Transient analysis for fluid injection into a dome reservoir

A dome-shaped layer can be selected as a storage site for fluid injection. In this study, we develop a mathematical model for simulating transient head distribution in a heterogeneous and anisotropic dome-shaped layer due to a constant-head injection in a fully penetrating well. In the model, a form of step change is adopted to approximate the upper and lower boundaries of the dome and then the layer is split into two regions. The Laplace-domain solution of the model is developed using the Laplace transform and method of separation of variables. The transient injection rate at wellbore can then be obtained based on Darcy’s law and Bromwich integral method. The predicted head contours from the head solution show significant vertical flow components near the location of step change in the dome reservoir. The results of sensitivity analysis indicate that the hydraulic conductivity is the most sensitive parameter and the specific storage is the least sensitive one to the injection rate after a short period of injection time. In addition, the injection rate for a dome reservoir is also very sensitive to the change of the height for the reservoir near the injection well (first region) at a very early injection time. In contrast, the injection rate is more sensitive to the change of the height of the second region than that of the first region at late time. This analytical solution may be used as a primary tool to assess the capacity of fluid injection to various dome reservoirs.