Finite Element Modelling of Sand Production Under Foamy Oil Flow in Heavy Oil Reservoirs

Abstract The motivation for studying sand production and foamy oil flow stems from the fact that a number of heavy oil solution gas drive reservoirs in Western Canada and Venezuela have consistently shown anomalously good primary performance, high oil production rates, and high primary recovery factors. We thus propose a mathematical model in which gas exsolution and gas bubble dispersions are described in a macroscopic manner through equations of states and relaxation, whereas sand production is viewed as an erosional hydrodynamics problem. The latter aspect has been investigated at length by the first author in a series of publications[9]–[12]. The formulation of the proposed model leads to a set of highly non-linear governing equations with primary field unknowns such as reservoir pressure, volume fraction of dispersed gas bubbles, concentration of fluidized solid and porosity. The numerical solutions of these equations are challenging and require special treatment such as least-squares finite element techniques in order to ensure stability and accuracy in results. Foamy oil flow with sand production around a wellbore is investigated using the proposed model. The numerical results are very consistent with the physics of gas exsolution and sand production as the reservoir pressure is depleted. For instance, oil production can be improved by increasing the depletion rate in terms of having higher volume fractios of dispersed gas bubble and produced sand. Exsoluted gas in the form of tiny dispersed bubbles has an effect of maintaining a high pressure gradient near the wellbore, hence enhancing the oil recovery factor. Since the pressure is decreased considerably by sand production, the increase in oil production when sand is produced is attributed to a permeability increase, according to Darcy's law. In trying to explain the improvement of oil production in a heavy oil solution gas drive reservoir, we claim that the effect of pressure maintenance caused by dispersed gas bubbles is much more significant than that due to a permeability increase by sand production. Introduction A number of heavy oil solution gas drive reservoirs in Western Canada and Venezuela have shown good performance and it has been observed that well-head samples coming from these reservoirs showed a foamy oil phase [1]. Several possible causes for this anomalous production behaviour of heavy oil reservoirs have been suggested. We will focus on the following two issues in order to introduce the motivations of this paper.Increase of the effective well radius due to geomechanical effects such as sand dilation and the development of wormholes or cavities around the wellbore both naturally present and created by sand production: At the same time, sand dilation results into an increase in absolute permeability due to the production of substantial volume of sand with the oil. Moreover, continued sand movement prevents the formation of pore blockages through fines trapping, asphaltene precipitation, and other nearwellbore mechanical skin effects.Enhancement of oil mobility by the nucleation of a large number of micro-bubbles to lead to the in-situ formation of continuous foam: During production, a non-equilibrium foamy (compressible) oil phase is generated that helps in maintaining the reservoir pressure, and hence provides the driving force for primary production..

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