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Anvarbek Meirmanov - One of the best experts on this subject based on the ideXlab platform.
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DOUBLE POROSITY MODELS FOR LIQUID FILTRATION IN INCOMPRESSIBLE POROELASTIC MEDIA
Mathematical Models and Methods in Applied Sciences, 2010Co-Authors: Anvarbek MeirmanovAbstract:Double porosity models for the liquid filtration in a Naturally Fractured Reservoir is derived from the homogenization theory. The governing equations on the microscopic level consist of the stationary Stokes system for an incompressible viscous fluid, occupying a crack-pore space (liquid domain), and stationary Lame equations for an incompressible elastic solid skeleton, coupled with the corresponding boundary conditions on the common boundary "solid skeleton-liquid domain". We assume that the liquid domain is a union of two independent systems of cracks (fissures) and pores, and that the dimensionless size δ of pores depends on the dimensionless size e of cracks: δ = er with r > 1. The rigorous justification is fulfilled for homogenization procedure as the dimensionless size of the cracks tends to zero, while the solid body is geometrically periodic. As the result we derive the well-known Biot–Terzaghi system of liquid filtration in poroelastic media, which consists of the usual Darcy law for the liquid...
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Double Porosity Models for Liquid Filtration in Incompressible Poroelastic Media
arXiv: Analysis of PDEs, 2009Co-Authors: Anvarbek MeirmanovAbstract:Double porosity models for the liquid filtration in a Naturally Fractured Reservoir is derived from the homogenization theory. The governing equations on the microscopic level consist of the stationary Stokes system for an incompressible viscous fluid, occupying a crack-pore space (liquid domain), and stationary Lame equations for an incompressible elastic solid skeleton, coupled with corresponding boundary conditions on the common boundary "solid skeleton-liquid domain". We suppose that the liquid domain is a union of two independent systems of cracks (fissures) and pores, and that the dimensionless size $\delta$ of pores depends on the dimensionless size $\varepsilon$ of cracks: $\delta=\varepsilon^{r}$ with $r>1$. The rigorous justification is fulfilled for homogenization procedure as the dimensionless size of the cracks tends to zero, while the solid body is geometrically periodic. As the result we derive the well-known Biot -- Terzaghi system of liquid filtration in poroelastic media, which consists of the usual Darcy law for the liquid in cracks coupled with anisotropic Lame's equation for the common displacements in the solid skeleton and in the liquid in pores and a continuity equation for the velocity of a mixture. The proofs are based on the method of reiterated homogenization, suggested by G. Allaire and M. Briane. As a consequence of the main result we derive the double porosity model for the filtration of the incompressible liquid in an absolutely rigid body.
Alireza Kazemi - One of the best experts on this subject based on the ideXlab platform.
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performance evaluation of an enhanced geothermal system in the western canada sedimentary basin
Renewable & Sustainable Energy Reviews, 2019Co-Authors: Alireza Kazemi, Seyedbijan Mahbaz, Alireza Dehghanisanij, Maurice B Dusseault, Roydon FraserAbstract:Abstract Sustainable low-carbon energy resources (e.g., geothermal energy) are important solutions to meet growing energy demand in developed and developing countries. Because of recent advances in drilling and hydraulic fracturing technologies for flow enhancement, Enhanced Geothermal Systems based on hot/warm fluids from deep geological formations have an increasingly interesting potential for power and heat supply. In this paper, a conceptual Sedimentary Enhanced Geothermal System in the Williston Basin is investigated numerically. Thermo-hydraulic and hydro-mechanical coupled models are used to assess the thermal performance and stress evolution of a geothermal doublet system. Using realistic properties of the target area, doublet spacing and recirculation flow rate are studied to evaluate the growth of the heat transfer volume. Introducing a more permeable zone (i.e., a fault or high permeability channel) across the flow path between wells does not shorten the useful Reservoir lifetime; in fact, it delays cold front advancement by lateral broadening of the heat transfer domain. As cold water is re-injected into the Reservoir in a recirculation approach, large stress changes are generated, and the stress distribution and local stress gradients change with time through combined convective and conductive heat transfer. Although the rock model used represents an unFractured sandstone with negligible permeability sensitivity to effective stress changes, the authors note that for a Naturally Fractured Reservoir the stress changes will have major impacts on flow paths (compressional versus extensional expansion) and hence temperature distributions and heat extraction behavior.
