An injection-well model is presented and used to history match a field injector's bottomhole pressures (BHPs) and injection profile (injection rate into each layer), taking into account plugging of formation caused by suspended solids in the injection water, poro- and thermoelastic stresses, injector shut-ins/restarts, and changes in both the injection rates and the average reservoir pressure. Fracture lengths and injection profile are estimated for a field injector as a case study. The injection-well fracture model is very similar to the Perkins and Gonzalez (1985) model except that it has integrated a more comprehensive and experimentally tested internal filtration model (Rajagopalan and Tien 1976; Pang and Sharma 1997; Gadde and Sharma 2001; Suri 2000; Wennberg and Sharma 1997) for calculating permeability reduction. It has also added a pressure-transient model that makes the earlier reservoir flow models more accurate.

The solids deposition is modeled using a filtration model (Rajagopalan and Tien 1976). The fluid flow in the reservoir is modeled using three approximated composite zones with uniform saturations and average mobilities, and the pressure for the fractured wellbore is calculated with the help of Gringarten's infinite-conductivity solution. The induced-fracture lengths are calculated on the basis of the Perkins and Gonzalez fracture-propagation model (1985) that accounts for the thermal and poroelastic stresses. The model is developed into a semianalytical numerical simulator that can predict and history match an injector's daily BHP, fracture lengths, and injection profile. Future estimates of pump pressures, BHP, injectivity, skin, front locations, fracture lengths, and injection profile can be obtained from this model. Both short-term pressure transients and long-term pseudosteady pressures observed over several years of injection can be history matched to capture effects that are important at both short and long time scales.

Finally a field-case injection-well study is presented in which BHP and injectivity are history matched over a period of 3 years. We show that the model can be used to estimate the minimum horizontal stresses in the layers if they are not known, which was the case. Estimates of fracture lengths, fraction of flow, permeability reduction, and skin and front locations are also obtained. There is significant uncertainty in the results because of uncertainty in the model inputs and in the completeness of the physics of the model of fracturing itself. Both the solids deposition and the opening/closing of the injection-induced fractures had to be accounted for to obtain the history match. The layer/sand stresses and the water quality are the most important parameters that determine the well's injectivity, fracture growth, and injection profile. Microseismic surveys are needed to delineate the fractures in injection wells.