Horizontal wells are increasingly used worldwide and are especially desirable offshore for water-flooding and reservoir pressure maintenance as they allow more access to the reservoir with large injectivities. Fracture growth in these horizontal injectors can play an important role in determining the injection rates, reservoir sweep and oil recovery.

A model is developed to estimate the growth of fractures in horizontal injectors. The model considers two orientations of fracture growth: 1) longitudinal fractures i.e. fracture along the horizontal well and 2) centered transverse fractures, i.e. at the center and perpendicular to the horizontal well.  Fracture growth is due to: 1) reduction of permeability around the horizontal well caused by particle deposition from injection fluids, 2) reduction in minimum horizontal stress due to cold fluid injection, and 3) injection of viscous polymer fluids. The model accounts for plugging of the horizontal well, the induced fracture and the formation around the fracture. It also calculates the thermal and pore pressure stresses to update the minimum horizontal stress around the fracture tip. It also allows injection of power-law fluids to model polymer injection in horizontal injectors.

It is shown that the injection well pressures are controlled by the minimum horizontal stress. The injection fluid quality, injection rate, and injection fluid temperature determine the rate of fracture growth in a horizontal injector. Fracture lengths are estimated for longitudinal and transverse fracture growth orientations as the lower and upper bound values.