Gas-Flow Simulation in Discrete Fracture-Network Models
- Remy Basquet (Institut Français du Pétrole) | Laurent Jeannin (Institut Français du Pétrole) | Arnaud Lange (Institut Français du Pétrole) | Bernard Bourbiaux (Institut Français du Pétrole) | Sylvain Sarda (Beicip-Franlab)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- October 2004
- Document Type
- Journal Paper
- 378 - 384
- 2004. Society of Petroleum Engineers
- 4.6 Natural Gas, 4.1.2 Separation and Treating, 5.1.5 Geologic Modeling, 5.1.2 Faults and Fracture Characterisation, 5.1 Reservoir Characterisation, 2.2.2 Perforating, 5.5 Reservoir Simulation, 3.3.2 Borehole Imaging and Wellbore Seismic, 4.1.5 Processing Equipment, 4.1.4 Gas Processing, 5.5.3 Scaling Methods, 4.3.4 Scale, 1.8 Formation Damage, 5.2.2 Fluid Modeling, Equations of State, 5.6.4 Drillstem/Well Testing, 5.8.6 Naturally Fractured Reservoir
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Advanced characterization methodologies are now able to provide realistic pictures of fracture networks. We recently developed software to simulate the transient and pseudosteady-state flows of a slightly compressible fluid in discrete fracture-network (DFN) models. This simulator is used to validate the fracture-network geometry and to calibrate the hydraulic properties of the fractures through dynamic data obtained from flowmeters, interference, and well tests. This paper is dedicated to the extension of the methodology to gas cases, taking into account the high fluid compressibility and the non-Darcy flow effects near the wellbore.
The main features of our simulator are described and illustrated through demonstrative examples. Our DFN simulation approach is based on an optimized explicit representation for both matrix and fracture media and a specific treatment for matrix/fracture and matrix/matrix exchanges. A pseudopressure function is included in the diffusivity equation to take into account highly compressible fluids. The hydrodynamic behavior of gas fluid flow near the wellbore is taken into account through a skin effect proportional to the flow rate for both matrix/well and fracture/well transmissivities.
This innovative numerical simulator is validated against existing analytical solutions and compared with finite-volume solutions computed with a suitable grid. Then, for application purposes, a complex realistic case involving a multiscale natural fracture network with small-scale fractures and major objects such as seismic and subseismic faults is presented. An interference test is simulated on a representative DFN model and on the equivalent dual-porosity model built thanks to upscaling procedures. This upscaled reservoir model is shown to remain consistent with the geological DFN model in terms of gas flow. This example illustrates the practical use of DFN models in our fractured-reservoir-modeling workflow.
Fractured gas fields can be found in many petroleum basins. To study the field development for such formations, we need to provide a realistic picture of fracture networks and characterize accurately the hydraulic parameters of the identified fracture patterns to do precise dynamic simulations. In opposition to liquid flow, the real-gas flow needs a specific treatment because of its high compressibility and the variation of viscosity and z-factor as a function of pressure. Besides, Darcy's law cannot always be applied to gas flow in a region near the wellbore. These two gas-flow specificities can be studied separately. Let us give a brief review of their treatment in the literature.
First, to take into account the variation of gas viscosity and z-factor as a function of pressure, Al-Hussainy et al.1 proposed a pseudopressure function to derive the governing partial-differential equations. This formulation also has been used by Wattenbarger and Ramey2 to extend the theory of hydraulically fractured gas-well testing to the flow of real gases. They determined the effects of wellbore storage and turbulence on well-test analysis by using a finite-difference model. They concluded that the drawdown tests for vertically fractured wells could be extended to the real-gas case by using the pseudopressure function.
Later, Camacho and Raghavan3 combined the double-porosity model of Barenblatt et al.4 with a pseudopressure formulation to deal with well-test analysis of solution-gas-drive systems for naturally fractured reservoirs.
We adopt in this paper the pseudopressure formulation in a system of equations similar to Barenblatt et al.4 model. A finite-volume method is used to solve those equations that are discretized on the geological model of fracture and matrix media.
In the vicinity of the wellbore, Darcy's law does not always apply to gas flow. A more general expression is needed for non-Darcy flow. The Forchheimer flow equation5 often has been used to represent turbulent fluid flow through porous media. Several studies have discussed the application of this type of equation to the flow of single-phase gas.6,7 In this work, we use a skin effect varying linearly with the flow rate. As proposed by Wattenbarger,7 we will be able to adopt a more realistic "turbulent" formulation by the introduction of a coefficient D function of the gas viscosity.
A methodology (Ref. 8) has been developed by IFP for several years to build flow-calibrated DFN models. This methodology includes the following steps:
The analysis of static data derived from outcrop, seismic, and borehole images.
The reconstruction of multiscale DFN models representative of the identified fracture patterns.
The simulation of dynamic data like buildup or interference tests on those DFN models to validate the fracture-network geometry and to calibrate the hydraulic parameters of each fracture set.
Taking into account the highly compressible fluid in a system of equations similar to Barenblatt et al., we are now able to extend our methodology of DFN characterization to real-gas fluid-flow problems.
After a presentation of the mathematical formulation used to simulate gas flow in DFN models, we propose validation cases through existing analytical solutions in the context of gas-well testing. This validation procedure is done in two steps: first, we focus on the pseudopressure formulation through a gas-well-test analysis with neither skin effect nor non-Darcy flow effect. Then, we introduce within the previous double-porosity model a rate-dependent skin to represent the formation damage skin and the non-Darcy flow effects.
Thanks to the agreement between the numerical results on the DFN model and the analytical solutions, we apply our DFN simulator to a realistic interference test and compare the results with simulations realized on a dual-porosity simulator. The DFN model is composed of a diffuse fracture pattern (small-scale fractures) and subseismic conductive faults that strongly affect fluid flow. The fracture cell attributes are determined from an upscaling method for the small-scale fractures and from the use of a modified transmissivity map for the faults and the subseismic faults. This case shows the applicability of our gas fluid-flow simulation approach to a realistic multiscale fracture network and the consistency of the workflow to convert geological images to a conventional double-porosity model.
The double-porosity concept was first introduced by Barenblatt et al.4 It assumes the existence of two porous regions of contrasted porosities and permeabilities within the formation.
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