NFR27 Using Embedded Discrete Fracture Models - Earthdoc

NFR27 Using Embedded Discrete Fracture Models (EDFMs) to Simulate Realistic Fluid Flow Problems A. Cominelli (Eni e&p), P. Panfili* (Eni e&p) & A. Scotti (Politecnico di Milano)

SUMMARY A large amount of world’s hydrocarbon reserves lies in reservoirs where one of the key features is the presence of a system of fractures spanning different length scales. Fractures may provide ways to drain the matrix, but they also drive gas and water towards wells. Fractures intensity, geometry and conductivity are characterised in conjunction with matrix properties using all possible data, such as production logging, mud-losses, image log, well test, geophysics and outcrops. This may lead to a geometrical characterisation in terms of a discrete fracture network (DFN), with the definition of a set of geometrical 2D objects embedded in the matrix domain. A DFN is a computational challenge for conventional dual-porosity simulators, where a dual medium formulation is cast in a corner point geometry grid (CPG). In this context small, with respect to CPG grid spacing, fractures can be easily incorporated using some practical recipes, see Dershowitz et al. (2000), in single porosity or in dual-porosity models. On the other hand, long range, interconnected fractures cannot be integrated in the simulation model unless some crude approximation is implemented in order to fit the fracture network geometry into the Warren and Root (1963) dual media framework, at least as it is available in conventional commercial simulators, see e.g, Eclipse (2011) . A more accurate solution is the implementation of unstructured gridding where the matrix is discretized by tetrahedral or more general polyhedra and the fractures are discretized using 2D polygons. These grids can be used with finite volume, connectivity based reservoir simulators (see Karimi-fard et al. (2004)), but the approach is computationally inefficient for most of the commercial simulators, and this motivated the development of the EDFM by Li and Lee (2008). In this approach the intersections between fractures and matrix blocks define the degrees of freedom (DOFs) for the high connectivity medium. Then, 2D flow between fracture DOFs and 1D flow between fractures and matrix can be integrated with 3D flow in the CPG grid representing the matrix. In a nut-shell, an unstructured grid for the fracture network is comined with a structured grid for the matrix. Differently from Li and Lee (2008), our implementation is not based on the customisation of the reservoir simulator. Rather, we exploit the capability of most commercial simulators to define non neighbouring connections across grid cells to implement EDFM in a non-invasive manner. Our results confirm that EDFM can be as effective as fully unstructured gridding but much more computationally efficient.

Second EAGE Workshop on Naturally Fractured Reservoirs 8-11 December 2013 Muscat, Oman

Introduction A large amount of world’s hydrocarbon reserves lies in reservoirs where one of the key features is the presence of a system of fractures spanning different length scales. Fractures may provide ways to drain the matrix, but they also drive gas and water towards wells. Fractures intensity, geometry and conductivity are characterised in conjunction with matrix properties using all possible data, such as production logging, mud-losses, image log, well test, geophysics and outcrops. This may lead to a geometrical characterisation in terms of a discrete fracture network (DFN), with the definition of a set of geometrical 2D objects embedded in the matrix domain. A DFN is a computational challenge for conventional dual-porosity simulators, where a dual medium formulation is cast in a corner point geometry grid (CPG). In this context small, with respect to CPG grid spacing, fractures can be easily incorporated using some practical recipes, see Dershowitz et al. (2000), in single porosity or in dualporosity models. On the other hand, long range, interconnected fractures cannot be integrated in the simulation model unless some crude approximation is implemented in order to fit the fracture network geometry into the Warren and Root (1963) dual media framework, at least as it is available in conventional commercial simulators, see e.g, Eclipse (2011) . A more accurate solution is the implementation of unstructured gridding where the matrix is discretized by tetrahedral or more general polyhedra and the fractures are discretized using 2D polygons. These grids can be used with finite volume, connectivity based reservoir simulators (see Karimi-fard et al. (2004)), but the approach is computationally inefficient for most of the commercial simulators, and this motivated the development of the EDFM by Li and Lee (2008). In this approach the intersections between fractures and matrix blocks define the degrees of freedom (DOFs) for the high connectivity medium. Then, 2D flow between fracture DOFs and 1D flow between fractures and matrix can be integrated with 3D flow in the CPG grid representing the matrix. In a nut-shell, an unstructured grid for the fracture network is comined with a structured grid for the matrix. Differently from Li and Lee (2008), our implementation is not based on the customisation of the reservoir simulator. Rather, we exploit the capability of most commercial simulators to define non neighbouring connections across grid cells to implement EDFM in a non-invasive manner. Our results confirm that EDFM can be as effective as fully unstructured gridding but much more computationally efficient. EDFM Implementation. In EDFM connected fracture corridors are explicitly represented in the simulation by defining a DOF every time the fracture intersects a CPG cell. Then, fluid in each fracture DOF may flow towards adjacent fracture DOFs according to properly calculated transmissibility. As regards the fracturematrix flow, the single phase unit mobility flux rate is the product of the pressure difference times a proper transport index. For a thorough description of the methodology, including definition of the transport terms, we refer to Li and Lee (2008). EDFM may be incorporated in standard reservoir simulators, e.g. Eclipse , by pre-processing the CPG grid and the DFN. The workflow can be summarised as follows: 1) the intersections of the fractures with the background matrix grid blocks are identified, then establishing the fracture DOFs; 2) fracture DOFS are characterised in terms of pore volume and transmissibility are provided between adjacent fracture DOFs; 3) matrix-fracture transport coefficient are computed: 4) the CPG grid is properly expanded to incorporate fracture DOFs as cells with consistent depth; 5) fracture-fracture transmissibility and matrix-fracture transport coefficient are included in the model as nonneighbouring connections.


