二次梯度非线性渗流问题求解

Solution for the Problem of Quadratic Gradient Nonlinear Percolation

通过建立考虑井储和表皮效应的均质油藏二次梯度真实井径不稳定渗流数学模型,选取不同的求解方法研究了二次梯度非线性渗流求解问题:由于模型严重的非线性特性,利用Laplace积分变换法求解极其困难而不可取;Duhamel叠加原理法有其自身的适用范围而不适用;Douglas-Jones预估-校正法可以解决这类非线性模型求解问题,但计算量大、耗时而不利于试井拟合解释。通过引入有效井径模型,比较容易地获得了井底压力动态响应关系曲线,避免了考虑表皮的真实井径模型求解难的问题,为多重介质等复杂介质油藏及复杂边界油藏的非线性渗流问题研究奠定了基础,提供了求解新思路。

By establishing a non-steady percolating model considering the actual well radius, skin effect of storage of geologic reservoirs, different solutions were selected for solving it, while the Duhamel superposition was not appropriate for its limited application ranges. Douglas-Jones predicting and connecting method was suitable for solving it , but its calculation was big and time consumption, was not suitable for interpreting well test. An effective well radius model was introduced, by which the curve of dynamic response of bottomhole pressure was easily obtained, the problem of difficult solution by using actual well radius model was effectively avoided, it provides a basis for studying the problem of nonlinear percolation in complex medium and complex boundary reservoirs.