一种新的计算泥浆侵入储层电阻率分布的数学模型

A Novel Mathematical Model to Calculate Distribution of Mud Invasion Formation Resistivity

水基钻井泥浆滤液侵入储层不仅是一个典型的水驱替油的过程 ,同时伴随着泥浆微粒的侵入和滤液中离子与储层水中离子的混合 ,改变储层的电阻率 ,影响测井解释结果。在经典油水两相驱替理论和微粒运移理论基础之上推导出了描述离子混合、泥浆微粒入侵、微粒在储层孔隙中运移、在孔隙表面沉积和在孔喉处被捕集的方程组 ;依据并联电路原理推导出了由岩石骨架 +死孔隙结构、泥浆微粒在孔隙表面和孔喉的滞留部分、剩余油、注入水与油层水的混合液 4部分并联电阻表达式。建立了一个计算泥浆侵入条件下电阻率剖面上分布的数学模型。用有限差分法进行了求解并给出了一个高侵算例。

The invasion of water-base drilling mud is not only a typical water-oil displacement process but also invasion of mud particles and mixing of ions in mud filtrate and formation water, which leads to change in formation resistivity and influences the results of well log interpretation. Based on the classical theories of water-oil displacement and particle migration, a set of equations, which describe mixing of ions, the invasion of mud particles, the migration of particles in formation, particle deposition on the surface of pore bodies and particle capture at pore throats, is derived. According to the principle of parallel circuit, an expression of formation resistivity paralleled by rock matrix and dead-end pores, retentive particles at pore bodies or throats, remaining oil, and blend of injection water and formation water, is also derived. A novel mathematical model to calculate the distribution of formation resistivity on radial profile considering mud invasion is presented, and the distribution is solved by the finite difference method. And a run for highly resistive mud filtrate invasion is given as an example.