The Numerical Simulation for Multi-Stage Fractured Horizontal Well in Low permeability reservoirs Based on Modified Darcy's Equation

Abstract

AbstractWith further progress of oilfields' development all over the world, more and more low permeability reservoirs are being put into production and a large number of multi-stage fractured horizontal wells were drilled. However, fluid flow in tight sandstone porous media does not obey Darcy's law any more, and instead conforms to the one of low-velocity non-Darcy seepage. So the multi-stage fractured horizontal well numerical simulation method has been developed.In this paper, Based on the nonlinear percolation theory, a new nonlinear seepage model of low permeability reservoir was established. Then, on the basis of core displacement laboratory experiment data and practical field data, an ideal three-phase and three-dimensional numerical reservoir simulation model for multi-stage fractured horizontal well was built. Under the same low permeability reservoir, taking the impacts of pressure sensitive effects and the threshold pressure gradient into consideration, the quasi-linear numerical model, Darcy numerical model and the non-Darcy numerical model were conducted. The effects of parameters including pressure sensitive effect, the threshold pressure gradient, were fully investigated. At last, the simulation results of pressure, water cut and recovery ratio for the non-Darcy numerical model of multi-stage fractured horizontal well were given.Research shows that most flow areas belong to nonlinear flow area; compared with the results of Darcy model, when considering non-linear flow, the energy consumption is higher, and the pressure level is lower, and the liquid production is smaller, and the water cut rising is slower. Sensitivity analysis shows that: For quasi-linear flow, Darcy flow and non-Darcy flow, with the increasing of non-linear flow coefficient, the flowing bottomhole pressure decreases quickly. When the injected fluid of the injection wells reaches the wellbore, the flowing bottomhole pressure increases quickly. However, the time of water front reaching the wellbore is different. For the non-Darcy flow, the recovery ratio is positive with the starting pressure gradient of water phase, but negative with starting pressure gradient of oil phase. With pressure sensitive coefficient decreasing, recovery ratio increases quickly. If producing pressure differential is maintained at proper value, then the effect of the pressure-sensitive on the permeability is reduced, which can help to improve recovery ratio. With the threshold pressure gradient becoming smaller, the recovery ratio becomes higher. The effect of the threshold pressure gradient on recovery ratio can be smaller or "eliminated" by using fracturing or advanced water injection.