Semi-analytical solutions to one-dimensional advection-diffusion equations with variable diffusion coefficient and variable flow velocity
Semi-analytical solutions to one-dimensional advection-diffusion equations with variable diffusion coefficient and variable flow velocity
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DOI：
10.1016/j.amc.2013.06.052
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发表时间：
2013-09
期刊：
影响因子：
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通讯作者：
Xinfeng Jia;F. Zeng;Yongan Gu
中科院分区：
文献类型：
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作者：
Xinfeng Jia;F. Zeng;Yongan Gu
在大多数先前的研究中，平流扩散传质过程中的扩散/分散系数和流速通常被认为是恒定平均值，这对于具有恒定粘度的不可压缩流体流动可能是合理的。然而，这一假设可能不适用于某些循环过程，例如稠油强化采油（EOR）过程中的吞吐二氧化碳注入和循环溶剂注入，其中扩散系数和流速均随时间和空间变化。本文开发了两种新颖的一维（1D）平流扩散数学模型：一种模型考虑恒定扩散系数和可变流速，另一种模型将这两个参数视为变量。两个新模型的半解析解是通过拉普拉斯变换和可变扩散系数和流速的特殊近似方案开发的。通过特殊平流扩散情况的解析解和数值解验证了半解析结果。发现恒定扩散系数和可变扩散系数的浓度分布具有截然不同的形状。在原油-溶剂传质过程中，流速比扩散系数发挥更大的作用，这意味着溶剂室和原油区之间的压力梯度可以大大增强溶剂在原油中的溶解。在某些基于溶剂的 EOR 方法中，重力可能会阻碍原油和溶剂的混合过程。
Diffusion/dispersion coefficient and flow velocity in an advection–diffusion mass-transfer process have both been commonly considered as constant mean values in most previous studies, which may be reasonable in incompressible fluid flow with a constant viscosity. However, this assumption may not be applicable for some cyclic processes, such as huff-n-puff CO2injection and cyclic solvent injection in heavy oil enhanced oil recovery (EOR) processes, in which both the diffusion coefficient and flow velocity vary with time and space.This paper develops two novel one-dimensional (1D) advection–diffusion mathematical models: one model considers a constant diffusion coefficient and a variable flow velocity, and the other one considers both parameters as variables. Semi-analytical solutions to both new models are developed through the Laplace transformation and a special approximation scheme to the variable diffusion coefficient and flow velocity. The semi-analytical results are validated by an analytical solution to a special advection–diffusion case as well as the numerical solutions.It is found that the concentration distribution for the constant and variable diffusion coefficients has quite different shapes. The flow velocity can play a much larger role than the diffusion coefficient does in the crude oil–solvent mass-transfer process, implying the pressure gradient between the solvent chamber and the crude oil zone can greatly enhance the solvent dissolution into the crude oil. Gravity force might hinder the mixing process of crude oil and solvent in some cases of solvent-based EOR methods.