An injection well model is presented that can be used to history match a field injector's bottom hole pressure (BHP) taking into account particle plugging due to injected solids, poro-elastic and thermo-elastic stresses, increase/decrease in injection induced fracture lengths, injector shut-ins / re-starts, changes in injection rates and average reservoir pressure. Estimates of fracture lengths and injection profile as a function of injection time are predicted for a field injector in a multi-layered reservoir.

The solids deposition is modeled accurately using filtration theory; the flow of the injection fluids is modeled using approximated composite zones (3 zones with uniform saturation and mobility) and the pressure at the wellbore is calculated using Gringarten's infinite conductivity fracture solution. The injection induced fracture lengths are calculated based on Perkins and Gonzalez fracture propagation model (1985) that accounts for the thermal and poro-elastic stresses. The model is a semi-analytical simulator that can predict injector performance through history matching an injectors' daily record of injection rate and BHP. More reliable future estimates of injectivity, skin, fracture lengths in a multi-layered reservoir, front locations, and injection fluid profile can be obtained. Both short term pressure transients and long term pressure transients observed over several years of injection need to be history matched to capture effects that are important at both short and long time scales.

Finally an example field case study is presented where BHP and injectivity of an ongoing injection well is history matched for both a few short term injection time intervals and over a period of 3 years. It is shown that both the solids deposition and the opening/closing of the injected induced fractures need to be accounted to obtain a good history match. These processes controlled by the layer stresses and the water quality are the most important physical processes determining the injector's injectivity and injection profile.