JP6855828B2 - Prediction method of particle size distribution of crystallized particles - Google Patents

Description

The present invention relates to a method for predicting the particle size distribution of crystallized particles.

Various types of particles (hereinafter, also referred to as "crystallized particles") are produced by crystallization. For example, in Patent Document 1, a mixed aqueous solution containing a nickel salt and a cobalt salt, an aqueous solution containing an ammonium ion feeder, and a caustic alkaline aqueous solution are supplied and reacted in a crystallization tank to react with a nickel-cobalt composite hydroxide. Particles are precipitated. The obtained nickel-cobalt composite hydroxide particles are used as a positive electrode active material for a lithium ion secondary battery.

Japanese Unexamined Patent Publication No. 2011-201764

R. David, P. Marshall; "Crystallization and precipitation engineering. III. A discrete formulation of the agglomeration rate of crystals in a crystallization process" Chem. Eng. Sci. 43,59-67 (1988) Yogesh M.H., Marco L. and Miroslav S; "Experimental and Modeling Study of Breakage and Restructuring of Open and Dense Colloidal Aggregates" Langmuir, 27,5739-5752 (2011) G. K. Batchelor, J. T. Green; "The hydrodynamic interaction of two small freely-moving spheres in a linear flow field" J. Fluid Mech., 56,375-400 (1972) C.J.Lin, K.J.Lee and N.F.Sather; "Slow Motion of Two Spheres in a Shear Field" J. Fluid Mech., 43,35-47 (1970) Saffman P.G. and Turner J.S .; "On the collision of drops in turbulent clouds" J. Fluid Mech., 1,16-30 (1956)

The growth process of particles by crystallization can be roughly divided into the process of precipitating solute components on the particle surface, the process of collision and coalescence of particles floating in the crystallization tank, and the process of re-dividing the once coalesced particles. including. Particle fragmentation can occur due to stirring with a stirring blade or the like.

Precipitation, collision / coalescence, and fragmentation are affected by crystallization conditions such as the volume of the crystallization tank and the type of stirring blade. The crystallization conditions are changed, for example, in order to cope with the difference between the laboratory machine and the mass production machine, for example, when the crystallization particles are commercialized.

Due to changes in crystallization conditions, precipitation, collision / coalescence, and fragmentation were affected, and the particle size distribution of the crystallized particles could change. The particle size distribution of the crystallized particles has a great influence on the performance of products manufactured using the crystallized particles.

Conventionally, regarding the particle size distribution of crystallization particles, it is necessary to actually manufacture the crystallization particles under the changed crystallization conditions and check the particle size distribution of the crystallization particles with a particle size distribution meter, before the change of the crystallization conditions. It was difficult to predict.

The present invention has been made in view of the above problems, and an object of the present invention is to provide a prediction method capable of accurately predicting the particle size distribution of crystallized particles.

In order to solve the above problems, according to one aspect of the present invention,
The particle size distribution of the crystallization particles produced by crystallization vessel a continuous, below formula (1), (8), predicted using (12) and (14), the particle size distribution of the crystallization particles Prediction method is provided.

According to one aspect of the present invention, there is provided a prediction method capable of accurately predicting the particle size distribution of crystallized particles.

It is a flowchart of the manufacturing method of the nickel-containing hydroxide according to one Embodiment. It is sectional drawing which simplifies the aggregate formed in the first half of the particle growth process by one Embodiment. It is sectional drawing which simplifies the outer shell formed in the latter half of the particle growth process by one Embodiment. It is a top view which shows the chemical reaction apparatus used in the manufacturing method of the nickel-containing hydroxide by one Embodiment. It is sectional drawing of the chemical reaction apparatus along the VV line of FIG. It is a schematic diagram which shows the outline of the probability density distribution with respect to the normalization rate α by one Embodiment. It is a schematic diagram which shows the coalescence and separation of the particle by one Embodiment. It is a figure which shows the actual measurement result and the calculation result of the particle size distribution of the particle crystallized under the stirring condition of Table 2.

Hereinafter, embodiments for carrying out the present invention will be described with reference to the drawings, but in each drawing, the same or corresponding configurations will be referred to with the same or corresponding reference numerals, and the description thereof will be omitted. In the following description, a method for producing a nickel-containing hydroxide and a method for predicting the particle size distribution of crystallization particles such as nickel-containing hydroxide will be described in this order. It goes without saying that the type of crystallization particles to which the method for predicting the particle size distribution of the present disclosure is applied is not limited to nickel-containing hydroxides.

