Time-Dependent Shape Factors for Uniform and Non-Uniform Pressure Boundary Conditions

Rangel-German, Edgar; Kovscek, Anthony R.; Akın, Serhat

doi:10.1007/s11242-009-9461-7

Cited by 16 publications

(7 citation statements)

References 15 publications

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“…The multiple interacting continua extension of the classical dual-porosity model (Pruess and Narasimhan, 1985;Karimi-Fard et al 2006;Rubin 2007;Gong et al 2008;Tatomir et al 2011) allows for local variations in saturation or concentration in the matrix. Time-dependent shape factors can model unsteady-state processes such as partially immersed fractures and nonuniform matrix saturations (Rangel-German and Kovscek 2006;Rangel-German et al 2010). These approaches are the numerical equivalent to our MRMT model: they attempt to approximate nonuniform saturation transients in the matrix and thus spatially and temporally varying transfer rates.…”

Section: Discussionmentioning

confidence: 99%

A Novel Multirate Dual-Porosity Model for Improved Simulation of Fractured and Multiporosity Reservoirs

Geiger¹,

Dentz

Neuweiler

2013

SPE Journal

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A major part of the world's remaining oil reserves is in fractured carbonate reservoirs, which are dual-porosity (fracture-matrix) or multiporosity (fracture/vug/matrix) in nature. Fractured reservoirs suffer from poor recovery, high water cut, and generally low performance. They are modeled commonly by use of a dual-porosity approach, which assumes that the high-permeability fractures are mobile and low-permeability matrix is immobile. A single transfer function models the rate at which hydrocarbons migrate from the matrix into the fractures. As shown in many numerical, laboratory, and field experiments, a wide range of transfer rates occurs between the immobile matrix and mobile fractures. These arise, for example, from the different sizes of matrix blocks (yielding a distribution of shape factors), different porosity types, or the inhomogeneous distribution of saturations in the matrix blocks. Thus, accurate models are needed that capture all the transfer rates between immobile matrix and mobile fracture domains, particularly to predict late-time recovery more reliably when the water cut is already high. In this work, we propose a novel multi-rate mass-transfer (MRMT) model for two-phase flow, which accounts for viscous-dominated flow in the fracture domain and capillary flow in the matrix domain. It extends the classical (i.e., singlerate) dual-porosity model to allow us to simulate the wide range of transfer rates occurring in naturally fractured multiporosity rocks. We demonstrate, by use of numerical simulations of waterflooding in naturally fractured rock masses at the gridblock scale, that our MRMT model matches the observed recovery curves more accurately compared with the classical dual-porosity model. We further discuss how our multi-rate dual-porosity model can be parameterized in a predictive manner and how the model could be used to complement traditional commercial reservoir-simulation workflows.

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Section: Discussionmentioning

confidence: 99%

A Novel Multirate Dual-Porosity Model for Improved Simulation of Fractured and Multiporosity Reservoirs

Geiger¹,

Dentz

Neuweiler

2013

SPE Journal

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“…They tried to overcome limitations by deriving a final form for the transfer function as: (19) For the particular case of two parallel fracture with pseudo-steady state pressure diffusion and instantaneously filled fracture, they define the shape factors in eqn. (19) by and (20) where b is a constant depending on the porous media properties. Good match was obtained with a reference solution using a fine grid model with ECLIPES 100 for a conceptual representation of a fractured reservoir with source and sink.…”

Section: Group Two: Transient Functionsmentioning

confidence: 99%

“…This formulation converges to for pseudo-steady state condition. In 2010, Rangel-German et al [19] solve the pressure diffusivity equation for single phase using non-uniform boundary conditions and approximating solution with an exponential function. They obtain values for in eqn.…”

Section: Group Two: Transient Functionsmentioning

confidence: 99%

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Fracture-matrix transfer function in fractured porous media

Mahmood¹

2013

WIT Transactions on the Built Environment

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One of the mathematical models dealing with fluid flow in fractured porous media is the dual porosity model. The key issue governing this model is the transfer function which representing fracture-matrix interaction. Many formulas for this function had been presented since the 1960s. In this work, a review for these formulations was done. Based on the assumption used in deriving the transfer function formulas, they are classified into two groups. The first group includes those derived assuming semi-steady (pseudo-steady) state flow and the second includes those assuming transient state flow. This work will help worker selecting the formulation that best represent the flow situation and the type of porous media.

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“…There are two different matrix and fracture systems with different physical characteristics inside such oil reserves. The mechanisms of production of this type of reservoirs are very different from conventional reservoirs (Rangel-German et al, 2010). Considering the juxtaposition of two matrix and fracture systems together (with considerable difference in size), the simulation of fractured reservoirs using single porosity models is very timeconsuming and even the simulation may not converge.…”

Section: Introductionmentioning

confidence: 99%

Modeling of transient shape factor in fractured reservoirs considering the effect of heterogeneity, pressure-dependent properties and quadratic pressure gradient

Abbasi¹,

Kazemi²,

Sharifi³

2019

Oil Gas Sci. Technol. – Rev. IFP Energies nouvelles

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Fractured reservoirs contain most of the oil in the world’s reserves. The existence of two systems of matrix and fracture with completely different characteristics has caused the modeling of the mechanisms of fractured reservoirs to be more complex than conventional ones. Modeling of this type of reservoirs is possible using two methods of single and dual porosity model. Modeling via single porosity scheme is very time-consuming as it takes into account huge matrix blocks (low permeability and high porosity) and small fractures (high permeability and low porosity) alongside each other explicitly. The dual porosity model, however, attempts to solve this problem using the concept of shape factor, which is defined as the amount of fluid transferred from the matrix to the fracture. The shape factor coefficients expressed so far have been derived via simplifying assumptions which keep them away from real conditions prevailing in fractured reservoirs. In this paper, shape factor is calculated more realistically with consideration of the quadratic pressure gradient in the diffusivity equation, the heterogeneity of the matrix block and the change of the rock properties by pressure change. For these three cases, the analytical modeling of the flow of fluid from the matrix to the fracture system has been discussed and its results with previous models have been compared. In addition, the dependence of shape factor on the stated parameters was evaluated and in order to validate the results of the proposed analytical model, its results were compared with the results of a commercial simulator. Investigating the shape factor with the assumptions about the physics of the fractured reservoirs will improve our understanding of the fluid transfer between the matrix and the fracture, and this capability will allow numerical and commercial simulators to predict the behavior of fractured reservoirs more accurately.

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Time-Dependent Shape Factors for Uniform and Non-Uniform Pressure Boundary Conditions

Cited by 16 publications

References 15 publications

A Novel Multirate Dual-Porosity Model for Improved Simulation of Fractured and Multiporosity Reservoirs

A Novel Multirate Dual-Porosity Model for Improved Simulation of Fractured and Multiporosity Reservoirs

Fracture-matrix transfer function in fractured porous media

Modeling of transient shape factor in fractured reservoirs considering the effect of heterogeneity, pressure-dependent properties and quadratic pressure gradient

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