Steam-Assisted Gravity Drainage (SAGD) is one of the successful in-situ thermal oil recovery methods in Alberta, Canada. There are several tools for design and evaluation of SAGD projects, for instance thermal reservoir simulators and simple analytical models. Although time consuming, reservoir simulators handle reservoir heterogeneities. On the other hand, existing analytical models are limited to simple configurations with constant rock and fluid properties. Therefore, providing a simple and fast analytical model that can accurately analyze a SAGD project with variable properties is very desirable.
In this study, a semi-analytical model is introduced to investigate the effect of temperature dependent properties such as thermal conductivity, heat capacity and rock density on the performance of SAGD process. The semi-analytical model solves transient nonlinear heat transfer equation coupled with the continuity equation in a sequential manner. First, nonlinear, transient partial differential heat transfer equation is transformed to an ordinary differential equation using Kirchhoff's transformation and Heat Integral Method (HIM). The ordinary differential equation is solved by fourth order Runge-Kutta method. Second, the continuity equation is solved using new temperatures and as a result, production rates and shape of steam chamber are determined. The stability of sequential methods is sensitive to the spatial and temporal discretization. A criterion for time step selection is defined based on the Courant number and Peclet number to guarantee the stability of this semi-analytical model. The Courant number depends on the steam temperature and fluid and rock properties of reservoir, i.e. absolute permeability, oil viscosity and porosity. Peclet number depends on the velocity of steam chamber interface, penetration depth of heat and thermal diffusivity at steam temperature.
The results of this study illustrate that the temperature dependent physical properties affect the temperature distribution ahead the steam chamber. The impact on the cumulative oil production and production rate is significant. Moreover, several field scale problems were simulated with both the proposed semi-analytical model and a commercial reservoir simulator. It is revealed that, the locations and shapes of steam chamber as well as production rates predicted from semi-analytical model and reservoir simulators are in an excellent agreement.
The proposed semi-analytical model runs in a small fraction of runtime of the numerical simulator, yet it provides reasonable results. Thus it has the potential to be used as a tool for quick SAGD evaluations. A runtime comparison between this model and the numerical simulator is also provided.