Numerical Coning Applications

Abstract

Abstract An analysis of water or gas coning behaviour is particularly important in determining the future performance of gas reservoirs and thick oil reservoirs of the Rainbow-Zama- Virgo types. Investigations of coning in these reservoirs have only recently become practical. This paper describes results from two numerical coning studies - one a gas-water problem, the other a three-phase problem in a Virgo reef. The implicit numerical model used is described in detail. INTRODUCTION THE CONTROL OF GAS AND WATER CONING in petroleum reservoirs is essential in optimizing recovery and minimizing operational costs. Coning is the result of high-pressure gradients around the producing well which cause the oil-water contact to rise and the gasoil contact to depress near the wellbore. Gravitational forces tend to segregate the fluids according to their densities. However, when gravitational forces are exceeded by the flowing pressure, a cone of water and/ or gas will penetrate the producing interval. Only recently has it become practical to investigate coning as a non-steady-state flow phenomenon with heterogeneous reservoir properties. These investigations are now practical utilizing numerical coning models. Coning is simulated with a 2D radial (R – Z) grid system extending out from the wellbore to some external radius (Re). To obtain proper definition of the gas and water cones, a fine grid is used near the wellbore. The pore volumes of these interior grid blocks are typically 1 to 10 barrels, At a normal producing rate and with a reasonable time-step size, the fluid throughput per time step of the inner blocks is many times the pore volume of the blocks. This high throughput causes large saturation changes per time step and, in the past, these large saturation changes have caused model instabilities. Normally, in a reservoir simulator the transmissibilities governing flow between blocks and the production rates of oil, gas and water are calculated explicitly using the saturation conditions existing at the beginning of the time step. If explicit transmissibilities and production terms are used in a coning model, a practical time-step size will cause the predicted saturations to become unstable and the GOR's and WOR's to oscillate, These instabilities can be controlled by treating the transmissibilities and production terms implicitly rather than excplicity. The computation required per time step increases with a totally implicit model, but the resulting increase in the time-step size which can be taken more than offsets the greater computation requirements. The net result is a numerical model which can be used routinely, at low cost, on practical problems. The Appendix describes in detail the mathematics of this coning model. The following section describes two coning studies. The first case is a gas pool with an underlying aquifer. The second is a single-well bioherm reef being produced under primary depletion. Initially, it is without a gas cap, but it does have a small underlying aq Uifer, Both studies used a fully compressible threephase 2D radial model.