(Manufacturing method of nickel-containing hydroxide)
FIG. 1 is a flowchart of a method for producing a nickel-containing hydroxide according to an embodiment. As shown in FIG. 1, the method for producing a nickel-containing hydroxide is to obtain particles of the nickel-containing hydroxide by neutralization crystallization, and the nucleation step S11 for generating the nuclei of the particles and the particles are formed. It has a particle growth step S12 for growing. Hereinafter, each step will be described, but before that, the nickel-containing hydroxide obtained will be described.

(Nickel-containing hydroxide)
Nickel-containing hydroxide is used as a precursor of a positive electrode active material of a lithium ion secondary battery. Nickel-containing hydroxide is, for example, (1) the general _{formula: Ni 1-x-y Co} x Al y (OH) 2 + α (0 ≦ x ≦ 0.3,0.005 ≦ y ≦ 0.15,0 ≦ or a nickel complex hydroxide represented by alpha ≦ 0.5), or, (2) the general _{formula: Ni x Co y Mn z M} t (OH) 2 + α (x + y + z + t = 1,0.1 ≦ x ≦ 0.7, 0.1 ≦ y ≦ 0.5, 0.1 ≦ z ≦ 0.8, 0 ≦ t ≦ 0.02, 0 ≦ α ≦ 0.5, M is Ti, V, Cr , Zr, Nb, Mo, Hf, Ta, and one or more additive elements selected from W), a nickel-cobalt-manganese composite hydroxide.

The nickel-containing hydroxide contains nickel, preferably a metal other than nickel. A hydroxide further containing a metal other than nickel is called a nickel composite hydroxide. The metal composition ratio of the nickel composite hydroxide (for example, Ni: Mn: Co: M) is maintained in the obtained positive electrode active material, so that it matches the metal composition ratio required for the positive electrode active material. Is adjusted to.

(Manufacturing method of nickel-containing hydroxide)
As described above, the method for producing a nickel-containing hydroxide includes a nucleation step S11 and a particle growth step S12. In the present embodiment, the nucleation step S11 and the particle growth step S12 are separately carried out by controlling the pH value of the aqueous solution in the crystallization tank using a batch type crystallization tank.

In the nucleation step S11, nucleation occurs prior to particle growth, and particle growth hardly occurs. On the other hand, in the particle growth step S12, particle growth takes precedence over nucleation and almost no new nuclei are generated. By separately carrying out the nucleation step S11 and the particle growth step S12, a homogeneous nucleus having a narrow particle size distribution range can be formed, and then the nucleus can be uniformly grown.

Hereinafter, the nucleation step S11 and the particle growth step S12 will be described. The pH value range is different between the aqueous solution in the crystallization tank in the nucleation step S11 and the aqueous solution in the crystallization tank in the particle growth step S12, but the range of ammonia concentration and the range of temperature are substantially the same. It's okay.

In this embodiment, a batch type crystallization tank is used, but a continuous type crystallization tank may be used. In the latter case, the nucleation step S11 and the particle growth step S12 are carried out at the same time. In this case, the range of the pH value of the aqueous solution in the crystallization tank is naturally the same, and may be set to, for example, in the vicinity of 12.0.

(Nucleation process)
First, a raw material solution is prepared. The raw material liquid contains at least a nickel salt, and preferably further contains a metal salt other than the nickel salt. As the metal salt, nitrate, sulfate, hydrochloride and the like are used. More specifically, for example, nickel sulfate, manganese sulfate, cobalt sulfate, titanium sulfate, ammonium peroxotitanate, potassium titanium oxalate, vanadium sulfate, ammonium vanadate, chromium sulfate, potassium chromate, zirconium sulfate, zirconium nitrate, Niobium oxalate, ammonium molybdate, sodium tungstate, ammonium tungstate and the like are used.

The metal composition ratio of the raw material liquid (for example, Ni: Mn: Co: M) is maintained in the obtained nickel composite hydroxide, so that it matches the composition ratio required for the nickel composite hydroxide. It will be adjusted.

Further, an alkaline aqueous solution, an ammonia aqueous solution, and an aqueous solution obtained by supplying and mixing water are stored in the crystallization tank. The mixed aqueous solution is hereinafter referred to as "pre-reaction aqueous solution". The pH value of the aqueous solution before the reaction is adjusted within the range of 12.0 to 14.0, preferably 12.3 to 13.5, based on the liquid temperature of 25 ° C. The concentration of ammonia in the pre-reaction aqueous solution is preferably adjusted within the range of 3 to 25 g / L, more preferably 5 to 20 g / L, and even more preferably 5 to 15 g / L. Further, the temperature of the aqueous solution before the reaction is preferably adjusted within the range of 20 to 60 ° C, more preferably 35 to 60 ° C.

