The kinetics observed in the leaching system often may contain more than one rate process. For example, the surface reaction acts simultaneously with the mass transfer process through the diffusion layer on the total kinetics. Then the surface reaction rate can be expressed by the following equation:
(1)
Where A- total area;
C s - surface concentration;
K s - the reaction rate constant of the surface reaction.
Under steady state conditions, C s can be obtained and brought into the above formula to obtain a mixed kinetic expression:
(2)
Where Δx is the thickness of the diffusion boundary layer, and the constant k 0 'is represented by the sum of the tandem reaction, ie, the mass transfer of the diffusion layer and the resistance of the surface reaction (the reciprocal of the rate), ie
(3)
If the area and Δx remain constant during the reaction, equation (2) becomes a simple first-order rate expression whose first-order rate constant k 0 ' contains D and K s with a complex temperature relationship. Usually D (solution diffusion coefficient) is less sensitive to temperature changes than K s with greater activation energy. Therefore K s will become much larger than D as the temperature increases. It is apparent from the formula (2) that diffusion at a high temperature is a rate controlling step, and at a low temperature, the surface reaction is a rate controlling step, and at a medium temperature, a mixing rate is controlled.
If the reaction causes the surface to form a product layer, diffusion occurs through the product layer, assuming that the surface area is constant, then equation (2) becomes
(4)
Where b(n 0 -n)=σΔx; n 0 is the number of moles of reactants in all ore blocks at the beginning of the reaction; n is the number of moles of residual reactant at any time t; n 0 -n represents The amount of reaction. Equation (4) can be integrated under the conditions of constant concentration and area.
(5)
This formula represents a linear parabolic rate and the sum rate, wherein the rate constant K p is equal to 2D / b. Equation (5) can also be written as
(6)
According to this formula, plotting t/Δn on Δn should result in a straight line whose slope contains the reciprocal of the parabolic rate constant K p and the intercept contains the reciprocal of the linear rate constant K s . It is reported that the Fe 3 + equation describes the initial stage of the oxidation leaching of copper ore.
In the study of mineral particle leaching process, the kinetic problem can often be treated by steady-state approximation. For example, stirring leaching must include steps of solution diffusion through the liquid boundary film, diffusion through the solid product layer, and surface reaction. For spherical particles, three successive kinetic processes are:
Boundary layer diffusion (7)
Diffusion through the product layer (8)
Surface reaction (9)
Under approximate steady-state conditions, each of the above rates is equal, so that a comprehensive expression can be derived (ignoring the inverse reaction):
(10)
The above formula can also be rewritten to express the rate using the reaction rate:
(11)
Formula (11) can be applied to a slurry composed of single-grained particles having an average radius of r 0 . For the case of having a particle size distribution characteristic, α = α I , that is, the reaction rate of the first particle having a particle size of r 0i , and then weighting the reaction rate of the individual particle size to obtain a total reaction rate α = . Under the condition of constant concentration, the integral equation (11) is obtained.
(12)
It is obvious from equation (12) that the integrated equation includes only the sum of the rate expressions of the boundary layer diffusion, the diffusion through the solid product layer, and the surface reaction. For the case where the concentration changes with time, as previously described, the concentration in equation (12) is C = C 0 (1-σba), at which point the equation must be numerically integrated.
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