基于卷积和矩阵变流量压降试井解释新方法

A new interpretation technique based on convolution and matrix for variable-rate falloff test

为解决油井压降测试过程中变流量下的压力动态响应问题,克服实际应用中缺少高精度压力数据的困难,使不稳定试井分析方法能够应用实际生产动态数据评价油气藏,应用杜哈美积分原理结合线性系统的卷积理论引出基于离散系统卷积和矩阵的压力动态响应关系式,选用单井径向流点源函数建立模型;利用油井实际压降测试数据和最优化方法求解符合该井实际生产动态的模型参数。利用离散系统卷积和矩阵关系式模型结合最优化方法求得的压力响应结果符合实际生产动态,求解得到理论解和实际测试结果误差较小;模型反映了油井的生产动态特性,可对油气藏历史生产状况进行评价,同时对生产动态预测具有较好应用价值。通过建立卷积和矩阵关系式模型,解决了变流量下的压力动态响应和缺少高精度压力条件下不稳定压力分析方法解释困难的问题。该模型可扩展性强,应用点源函数理论可推广到不同的实际油藏模型。

To highlight dynamic pressure responses under variable flow during falloff test of oil wells for providing high-resolution pressure data to facilitate the pressure transient well testing in reservoir assessment,the Duhamel integral principle and the convolution theory for linear system were combined to generate the correlation between discrete system convolution sum matrix for identifying dynamic pressure responses.Then,the model was constructed by using radial flow point-source function of a well,and actual falloff test data and optimal method were used jointly to derive the model parameters conforming to the actual production performance of the well.It is indicated that the pressure responses derived by using the model constructed according to the discrete system convolution sum matrix correlation together with the optimal method coincide well with actual production performance.Minor errors are observed between actual testing data and the theoretical solution derived through optimal solution of the model.The proposed model reflects the production performance of oil well,and it can be used to assess the production history of reservoirs and also predict the production performance.The model based on the convolution sum matrix correlation can derive the dynamic pressure responses under variable flow and provides a technique of transient pressure analysis without high-precision pressure data.This model is expandable and can be extended to different reservoirs in conjunction with the point-source function.