Layer | Fill | Outline |
---|
Map layers
Theme | Visible | Selectable | Appearance | Zoom Range (now: 0) |
---|
Fill | Stroke |
---|---|
Collaborating Authors
Results
Abstract Modeling of naturally fractured reservoirs is the first step to develop best scenarios for hydraulic fracture treatment, the design of an optimum production method and to evaluate reservoir potential. This paper reviews the state-of-the-art in current methods; hence, presents an integrated modeling methodology, utilizing object-based modeling, stochastic simulation and global optimization. Firstly, as an object-based model, each fracture is presented and treated as a discrete object. A stochastic simulation is carried out to generate an initial fracture network. An objective function is then formulated as the difference in statistics between the initial network and the target. Semi-variogram and other spatial statistical properties (cross variogram, multi-histogram mean and variogram distance) of fracture parameters are included so that the objective function is able to statistically describe representative field data. Subsequently, we use a global optimization algorithm to optimize the objective function. A case study is performed on an actual outcrop fault map to illustrate the proposed methodology's capacity. The results map the outcrop faults very closely. Introduction Due to geological reasons, many of the naturally fractured reservoirs (NFR) possess very low permeability, which is inadequate for economic production. Therefore, some permeability enhancement techniques are essential for these reservoirs. However, the underlying principles of such techniques, such as hydraulic fracture stimulation, are complex and progress is hindered due to lack of appropriate geo-statistical fracture description models. Thus, there are three main reasons for a detailed fracture distribution:To site best locations for production wells; To study the response of natural fractures under stimulation pressure; hence, to develop a best scenario for hydraulic fracture treatment; and To design an optimum production method and evaluate reservoir potential. In order to achieve the prescribed objectives, NFR need to be characterized and modeled, which would include descriptions of reservoir boundaries, major faults and medium to small-scale fracture networks. Fracture Modeling Techniques: State-of-the-Art Mathematical and Geo-Mechanical Models Several techniques to simulate NFR have been documented in the literature. Firstly, there are mathematical and geo-mechanical models. Earlier mathematical methods to simulate NFR and fluid flow through them include equivalent continuum, discrete network and hybrid models. The usual approach relies on simplistic geometrical descriptions of fracture systems (e.g. homogeneous reservoirs, parallel plate fractures, etc.) with primary efforts spent on flow behaviours. Many authors use different geo-mechanical approaches for modeling NFR, such as simple curvature analysis, field stress and fracture growth mechanism, and numerical analysis by solving systems of non-linear continuum mechanics equations using finite element methods. However, due to the complex nature of fracture systems, most studies so far have succeeded only in modeling unrealistic homogeneous reservoirs. Moreover, most of these techniques use only a limited source of data, such as seismic or well logs. Hence, in modeling NFR, it is necessary to utilize all data sources in an integrated manner to reach a more comprehensive model. Stochastic Simulation Stochastic simulation is one of the integrated reservoir modeling approaches. Since explicit fracture information is only
- North America (1.00)
- Asia (0.94)
- Oceania > Australia (0.47)
- Europe > United Kingdom (0.28)
- Geophysics > Seismic Surveying (0.48)
- Geophysics > Borehole Geophysics (0.34)
Simulation of Production from Naturally Fractured Reservoirs with the Use of Effective Permeability Tensor
Teimoori, A. (The University of New South Wales) | Tran, N.H. (The University of New South Wales) | Chen, Z. (The University of New South Wales) | Rahman, S.S. (The University of New South Wales)
Abstract This paper presents a numerical model for simulating fluid flow and production from naturally fractured reservoir based on a flux continuous control volume mixed finite element approach. The main features of the present model are that it accounts for the heterogeneity of the fractured media by applying effective permeability tensor in each grid block and allows the direct calculation of fluid flow velocity. Flux continuous control volume mixed finite element technique is used to simultaneously solve two coupled partial differential equations for fluid pressure and velocity. Effective permeability tensor represents directional permeability in fractured media. Thus the model overcomes the existing problems in previous models in relation to irregular fracture patterns, flow interactions between matrix and fractures and effects of fracture characteristics (dimension, density and orientation). The model is validated against data published in literature and applied to a typical naturally fractured reservoir, where the fracture network was characterized by a hybrid object-based fracture characterization technique. Introduction Characterization and simulation of fluid flow in naturally fractured reservoirs are challenging issues in petroleum engineering and hydrology. The current simulation techniques for these reservoirs have been limited either