Comparison of A Three-dimensional Numerical Simulation With A Itot Water Drive Physical Model Experiment

Abstract

Abstract A three-dimensional hot water drive simulation is compared with a physical model experiment. The main purpose oj the paper is to show the degree of agreement that can be achieved when a carefully controlled experiment is compared with numerical simulation. The over-all accuracy is 5% on production curves and 10% on temperature profiles. Introduction This paper describes a comparison of a three-dimensional numerical simulation of a hot water flood, with a physical model experiment. Cold water drives can often be reduced in dimension by using the concepts of vertical equilibrium and gravity segregation(1). However, hot water drives are not so readily amenable to a similar treatment, the reason being the difficulties associated with the description of the temperature profile in the vertical direction. Hence, a three-dimensional hot water injection process must of necessity be carried out in a three-dimensional numerical simulator. Many experiments of the type described have been performed in Shell's research laboratories during the last ten years, and compared with numerical simulation. The purpose of this paper is to show the order of agreement that can be achieved when carefully controlled experiments are compared with numerical simulations. In this respect, the degree of agreement obtained is typical of the many comparisons that have been made. The Numerical Model The numerical model used a standard finite-diffierence IMPES(2,3) technique with central differences in space and backward differences in time. In the convection terms, a two-point upstream formulation(4) was available for both the mobilities in the mass flow terms and the enthalpies in the energy convection terms. The simulator did not contain any arbitrary parameters or empirical correlations. All data required by the simulator are, in principle, measurable. A further detailed description of the numerical model can be found in reference 5, together with a bibliography for similar models and published numerical methods. The model has been well validated by comparison with known analytical solutions and comparison with 16 physical model experiments, and it has been successfully run on a number of field cases. The data sources used for this simulation are recorded in Appendix A, together with some discussion on their reliability. Experimental Set-Up The object of the experiment was to study the effect of secondary recovery by hot water injection in a particular reservoir. Figure 1 shows the experimental set-up. It depicts a rectangular box at an angle of 9 degrees to the horizontal. The model was packed with sand using Wygall's method(6). The experiment consisted of two stages. The first comprised a short period of flank cold water injection through seven injection wells, with production from wells 2 and 3. During this stage, the injection wells were held at a constant bottom-hole pressure of 12.0 atm (1.216 × 106 Pa), and the producers at 11.6 atm (1.175 × 106 Pa). The second stage consisted of production through wells 2 and 3 at a constant rate, with injection of hot water in well 1 at a constant bottom-hole pressure of 12.0 atm (1.216 × 106 Pa).