Modeling SAGD with a Black-Oil Proxy

Abstract This paper describes a new approach to model steam-assisted gravity drainage (SAGD) using 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 where solution gas-oil ratio (Rs) is used as an "equivalent temperature variable". In the black-oil formulation: (1) fully saturated oil viscosity (μo*) at reservoir pressure equals μo that would be attained at steam-chamber temperature (T*) in the actual SAGD process; (2) initial oil viscosity (μoi) with initial Rs=0, represents initial oil viscosity at reservoir temperature; and (3) black-oil gas properties represent steam at T*. Upon careful analysis of the SAGD process, one finds that oil flows only along a narrow zone along the outer edge of the steam chamber – "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 black-oil model solubility gradient also varies, analogous to temperature in a thermal model, from zero to fully-saturated (Rs*) with an associated drop in oil viscosity from μoi to μo*. 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 black-oil proxy model runs up to 10 times faster than a thermal model, while maintaining similar performance behavior. The proxy model saturated pseudo-oil viscosity μo(p) relation used is found by history matching a full-physics thermal model performance prediction of oil rate, BHFP, and cumulative oil for a 2D homogeneous model. We have found a single-constant μo(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 Rs is not physical, but reflects the use of Rs as a transform variable for temperature, capturing the strong spatial variation of temperature and oil viscosity within the localized steam-oil boundary region where oil has been mobilized. The pseudo-oil viscosity relation, defined by a single empirical best-fit constant n – for a given T* and 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 black-oil proxy model for SAGD optimization of T*, control rates, and well placement, at a fraction of the CPU cost. We also see the potential of using the black-oil 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.