Simulação numérica do escoamento água-gás em reservatórios de baixa permeabilidade

Abstract

Natural gas recovery has increased with the exploitation of unconventional reservoirs with low and very low permeability. In these reservoirs, production is favored, for instance, by the use of horizontal wells and due to the gas slippage effect. In this work, a numerical simulation of the two-phase isothermal water-gas flow is performed, accounting for the impact of gas slippage and the variation of permeability as a function of the change in stress acting on the porous matrix. This is justified because analytical solutions are limited to particular cases with simplifying assumptions, and field-scale experiments are difficult to perform and costly — with well pressure tests being the closest alternative. The governing equations are discretized using the Finite Volume Method and the systems of algebraic equations are linearized and solved by applying a Picard-Newton solution strategy, an operator decomposition and the iterative method of the preconditioned Stabilized Biconjugate Gradient. The use of the Finite Volume Method ensures the conservation of the involved quantities, while the Picard-Newton strategy is adopted due to the need for linearizations. Additionally, the operator decomposition allows for solving two subsystems with lower computational cost compared to solving a single larger system (two systems of order 2N2 instead of one system of order 4N2 ). The results obtained are made available in terms of instantaneous flow rate and volume of recovered gas, considering several production scenarios. In conclusion, they showed that it was possible to capture the physical effects, with the slippage favoring production and the reduction in reservoir pressure leading to a decrease in apparent permeability.