Abstract: A mathematical model,which is about a partial differential equation mixture problem,for the contamination of formation due to solid particle invasion,has been put forward by applying stochastic process theory.The function relationship between contamination degree and contamination distance can be obtained by numerical solutions under given time t(the definition of contamination density is also given.).And the permeability K of formation decreases with the increase of contamination degree.The variation of contamination distance with time is finally determined when the permeability K is lowered to a given value K.The calculated results accord with the real case.

Key words: contamination of formation, micrograin stoppage, invasion depth, stochastic process

摘要： 从随机过程中的扩散过程理论出发,并利用接触过程的有关结果,建立了偏微分方程混合问题的固体颗粒污染地层数学模型.数值求解后,可给出任一时间t值下,污染程度(定义了污染密度)随距离y值而变的函数关系.污染密度增大,使渗透率K降低,以K值低到某定值K所对应的距离y*(t)为t时的污染距离,则最终给出污染距离随时间的变化规律.试算结果与实际情况相符合.

关键词: 油层污染, 微粒堵塞, 侵入深度, 随机过程