A.T. Watson

History Matching in Two-Phase Petroleum Reservoirs

An automatic history-matching algorithm based on an optimal control approach has been formulated to estimate jointly spatially varying permeability and porosity and coefficients of relative permeability functions in 2-phase reservoirs. The algorithm utilizes pressure and production rate data simultaneously. The performance of the algorithm for the waterflooding of one- and two-dimensional hypothetical reservoirs is examined, and properties associated with the parameter estimation problems are discussed.

Relative-permeability estimation from displacement experiments: an error analysis

Parameter estimation can be a superior method of estimating relative permeabilities from displacement (unsteady-state) coreflood experiments. To use the parameter-estimation method, one must choose functional representations of the relative permeability curves. In previous work, only a simple exponential function was used, which can result in very large errors in estimation of relative permeabilities. In this work, the authors extend the parameter-estimation method to consider the use of several alternative functional forms, including highly flexible cubic splines, which should be better able to represent a wide variety of relative-permeability curves. In this way, the error associated with the assumption of a simple functional representation can be greatly decreased. They also develop a procedure to analyze the accuracy with which relative permeabilities may be estimated by parameter estimation. The analysis is used to evaluate the performance of different functional representations in the parameter estimation method. Furthermore, it can also be used to assess quantitatively the effect of experimental design on the accuracy of estimates of relative permeability.

Image processing of tracer particle motions as applied to mixing and turbulent flow—I. The technique

Abstract Techniques of digital image processing of stereoscopic motion pictures are presented which were used to automate the tracking of neutrally buoyant tracer particles in turbulent flow. A software package is described which performed the following tasks: (1) particle image identification, (2) particle image tracking and (3) stereo pair matching of particle trajectories. Various criteria and objective functions are given which were used to accomplish the tasks.

Adsorption Studies of Natural Gas Storage in Devonian Shales

Significant amounts of natural gas exist as an adsorbed, or condensed, phase in Devonian shale formations and other unconventional gas resources. The amount of the adsorbed phase depends on the pressure and temperature. The Langmuir isotherm has been used to describe the pressure dependence. However, temperature dependence has not been explored. This is important to evaluate thermal simulation as a recovery method and to extrapolate laboratory measurements to reservoir conditions. The authors investigate adsorption as a function of both pressure and temperature. They found that the effects of temperature are significant and that the Langmuir model does not describe adsorption adequately. They reconciled the data with bi-Langmuir models.

A Bayesian methodology for estimating relative permeability curves

Among the various properties important for simulating reservoir behavior, relative permeability curves may be the most poorly determined by current methods. This paper presents a method for obtaining improved estimates of relative permeability curves. A Bayesian-type performance index is used to incorporate prior estimates of relative permeability curves into an automatic history-matching algorithm. Estimates obtained with the method are consistent with the reservoir production and yet conform to the prior estimates.

A Regression-Based Method for Estimating Relative Permeabilities From Displacement Experiments

The authors address the process of estimating relative permeability curves from data collected during unsteady-state displacement experiments. They introduce B-splines for use as functional representations of relative permeability curves. With B-splines, polynomial splines of any order can be conveniently implemented in the estimation procedure. This feature allows greater flexibility for incorporating inequality constraints into the parameter-estimation process. The authors present a method for choosing an appropriate number of spline partitions for representing permeability curves. The method is based on considerations for obtaining the most accurate estimates of the relative permeability curves. They illustrate the method with both hypothetical and actual experimental data. They demonstrate that serious estimation errors may be encountered when relative permeability curves are represented with functions containing too few parameters - e.g., power-law functions.

Use of in situ saturation data in estimation of two-phase flow functions in porous media

Abstract Accurate estimates of multiphase flow functions (relative permeability and capillary pressure) are necessary for reliable prediction of oil recovery from a reservoir and nonaqueous phase (NAPL) contaminants from aquifers. Current methods of estimating two-phase relative permeabilities from unsteady state displacement experiments are based on Buckley-Leverett model. This model assumes that the medium is homogeneous, flow is one-dimensional and capillary effects are negligible. These assumptions are not valid for many reservoir rock samples. In this work, we have used a parameter estimation procedure to predict simultaneously relative permeabilities and capillary pressure functions from production, pressure drop as well as in situ saturation data of unsteady state displacements. Heterogeneities in porosity, permeability, residual oil saturation and initial saturation are accounted for in our model. Experimental data, estimated flow functions, and associated uncertainties are presented for two reservoir rock samples. The in situ saturation profiles are better matched by our technique over the JBN method because the heterogeneities of the sample are incorporated into our estimation procedure. Use of in situ saturation profile reduces the uncertainties in the estimations.

Accuracy of JBN Estimates of Relative Permeability: Part 1 - Error Analysis

The accuracy of relative permeabilities estimated from displacement experiments by the Johnson, Bossler, and Naumann (JBN) method is considered. A Monte Carlo error analysis is developed to provide quantitative measures of that accuracy. The Monte Carlo error analysis is used to investigate the effect of different experimental operating conditions on the accuracy of relative permeability estimates.

Characterization of Devonian shales with X-ray computed tomography

The paper investigates use of X-ray computed tomography (CT) for determining properties of Devonian shales. A dual-scan method is used to determine storage distribution quantitatively. Fractures considerably smaller than the resolution of the instrument were detected. Features observed in the CT images were validated by thin-section analysis.

Estimating parameters in scientific computation - A survey of experience from oil and groundwater modeling

and engineering depends upon the accuracy of numerical models. On what does the accuracy of the models depend? Several things: the correctness of the underlying mathematical formulation, the numerical discretization used, the solution algorithms employed, and the accuracy of values for the physical parameters that appear in the model. It is this last factor that we want to examine in some depth. First, what do we mean by a parameter? In physics, a parameter typically describes a property of a material (such as mass, viscosity, or density) that can vary without changing the underlylng natural laws. For example, consider a group of particles moving about in a closed container. The number of particles, their masses, and their charge are parameters. Other parts of a physical model are not parameters. The fact that the equations of motion are given by a sytem of second-order differential equations, for instance, is not describable by a parameter-it is a fundamental characteristic of the model.