the hydrotreating reaction of heavy hydrocarbon oils, etc.). The output unit 20 may also be a combination of these.

The pressure loss estimation derivation device 10 of this embodiment may be a device that derives only an estimate of the pressure loss in the reactor when the fluid is one phase, that is, gas or liquid, or a device that derives only an estimate of the pressure loss in the reactor when the fluid is two phases, that is, gas and liquid, or a device that derives both an estimate of the pressure loss in the reactor when the fluid is one phase and an estimate of the pressure loss in the reactor when the fluid is two phases.

When the device derives both an estimated value of the pressure loss in the reactor when the fluid is one phase and an estimated value of the pressure loss in the reactor when the fluid is two phases, it is preferable that the device is equipped with a fluid phase number information acquisition unit (not shown) that acquires information by having the reaction operator input in acquisition unit 11 whether the fluid is one phase or two phases.

The fluid phase number information is transmitted to the computer main body 14, whereby an equation for calculating the _pressure drop based on the fluid viscosity, the fluid linear velocity, the fluid density, and the porosity of the solid catalyst layer in the reactor, which is used in the ΔP cal derivation unit 17, is appropriately selected.

Each component of the pressure loss estimation device 10 may be configured using hardware logic, or may be realized using software using a CPU as follows:

That is, the pressure loss estimation derivation device 10 includes a CPU (central processing unit) that executes the commands of a control program that realizes each function, a ROM (read only memory) that stores the program, a RAM (random access memory) that expands the program, and a storage device (recording medium) such as a memory that stores the program and various data. The object of the present invention can also be achieved by supplying a recording medium on which the program code (executable program, intermediate code program, source program) of the control program of the pressure loss estimation derivation device 10, which is software that realizes the above-mentioned functions, is recorded in a computer-readable manner to the pressure loss estimation derivation device 10, and having the computer (or CPU or MPU) read and execute the program code recorded on the recording medium.

Examples of the recording medium that can be used include tape-based devices such as magnetic tape and cassette tape, disk-based devices including magnetic disks such as flexible disks and hard disks, and optical disks such as CD-ROMs, MOs, MDs, DVDs, and CD-Rs, card-based devices such as IC cards (including memory cards) and optical cards, and semiconductor memory-based devices such as mask ROMs, EPROMs, EEPROMs, and flash ROMs.

The pressure loss estimation derivation device 10 may be configured to be connectable to a communication network, and the program code may be supplied via the communication network. The communication network is not particularly limited, and may be, for example, the Internet, an intranet, an extranet, a LAN, ISDN, VAN, a CATV communication network, a virtual private network, a telephone line network, a mobile communication network, a satellite communication network, or the like. The transmission medium constituting the communication network is not particularly limited, and may be, for example, a wired medium such as IEEE1394, USB, power line carrier, cable TV line, telephone line, or ADSL line, or may be a wireless medium such as infrared such as IrDA or a remote control, Bluetooth (registered trademark), 802.11 wireless, HDR, a mobile phone network, a satellite line, or a terrestrial digital network. The present invention may also be realized in the form of a carrier wave or a data signal sequence in which the program code is embodied by electronic transmission.

The present invention will be explained in more detail below with reference to examples, but the present invention is not limited to the following examples.

[Measurement of metal impurity concentration in heavy hydrocarbon oil]
The metal impurity concentrations in the heavy hydrocarbon oil were measured by ICP-OES. Specifically, the metal-equivalent concentrations of Ni, V, and Fe in the heavy hydrocarbon oil before it flowed into the reactor and the metal-equivalent concentrations of Ni, V, and Fe in the heavy hydrocarbon oil after it flowed out of the reactor were measured by ICP-OES.