As the alkaline aqueous solution, for example, one containing an alkali metal hydroxide such as sodium hydroxide and potassium hydroxide is used. The alkali metal hydroxide may be supplied as a solid, but is preferably supplied as an aqueous solution.

As the aqueous ammonia solution, one containing an ammonia feeder is used. As the ammonia feeder, for example, ammonia, ammonium sulfate, ammonium chloride, ammonium carbonate, ammonium fluoride and the like can be used.

In the present embodiment, an ammonia feeder is used as the non-reducing complexing agent, but ethylenediaminetetraacetic acid, nitritotriacetic acid, uracil diacetic acid, glycine and the like may be used. The non-reducing complexing agent may be any one capable of forming a complex by bonding nickel ions or the like in an aqueous solution in a crystallization tank.

After adjusting the pH, ammonia concentration, temperature, etc. of the pre-reaction aqueous solution, the raw material solution is supplied into the crystallization tank while stirring the pre-reaction aqueous solution. As a result, a reaction aqueous solution in which the pre-reaction aqueous solution and the raw material solution are mixed is formed in the crystallization tank, nucleation is generated by neutralization crystallization, and the nucleation step S11 is started.

In the nucleation step S11, when the pH value of the reaction aqueous solution is 12.0 or more, nucleation becomes dominant over particle growth. Further, in the nucleation step S11, when the pH value of the reaction aqueous solution is 14.0 or less, it is possible to prevent the nuclei from becoming too fine and to prevent the reaction aqueous solution from gelling. In the nucleation step S11, the fluctuation range (the range between the maximum value and the minimum value) of the pH value of the reaction aqueous solution is preferably 0.4 or less.

Further, in the nucleation step S11, when the ammonia concentration in the reaction aqueous solution is 3 g / L or more, the solubility of metal ions can be kept constant, and nuclei having a uniform shape and particle size can be easily generated. Further, in the nucleation step S11, when the ammonia concentration in the reaction aqueous solution is 25 g / L or less, the metal ions remaining in the liquid without precipitation are reduced, and the production efficiency is improved. In the nucleation step S11, the fluctuation range (the range between the maximum value and the minimum value) of the pH value of the reaction aqueous solution is preferably 5 g / L or less.

Further, in the nucleation step S11, when the temperature of the reaction aqueous solution is 20 ° C. or higher, the solubility of the nickel-containing hydroxide is high, so that nucleation occurs slowly, and the control of nucleation is easy. On the other hand, when the temperature of the reaction aqueous solution is 60 ° C. or lower, the volatilization of ammonia can be suppressed, so that the amount of ammonia water used can be reduced and the production cost can be reduced.

In the nucleation step S11, an alkaline aqueous solution and an ammonia aqueous solution are supplied into the crystallization tank in addition to the raw material solution so that the pH value, ammonia concentration, and temperature of the reaction aqueous solution are maintained within the above ranges. As a result, the formation of nuclei continues in the reaction aqueous solution. Then, when a predetermined amount of nuclei are generated, the nucleation step S11 is completed. Whether or not a predetermined amount of nuclei are produced can be estimated from the amount of metal salt supplied.

(Particle growth process)
After the completion of the nucleation step S11 and before the start of the particle growth step S12, the pH value of the reaction aqueous solution in the crystallization tank was adjusted to 10.5-12.0, preferably 11.0 to 12.0 based on the liquid temperature of 25 ° C. The pH value is adjusted to 12.0 and lower than the pH value in the nucleation step S11. To adjust the pH value, stop the supply of the alkaline aqueous solution into the crystallization tank, and supply an inorganic acid (for example, sulfuric acid in the case of sulfate) in which the metal of the metal salt is replaced with hydrogen into the crystallization tank. It can be adjusted by things.

After adjusting the pH, ammonia concentration, temperature, etc. of the reaction aqueous solution, the raw material solution is supplied into the crystallization tank while stirring the reaction aqueous solution. As a result, the growth of nuclei (particle growth) is started by neutralization crystallization, and the particle growth step S12 is started. In the present embodiment, the nucleation step S11 and the particle growth step S12 are performed in the same crystallization tank, but may be performed in different crystallization tanks.

In the particle growth step S12, if the pH value of the reaction aqueous solution is 12.0 or less and lower than the pH value in the nucleation step S11, almost no new nuclei are generated, and the particle growth is more than the nucleation. It occurs with priority.

