低渗透气藏压裂井三项式方程推导及应用

低渗透气藏压裂前自然产能很低或基本无产能，压裂是低渗透气藏增产和保持经济开采的重要措施。传统的二项式产能方程只能描述高速非达西渗流，对于这种低渗压裂井，地层的低渗透性和裂缝的高导流能力使得其渗流规律已经和压裂前大不一样，二项式产能方程已无法描述气井的生产状况，必须建立新的产能方程。文章从渗流力学基本理论出发，建立了低渗透气藏压裂井三项式产能方程。该模型全面考虑低渗透气藏压裂井的低速非达西渗流和高速非达西渗流的影响，得出了低渗透气藏压裂井渗流阻力由三部分组成，即启动压力阻力、粘滞阻力、惯性阻力，三者同时存在使得渗流阻力加大，并提出了低渗压裂井产能预测方法，能够更精确地确定渗流阻力系数和合理产量等重要参数，为科学合理开发低渗透气藏提供了理论依据。

RESEARCH ON THE DERIVATION AND APPLICATION OF TRINOMIAL EQUATION OF THE FRACTURED WELLS IN LOW-PERMEABILITY GAS RESERVOIRS

Natural productivity of low-permeability gas reservoirs is extremely low or almost nil before fracturing. Fracturing treatment is an important measure to economically develop and stimulate low-permeability gas reservoirs. Conventional binomial production equation can only describe high-velocity Non-Darcy flow. Due to low formation permeability and high fracture conductivity, percolation rules of fractured well on low-permeability reservoirs differ significantly from that before fracturing, binomial equation can no longer describe production status of gas well and new production equation should be established. It is set up trinomial equation for fractured well on low-permeability gas reservoirs based on percolation mechanics. The model considered the effects of both low and high velocity non-Darcy flow on fractured well and concluded that both startup pressure resistance, viscous resistance and inertial resistance contribute to and increase filtrational resistance in fractured well. This paper also puts forward productivity prediction method of low-permeability fractured well that achieves more accurate determination of important parameters such as the filtrational resistance coefficient and rational production, which provides theoretical basis for developing low-permeability gas reservoirs scientifically.