to basic flow calculation through a system of connected fractures embedded in zero matrix permeability rock1, or to unrealistic dual porosity model, where naturally fractured reservoirs are often assumed to be parallel layers separated by fractures. The idea of using control volume mixed finite element (here after CVMFE) method is to solve a simple system of lower order equations for the velocity and pressure, instead of complicated differential equations when modeling multi-phase fluid flow in porous media. This leads to a system of first order equations of flow and conservation of immiscible incompressible phases in a porous media. In this work we use the block-centered CVMFE method to calculate pressure at the block centers and velocity on the block edges. In this method, the fluid pressure field is calculated implicitly using pressure equation while the velocity field is simultaneously calculated explicitly using control volume method. The system of equations can be solved by mixed finite element or CVMFE methods. The system of linear equations produced in mixed finite element method are not positive definite and cannot be solved by straightforward applications of well-known iterative solvers. However, block-centered CVMFE method in this paper produces a symmetric positive definite system of equations. In recent years, use of the effective permeability tensor has been recognized as one of the most effective ways to represent the heterogeneity of permeability and simulation of fractured reservoirs. It is assumed that a fractured grid-block can be replaced with a homogeneous grid-block having an equivalent permeability taking into account the geometry of the actual fracture system. Teimoori et al. presented a model which employs periodic boundary conditions and boundary element method to calculate the full symmetric and positive definite effective permeability tensor. There are considerable works conducted recently in the simulation of fluid flow using the full effective permeability tensor. Lee et al. presented a method to simulate reservoirs using a flux-continuous finite difference method and full effective permeability tensor. One of the advantages of this method is the applicability of the model in simulation of heterogeneous reservoirs with up-scaled permeability tensor. The main drawback of their model was that it is only applicable to the reservoirs with regular grid blocks. Cai et al. presented a mathematical model based on CVMFE method to simulate pressure and flow in a reservoir with regular or irregular block-centered grid blocks. Sutopo et al. also used CVMFE in the simulation of production from naturally fractured reservoirs.
- North America > United States (0.69)
- Oceania > Australia (0.46)
An Integrated Model for the Design and Evaluation of Multiwell Hydraulic Fracture Treatments for Gas-Condensate Reservoirs
Valencia, K.L. (The University of New South Wales) | Chen, Z. (The University of New South Wales) | Rahman, M.K. (The University of Western Australia) | Rahman, S.S. (The University of New South Wales)
Abstract This paper presents a hydraulic fracture treatment design optimization scheme which integrates a hydraulic fracture geometry model, a production model and an economic model. The hydraulic fracture geometry model is used to determine the final fracture geometry and select the treatment parameters for a given stress and reservoir condition. Production from the treated well is estimated for pseudo-steady state condition using a model equivalent to a compositional simulator. A genetic-evolutionary optimization algorithm is used to obtain the optimum treatment parameters for maximum production or NPV. The integrated model has been used to investigate different field scenarios of a multiwell gas-condensate reservoir, including optimization of well locations and hydraulic fracture treatment parameters for any well type, achievement of target production and maximization of NPV with simultaneous minimization of the associated treatment costs. Introduction To increase ultimate recovery with minimum treatment cost, hydraulic fracture treatments are optimized by coupling a hydraulic fracture geometry model, a production model and an economic model. A three-step calculation procedure is then conducted repeatedly to obtain the best combination of hydraulic fracture treatment parameters. Previous works in hydraulic fracture treatment design optimization were devoted mainly in the development of a search scheme for the optimum design. The main drawbacks of these tools include absence of global optimization procedure and limited number of design variables. In our previous work, we have addressed these shortcomings and we formulated geometric and operational constraints to ensure a reliable optimum treatment design. The search scheme used is a hybrid of genetic algorithm and evolutionary operation. In our current work, we have incorporated an improved objective function into the optimization scheme and applied it to a specific gas-condensate reservoir. Previous studies simplified the production model by considering the ideal case of a single well, centrally located in a square or circular drainage area. In practice, however, a candidate for a fracture treatment could be part of a multiwell system. To date, several analytical models applicable to multiple wells have been published in literature. Notable is Rodriguez and Cinco-Ley's pioneering work which was further improved by Camacho-V. et al. Most recently, Ozkan introduced