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fluid flow in Fractured Reservoirs exact analytical solution for transient dual porosity model with variable rock matrix block size
Journal of Petroleum Science and Engineering, 2018Co-Authors: Mahdi Abbasi, Mohammad Madani, Mohammad Sharifi, Alireza KazemiAbstract:Abstract Dual porosity Reservoirs consist of two comparatively independent systems of fractures and matrix blocks with high and low permeability values, respectively. Semi-analytical and numerical studies on Naturally Fractured Reservoirs have been already cited in the literature. The present study focuses on investigation of a linear double porosity model of a semi-infinite-acting Naturally Fractured Reservoir using an exact analytical method. Different matrix block size distributions are embedded into a transient model to consider the effects of heterogeneity in Fractured formations. In order to take into account transient fracture-matrix exchange, an analytical method is proposed to solve the coupled fracture and matrix equations. Gauss Legendre quadrature is employed to evaluate the double integral of general transient solution. Moreover, the corresponding shape factor was evaluated in a double porosity transient model coupled with variable matrix block size distribution. Results demonstrated that matrix block size distributions strongly affect the fluid transfer during the early time region. Also, the presented model was employed to generate interference test curves which in turn were studied to investigate the impacts of storativity ratio and matrix block size distributions on the fracture-matrix fluid transfer. Results illustrated that a series of obtained pressure data from an observational well along with the proposed model may be considered a robust method in fracture intensity assessment. Fast sensitivity analysis and very efficient computational cost are the benefit of the derived analytical solutions with respect to previous numerical solutions.
Pedro Marcelo - One of the best experts on this subject based on the ideXlab platform.
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Análise avançada de dados de produção em reservatórios naturalmente fraturados
[s.n.], 2018Co-Authors: Adrian Herbas, Pedro MarceloAbstract:Orientador: Rosângela Barros Zanoni Lopes MorenoDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica e Instituto de GeociênciasResumo: Nos últimos anos tem havido um interesse crescente no uso dos métodos de Análise Avançada de Dados de Produção (AADP) para a descrição dinâmica do reservatório. A partir destes métodos analisam-se dados de produção diárias disponíveis, reduzindo a necessidade de operações de teste de poço, evitando perda de produção e com uma exatidão comparável à Análise de Transiente de Pressão. Diferentes modelos AADP têm sido propostos para reservatórios de óleo e gás homogêneos, de metano em camadas de carvão e de gás de xisto. No entanto, a produção de reservatórios naturalmente fraturados, tais como rochas carbonáticas ou siliciclásticas, ainda está sendo analisada como sistemas homogêneos utilizando métodos AADP atuais. Este trabalho apresenta a derivação analítica de dois métodos de AADP (Balanço de materiais dinâmico e curvas tipo de Blasingame) baseados no modelo de dupla porosidade, para analisar a produção diária de reservatórios naturalmente fraturado. Foram avaliados a transferência matriz-fratura pseudo-permanente e transiente (camadas e esferas). O desenvolvimento foi baseado nas soluções aproximadas de longo tempo da equação da difusividade em sistemas de dupla porosidade, para vazão constante em reservatórios fechados sem fluxo na fronteira. As aproximações foram comparadas com a solução exata, dada pela inversa da solução no espaço Laplace, obtida aplicando o algoritmo de Gaver-Stehfest. A validação foi feita usando dados de produção e pressão de fluxo sintéticos, gerados por um simulador numérico, e dados reais de campo de um reservatório de gás-condensado naturalmente fraturado. Os resultados confirmaram que reservatórios naturalmente fraturados com fluxo interporoso pseudo-permanente podem apresentar dois comportamentos dominado pelos limites do reservatório (fraturas y sistema total). A permeabilidade da fratura e o dano do poço são dependentes variáveis ômega e lambda. Reservatórios fraturados com fluxo interporoso transiente podem ser analisados utilizando técnicas de AADP atuais desenvolvidas para sistemas homogêneosAbstract: In recent years there has been an increasing interest in the use of Advanced Production Data Analysis (APDA) methods for dynamic Reservoir description. These methods analyze available daily production data, reducing the need of well testing operations, avoiding production loss, with accuracy comparable to Pressure Transient Analysis (PTA). Different APDA models have been proposed for homogeneous, coalbed methane and shale gas Reservoirs. Nevertheless, production from Naturally Fractured Reservoirs, such as Carbonates or Siliciclastic, is still being analyzed as homogeneous systems with current APDA techniques. This work presents the analytical derivation of two APDA methods (Dynamic Material Balance and Blasingame Type Curves) based on the dual porosity model, to analyze daily production of Naturally Fractured Reservoirs (NFR). Both interporosity flow models between matrix and fractures, pseudosteady-state and transient (slabs and spheres), were evaluated. The development was based on long-time approximate solutions of diffusivity equation for constant flow rate in a closed system with no-flow boundary. These approximations were compared with the exact solution given in Laplace space, inverted to time domain applying the Gaver-Stehfest algorithm. The validation of the derived methods was made using synthetic production and flowing pressure data, generated by a numerical simulator, and real field data from a gas-condensate Naturally Fractured Reservoir. Results confirmed that Naturally Fractured Reservoirs with pseudosteady-state interporosity flow could present two boundary-dominated behaviors (fracture and total systems). Fracture permeability and wellbore skin are functions of omega and lambda variables. Fractured Reservoirs with transient interporosity flow between matrix and fracture system, can be analyzed using current APDA techniques developed for homogeneous systemsMestradoReservatórios e GestãoMestre em Ciências e Engenharia de Petróleo33003017CAPE
Pedro Marcelo Adrian Herbas - One of the best experts on this subject based on the ideXlab platform.
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Análise avançada de dados de produção em reservatórios naturalmente fraturados
2017Co-Authors: Pedro Marcelo Adrian HerbasAbstract:Resumo: Nos últimos anos tem havido um interesse crescente no uso dos métodos de Análise Avançada de Dados de Produção (AADP) para a descrição dinâmica do reservatório. A partir destes métodos analisam-se dados de produção diárias disponíveis, reduzindo a necessidade de operações de teste de poço, evitando perda de produção e com uma exatidão comparável à Análise de Transiente de Pressão. Diferentes modelos AADP têm sido propostos para reservatórios de óleo e gás homogêneos, de metano em camadas de carvão e de gás de xisto. No entanto, a produção de reservatórios naturalmente fraturados, tais como rochas carbonáticas ou siliciclásticas, ainda está sendo analisada como sistemas homogêneos utilizando métodos AADP atuais. Este trabalho apresenta a derivação analítica de dois métodos de AADP (Balanço de materiais dinâmico e curvas tipo de Blasingame) baseados no modelo de dupla porosidade, para analisar a produção diária de reservatórios naturalmente fraturado. Foram avaliados a transferência matriz-fratura pseudo-permanente e transiente (camadas e esferas). O desenvolvimento foi baseado nas soluções aproximadas de longo tempo da equação da difusividade em sistemas de dupla porosidade, para vazão constante em reservatórios fechados sem fluxo na fronteira. As aproximações foram comparadas com a solução exata, dada pela inversa da solução no espaço Laplace, obtida aplicando o algoritmo de Gaver-Stehfest. A validação foi feita usando dados de produção e pressão de fluxo sintéticos, gerados por um simulador numérico, e dados reais de campo de um reservatório de gás-condensado naturalmente fraturado. Os resultados confirmaram que reservatórios naturalmente fraturados com fluxo interporoso pseudo-permanente podem apresentar dois comportamentos dominado pelos limites do reservatório (fraturas y sistema total). A permeabilidade da fratura e o dano do poço são dependentes variáveis ômega e lambda. Reservatórios fraturados com fluxo interporoso transiente podem ser analisados utilizando técnicas de AADP atuais desenvolvidas para sistemas homogêneos.Abstract: In recent years there has been an increasing interest in the use of Advanced Production Data Analysis (APDA) methods for dynamic Reservoir description. These methods analyze available daily production data, reducing the need of well testing operations, avoiding production loss, with accuracy comparable to Pressure Transient Analysis (PTA). Different APDA models have been proposed for homogeneous, coalbed methane and shale gas Reservoirs. Nevertheless, production from Naturally Fractured Reservoirs, such as Carbonates or Siliciclastic, is still being analyzed as homogeneous systems with current APDA techniques. This work presents the analytical derivation of two APDA methods (Dynamic Material Balance and Blasingame Type Curves) based on the dual porosity model, to analyze daily production of Naturally Fractured Reservoirs (NFR). Both interporosity flow models between matrix and fractures, pseudosteady-state and transient (slabs and spheres), were evaluated. The development was based on long-time approximate solutions of diffusivity equation for constant flow rate in a closed system with no-flow boundary. These approximations were compared with the exact solution given in Laplace space, inverted to time domain applying the Gaver-Stehfest algorithm. The validation of the derived methods was made using synthetic production and flowing pressure data, generated by a numerical simulator, and real field data from a gas-condensate Naturally Fractured Reservoir. Results confirmed that Naturally Fractured Reservoirs with pseudosteady-state interporosity flow could present two boundary-dominated behaviors (fracture and total systems). Fracture permeability and wellbore skin are functions of omega and lambda variables. Fractured Reservoirs with transient interporosity flow between matrix and fracture system, can be analyzed using current APDA techniques developed for homogeneous systems
Hassan Hassanzadeh - One of the best experts on this subject based on the ideXlab platform.
