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到目前为止,人们在进行酸压施工设计,求解描述酸液浓度沿裂缝分布状况的对流扩散方程时,由于某些技术上原因均未考虑氢离子有效传质系数D_e随酸浓度C_D的变化规律。本文给出了在考虑D_e随C_D变化的条件下,用有限差分法求解对流扩散方程的过程。给出了对流扩散方程差分格式稳定性的求证方法以及该差分格式的稳定条件,并进一步给出了利用此稳定条件选取合理计算步长进行计算的结果。 在进行数理推证时,充分考虑了每一个物理量的特征,从而使推证简化。展示了数理方法求解工程问题的一个途经。
Up till now, people did not consider the law of the effective mass transfer coefficient D_e of hydrogen ion with the change of acid concentration C_D, because of some technical reasons when designing the acid pressure construction and solving the convection-diffusion equation describing the distribution of acid concentration along the fracture. . In this paper, the process of solving the convection-diffusion equation by finite difference method is given under the condition that D_e changes with C_D. The method of verifying the stability of convection-diffusion equations in differential format and the stability conditions of the difference scheme are given. The results of selecting reasonable calculation steps using this stability condition are given. In the mathematical reasoning, fully considered the characteristics of each physical quantity, so that the simplification of the proof. A mathematical approach to solving engineering problems is presented.