Since the pH value is 12.0, which is a boundary condition between nucleation and particle growth, the priority order changes depending on the presence or absence of nuclei present in the reaction aqueous solution. For example, if the pH value of the nucleation step S11 is set higher than 12.0 to generate a large amount of nuclei and then the pH value is set to 12.0 in the particle growth step S12, a large amount of nuclei are present in the reaction aqueous solution. , Particle growth takes precedence. On the other hand, when there are no nuclei in the reaction aqueous solution, that is, when the pH value is set to 12.0 in the nucleation step S11, nucleation is prioritized because there are no nuclei to grow. After that, if the pH value is made smaller than 12.0 in the particle growth step S12, the produced nuclei grow. In order to clearly separate nucleation and particle growth, the pH value of the particle growth step is preferably 0.5 or more lower than the pH value of the nucleation step, and more preferably 1.0 or more.

Further, in the particle growth step S12, when the pH value of the reaction aqueous solution is 10.5 or more, the solubility by ammonia is low, so that the metal ions remaining in the liquid without precipitation are reduced, and the production efficiency is improved.

In the particle growth step S12, an alkaline aqueous solution and an ammonia aqueous solution are supplied into the crystallization tank in addition to the raw material solution so that the pH value, the ammonia concentration, and the temperature of the reaction aqueous solution are maintained within the above ranges. As a result, particle growth is continued in the reaction aqueous solution.

The particle growth step S12 can be divided into the first half and the second half by switching the atmosphere in the crystallization tank. The atmosphere in the first half is an oxidizing atmosphere as in the nucleation step S11. The oxygen concentration in the oxidizing atmosphere is 1% by volume or more, preferably 2% by volume or more, and more preferably 10% by volume or more. The oxidizing atmosphere may be an atmospheric atmosphere (oxygen concentration: 21% by volume) that is easy to control. The upper limit of the oxygen concentration in the oxidizing atmosphere is not particularly limited, but is 30% by volume or less. On the other hand, the atmosphere in the latter half is a non-oxidizing atmosphere. The oxygen concentration in the non-oxidizing atmosphere is 1% by volume or less, preferably 0.5% by volume or less, and more preferably 0.3% by volume or less. The oxygen concentration of the non-oxidizing atmosphere is controlled by mixing the oxygen gas or the atmosphere with the inert gas.

FIG. 2 is a schematic cross-sectional view of the agglomerates formed in the first half of the particle growth step according to the embodiment. FIG. 3 is a schematic cross-sectional view of the outer shell formed in the latter half of the particle growth step according to the embodiment.

In the first half of the particle growth step S12, the seed crystal particles 2 are formed by the growth of the nucleus, and when the seed crystal particles 2 become large to some extent, the seed crystal particles 2 collide with each other, and the seed crystal particles 2 start to collide with each other. Aggregates 4 are formed. On the other hand, in the latter half of the particle growth step S12, a dense outer shell 6 is formed around the aggregate 4. As a result, particles composed of the aggregate 4 and the outer shell 6 are obtained.

The structure of the nickel-containing hydroxide particles is not limited to the structure shown in FIG. For example, when the nucleation step S11 and the particle growth step S12 are carried out at the same time, the structure of the particles obtained at the completion of the neutralization crystallization is different from the structure shown in FIG. The structure is, for example, a mixture of those corresponding to the seed crystal particles 2 and those corresponding to the outer shell 6 to form a uniform structure in which the boundary is not easily known.

When the nickel-containing hydroxide particles have grown to a predetermined particle size, the particle growth step S12 is terminated. The particle size can be estimated from the amount of metal salt supplied in each of the nucleation step S11 and the particle growth step S12.

After the nucleation step S11 is completed, in the middle of the particle growth step S12, the supply of the raw material liquid and the like may be stopped, the stirring of the reaction aqueous solution may be stopped, the particles may be precipitated, and the supernatant liquid may be discharged. Thereby, the metal ion concentration in the reaction aqueous solution reduced by the neutralization crystallization can be increased.

FIG. 4 is a top view showing a chemical reaction apparatus used in the method for producing a nickel-containing hydroxide according to one embodiment. FIG. 5 is a cross-sectional view of the chemical reaction apparatus along the VV line of FIG.

The chemical reaction apparatus 10 includes a crystallization tank 20, a stirring blade 30, a stirring shaft 40, and a baffle 50. The crystallization tank 20 houses the reaction aqueous solution in a columnar internal space. The stirring blade 30 stirs the reaction aqueous solution in the crystallization tank 20. The stirring blade 30 is attached to the lower end of the stirring shaft 40. The stirring blade 30 is rotated by rotating the stirring shaft 40 by a motor or the like. The center line of the crystallization tank 20, the center line of the stirring blade 30, and the center line of the stirring shaft 40 may coincide with each other and may be vertical. The baffle 50 is also called a baffle plate. The baffle 50 protrudes from the inner peripheral surface of the crystallization tank 20 and interferes with the rotating flow to generate an ascending flow and a descending flow, improving the stirring efficiency of the reaction aqueous solution.

