Modeling Steam-Assisted Gravity Drainage With a Black-Oil Proxy

This paper describes an alternative approach to model steam-assisted gravity drainage (SAGD) with an isothermal black-oil (BO) reservoir simulator. The oil-viscosity reduction caused by heating in the actual SAGD process is emulated by a tuned saturated pseudo-oil viscosity relation in which solution gas/oil ratio (R-s) is used as a "proxy for temperature." In the BO formulation, fully saturated oil viscosity (mu(o)*) at reservoir pressure equals mu(o) that would be attained at steam-chamber temperature (T*) in the actual SAGD process; initial oil viscosity (mu(oi)) with initial R-s = 0 represents initial oil viscosity at reservoir temperature; and BO gas properties represent steam at T*. After careful analysis of the SAGD process, one finds that oil flows only along a narrow zone along the outer edge of the steam chamber-the "edge oil-flow zone." The temperature gradient within this narrow zone is perpendicular to the oil-flow direction and is practically impossible to model with any precision because of the large temperature variation and dynamic steam-chamber shape over time. The BO-model solubility gradient also varies, analogous to temperature in a thermal model, from zero to fully saturated (R-s*) with an associated drop in oil viscosity from mu(oi) to mu(o)*. SAGD design requires many hundreds of runs to find operational conditions that maximize economic value (e.g., injector and producer location, rates, pattern spacing, and steam-chamber temperature T*). The proposed BO proxy model runs several times faster than a thermal model while maintaining similar performance behavior. The proxy-model saturated pseudo-oil viscosity mu(o)(p) relation used is found by history matching a full-physics thermal-model performance prediction of oil rate, bottomhole flowing pressure, and cumulative oil for a 2D homogeneous model. We have found a single-constant mu(o)(p) equation that yields a good match to thermal SAGD performance. The tuned pseudo-oil viscosity relation honors the measured initial reservoir and fully heated (at T*) oil viscosities. Its dependence on R-s is not physical, but reflects the use of R-s as a transform variable for temperature, capturing the strong spatial variation of temperature and oil viscosity within the localized steam/oil boundary region in which oil has been mobilized. The pseudo-oil viscosity relation, defined by a single empirical best-fit constant n-for a given T* and a set of thermal properties-appears to be applicable for a wide range of reservoir heterogeneity, injection and production rates, and well placement. Consequently, it should be possible to use the BO proxy model for SAGD optimization of T*, control rates, and injector/producer vertical-depth difference. We also see the potential of using the BO proxy model for solvent-based SAGD, with the pseudo-oil viscosity model depending on both T* and solvent; thermal compositional modeling is yet even slower and less suitable for optimization.