第二节势的叠加原理 The line absorbing fluid from formation is called line sink The line sink is equivalent to production well 线源向地层供给液体的点相当于注入井 The line supplying fluid into formation is called line source The line source is equivalent to injection well 线汇(源)的强度单位有效厚度的油层的产量或 注入量q,规定线汇的强度为负,线源的强度为正。 The production or injection of oil layer of unit effective thickness q is called the intensity of line sink(source). It is set that the intensity of line sink is negative and that of line source is positive 对于水平等厚地层,只需讨论它的一个水平截面就够了,此时线汇 (源)就变成点汇(源)。今后对线汇(源)和点汇(源)不加区分。 本章中为行文简洁,一律假设地层厚度h=1
第二节势的叠加原理 设均质不可压缩液体在均质不可压缩地层中渗流,求无 限大地层上强度为一q的点汇所造成的压力分布 取点汇为极坐标系的原点,由于地层和液体都是均质的 拉氏方程为: 0 (31)1 p=CInr +C? (3-2) 、C2为任意常数,两边同时对r求导得 (3-3) dr
第二节势的叠加原理 已知点汇的强度为一q,则有: arK ap 2KC q mr u dr 因此 qu 2K 将C1值代入式(3-2)可得无限大平面地层上强度为 q的点汇所造成的压力分布为: D≈qnr+C2 (3-4) 2TK 我们引入势的概念:①=p+C3 (3-5) Φ称为势,C3是任意常数
第二节势的叠加原理 有了势的概念,达西方程可以写为 v=-grad① (3-6) 对于平面径向流就有: dap (3-7) 联立式(3-4)和式(3-5)可得: Φ=qnr+C (3-8) 2丌
势的叠加原理:若均质等厚不可压缩的无限大地层上有许多点 汇、点源同时工作,我们自然就会想到地层上任意一点的势应 该等于每个点源、点汇单独工作时在该点所引起的势的代数 和 If there are lots of point sink and point source working simultaneously in the homogeneous isopachous incompressible infinite formation, we will naturally call to mind that the potential of a arbitrary point in formation should be equal to the algebraic sum of potential on this point caused by each point sink and point source when working independently, and this is the superposition principle of potentia 设n个点汇(源)的强度为q;(i=1,…,n),地层中任 点M距各个点汇(源)的距离分别为r;(i=1,2,,n), 则M点的势为 ∑土qInr+C (3-9) 对于点源q的前面应取负值,这是因为点源是负 点汇的缘故