Further, the chemical reaction apparatus 10 includes a raw material liquid supply pipe 60, an alkaline aqueous solution supply pipe 62, and an ammonia water supply pipe 64. The raw material liquid supply pipe 60 supplies the raw material liquid into the crystallization tank 20. The alkaline aqueous solution supply pipe 62 supplies the alkaline aqueous solution into the crystallization tank 20. The ammonia water supply pipe 64 supplies ammonia water into the crystallization tank 20.

(Method for predicting particle size distribution of crystallization particles such as nickel-containing hydroxide)
In the prediction method of the present disclosure, the particle size distribution of crystallization particles such as nickel-containing hydroxide is predicted by using the following formula (15). Hereinafter, the process of deriving the following equation (15) will be described. First, Table 1 below shows the meanings of the symbols used in the following derivation process.

表１において単位が［-］であることは、無次元量であることを表す。尚、表１には記載されていないが、以下の説明において、下付き添え字「ｉ」は大きい粒子を、下付き添え字「ｊ」は小さい粒子を表す。晶析粒子がニッケル含有水酸化物である場合、「晶析槽への総供給流量Ｑ」とは、原料液、アルカリ水溶液およびアンモニア水溶液の合計の単位時間当たりの供給量を意味する。

When the unit is [-] in Table 1, it means that it is a dimensionless quantity. Although not shown in Table 1, in the following description, the subscript "i" represents a large particle and the subscript "j" represents a small particle. When the crystallization particles are nickel-containing hydroxides, the "total supply flow rate Q to the crystallization tank" means the total supply amount of the raw material solution, the alkaline aqueous solution and the ammonia aqueous solution per unit time.

(Grain growth equation and growth function in crystallization reaction)
In the prediction method of the present invention, based on the conservation equation of the number of particles introduced in Non-Patent Documents 1 and 2, all the effects of precipitation, collision / coalescence, and fragmentation are incorporated into the growth function Ω, and the particle number density Ψ (r. The conservative equation of, t) is expressed by the following equation (2). Here, the growth function Ω is a function representing the time change of the particle size, and its magnitude depends on the particle size.

本発明の予測方法では、連続晶析型の量産装置から定常的に産出される粒子の粒径分布を解析対象にするため、上記式（２）から時間依存の項を消去する。また、粒子の成長過程のみを扱うため、核生成する粒子については、粒子径の最小値r₀を有する粒子が晶析槽に数密度Ψ₀で流入するものと近似して取り扱う。核生成理論を含まない、単純化された粒径成長に関する方程式は、成長関数Ωの積分形として下記の式（３）で表される。

In the prediction method of the present invention, the time-dependent term is eliminated from the above equation (2) in order to analyze the particle size distribution of particles constantly produced from the continuous crystallization type mass production apparatus. In addition, since only the growth process of the particles is dealt with, the nucleated particles are treated as if the particles _{having the minimum particle size r 0} flow into the crystallization tank at a number density of Ψ _0. The simplified equation for particle size growth, which does not include the theory of nucleation, is expressed by the following equation (3) as an integral form of the growth function Ω.

粒子が析出のみで成長して、その成長速度が粒径に依らず一定と考えると、上記式（３）で表される粒径分布は、指数関数的に単調減少する。ここに衝突・合体による成長が加わると、成長関数Ωは粒径に依存するようになり、ある粒径でピークを有する分布になる。析出と衝突・合体による粒子の成長過程をモデル化して成長関数Ωを求めることにより、上記式（３）から粒径分布Ψ(r)を計算できる。

Assuming that the particles grow only by precipitation and the growth rate is constant regardless of the particle size, the particle size distribution represented by the above formula (3) decreases exponentially and monotonically. When growth due to collision / coalescence is added here, the growth function Ω becomes dependent on the particle size, and the distribution has a peak at a certain particle size. The particle size distribution Ψ (r) can be calculated from the above equation (3) by modeling the growth process of particles due to precipitation and collision / coalescence to obtain the growth function Ω.

(Growth of particle size due to collision / coalescence)
While the particles float on the flow in the crystallization tank, they coalesce with other particles while repeatedly colliding with each other to form an agglomerate. When passing through the stirring blade, a part of this agglomerate is separated again by being pulled or sheared by the action of flow as described in Non-Patent Document 2. The particles grow as agglomerates by the collision / coalescence mechanism including this separation.

The number of times a particle collides with another particle per unit time (collision frequency) is expressed as the product of the collision cross-sectional area of the particle, the relative velocity, and the number density of the collided particle. Of the particles that collide at this frequency, the particles coalesce when the energy lost in the inelastic collision is less than the energy of the bond. The binding energy is due to the particle junction being filled with a new growth phase of the crystal by surface precipitation, and the rate of this collision coalescence is probable by the magnitude of the kinetic energy based on the relative velocity of the fluid fluctuation trying to break the bond. Is dominated.