[Measurement of density and viscosity of heavy hydrocarbon oil]
The density of the heavy hydrocarbon oil was obtained by correcting the density converted to 15° C. measured in accordance with JIS K2249 "Crude oil and petroleum products -- Density test method and density, mass and volume conversion table" by the reaction temperature.
The viscosity of the heavy hydrocarbon oil was obtained by multiplying the result obtained in accordance with JIS K 2283 "Crude oil and petroleum products -- Test method for kinematic viscosity and calculation method for viscosity index" by the density converted to 15°C measured in accordance with JIS K2249 "Crude oil and petroleum products -- Test method for density and density, mass, and volume conversion table" and converting the result into a temperature value.

[Measurement of density and viscosity of hydrogen]
The density of hydrogen was obtained by correcting the density corresponding to the composition obtained by composition analysis using gas chromatography for temperature and pressure.
The viscosity of hydrogen was obtained by inputting the composition analysis results obtained by gas chromatography into a process simulator and calculating it.

The reaction temperature was measured using a thermometer inside the reactor, and the maximum temperature was used.

[Example 1]
Four different types of heavy hydrocarbon oil hydrotreating catalysts (molybdenum-nickel catalysts in which molybdenum and nickel are supported on gamma alumina, shape: four-leaf clover) A to D were packed into a reactor, respectively, to form four solid catalyst layers. At this time, the layer height H (m) of each solid catalyst layer was measured by a scale. The layer height H of each solid catalyst layer was multiplied by the cross-sectional area (m ² ) of the reactor (cylindrical tubular reactor) to calculate the packing volume V _cat (m ³ ) of each solid catalyst layer. Furthermore, BD = W _cat /V _cat was calculated from the packing volume V _cat and the packing weight W _cat (kg) of each solid catalyst layer, and the packing density BD (kg/m ³ ) of each solid catalyst layer was obtained. From the packing density BD of each solid catalyst layer, the true density ρ _cat (kg/m ³ ) of each solid catalyst, and the pore volume PV (m ³ /kg) of each solid catalyst, ε ₀ =1-(BD×(1/ρ _cat +PV)) was calculated, and ε ₀ of each solid catalyst layer was calculated.
The true density of the solid catalyst was determined by the pycnometer method (liquid phase method). The pore volume of the solid catalyst was measured by mercury intrusion porosimeter (MICROMERITICS AUTO-PORE 9200, manufactured by Shimadzu Corporation) as the mercury intrusion device.

From the average major axis and the average minor axis of each solid catalyst, the spherical diameter dp was calculated by the above formula (8-3) assuming that each solid catalyst was a sphere.
Table 1 shows the dp, H, ε ₀ and layer structure of the hydrotreating catalysts A to D. In Table 1, zone 1 is the reactor inlet side, and zone 4 is the reactor outlet side.

Heavy hydrocarbon oil heated to the reaction temperature and hydrogen were introduced from the top of the reactor, and hydrotreating was carried out under the following conditions:

Reaction conditions:
Reaction temperature: 377°C
Pressure (hydrogen partial pressure): 10.3 MPa
Liquid space velocity; 0.2h ^-1
Linear speed (oil): 0.0043m/s
Linear speed (hydrogen): 0.067 m/s
Hydrogen/oil ratio: 860 ^m3 / ^m3
Sulfur content in produced oil: 0.30 mass%

Characteristics of feedstock oil:
Oil type: Middle Eastern crude oil atmospheric distillation residue Density (15°C): 0.9616g/ ^cm3
Sulfur component: 2.97% by mass
Vanadium: 15 ppm
Nickel: 31 ppm
Iron: 18 ppm
Kinematic viscosity: 369 mm ³ /s (50°C)
Properties of the resulting oil:
Vanadium: 6 ppm
Nickel: 9 ppm
Iron: 13 ppm
The sulfur content was measured in accordance with JIS K2541 "Crude oil and petroleum products -- Determination of sulfur content."
The above reaction conditions are average values over the entire reaction period.

