Understanding and modeling of gas-condensate flow in porous media

 Well deliverability impairment due to liquid dropout inside gas-condensate reservoirs below dew-point pressure is a common production problem. The operating conditions and the thermodynamic properties of the condensate govern the production performance of this type of reservoir. Modeling condensate production using analytical, semi-analytical or empirical formula for quick assessment of reservoir performance is a complicated method due to the complex thermodynamic behavior. The objective of this study is to provide a fundamental understanding of the flow and thermodynamics of gas-condensate fluid to develop tools for the production prediction. The prior developments of flow modeling of gas-condensate are briefly reviewed. The multi-phase flow and the depletion stages during production are discussed. Each component of pseudo-pressure calculations to determine the condensate flow rate is explained. Thermodynamic properties and laboratory experiment relevant to the flow of condensate are also explored. Pressure-volume-temperature properties such as two-phase envelope, constant composition expansion and constant volume depletion are demonstrated for three different gas-condensate fluids namely lean, intermediate and rich. This article is also useful for future developments of the production model for a gas-condensate under various operational and completion scenarios such as horizontal wells and hydraulic fractures in tight formations.Cited as: Panja, P., Velasco, R., Deo, M. Understanding and modeling of gas-condensate flow in porous media. Advances in Geo-Energy Research, 2020, 4(2): 173-186, doi: 10.26804/ager.2020.02.06

Estudo e implementação de um modelo composicional para a simulação de reservatórios de petróleo

Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Engenharia Mecânica, Florianópolis, 2013.Este trabalho apresenta o estudo e a implementação de um modelo composicional para a simulação do escoamento isotérmico em reservatórios de petróleo com malhas não-estruturadas e utilizando o método dos volumes finitos baseado em elementos (EbFVM). O modelo utilizado consiste em uma formulação totalmente implícita com a solução simultânea das equações de conservação e das equações de equilíbrio químico pelo método de Newton-Raphson. O modelo considera reservatórios com propriedades heterogêneas e anisotrópicas, efeitos da pressão capilar e gravitacionais, entre outros fatores físicos relevantes. A formulação assume um número arbitrário de componentes, distribuídos nas fases óleo e gás, além do componente água presente apenas na fase água. Trata-se portanto de um modelo trifásico, mas com solução do equilíbrio químico apenas nas fases óleo e gás. No modelo, são feitos cálculos de flash e teste de estabilidade baseado na minimização da energia livre de Gibbs utilizando métodos de solução mais avançados e robustos, combinando o método de Newton-Raphson com o procedimento de substituições sucessivas. Para validação do modelo, os resultados são comparados com os de simuladores composicional e black oil comerciais apresentando boa concordância. A implementação do modelo e de todos os módulos numéricos utilizados no trabalho foi feita através de uma programação avançada em C++, permitindo a reutilização do código para solução de problemas termodinâmicos multicomponentes, que exigem a utilização de uma equação de estado cúbica. Para exemplificar esta característica do código, um procedimento para calcular propriedades do modelo black oil a partir de uma análise composicional também é apresentada. Abstract : This dissertation presents the study and implementation of a compositional model for the simulation of the isothermal flow in oil reservoirs with unstructured meshes using the element-based finite volume method (EbFVM). The model consists of a fully implicit formulation with a fully coupled solution of mass balance and chemical equilibrium equations using the Newton-Raphson method. The model considers reservoirs with heterogeneous and anisotropic properties, effects of capillary pressure and gravity, among other relevant physical factors. The formulation assumes an arbitrary number of components distributed in the oil and gas phases, and the component water is present only in the water phase. It is therefore a three-phase model but with the chemical equilibrium being solved only in oil and gas phases. In the model, flash calculations and the stability test based on the minimization of Gibbs free energy are solved using a more advanced and robust procedure, combining the Newton-Raphson method with a successive substitution procedure. To validate the model, comparisons are made with the results obtained with comercial compositional and black oil simulators and the results showed good agreement. The implementation of the model and all the numerical modules used in this work were done with advanced programming techniques in C++, allowing code reuse for solving multicomponent thermodynamic problems, which require the use of a cubic equation of state. To illustrate this feature of the code, a procedure for calculating black oil model properties from a compositional analysis is also presented

Mathematical Models and Numerical Methods for Porous Media Flows Arising in Chemical Enhanced Oil Recovery

We study multiphase, multicomponent flow of incompressible fluids through porous media. Such flows are of vital interest in various applied science and engineering disciplines like geomechanics, groundwater flow and soil-remediation, construction engineering, hydrogeology, biology and biophysics, manufacturing of polymer composites, reservoir engineering, etc. In particular, we study chemical Enhanced Oil Recovery (EOR) techniques like polymer and surfactant-polymer (SP) flooding in two space dimensions. We develop a mathematical model for incompressible, immiscible, multicomponent, two-phase porous media flow by introducing a new global pressure function in the context of SP flooding. This model consists of a system of flow equations that incorporates the effect of capillary pressure and also the effect of polymer and surfactant on viscosity, interfacial tension and relative permeabilities of the two phases. We propose a hybrid method to solve the coupled system of equations for global pressure, water saturation, polymer concentration and surfactant concentration in which the elliptic global pressure equation is solved using a discontinuous finite element method and the transport equations for water saturation and concentrations of the components are solved by a Modified Method Of Characteristics (MMOC) in the multicomponent setting. We also prove convergence of the hybrid method by assuming an optimal O(h) order estimate for the gradient of the pressure obtained using the discontinuous finite element method and using this estimate to analyze the convergence of the MMOC method for the transport system. The novelty in this proof is the convergence analysis of the MMOC procedure for a nonlinear system of transport equations as opposed to previous results which have only considered a single transport equation. For this purpose, we consider an analogous single-component system of transport equations and discuss the possibility of extending the analysis to multicomponent systems. We obtain error estimates for the transport variables and these estimates are validated numerically in two ways. Firstly, we compare them with numerical error estimates obtained using an exact solution. Secondly, we also compare these estimates with results obtained from realistic numerical simulations of flows arising in enhanced oil recovery processes. This mathematical model and hybrid numerical procedure have been successfully applied to solve a variety of configurations representing different chemical flooding processes arising in EOR. We perform numerical simulations to validate the method and to demonstrate its robustness and efficiency in capturing the details of the various underlying physical and numerical phenomena. We introduce a new technique to test for the influence of grid alignment on the numerical results and apply this technique on the hybrid method to show that the grid orientation effect is negligible. We perform simulations using different types of heterogeneous permeability field data which include piecewise discontinuous fields, channel-like fractures, real world SPE10 models and multiscale fields generated using a stationary, isotropic, fractal Gaussian distribution. Finally, we also use the method to compare the relative performance of flooding schemes with different injection profiles both in a quarter five-spot as well as a rectangular reservoir geometry