In the prediction method of the present invention, as a result of the large particle i colliding with and coalescing with the small particle j, the large particle i increases the volume, while the small particle j decreases the number, and the number and volume of particles between the particles are increased. I made a balance. Taking the above into consideration, the volume at which large particles i grow due to collision / coalescence is expressed by the following equation (4).

同時に、小さな粒子jの消失数は下記の式（５）で表される。

At the same time, the number of disappearances of the small particles j is expressed by the following equation (5).

粒子の衝突断面積は、次のように取り扱う。粒子同士が接近すると、非特許文献３、４に記載のように互いの粒子の軌道が変化して衝突が回避される傾向がある。本発明の予測方法では、大きな粒子が移動するとき、その外周部に沿って小さな粒子は通過しようとすると考えられるので、大きな粒子と小さな粒子の半径を足し合わせた外円から、大きな粒子の内円を差し引いた環状面を衝突断面積とした。

The collision cross section of particles is treated as follows. When the particles approach each other, the trajectories of the particles change as described in Non-Patent Documents 3 and 4, and collisions tend to be avoided. In the prediction method of the present invention, when a large particle moves, it is considered that the small particle tries to pass along the outer peripheral portion thereof. Therefore, from the outer circle obtained by adding the radii of the large particle and the small particle, the inside of the large particle The annular surface obtained by subtracting the circle was defined as the collision cross-sectional area.

Regarding the relative velocity of particles, the turbulent collision theory described in Non-Patent Document 5 is cited. With reference to the center of the large particle i, _{the relative velocity at a position separated by the collision distance r i} + r _j follows the differential of the particle based on the velocity gradient of the laminar shear flow field, and the average value is calculated by the following equation. It is represented by (6).

粒子の相対運動は、実際には一様ではなく、例えば図６に示すような確率密度分布に基づく速度の揺らぎを有すると考えられる。この粒子の相対運動の揺らぎにより、衝突・合体頻度も確率分布を有すると考えられる。本発明の予測方法ではまず、粒子の相対速度を下記の式（７）に示すように平均速度で規格化した。規格化速度αに対する確率密度分布は図６に示すマックスウエル-ボルツマン分布を想定し、粒径に依らず一定であると近似した。

The relative motion of the particles is not actually uniform, and it is considered that the particles have velocity fluctuations based on the probability density distribution as shown in FIG. 6, for example. It is considered that the collision / coalescence frequency also has a probability distribution due to the fluctuation of the relative motion of the particles. In the prediction method of the present invention, first, the relative velocity of the particles was normalized by the average velocity as shown in the following equation (7). The probability density distribution with respect to the normalized velocity α assumes the Maxwell-Boltzmann distribution shown in FIG. 6 and is approximated to be constant regardless of the particle size.

従って、合体の割合はある結合エネルギーより小さな運動エネルギーである積算割合であるから、その割合をエネルギー比の指数関数（下記の式（８）参照）で近似する。規格化速度αで表現される同じ形の確率分布関数を用いれば、この合体確率はどの粒子径でも同様の表式になる。さらに、粒子の合体過程は、粒子の結合の強さに対して、他の粒子の衝突や流体による引張りやせん断による破壊作用が大きくなるとき、粒子が再び分離する場合があるが、これらの複雑な行程も下記の式（８）の指数関数型の合体確率で表現できるものとした。

Therefore, since the coalescence ratio is an integrated ratio that is a kinetic energy smaller than a certain binding energy, the ratio is approximated by an exponential function of the energy ratio (see the following equation (8)). Using the same form of probability distribution function expressed by the normalized velocity α, this coalescence probability has the same expression for any particle size. In addition, the particle coalescence process is complicated by the fact that the particles may separate again when the collision strength of the particles is increased by the collision of other particles or the destructive action of tension or shear by the fluid. It is assumed that such a process can be expressed by the exponential type coalescence probability of the following equation (8).