24 hours after the start of the reaction, the metal impurity concentration in the heavy hydrocarbon oil before flowing into the reactor was measured, and the product of this and the total amount of heavy hydrocarbon oil flowing into the reactor during 24 hours was calculated to obtain the total amount of impurities S _IN (kg/24h) in the heavy hydrocarbon oil flowing into the reactor during 24 hours after the start of the reaction. 24 hours after the start of the reaction, the metal impurity concentration in the heavy hydrocarbon oil after flowing out from the reactor was measured, and the product of this and the total amount of heavy hydrocarbon oil flowing out from the reactor during 24 hours was calculated to obtain the total amount of impurities S _OUT (kg/24h) in the heavy hydrocarbon oil flowing out from the reactor during 24 hours after the start of the reaction.
The ε ₀ , S _IN and S _OUT of the solid catalyst layer in each zone were substituted into the formula (1-B) to obtain the ε _24h of the solid catalyst layer in each zone as a function of α _const . The ε _24h , the density, linear velocity and viscosity of the heavy hydrocarbons after 24 hours, the density, linear velocity and viscosity of hydrogen, and the dp and H of the catalyst were substituted into the formulas (9) to (14) to obtain the calculated pressure loss ΔP _cal(n) (ΔP2 _cal(n) ) of the solid catalyst layer in each zone after 24 hours as a function of α _const (n=4). Next, the calculated pressure loss of the solid catalyst layers in zones 1 to 4 was summed up to obtain the calculated pressure loss ΔP _cal (ΔP2 _cal ) of the entire solid catalyst layer as a function of α _const . The calculated pressure drop ΔP _cal (ΔP2 _cal ) of the all-solid catalyst layer was substituted into the above formula (2) to obtain an estimated pressure drop ΔP _sim (ΔP2 _sim ) of the all-solid catalyst layer as a function of α _const and σ.
Thereafter, the above pressure loss estimation work was performed every 24 hours, and the estimated pressure loss ΔP _sim (ΔP2 _sim ) was obtained as a function of α _const and σ. α const and σ were adjusted so that the ratio ΔP _{(ave ) /} ΔP _{sim (ave)} , which is the average value of the actual pressure loss _value ΔP and the estimated pressure loss value ΔP _{sim over 15 reaction points from the start of the reaction, approached 1. It was found that the actual measurement value and the estimated value matched well when α const =} 0.0065 and σ = -0.19.

The above-mentioned pressure loss estimation work was performed every 24 hours with α _const = 0.0065 and σ = -0.19. Figure 4 shows a graph of the actual measured value (achieved value) and the estimated value of the pressure loss versus the reaction time.

As shown in FIG. 4, the values of α _const and σ were not changed until 269 days had passed, but the average value of ΔP/ΔP _sim during that time was 1.06, and the pressure loss could be estimated with a very high degree of accuracy. Since the value of ΔP/ΔP _sim gradually increased (after 264 days: 1.09, after 265 days: 1.16, after 266 days: 1.20, after 267 days: 1.24, after 268 days: 1.28, after 269 days: 1.30), the value of α _const was changed to 0.03 after 270 days had passed (σ was not changed), and the reaction was carried out for a total of about 300 days. The actual and estimated values of the pressure loss during the entire reaction period were in good agreement. The average value of ΔP (actual value)/ΔP _sim (estimated value) during this period was 1.06.

