Abstract
Abstract
The prediction of relative permeability has been in the past and is currently a very active research area, with theoretical, experimental and empirical approaches under consideration. However, it is fair to say that the complexities of relative permeability have to date eluded researchers and practitioners alike, in that there is no universal formulation that is able to predict two-phase relative permeability for the wide range of rock and wettability characteristics observed. This paper presents a new, generalised formulation, one that is truly predictive, and compares the same with the industry standard - the modified Brooks-Corey (MBC) formulation.
The MBC formulation is perhaps the most widely used, practical method describing laboratory-derived relative permeability relationships in terms of simple power functions. The shortcomings of this formulation are that it has no real predictive capability and the relative contributions due to pore structure components as compared to variation in wettability cannot be resolved. The new two-phase flow formulation presented is based on a phenomenological approach related to the Carman-Kozeny equation, and is able to resolve the above mentioned shortcomings.
Included are several laboratory examples and the results of a comparison of the two formulations is presented. It is shown how the new formulation is able to predict "the curvature" of relative permeability curves when only the endpoints are known, duplicating observed behaviour from steady-state relative permeability experiments. Alternatively, if the endpoints can be derived, correlated or estimated with the use of more fundamental data, the entire prediction of relative permeability is possible.
In conclusion, the formulation presented is able to predict two-phase relative permeability under steady-state conditions, not just merely fit data. The second advantage of this method is that it is theoretically based and does not involve any fitting parameters but involves relatively simple analytical expressions.
Introduction
Unlike conventional core analysis, involving the measurement of permeability and porosity, advanced (or special) core analysis (SCAL) is more expensive and time consuming. For these reasons, the number of plugs used for SCAL for a particular field tends to be limited, often not covering all existing depositional environments and flow zone units adequately and leading to poor reservoir representation.
Prediction models provide a means to augment a data set and to validate the latter, allowing the characterization of a reservoir. In a more abstract sense, capillary pressure and statistical models for relative permeability have their own assumptions and rely purely on theory, making them less practical. Network models may be highly plug-specific. It is also difficult to translate results from experiments performed on standard core material, such as Berea sandstone, to other types of reservoir rock. Purely empirical models, on the other hand, are perhaps the most widely used in the petroleum industry, but they may not be universally applicable. Finally, empirical models based on theoretical concepts tend to be more satisfactory and may lead to greater universality(1).
Research in the area of single-phase flow and flow zone unit identification have led to the conclusion that the theoretical Carman-Kozeny equation(2, 3) is an ideal formulation for bridging the gap between the views of geologists and engineers. Good results obtained in previous research(4) utilizing the Carman-Kozeny (C-K) equation was then the impetus for investigating two-phase flow using a modified C-K formulation. The modification required for a two-phase formulation involved adaptation of certain parameter groups, to allow the inclusion of the second phase. The new model was tested using a large number of relative permeability data sets which were generated by service laboratories, several hundred relationships, mainly for Australian fields.
The purpose of the research described, part of a larger objective, is to compare the performance of a new mechanistic model, based on the Carman-Kozeny equation, with the Brooks and Corey model. Before presenting results from such comparison, a summary of respective formulations is given, for the Modifed Brooks and Corey model and the new relative permeability model.