邪魔板付きの晶析槽では、撹拌軸を対称とした上下循環の軸流が形成される。粒子はこの軸流に乗って撹拌翼を通過して、このときに最も大きな破壊作用を受けると考えられる。本発明の予測方法では、撹拌翼における乱流エネルギー消散速度εから、上記式（６）を用いて撹拌翼通過時の粒子の相対運動に基づく運動エネルギーを求め、それを粒子の結合を破壊するエネルギーとして近似した。なお、本発明の予測方法では、衝突・合体した粒子の結合が破壊される効果のみを考慮しており、粒子自身が破壊されて元の大きさよりも小さくなる効果は取り入れていない。

In the crystallization tank with a baffle plate, an axial flow of vertical circulation is formed with the stirring axis symmetrical. It is considered that the particles ride on this axial flow and pass through the stirring blade, and at this time, undergo the greatest destructive action. In the prediction method of the present invention, the kinetic energy based on the relative motion of the particles when passing through the stirring blade is obtained from the turbulent energy dissipation rate ε in the stirring blade using the above equation (6), and the binding of the particles is broken. Approximate as energy. In the prediction method of the present invention, only the effect of breaking the bond of the colliding / coalescing particles is considered, and the effect of breaking the particles themselves to become smaller than the original size is not incorporated.

The particles that come into contact with each other due to collision are bonded by filling the joint between the particles by the precipitation of crystals. In the prediction method of the present invention, the magnitude of this binding energy is considered to be equal to the surface energy that increases when the binding surface is divided and exposed as a new surface, and as shown in FIG. 7, it is considered to be equal to the area of the binding surface. From the surface energy per unit area, it was expressed by the following formula (9). 7A and 7B are schematic views showing particle coalescence and separation according to one embodiment, FIG. 7A is a schematic diagram showing particle coalescence, and FIG. 7B is a schematic diagram showing particle separation.

粒子表面に析出する結晶の厚さをδとすると、結合面の面積Ｓは幾何学的な関係から下記の式（１０）で求めることができる。

Assuming that the thickness of the crystal precipitated on the particle surface is δ, the area S of the bonding surface can be obtained by the following equation (10) from the geometrical relationship.

粒子の析出反応は、粒子表面への溶質の輸送が律速になっていると近似すると、その速度はバルクの溶質濃度Cに比例するため下記の式（１１）で表される。

The particle precipitation reaction is expressed by the following formula (11) because the rate is proportional to the bulk solute concentration C, assuming that the transport of the solute to the particle surface is rate-determining.

本発明の予測方法では、ある条件で実際に晶析された粒子の粒径分布を参照して、モデルによる計算結果がその形状を再現できるように、上記式（１１）の物質移動係数kの大きさを調整して求めた。この値を晶析工程に共通なモデル定数として、別の晶析条件における粒径分布の計算にも適用した。

In the prediction method of the present invention, the mass transfer coefficient k of the above formula (11) can be reproduced by referring to the particle size distribution of the particles actually crystallized under a certain condition so that the calculation result by the model can reproduce the shape. It was calculated by adjusting the size. This value was used as a model constant common to the crystallization process and was also applied to the calculation of the particle size distribution under different crystallization conditions.

Based on the above considerations, the growth function due to precipitation is represented by the above equation (11), and the growth function due to collision / coalescence is represented by the above equation (4). By adding these, the growth function Ω due to precipitation and collision / coalescence is expressed by the following equation (12).

一方、粒子間の衝突・合体の結果として、粒径分布を表す方程式は下記の式（１３）のように補正される。

On the other hand, as a result of collision / coalescence between particles, the equation representing the particle size distribution is corrected as in the following equation (13).

ここでG(r)は粒子数密度の補正関数であり下記の式（１４）で表される。

Here, G (r) is a correction function of the particle number density and is expressed by the following equation (14).

上記式（３）と上記式（１３）と上記式（１４）を整理すると、粒径分布は下記の式（１５）で表される。下記の式（１５）は、セルフコンシステント（self-consistent）な方程式である。

When the above formula (3), the above formula (13) and the above formula (14) are arranged, the particle size distribution is represented by the following formula (15). Equation (15) below is a self-consistent equation.

上記式（１５）はセルフコンシステント法で解くことができる。例えば、晶析槽の容積の変更（主に大容積化）などが行われる場合に、つまり、晶析条件の変更が行われる場合に、上記式（１５）を用いて晶析粒子の粒径分布を予測することにより、その晶析条件の変更が妥当なものか検討するツールとして活用することができる。

The above equation (15) can be solved by the self-consistent method. For example, when the volume of the crystallization tank is changed (mainly increased in volume), that is, when the crystallization conditions are changed, the particle size of the crystallization particles is changed using the above formula (15). By predicting the distribution, it can be used as a tool to examine whether the change in the crystallization conditions is appropriate.

In order to verify the validity of the above formula (15), an experiment was conducted in which nickel sulfate and caustic soda were reacted in a crystallization tank as a laboratory machine to prepare nickel hydroxide particles. The actual measurement result of the particle size distribution of the particles obtained in the experiment (hereinafter, also simply referred to as "actual measurement result") and the calculation result using the above formula (15) (hereinafter, also simply referred to as "calculation result"). Was compared.

