基于数值模型的气井现代产量递减分析及动态预测

Advanced production decline analysis and performance forecasting of gas wells based on numerical model

传统的气井生产动态预测方法常采用拟稳态产能方程结合物质平衡方程来进行,由于低渗、致密储层流动很难达到拟稳态,预测结果可能存在较大误差。现代产量递减分析技术已成为单井动态预测的新技术,但还停留在解析模型阶段,通常采用叠加原理进行全程历史拟合。由于气井生产阶段产量波动大、流动阶段多,历史拟合计算周期长,解析法难以满足现场需求。针对上述问题,以垂直压裂井为例,建立了不稳定渗流数学模型,采用混合有限元方法获得了定产降压、定压降产和变产变压等3种生产模式的数值解。并根据定产降压解绘制了现代产量递减分析曲线,变产变压解进行全程历史拟合以及先定产降压、后定压降产的组合进行气井生产动态预测。模型结果与Topaze商用软件的计算结果一致,且数值模型的全程历史拟合速度具有明显优势,与传统生产动态预测方法的结果对比以及现场实例分析结果表明,新模型结果准确且方法实用、可靠。

The pseudo-steady state productivity equation in combination with material balance equation is always used as the traditional performance forecasting method of gas-well production.Due to low permeability,the flow of tight reservoirs is difficult to reach a pseudo-steady state,so that big errors may exist in the forecasting results.The advanced production decline analysis has been a new technology for single-well performance forecasting,but still at the analytical model stage,and thus the superposition principle is commonly used for whole-course history matching.Because of the large yield fluctuation at gas-well production stage and the multiple flow stages,history matching shows a long computation period,so the analytical method is difficult to meet the onsite demand.In view of above questions,a type of unstable porous flow mathematical model was established by taking the vertical fractured well as an example,and the numerical solutions to three kinds of production patterns including producing at a constant rate,producing at a constant bottom hole flowing pressure and variable pressure and variable rate were obtained using the mixed finite element method.The advanced production decline analysis curve was drawn based on the solution of constant rate production,the whole-course history matching was conducted by variable pressure and variable rate solutions,and the production performance forecasting of gas wells was carried out according to the combination of the constant rate production and the later constant pressure production.By comparison,the model results and the calculation results of Topaze commercial software are consistent,and the whole-course history matching rate of numerical model has significant advantages.The comparison with the results of traditional production performance forecasting method and the field-case analysis results show that the model results of this study are accurate and the used methods are practical and reliable.