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Summary We describe a novel methodology for the determination of three-phase relative permeability functions at reservoir conditions. Two- and three-phase displacement experiments are conducted on a low-permeability chalk sample, and estimates of the three-phase relative permeability and capillary pressure functions are obtained. Three-phase relative permeabilities are also calculated using the Stone correlation, and they are evaluated by simulating the experimental data. Introduction Determination of relative permeability functions from displacement experiments has received a lot of attention over the past 50 years. The vast majority of the work has been directed towards determination of two-phase properties from laboratory experiments. Most applications involving three- phase relative permeabilities have utilized correlations in which two-phase relative permeability data are extrapolated into three-phase regions. Although this would be tractable, if accurate, these correlations have largely remained untested due to the lack of sufficient measurements of three-phase relative permeability functions. Analysis of three-phase experimental data has often been based on several generally unsupported simplifications (e.g.. the neglect of capillary pressure, incompressible fluids, uniform saturation profiles, and each relative permeability being a function of its own saturation only). In an effort to meet such simplifications, experiments have frequently been conducted under flowing conditions that are unrepresentative of those encountered within the reservoir. Consequently, the estimated three-phase properties may not be suitable for describing reservoir flow. We report here the application of a methodology to overcome these problems. We have constructed an experimental apparatus whereby two- and three-phase displacement experiments may be performed at reservoir conditions. The experimental process is modeled by a general purpose three-phase simulator which includes all the pertinent physical effects. We then choose the appropriate relative permeability and capillary pressure functions, through solution of a series of optimization problems, so that the quantities calculated with the simulator are consistent with the measured values. This methodology is demonstrated with a low-permeability chalk sample. We also calculate three-phase relative permeabilities from the two-phase data using the Stone model, and evaluate the effectiveness of that model by simulating the data collected during the experiment. The estimates of the three-phase relative permeabilities obtained with the Stone model do not accurately reconcile the experimental data. Three-Phase Flow Apparatus The schematic of the flow apparatus is shown in Fig. 1. It consists of a pumping system, a three-phase separator, a core holder and a X-ray scanner system for in-situ saturation measurements. Each of these components is described below. For further details on experimental set-up, see Ebeltoft et al. Pumping system. The pumping system consist of eight computer controlled cylinders that pumps reservoir fluids into the core sample at reservoir conditions. Cylinders are paired to act as a pump.

Properties important for describing the flow of multiple fluid phases through porous media are represented as functions of state variables (fluid saturations). A generalized procedure is presented to obtain the most accurate estimates of the multiphase flow functions from the available experimental data. The procedure is demonstrated for several different experimental designs, including a novel experiment in which fluid saturations are measured using nuclear magnetic resonance imaging. A method to evaluate the accuracy of the estimates is presented, and its use for assessing experimental design is demonstrated.

We have developed a new design of steady-state type experiments for simultaneous estimation of relative permeability and capillary pressure functions ͑collectively called multiphase flow functions͒ from measured pressure-drop and production data. The multiphase flow functions are represented by B-splines to ensure a flexible representation, and the coefficients in the representation are determined using a regression-based approach. The methodology is demonstrated using synthetic data. Further, we show that both relative permeability and capillary pressure functions can be estimated, and we were able to reconcile all pressure-drop and production data from the steady-state type experiment conducted. An analysis of the accuracy of the estimated functions showed that they were accurately determined over a large saturation interval.

TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractProduction forecasts are essential for sound reservoir management. The foundation for such forecasts is a characterization of relevant reservoir properties. These properties are usually determined through history matching, using production data, static well data (hard data), and the upscaled geological model (prior model), simultaneously. This process if often very complex and costly, both in terms of CPU-time and man-hours. To reduce cost and complexity of reservoir characterization, we propose an alternative methodology; scale splitting. This approach utilizes the fact that production data often contain information about variability of reservoir properties on a much coarser length scale than the other data do. Hence, production data alone can be used to determine the large-scale variation in the estimated properties. The selection of parameters that can be estimated from the production data are determined through a data driven, top-down search, starting with a single parameter representing the average property for the reservoir structure in question. One of the primary objectives of this search is to keep the number of parameters as low as possible, without sacrificing the match quality. The prior model and the hard data need to be integrated to allow also for finer-scale property variation, and to match hard data at well locations. With scale splitting this is done at low cost after the history match of production data. We present the scale splitting approach for absolute permeability estimation and give examples where it is compared to other approaches in terms of match quality and work load. y J J J J y y J r