古典渗流理论常被简化为简单的常规线性渗流,这与实际情况有很大误差.针对双重介质油藏,从质量守恒原理出发,详细地推导出了二次压力梯度非线性渗流偏微分方程,发现线性渗流是非线性渗流的近似、简化与处理;建立了考虑二次压力梯度的双重介质不稳定渗流试井数学模型;对其变量代换,最后利用Douglas-Jones预估-校正数值解法进行求解.绘制了该模型的试井样版曲线并对不同参数进行了敏感性分析、二次压力梯度引起的误差分析,结果表明考虑二次压力梯度的影响更符合实际油藏,不应被忽略.%The classical filtering flow theory is usually simplified into the common linear filtering flow. This makes some differences with the case in reality. The complicated nonlinear filtering flow mechanics marks a new direction of the development of the modern filtering flow mechanics. This paper mainly focuses on the reservoir with dual medium. In terms of the conservation law of mass, It deduces the quadratic pressure gradient nonlinear filtering flow partial differential equation. It discovers that the linear filtering flow is the approximation, simplification, and processing of the nonlinear one. Meanwhile, It establishes the dual medium unstable filtering flow mathematical model for well testing taking the quadratic pressure gradient terms into consideration. With the variable substitutions, It finally obtains its solution by using the Douglas-Jones estimate-calibrate numerical method. Moreover, it draws up the type curves for this model and makes the sensitivity analysis for various parameters as well as the error analysis resulting from quadratic pressure gradient terms. The results demonstrate that the consideration of quadratic pressure gradient terms fits the actual reservoir well and should not be ignored.
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