In general, hydraulic fractures propagate perpendicular to the horizontal well axis whenever the drilling direction is parallel to the principal minimum stress plane. However, operators frequently drill horizontal wells parallel to lease boundaries resulting in slanted hydraulic fracture planes at angles less than 90 degrees from the well axis. This study provides a model for the inclined fracture case. It applies and further extends the unified fracture design approach for rectangular drainage areas, relating the dimensionless proppant number to the maximum productivity index in pseudo-steady state conditions. When simulating flow in shale reservoirs, the stimulated shale volume was represented as a rectangular drainage area that varies with changing angle, but preserves total area. Similarly, fracture length and width varies with changing angle, but total propped fracture volume stays constant. Results show that for any given set of reservoir and proppant properties along with a given proppant mass, as long as the created fractures drain the same stimulated rock volume, there exists a well direction resulting in maximized well productivity that is not necessarily parallel to the minimum stress direction. In addition, results yield two main correlations. The first one relates the optimal fracture angle to proppant number, for a given ratio of well spacing to primary-fracture spacing. In this way, operators can choose the drilling azimuth that would maximize production. The second correlation determines the optimal ratio of well spacing to primary-fracture spacing as a function of proppant number for a given fracture angle. This can be applied when selecting the optimum number of fracture stages given a well spacing plan and fracture angle. Two case studies show the application of these findings. In the end, this work provides a simple framework for well design incorporating slanted hydraulic fractures.

Summary Hydraulic fractures propagate perpendicular to the horizontal-well axis whenever the drilling direction is parallel to the minimum-principal-stress direction. However, operators frequently drill horizontal wells parallel to lease boundaries, resulting in hydraulic-fracture vertical planes slanted at angles less than 90° from the well axis. The stimulated-rock-volume (SRV) dimensions are defined by fracture height, well length, and fracture length multiplied by the sine of the angle between fracture planes and the horizontal-well axis (fracture angle). The well productivity index (PI) under boundary-dominated flow (BDF) is given by the PI for one fully penetrating fracture multiplied by the number of fractures. An extension of the unified-fracture-design (UFD) approach for rectangular drainage areas enables determination of the unique number of fractures that will maximize well productivity under BDF conditions given the formation permeability, proppant mass, fracture angle, and well spacing. Fracture length and width vary depending on the fracture angle, but the total-propped-fracture volume remains constant. Because the likely reason for drilling at an angle to the minimum-stress direction is to better cover a lease area with north/south and east/west boundaries, the smallest fracture angle will be 45°, corresponding to northwest/southeast or northeast/southwest minimum-stress direction. This results in the need to lengthen fractures by at most 40% to preserve the SRV for a given horizontal-well length and spacing. For the same sufficiently large proppant mass, this will reduce fracture conductivity by the same factor. However, because the flow area has increased, the result will be greater well productivity. This study shows a simple strategy for designing wells to maximize productivity even when not drilled in the minimum-stress direction.