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One-Dimensional Matrix-Fracture Transfer in Dual Porosity Systems with Variable Block Size Distribution
Transport in Porous Media, 2012Co-Authors: Ehsan Ranjbar, Hassan Hassanzadeh, Zhangxin ChenAbstract:Most of the developed models for Fractured Reservoirs assume ideal matrix block size distribution. This assumption may not be valid in reality for Naturally Fractured Reservoirs and possibly lead to errors in prediction of production from the Naturally Fractured Reservoirs especially during a transient period or early time production from the matrix blocks. In this study, we investigate the effect of variable block size distribution on one- dimensional flow of compressible fluids in Fractured Reservoirs. The effect of different matrix block size distributions on the single phase matrix-fracture transfer is studied using a recently developed semi-analytical approach. The proposed model is able to simulate fluid exchange between matrix and fracture for continuous or discrete block size distributions using probability density functions or structural information of a Fractured formation. The presented semi-analytical model demonstrates a good accuracy compared to the numerical results. There have been recent attempts to consider the effect of variable block size distribution in Naturally Fractured Reservoir modeling for slightly compressible fluids with a constant viscosity and compressibility. The main objective of this study is to consider the effect of variable block size distribution on a one-dimensional matrix-fracture transfer function for single-phase flow of a compressible fluid in Fractured porous media. In the proposed semi-analytical model, the pressure variability of viscosity and isothermal compressibility is considered by solving the nonlinear partial differential equation of compressible fluid flow in the Fractured media. The closed form solution provided can be applied to flow of compressible fluids with variable matrix block size distribution in Naturally Fractured gas Reservoirs.
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Shape factor in the drawdown solution for well testing of dual-porosity systems
Advances in Water Resources, 2009Co-Authors: Hassan Hassanzadeh, Mehran Pooladi-darvish, Shahram AtabayAbstract:Abstract One of the important parameters in existing commercial dual-porosity Reservoir simulators is matrix–fracture shape factor, which is customarily obtained by assuming a constant pressure at the matrix–fracture boundary. In his work, Chang [1] , [2] addressed the impact of boundary conditions at the matrix–fracture interface and presented analytical solutions for the transient shape factor and showed that for a slab-shaped matrix block a constant pressure boundary condition leads to an asymptotic (long-time) shape factor of π2/L2, and that a constant volumetric flux leads to an asymptotic shape factor of 12/L2. In a recent paper [3] , we reconfirmed Chang’s [1] , [2] results using a Laplace transform approach. In this study, we extend our previous analysis and use infinite-acting radial and linear dual-porosity models, where the boundary condition is chosen at the wellbore, as opposed to at the matrix boundary. The coupled equations for fracture and matrix are solved analytically, taking into account the transient exchange between matrix and fracture. The analytical solution that invokes the time dependency of fracture boundary condition under constant rate is then used to calculate the transient shape factors. It is shown that, for a well producing at constant rate from a Naturally Fractured Reservoir, the appropriate value of stabilized shape factor is 12/L2. This contrasts with the commonly used shape factor for a slab-shaped matrix block that is subject to a constant pressure boundary condition, which is π2/L2. The errors in the matrix–fracture exchange term in a dual-porosity model associated with the use of a shape factor derived based on constant pressure boundary condition at the matrix boundary are then evaluated.
