The Kolmogorov model and Schneider rate equation
were successfully applied to simulate the crystallization behavior of neat polymers under complex thermal and flow histories.
Therefore, the flow rate equation
must be corrected considering theses effects.
Method for determining the rate equation
of the pyrolysis of oil shale
According to the research of hot deformation data, Sellar and Tegart developed an Arrhenius kinetic rate equation
which includes the activation energy and the temperature .
The model mainly contains three parts: (1) the fluid flow at the REV scale which is governed by the generalized Navier-Stokes equations, (2) the mass transfer in porous media with respect to the effective diffusivity and a source/sink term solved by the advection-diffusion equation, and (3) the gas-solid adsorption process in the porous matrix which is governed by the typical Langmuir adsorption rate equation
. The remaining parts are organized as follows: In Section 2, a generalized LB model for fluid flow in porous media is revisited briefly.
First, given a "rate constant" for each reaction, one can write down a differential equation called the rate equation
, which describes the time evolution of the concentration of each species in a deterministic way.
The movement of solute molecules on to solid surface particulates from the aqueous phase, and then diffusion of the solute molecules into the pore interiors  could be described by the intra-particle diffusion rate equation
and is given as .
The corresponding pseudo-second order rate equation
is given as,
Despite the above-mentioned achievements in this particular research field, there is a lack of systematic investigation on an analytical solution for the dissolution rate equation
of rock salt, so that more in-depth study is required.
A brief derivation of a nucleation rate equation
based on this framework is given in the preface.
Equation A1 is called the Minimum Error Rate Equation