Production performance analysis model of partially penetrated fractured vertical well in reservoir with high formation-saturation pressure difference
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摘要:
针对高地饱压差油藏早期衰竭式开发过程中,原油物性变化及地层渗透率应力敏感引发渗流控制方程强非线性的问题,通过定义拟压力函数与拟时间因子对该方程进行线性化处理,同时考虑油井压裂后裂缝在纵向上部分打开,建立了高地饱压差油藏部分压开垂直裂缝井渗流数学模型。利用Laplace变换、有限Fourier余弦变换及点汇叠加原理,求解得到部分压开无限导流垂直裂缝井的井底压力解;进一步结合导流能力影响函数、Duhamel褶积原理及封闭油藏纯弹性驱物质平衡方程,得到有限导流裂缝井的产量解。参数敏感性分析结果表明:对于存在渗透率应力敏感性的高地饱压差油藏,制定合理的生产制度可有效避免过大生产压差造成的地层渗透率损害,以及压力快速下降引发的原油过早脱气风险;压裂设计时应以裂缝位于储层中部、地层纵向压开程度大于0.5为目标,并结合地质特点、施工条件等因素综合确定最优的人工裂缝半长及渗透率。研究成果为高地饱压差油藏部分压开垂直裂缝井产量动态预测、地层参数反演提供了有效方法,同时也为该类井的生产制度优化及地层能量补充时机确定奠定了理论依据。
Abstract:As the changes of oil properties and stress-sensitive formation permeability, the flow governing equations for early-stage depletion development in reservoirs with high formation-saturation pressure difference is strong nonlinear. By the definition of pseudo-pressure function and pseudo-time factor and considering partially penetrated vertical fracture wells in such reservoirs, the mathematical model was established. Using Laplace transform, finite Fourier cosine transform, and the point sink superposition principle, the bottomhole pressure solution for a partially penetrated infinite-conductivity vertical fracture well was obtained. By incorporating the conductivity influence function, Duhamel’s convolution principle and material balance equation of closed reservoir, the production solution for a finite-conductivity fracture well was further derived. Parameter sensitivity analysis demonstrates that: for reservoirs with high formation-saturation pressure difference exhibiting stress sensitivity, implementing a rational production strategy can effectively avoid both formation permeability damage caused by excessive drawdown and the risk of dissolved gas liberates due to rapid pressure decline. The objectives should be central fracture placement within the reservoir and a vertical penetration ratio exceeding 0.5 when fracturing designing. Besides, the optimal fracture half-length and permeability should be determined based on geological characteristics and operational constraints. This study provides a methodology for forecasting production performance and inverting formation parameters of partially penetrated wells in reservoirs with high formation-saturation pressure difference. It also offers a theoretical basis for optimizing production strategies and determining the timing for formation energy replenishment in such reservoirs.
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