Abstract
It has been repeatedly noted in the literature that the physic-chemical properties of oil extracted at different stages of exploitation can vary significantly. We have investigated a modification of the Buckley — Leverett model (BL model) in our previous works to study the influence of oil viscosity change on the solutions of twophase filtration problems. In this model the change in oil viscosity was modeled using the dependence of the viscosity ratio on dynamic water saturation. The solutions to the linear displacement problem at a given total filtration rate were analyzed. This article considers a modification of the two-phase isothermal Muskat — Leverett model (ML model), which takes into account capillary forces. The influence of oil viscosity change in the process of oil production on the structure of the solution is studied numerically a case study of the problem of radial displacement with a given pressure drop.
Highlights
We have investigated a modification of the Buckley — Leverett model (BL model) in our previous works to study the influence of oil viscosity change on the solutions of twophase filtration problems
In this model the change in oil viscosity was modeled using the dependence of the viscosity ratio on dynamic water saturation
This article considers a modification of the two-phase isothermal Muskat — Leverett model (ML model), which takes into account capillary forces
Summary
Систему уравнений плоской радиальной изотермической фильтрации двухфазной несжимаемой жидкости в однородной пористой среде можно записать в виде [6, 7]. P2 − p1 = pc (s) = (m0 / K0 )1/ 2σj(s), s1 + s2 = 1, где r — пространственная переменная, 0 ≤ r ≤ R, R — радиус контура питания;. T — время; s — динамическая водонасыщенность порового пространства, определяемая по формуле s Si — истинная насыщенность флюидом порового пространства (индекс i = 1 соответствует вытесняющей фазе — «воде», а i = 2 — нефти), Si0 — остаточная насыщенность i-й фазы; pi — давление в i-й фазе; m m0(1 −. В данной работе изучаются решения в условиях несжимаемости жидкостей, в горизонтальном, несжимаемом, однородном нефтяном пласте (m0 = const, K0 = const). Поэтому для моделирования эффекта увеличения вязкости нефти в процессе эксплуатации месторождения можно использовать следующую зависимость μ2 от степени обводненности s(r, t): μ2 (s) μ. — значение вязкости нефти на конечной стадии разработки месторождения при s = 1. Волна над безразмерными переменными далее опускается, и уравнение (2) запишется в виде
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