考虑页岩气赋存及非线性流动机理的产能预测半解析方法

A semi-analytical method of production prediction for shale gas wells considering multi-nonlinearity of flow mechanisms

常规油气井可较容易求得解析产能,而页岩气的解吸、滑脱和扩散等非线性流动机理导致产能模型具有严重的非线性.本文运用三线性流模型,引入新的拟压力和拟时间处理页岩气的解吸和压缩性的非线性,运用逐次替换法处理滑脱和扩散的非线性.引入动用范围的概念,结合物质平衡方法和牛顿迭代法求得不同时间下的平均压力,以此不断更新模型参数,获得产能的半解析解.结果表明:(1)该方法能高效处理模型的非线性,准确快速地获得页岩气井的产能;(2)忽略气体的压缩性会严重低估气井产能;滑脱和扩散提高了气井产能,但加剧了产量递减;吸附解吸提高了中后期的产能,减缓了产量递减;(3)该方法能很好地拟合矿场生产数据,并预测气井的产能和可采储量.

Unlike conventional reservoirs, production prediction for shale gas wells is not easy with analytical models for model nonlinearity caused by multi flow mechanisms of shale gas, such as desorption, slippage flow and diffusion. This paper presents a method to linearize the production prediction model based on the trilinear flow model. The nonlinearity of desorption and gas compressibility is linearized by defining a pseudo-pressure and pseudo-time, and the nonlinearity of apparent permeability is dealt with iterations. Average pressure in the investigation is applied to convert the pseudo-time to real time, which is calculated with material balance equation and Newton iteration. The results show that： （1） The production predicted with the semi-analytical method is accurate for the nonlinearity in the model being dealt properly; （2） Neglecting the compressability of gas has a great influence on precision of production prediction; slippage flow and diffusion of shale gas increase the productivity of shale gas wells, but they aggravate the decline of production; desorption in shale matrix can enhance middle and long term production, and alleviate production decline; （3） The field case shows the veracity of the semi-analytical model, and gas production and EUR can be evaluated with the model.