[Example 2]
When T _B was obtained on an actual scale in accordance with the above-mentioned method 2 for obtaining the threshold value T _B for coking, T _B was 370° C. In addition, in the method 2 for obtaining the threshold value T _B for coking, line 1 was y = 0.0002x + 0.0372, and line 2 was y = 0.0163x - 5.9256.
Therefore, until the reaction temperature _Tt exceeded 370° C., the estimated value of the pressure loss was calculated using ε _x calculated by the formula (1) in the method of Example 1 described above (α=0.0065, σ=−0.19 as in Example 1).
After 101 days, the reaction temperature _Tt reached 371°C, exceeding _Tb of 370°C.
The metal impurity concentration in the heavy hydrocarbon oil before flowing into the reactor after 101 days was measured, and the product was calculated by multiplying the total amount of heavy hydrocarbon oil flowing into the reactor between 100 days and 101 days to obtain the total amount of impurities S _IN (kg/24h) in the heavy hydrocarbon oil flowing into the reactor between 100 days and 101 days. The metal impurity concentration in the heavy hydrocarbon oil after flowing out from the reactor after 101 days was measured, and the product was calculated by multiplying the total amount of heavy hydrocarbon oil flowing out from the reactor between 100 days and 101 days to obtain the total amount of impurities S _OUT (kg/24h) in the heavy hydrocarbon oil flowing out from the reactor between 100 days and 101 days.
The ε _{100 days} , S _IN , S _OUT , R, T _B , and T _t(x) of the solid catalyst layer in each zone were substituted into the formula (1-1) to obtain the ε _{101 days} of the solid catalyst layer in each zone as a function of β and γ. In accordance with the above-mentioned setting method 2 of tuning factors β and γ, β=1 was substituted as a provisional value to obtain the ε _{101 days} as a function of γ. The ε _{101 days} , the density, linear velocity, and viscosity of the heavy hydrocarbons after 101 days, the density, linear velocity, and viscosity of the hydrogen, and the dp and H of the catalyst were substituted into the formulas (9) to (14) to obtain the calculated value ΔP _cal(n) of the pressure loss of the solid catalyst layer in each zone after 101 days as a function of γ. Next, the calculated values of the pressure loss of the solid catalyst layers in zones 1 to 4 were summed up to obtain the calculated value ΔP _cal of the pressure loss of the entire solid catalyst layer as a function of γ. The calculated pressure drop ΔP _cal of the all-solid catalyst layer was substituted into the above formula (2) to obtain an estimated pressure drop ΔP _sim of the all-solid catalyst layer as a function of γ. When the actual pressure drop ΔP after 101 days had elapsed and the above ΔP _sim were calculated so that ΔP = ΔP _sim , γ was 340.
Thereafter, the above-mentioned pressure loss estimation work was performed every 24 hours, and since ΔP/ΔP _sim was within the range of 0.5 to 1.5 at 15 points thereafter, the pressure estimation work was continued with β=1 and γ=340.
FIG. 5 shows a graph of the measured and estimated pressure drop versus reaction time.

As shown in Fig. 5, the measured and estimated values of pressure drop during the entire reaction period were in good agreement. Moreover, there was no need to change the tuning parameter α, as in Example 1. The average value of ΔP (measured value)/ΔP _sim (estimated value) during this period was 1.01.

Reference Signs List 10: Pressure loss estimation derivation device, 11: Acquisition unit, 12: Fluid information acquisition unit, 13: Impurity information acquisition unit, 14: Calculator, 15: Calculation unit, 16: Porosity derivation unit, 17: ΔP _cal derivation unit, 18: Pressure loss estimated value derivation unit, 19: Temperature information acquisition unit, 20: Output unit

Claims (7)