a model that takes into account the transient and pseudo-steady state flow regimes and allows for possibility of any well combination and variable rates. On the other hand, using the matrix approach, Valko et al. introduced a simpler model which is applicable for pseudo-steady state flow regime. In order to obtain the optimum values of the hydraulic fracture treatment parameters, an accurate production estimate for a given reservoir condition is necessary. Some of the published works on the subject coupled a stochastic optimization algorithm with a production model that uses idealized dry gas reservoir or single phase oil reservoir. Others used a reservoir simulator for a more accurate production estimate and employed parametric sensitivity analysis to get the optimum treatment parameters. The latter gives improved production estimate but does not explore the whole search space for the global optimum design as it is computationally tedious and time consuming whereas the former gives inaccurate production estimate for reservoirs other than the ideal case but efficiently searches for the optimum values of treatment parameters. In order to overcome the foregoing weaknesses, a generalized production model applicable to gas or gas-condensate reservoir is incorporated in the optimization scheme. This guarantees speedier evaluation of the objective function. Coupling the production model with an efficient optimization algorithm provides solutions to field development problems. Particular attention is given to gas-condensate reservoirs as the need to hydraulically fracture multiple wells in gas-condensate reservoirs arises since exploitation of higher temperature and pressure reservoirs is becoming increasingly important.
Calculation Of Permeability Tensor Using Boundary Element Method Provides A Unique Tool To Simulate Naturally Fractured Reservoirs
Teimoori, A. (The University of New South Wales) | Chen, Z. (The University of New South Wales) | Rahman, S.S. (The University of New South Wales) | Tran, T. (The University of New South Wales)
Abstract This paper presents a numerical model to calculate effective permeability tensor in naturally fractured reservoirs. Darcy's law and Navier-stoke's equation are used to formulate fluid flow in rock matrix and fractures, respectively. Fractures of different scales based on their length are considered. Short fractures are considered as an enhancement of matrix permeability by applying the interface boundary condition. Long fractures intersecting more than one block are treated as a source/sink in the corresponding blocks. Fluid flow in porous matrix around the medium and long fractures is modeled by Poisson's equation. Periodic boundary condition is applied on the grid-block boundaries to calculate the elements of effective permeability tensor. The model has been validated against analytical results and applied to a number of cases where arbitrary fractures of different sizes are assumed within the grid-blocks. Introduction Modeling of fluid flow in naturally fractured reservoirs is an important issue in the areas of petroleum engineering and hydrology. Currently, dual porosity and discrete fracture models are the main approaches to simulate fluid flow in naturally fractured reservoirs. In dual porosity model fractures are assumed to be infinitely long and distributed in a regular pattern. However, real fracture system does not appear to have these properties. The discrete fracture model on the other hand, considers real fracture dimension and focuses on fracture permeability. This approach has the drawback that fluid flow can only take place through a network of connected fractures and flow through the matrix and isolated fractures are not considered. In recent years, calculation of the effective permeability tensor has been recognized to be the most effective way to represent the permeability in a fractured formation. It is assumed that a fractured grid-block can be replaced with a homogeneous grid-block having an equivalent permeability tensor taking into account the geometry of the actual fracture system. Effective permeability was first introduced for a set of parallel fractures with the assumption of zero matrix permeability. Snow developed a basic mathematical model to calculate permeability of an individual or an arbitrary set of parallel fractures. Fractures were assumed to be smooth and infinite parallel plates. Based on Snow's model, Chen et al. evaluated analytically the equivalent permeability of a system with multiple sets of parallel fractures. Long et al. studied a system of arbitrary distributed fractures with the consideration of fracture connectivity. Oda applied a line source-sink to represent randomly distributed fractures in the calculation of effective permeability. Gupta et al., based on Oda's model, proposed a procedure to calculate permeability tensor and calibrate the results using well log, well test and seismic data. Matrix permeability, however, was not considered in the above mentioned models. Some improvements were made by Rasmussen et al. with consideration of fluid flow in the matrix. They used boundary element method to study the effect of vertical fracture/matrix permeability ratio on hydraulic conductivity in a simple fracture system. Fractures were treated as a separate system ignoring fluid flow from fracture to the matrix. They reported that the model was sensitive to the ratio of the distance between mesh points on fracture faces and the fracture aperture.
