A productivity equation of horizontal wells in the bottom water drive reservoir with an interlayer

The interlayer can effectively prevent the ridge of bottom water and has a non-negligible influence on the flow dynamics of oil and gas in the reservoir. In view of the above problems, this paper studies the influence of a bottom water reservoir with an interlayer on the critical productivity of horizontal wells and establishes a coupling model of seepage and wellbore flow in a bottom water reservoir with an interlayer. The critical productivity of horizontal wells in a bottom water reservoir with an interlayer can be evaluated more accurately. Firstly, the three-dimensional seepage field is approximately decomposed into internal and external seepage fields, and the critical productivity formulas of internal and external seepage fields are solved, respectively. Using the equivalent seepage resistance, the critical productivity formula of horizontal wells in interlayer bottom water reservoirs is obtained. The results are compared with the calculation results of the traditional productivity formula and the simulation results of the commercial software ECLIPSE. Second, based on the mass conservation principle and momentum conservation principle, the wellbore-reservoir coupling mathematical model of a horizontal well is established by the discrete method. Finally, the sensitivity analysis of the selected parameters is discussed in detail. The results show that: (1) compared with the traditional productivity algorithm, the algorithm considers the influence of interlayers on productivity and gives a detailed theory, a specific calculation process, and the importance of accurate prediction of wellbore flow. (2) The model is calculated by an example, and the calculation results are compared with the traditional formula and the commercial simulator ECLIPSE. The results show that the horizontal well productivity formula considering the influence of interlayer is closer to the simulation results of commercial software ECLIPSE, and the relative error is 8.56%. (3) The established coupling model considers the influence of interlayer radius length and horizontal well length. The general trend is that productivity gradually increases with an increase in interlayer radius length or horizontal well length, but the growth rate gradually decreases.