Integrating Pressure and Fractional Flow Data in Reservoir Modeling With Fast Streamline-Based Inverse Method

Abstract Generation of a reservoir model's spatial permeability distribution directly from historical multiple-well pressure and fractional flow rate data requires an inverse solution of the flow equations. This computation generally utilizes a gradient method to solve the minimization problem. A previously reported geostatistically-based inverse sequential self-calibration (S SC) technique has been shown to significantly reduce the computer time as compared to full inversion solutions and to yield excellent results for single-phase pressure. In this paper we extend the SSC to jointly invert multiple well pressure and multiphase fractional flow data by:adapting a fast streamline simulator for the forward flow solution; andimplementing a new method for computing the sensitivity coefficients for fractional flow rate. The method is fast and robust, and an important consequence of the method is that the spatial correlation structure is honored through the kriging equations in the SSC. This leads to well-behaved objective functions with low final values and preserves the prior model spatial characteristics. The paper demonstrates the extended SSC for generating permeability realizations from production data using a synthetic reservoir model. The paper systematically compares the quality of the production data matches for inversion of pressure data alone, fractional flow rate data alone, and the combination of fractional flow rate and pressure data. For the synthetic model, pressure data alone provides coarse information primarily near the wells, whereas the fractional flow data provide more information on interwell spatial reservoir permeability. Inverting pressure and fractional flow data jointly lead to significant improvement of the representation of reservoir heterogeneity and reduction in uncertainty. The paper shows that the accuracy of reservoir performance predictions at wells can be dramatically improved by building the models using the historical production data from those wells. However, if only production data have been used to build a model, the results also indicate that the prediction capability may be limited for new wells drilled in areas outside the influence region of existing wells or under flow or well conditions different from those used for the inversion. Future research directions are discussed at the end. P. 161