油田注入水中固体颗粒对地层伤害的数学模型

建立了模拟注水过程中由于固体颗粒侵入造成地层伤害的一维（径向）两相（油、水）数学模型。该模型为一组非线性偏微分方程，它反映了固体颗粒在地层孔道中的运移、孔壁深积与孔喉堵塞引起的颗粒滞留及其对地层孔隙度、渗透率及油水两相流动状况的影响。用有限差分方法求解数学模型，编制了模拟计算程序。举例说明了数学模型在３个方面的应用：分析注入水中颗粒浓度对地层伤害程度的影响；预测不同注水量下地层伤害程度；求出地层伤

A Mathematical Model for Simulating Formation Damage due to Solid Particles Invasion during Water Injection

A mathematical model of one-dimension(radial),two-phase(oil and water)flow applied to simulate formation damage due to solid particles invasion during water injection processes is presented. It consists of a group of nonlinear partial differential equations. The migration of particles in a porous medium, the particle retention resulting from pore surface deposition and pore throat blocking and the effect of the particle retention on the formation porosity and permeability and on the flow of oil and water are considered in the model. The simulator based on the model has been developed. The application of the model are illustrated in three aspects.The model has been used to analyse the effect of the particle concentration of injection water on formation damage, to predict formation damage with different volumes of water injection, to estimate the damage radius,permeability in the damage area and skin factor which are the necessary design parameters for the treatment of the elimination damage.