A method for estimating a pressure drop in a reactor at any reaction time _tx in a fixed bed flow reaction in which a one-phase fluid of gas or liquid, or a two-phase fluid of gas and liquid, is circulated through a reactor packed with a solid catalyst, the method comprising the steps of:
Acquiring the viscosity μ of the fluid, the linear velocity u of the fluid, and the density ρ of the fluid at the reaction time t _x ;
A step of acquiring a total amount of impurities S IN in the fluid flowing into the reactor during a period (t _x -t _x-1 ) between another arbitrary reaction time t _x-1 before the reaction time t _x and the reaction time t _x , and a total amount of impurities S _OUT in the fluid flowing out of the _reactor ;
and substituting the obtained S _IN and S _OUT into the following formula (1) to derive the porosity ε _x of the solid catalyst layer in the reactor at the reaction time t _x ,
The obtained μ, u, ρ, and ε _x are substituted into an equation for calculating a pressure drop based on the viscosity of the fluid, the linear velocity of the fluid, the density of the fluid, and the porosity of the solid catalyst layer in the reactor, to derive a calculated value of the pressure drop, ΔP _cal ;
A method for estimating a pressure drop in a reactor, comprising: substituting the obtained ΔP _cal into the following formula (2) to obtain an estimated value ΔP _sim of the pressure drop in the reactor at the reaction time t _x ,
The method for estimating pressure drop in a reactor, wherein a formula for calculating the pressure drop based on the void ratio of the solid catalyst layer in the reactor is the Ergun formula, the Blake-Kozeny formula, the Burke-Plummer formula, the Kozeny-Carman formula, or the Fanning formula when the fluid is a single phase of gas or liquid, and is the Ergun-Larkins formula when the fluid is a two-phase of gas and liquid .
(In formula (1), ε _x-1 is the void fraction of the solid catalyst layer in the reactor at the reaction time t _x-1 , and α is a tuning factor.)
(In formula (2), σ is a tuning factor.) Further, the method includes a step of acquiring a reaction temperature T _t(x) at a reaction time t _x ,
2. The method for estimating a pressure drop in a reactor according to claim 1, wherein, when a relationship between the Tt _(x) and a coking threshold T _B , which is a temperature at which coke is generated and begins to deposit on the solid catalyst layer, satisfies Tt _(x) > T _B , in the step of deriving a porosity ε _x of the solid catalyst layer in the reactor, the S _IN , the S _OUT , the T _B , and the Tt _(x) are substituted into the following formula (1-1) instead of the formula (1) to derive the porosity ε _x of the solid catalyst layer in the reactor at the reaction time t _x .
(In formula (1-1), R is a gas constant, and β and γ are tuning factors.) A reaction method for controlling a pressure drop in a reactor at any reaction time t _x in a fixed bed flow reaction in which a one-phase fluid of gas or liquid, or a two-phase fluid of gas and liquid is flowed through a reactor packed with a solid catalyst, comprising the steps of:
A step of acquiring a total amount of impurities S IN in the fluid flowing into the reactor during a period (t _x -t _x-1 ) between another arbitrary reaction time t _x-1 before the reaction time t _x and the reaction time t _x , and a total amount of impurities S _OUT in the fluid flowing out of the _reactor ;
and substituting the obtained S _IN and S _OUT into the following formula (3) to derive the porosity ε _x of the solid catalyst layer in the reactor at the reaction time t _x ,
The desired pressure drop ΔP _x in the reactor is substituted into the following formula (4) to derive ΔP _cal ,
The obtained ΔP _cal and the ε _x are substituted into an equation for calculating the pressure drop based on the viscosity of the fluid, the linear velocity of the fluid, the density of the fluid, and the void fraction of the solid catalyst layer in the reactor,
A reaction method for controlling a pressure drop in a reactor, comprising: adjusting a viscosity μ of a fluid, a linear velocity u of the fluid, and a density ρ of the fluid so that the equation for calculating the pressure drop is satisfied ;
A reaction method for controlling pressure drop in a reactor, wherein a formula for calculating the pressure drop based on the void ratio of the solid catalyst layer in the reactor is the Ergun formula, the Blake-Kozeny formula, the Burke-Plummer formula, the Kozeny-Carman formula, or the Fanning formula when the fluid is a single phase of gas or liquid, and is the Ergun-Larkins formula when the fluid is a two-phase of gas and liquid .
