Performance Model for Vertical Wells with Multi-stage Horizontal Hydraulic Fractures in Water Flooded Multilayer Reservoirs

For the characteristics of horizontal fractures in shallow low-permeability oil layers after hydraulic fracturing in multilayer reservoirs, horizontal fractures are taken equivalent to an elliptical cylinder with the reservoir thickness using the equivalent permeability model; then, upon the elliptic seepage theory, the seepage field which has led by a vertical well with horizontal fractures is divided into two parts: (1)radial flow from the external formation to the equivalent area of horizontal fracture and (2) elliptic flow in the equivalent area of horizontal fracture. The loss of pressure caused by threshold pressure gradient, material balance in the reservoir, and multi-well pressure superposition principle are synthesized to calculate the performance. Finally, separate-layer multi-stage horizontal fractured well performance is deduced by summing the performance of high-permeability oil layers and fractured thin low-permeability oil layers. Low-permeability thin oil layers in Xing Shu-Gang oilfield are taken as practical cases, and the well space limits and economic reservoir thickness limits are calculated by the performance model; the relationship among recovery and productivity intensity, and the ratio of thin low-permeability oil layers thickness to the total thickness are also discussed.