Compressible streamlines and three-phase history matching

Reconciling high-resolution geologic models to field production history is still by far the most time-consuming aspect of the workflow for both geoscientists and engineers. Recently, streamline-based assisted and automatic history-matching techniques have shown great potential in this regard, and several field applications have demonstrated the feasibility of the approach. However, most of these applications have been limited to two-phase water/oil flow under incompressible or slightly compressible conditions. We propose an approach to history matching three-phase flow using a novel compressible streamline formulation and streamline-derived analytic sensitivities. First, we use a generalized streamline model to account for compressible flow by introducing an 11 effective density" of total fluids along streamlines. This density term rigorously captures changes in fluid volumes with pressure and is easily traced along streamlines. A density-dependent source term in the saturation equation further accounts for the pressure effects during saturation calculations along streamlines. Our approach preserves the 1D nature of the saturation equation and all the associated advantages of the streamline approach with only minor modifications to existing streamline models. Second, we analytically compute parameter sensitivities that define the relationship between the reservoir properties and the production response, viz. water-cut and gas/oil ratio (GOR). These sensitivities are an integral part of history matching, and streamline models permit efficient computation of these sensitivities through a single flow simulation. Finally, for history matching, we use a generalized travel-time inversion that has been shown to be robust because of its quasilinear properties and converges in only a few iterations. The approach is very fast and avoids much of the subjective judgment and time-consuming trial-and-error inherent in manual history matching. We demonstrate the power and utility of our approach using both synthetic and field-scale examples. The synthetic case is used to validate our method. It entails the joint integration of water cut and gas/oil ratios (GORs) from a nine-spot pattern in reconstructing a reference permeability field. The field-scale example is a modified version of the ninth SPE comparative study and consists of 25 producers, 1 injector, and aquifer influx. Starting with a prior geologic model, we integrate water-cut and GOR history by the generalized travel-time inversion. Our approach is very fast and preserves the geologic continuity.