Logistic和Generalized-Arc-Tangent产量递减方程理论推导

为了揭示Logistic和Generalized-Arc-Tangent产量递减方程的渗流特征，选取特殊的油相相渗关系式，按照Arps产量递减方程理论，推导出了Logistic和Generalized-Arc-Tangent产量递减方程及其对应水相相渗关系式。研究结果表明，在注水保持地层压力的条件下，产量递减类型主要由油水两相渗流特征共同决定。推导出的油水两相相渗关系式均是以出口端含水饱和度为变量，符合行业相渗关系式标准，克服了以往产量递减方程理论推导时采用平均含水饱和度为变量的拟相渗关系式缺陷。通过吐哈丘陵油田、温五区块的应用，实际产量与经油水两相相渗关系式分别确定的产量基本一致。

Theoretical Derivation of Logistic and Generalized-Arc-Tangent Production Decline Equations

To reveal the flow characteristics of Logistic and Generalized-Arc-Tangent production decline equations, the paper selects a special oil-phase relative permeability relation and deviates Logistic and Generalized-Arc-Tangent production decline equations and its corresponding water-phase relative permeability formula according to the derivation process of Arps production decline equation. The results show that the type of production decline is mainly determined by the characteristics of oil-water two-phase flows under the condition of maintaining formation pressure by water injection. The relative permeability relations of oil and water phases take the water saturations at the outlet as variables, which complies with the industrial standards of relative permeability relations and avoids the defects of the pseudo-relative permeability relations using the average water saturation as a variable during previous decline equation derivation. The actual applications in Qiuling oilfield and Block Wen-5 in Tuha oilfield show that the actual production is consistent with the results obtained from the production decline equation determined by relative permeability relations of oil and water phases, respectively