In the experiment, a continuous crystallization tank was used. The crystallization tank is filled with water adjusted to a predetermined pH, and the nickel sulfate aqueous solution and the caustic soda aqueous solution are supplied from the nozzle so as to be stoichiometrically equal while stirring the liquid by operating the stirring blade at a predetermined rotation speed. And reacted. The liquid flowing out of the crystallization tank was periodically sampled, and the particle size distribution of the particles contained in the liquid was measured by Microtrack MT3300EXII manufactured by Microtrack Bell. The crystallization experiment was continued until the change in particle size distribution with time disappeared. As shown in Table 2 below, four levels of tests were conducted in which the number of rotations of the stirring blade, the type of stirring blade, and the liquid volume of the crystallization tank were changed.

表２において、「6DT」は6枚ディスクタービン翼を、「4PP」は4枚ピッチドパドル翼を表す。

In Table 2, "6DT" represents 6 disc turbine blades and "4PP" represents 4 pitched paddle blades.

The conditions for solving the above equation (15) include the liquid volume of the crystallization tank, the supply flow rate of the raw material liquid, the kinematic viscosity of the fluid charged in the crystallization tank, the density of the particles, and the relative velocity of the particles. To calculate, the turbulent energy dissipation rate of the fluid surrounding the particle is required. Here, using the general-purpose thermo-fluid analysis software CFX15.0 manufactured by ANSYS, the turbulent energy dissipation rate when the particles pass through the stirring blade was obtained from the fluid simulation of the crystallization tank. In addition, the surface energy was obtained from the energy difference between the bulk and the surface structure using the most stable (001) plane from the crystal structure of nickel hydroxide. Energy was calculated using VASP (Vienna Ab initio Simulation Packege) using density functional theory.

In the calculation model of the particle size distribution, as an initial condition, a particle size cell having a size of 0.5 μm to 30 μm divided into 100 was prepared. The initial number of particles in each particle size cell was given an exponentially monotonically decreasing distribution from 0.5 μm to 30 μm. In addition, the nucleated particles were treated as if a predetermined number of particles having a minimum particle size of 0.5 μm flowed into the crystallization tank. The particle size distribution function represented by the above equation (15) is iteratively calculated under a predetermined calculation time step Δt, and when both Ψ (r) and Ψ'(r) match with sufficient accuracy, It was used as a stationary solution of the particle size distribution.

FIG. 8 is a diagram showing actual measurement results and calculation results of the particle size distribution of the particles crystallized under the stirring conditions of Table 2. In FIG. 8, the solid line shows the actual measurement result, and the broken line shows the calculation result. FIG. 8 (a) is a diagram showing actual measurement results and calculation results of the particle size distribution of the particles crystallized under the stirring conditions of (a) in Table 2. The shape of the probability distribution function with respect to the normalization coefficient of the relative velocity of the particles and the mass transfer coefficient of the precipitation reaction were adjusted so that the width of the particle size distribution, the peak particle size, and the peak frequency generally match. FIG. 8 (b) is a diagram showing actual measurement results and calculation results of the particle size distribution of the particles crystallized under the stirring conditions of (b) in Table 2. FIG. 8 (c) is a diagram showing actual measurement results and calculation results of the particle size distribution of the particles crystallized under the stirring conditions of (c) in Table 2. FIG. 8 (d) is a diagram showing actual measurement results and calculation results of the particle size distribution of the particles crystallized under the stirring conditions of (d) in Table 2.

As is clear from FIG. 8, it was confirmed that the calculation result can well reproduce the difference in the particle size distribution depending on the rotation speed and type of the stirring blade and the volume of the crystallization tank. Therefore, the prediction method using the above formula (15) is useful as a study tool for determining crystallization conditions such as the volume of the crystallization tank.

(Transformation, improvement)
Although the embodiment of the method for predicting the particle size distribution of the crystallized particles has been described above, the present invention is not limited to the above embodiment, and various modifications and improvements are made within the scope of the gist described in the claims. Is possible.

Prediction method of the present disclosure can be applied to predict the particle size distribution of the crystallization particles produced in a continuous crystalliser.

2 Seed crystal particles 4 Aggregates 6 Outer shell 10 Chemical reactor 20 Crystallization tank 30 Stirring blade 40 Stirring shaft 50 Baffle 60 Raw material liquid supply pipe 62 Alkaline aqueous solution supply pipe 64 Ammonia water supply pipe

Claims (1)

The particle size distribution of the crystallization particles produced by crystallization tank continuous, be predicted using the following formula (A) ~ (D), the prediction method of the particle size distribution of the crystallization particles.

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