Abstract Modelling of naturally fractured reservoirs is the first step to develop best scenarios for hydraulic fracture treatment, design an optimum production method and evaluate reservoir potential. This paper reviews the state of the art in current methods and presents an integrated modelling methodology utilizing object-based modelling, stochastic simulation and global optimization. Firstly, as an object-based model, each fracture was presented and treated as a discrete object. A stochastic simulation was carried out to generate an initial fracture network. An objective function was then formulated as the difference in statistics between the initial network and the target. Semi-variogram and other spatial statistical properties (cross variogram, multi-histogram mean and variogram distance) of fracture parameters were included, so that the objective function was able to statistically describe representative field data. Subsequently, a global optimization (simulated annealing) algorithm was used to optimize the objective function. An application study of a 2D fracture network showed that the modelling methodology have mapped discrete fracture network very closely to the observed physical distribution of fractures and their properties. Introduction Background Due to geological reasons, many of the naturally fractured reservoirs possess very low permeability, which is inadequate for economic production. Therefore, some permeability enhancement techniques are essential for these reservoirs. However, several authors(1)(2) have identified that underlying principles of such techniques, such as hydraulic fracture stimulation, are complex and progress is hindered due to lack of appropriate geo statistical fracture description models. Thus, there are three main reasons for a detailed fracture distribution:To site best locations for production wells To study the response of natural fractures under stimulation pressure, hence, to develop a best scenario for hydraulic fracture treatment. To design an optimum production method and evaluate reservoir potential In order to achieve the prescribed objectives, naturally fractured reservoirs need to be characterized and modeled, which include description of reservoir boundaries, rock heterogeneity, major faults and medium to small-scale fracture networks . Fracture Modelling Techniques: State of the Art Mathematical and Geo-Mechanical Models Several techniques to simulate naturally fractured reservoirs have been documented in literature. Firstly, there were mathematical and geo-mechanical models. Earlier mathematical methods to simulate natural fracture networks and fluid flow through them included equivalent continuum , discrete network and hybrid models . The usual approach relied on simplistic geometrical description of fracture systems (e.g. homogeneous reservoirs, parallel plate fractures, etc.), with primary efforts spent on flow behaviors. Many authors have used different geo-mechanical approaches for modelling fractured reservoirs, such as simple curvature analysis, field stress and fracture growth mechanism, and numerical analysis by solving systems of non-linear continuum mechanics equations using finite element methods . However, due to the complex nature of fracture systems, most studies so far have succeeded only in modelling of unrealistic homogeneous reservoirs. Moreover, most of these techniques used only a limited source of data, such as seismic or well logs. Hence, in modelling naturally fracture reservoirs, it is necessary
- Europe (0.46)
- North America > Canada (0.28)
- Geophysics > Seismic Surveying (0.48)
- Geophysics > Borehole Geophysics (0.34)