A Semi-Analytical Model for the Prediction of CO2 Injectivity into Saline Aquifers or Depleted Hydrocarbon Reservoirs

Abstract

As carbon dioxide (CO2) is injected into a reservoir (for CO2 sequestration in a saline aquifer or depleted reservoir, or even for enhanced oil recovery in the case of a less depleted reservoir), a region around the well becomes saturated and expands with time. From a pressure transient perspective, by making some simple assumptions the resulting reservoir configuration at any given moment can be approximated by a two-region radial composite system. As well as its radial extent, the inner region is defined by its diffusivity and mobility, both of which differ from those of the outer region as a result of the CO2 saturation. The CO2 viscosity and compressibility at reservoir pressure and temperature are the essential properties that impact the diffusivity and mobility. Knowing the three variables, radius, diffusivity ratio and mobility ratio, the constant rate pressure transient response is readily computed from existing analytical radial composite model solutions. These are commonly used in the petroleum industry to analyse well test behaviour and can be configured with a variety of boundary conditions (no flow, constant pressure or infinite, usually in the shape of a rectangle). The problem with CO2 injection is that the radius and properties of the inner zone vary with time and hence any single radial composite model does not apply. The solution approach in this paper is to apply superposition. At each discretised time step, the well is simultaneously injected at a constant rate assuming the current configuration and shut in with the previous configuration. The shut-in "cancels out" the previous model and the current model applies. At each time step, the injected volume is calculated, the material balance and associated reservoir pressure computed along with the new inner zone radius, diffusivity and mobility and hence the model for the next time step is defined. An additional iterative loop allows for the injection rate to decrease if the injection pressure exceeds a maximum constraint. The method is simple and fast and appears to match the pressure response of numerical simulations of the same problem using more detailed physics, without the associated noisy derivative often associated with grid-based solutions. It implicitly assumes a piston like displacement which results in an unrealistic saturation profile that differs from the more rigorous numerical models where gravity and capillary effects are included. However, comparisons with such models indicate that the prediction of well pressure and hence injectivity is sufficiently accurate for practical purposes despite this approximation. The application of superposition in time - a method usually associated with solving linear problems – is demonstrated to adequately solve the complex non-linear problem of CO2 injectivity and, because the method includes material balance, it can help to define storage efficiency factors which are critical for the evaluation of storage capacity.