A Streamline Approach for Ranking Reservoir Models that Incorporates Production History
Authors: Wang Y. , Kovscek A.R. 
Published: December 2007

Abstract
The reservoir models generated by geostatistical techniques but unconstrained to production history provide equally probable reservoir descriptions that honor observed geology. However, flow simulation results on these models may vary widely indicating uncertainty. Constraining geostatistical models to known production history reduces uncertainty. To this end, a streamline-based algorithm for ranking geostatistical realizations with regard to production history is proposed. First, a rapid, streamline-based inversion method is applied to obtain a history-matched reservoir model. Then, unit mobility ratio streamline geometries are computed, without full flow simulation, for the history-matched model and the geostatistical models considered. Each model is then compared to the history-matched model with regard to streamline properties, such as time-of-flight. In this way, reservoir models that match production history and honor known geological information are obtained. Synthetic examples using up to 600 distinct reservoir models demonstrate computational efficiency and also shows that the method easily selects the most appropriate permeability fields. Flow simulations confirm that selected permeability fields are satisfactory. The technique also appears to be appropriate for downscaling history-matched permeability fields from coarse to fine grids.

Introduction
Geostatistical techniques are used primarily to generate realistic equally probable numerical reservoir models that honor known geological information. However, significant uncertainty exists in the detailed distribution of reservoir properties such as permeability1 because the known data is relatively sparse. If flow simulation is performed on various realizations to predict reservoir performance, the geological reservoir model uncertainty is transferred into uncertainty of flow simulation results. If production history is present, integration of this data with geostatistical realizations can reduce uncertainty. In turn, future reservoir performance should be better predicted.
Numerous history-matching methods have been discussed in the literature2–11. Most employ ideas such as sensitivity coefficients (of the objective function) evaluated for each gridblock and apply techniques such as simulated annealing to minimize the error between observed and simulated data. Even though various techniques have been proposed to accelerate the process, most history-matching methods require a large number of flow simulations and are therefore computationally intensive. Their application to problems with a large number of variables is difficult.
Previously, a streamline approach was proposed for history-matching production data12. Streamline properties are used in an estimation method to obtain the permeability changes needed to match production data. The method works in two steps:the error between measured and computed producer water-cut is related to the error in effective permeability of streamlines; andthe perturbation in streamline effective permeability is computed analytically and mapped into a change of permeability for individual grid cells. This method is rapid and applies well in water-flood cases with no infill wells to be matched. Agarwal &Blunt13 applied this same method to cases with gravity and compressibility. Data from a North Sea Field was used to test the technique and they observed reasonable history match and prediction of future performance. In both cases, the history-matched reservoir models were not constrained to geological information.