(In formula (3), ε _x-1 is the void fraction of the solid catalyst layer in the reactor at the reaction time t _x-1 , and α is a tuning factor.)
(In equation (4), σ is a tuning factor.) Further, the method includes a step of acquiring a reaction temperature T _t(x) at a reaction time t _x ,
4. The reaction method for controlling a pressure drop in a reactor according to claim 3, wherein, when the relationship between Tt ₍ x) and the coking threshold value T _B satisfies Tt _(x) > T _B , in the step of deriving the porosity ε _x of the solid catalyst layer in the reactor, the S _IN , the S _OUT , the T _B , and the Tt _(x) are substituted into the following formula (3-1) instead of the formula (3) to derive the porosity ε _x of the solid catalyst layer in the reactor at the reaction time t _x .
(In formula (3-1), R is a gas constant, and β and γ are tuning factors.) A pressure drop estimation device for deriving a pressure drop in a reactor at any reaction time _tx in a fixed bed flow reaction in which a one-phase fluid of gas or liquid, or a two-phase fluid of gas and liquid, is circulated through a reactor packed with a solid catalyst, the device comprising:
A fluid information acquisition unit that acquires the viscosity μ of the fluid, the linear velocity u of the fluid, and the density ρ of the fluid at the reaction time t _x ;
an impurity information acquisition unit that acquires a total amount S IN of impurities in the fluid flowing into the reactor during a period (t _x -t _x-1 ) between another arbitrary reaction time t _{x -1} before the reaction time t _x and the reaction time t _x and a total amount S _OUT of impurities in the fluid flowing out of the reactor;
a porosity deriving unit that derives the porosity ε _x of the solid catalyst layer in the reactor at the reaction time t _x by substituting the obtained S _IN and S _OUT into the following formula (5);
a ΔP cal derivation unit that substitutes the obtained μ, u, ρ, and ε _x into an equation for calculating a pressure drop based on a viscosity of a fluid, a linear velocity of the fluid, a density of the fluid, and a porosity of a solid catalyst layer in a reactor, and derives a calculated value of the pressure drop, ΔP _{cal ;}
a pressure loss estimated value deriving unit that substitutes the obtained ΔP _cal into the following formula (6) to derive an estimated value ΔP _sim of the pressure loss in the reactor at the reaction time t _x ;
an output unit that outputs the estimated pressure loss value ΔP _sim ;
A pressure loss estimation device comprising:
The pressure loss estimation deriving device, wherein an equation for calculating the pressure loss based on the porosity of the solid catalyst layer in the reactor is the Ergun equation, the Blake-Kozeny equation, the Burke-Plummer equation, the Kozeny-Carman equation, or the Fanning equation when the fluid is a single phase of gas or liquid, and is the Ergun-Larkins equation when the fluid is a two-phase of gas and liquid .
(In formula (5), ε _x-1 is the void fraction of the solid catalyst layer in the reactor at the reaction time t _x-1 , and α is a tuning factor.)
(In equation (6), σ is a tuning factor.) Further, a temperature information acquisition unit is provided for acquiring a reaction temperature T _t(x) at a reaction time t _x ,
6. The pressure loss estimation deriving device according to claim 5, wherein, when a relationship between the Tt _(x) and a coking threshold T _B , which is a temperature at which coke is generated and begins to deposit on the solid catalyst layer , satisfies Tt _(x) > T _B , a porosity deriving unit that derives the porosity ε _x of the solid catalyst layer in the reactor is configured to substitute the S _IN , the S _OUT , the T _B , and Tt _(x) into the following formula (5-1) instead of the formula (5) to derive the porosity ε _x of the solid catalyst layer in the reactor at the reaction time t _x .
(In formula (5-1), R is a gas constant, and β and γ are tuning factors.) A pressure loss estimation program for causing a computer to function as fluid information acquisition means in the fluid information acquisition unit, impurity information acquisition means in the impurity information acquisition unit, porosity derivation means in the porosity derivation unit, ΔP cal derivation means _in the ΔP _cal derivation unit , pressure loss estimated value derivation means in the pressure loss estimated value derivation unit, and output means in the output unit of the pressure loss estimation derivation device according to claim 5 or 6.

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