Comparison of EDFM with analytical Solutions To prove the effectiveness of our EDFM implementation we numerically simulated the pressure transient behaviour of a multi-fractured horizontal well and compared the results against available analytical solutions (see Raghavan et al (1997)). The physical problem consists of a rectangular reservoir with dimension 3000x4000x1 ft3 and uniform porosity (20%) and permeability (0.1 mD). A multifractured horizontal well with radius equal to 0.35 ft and length equal to 2000 ft is defined in the centre of the reservoir domain; three fractures are located at the beginning, at the end and at the centre of the well. Fractures half length is equal to 100ft, permeability is 10000 mD and fracture aperture is 0.01 ft. Two cases were considered: in the former the grid is oriented along the fracture direction, in the latter the grid is rotated of 45° with respect to the fractures direction. EDFM numerical results are compared to the analytic solution in terms of pressure derivative vs time in Figure 1. In both cases the two solution are completely consistent. Notably EDFM is not affected by orientation of the grid.

Figure 1 Multifractured Horizontal well Pressure Derivative vs Time obtained using analytical solution (blue line) and EDFM (red line), with the simulation grid oriented along fractures direction (left) and with the simulation grid rotated of 45° with respect to fractures direction (right). Simulation of a First Contact Miscible injection process using EDFM Simulation of gas injection processes in naturally fractured reservoir is of strategic relevance to optimize oil recovery, and this requires to properly model gas break-through due to the presence of fracture corridors. Then, an accurate characterization of the actual fracture network by means of DFN distributions can be helpful. Accurate and efficient simulation of fluid flow inside such fractures corridors is then a key issue. In particular our focus was to simulate a first contact miscible (FCM) gas injection in a representative, highly fractured, carbonate reservoir sector. The main fracture corridors were characterized by a DFN consisting of a set 76 fractures with length ranging from 1200 to 8200 ft. To validate the methodology in this context, fracture properties were assumed to be constant (permeability equal to 106 mD and aperture equal to 0.01 m) and back ground matrix was considered homogeneous (permeability is set equal to 1 mD and porosity to 0.2). Matrix and fracture parameters were chosen with the purpose of emphasising the role of the corridors in the transport.


Two wells, one producer and one gas injector, both intercepting fractures, were defined in the sector. The gas injection stream composition was assumed constant in time. Wells operated at constant BHP. Different EDFMs were built using different CPG grid resolutions (with a lateral resolution of 775x775 ft, 388x388 ft and 258x258 ft respectively). FCM gas injection was simulated using a commercial compositional model (Eclipse 300). As reference solution, an unstructured DFM was constructed following Karimi-fard et al. (2004).The FCM gas injection in the unstructured model, was simulated using a grid-agnostic simulator, Intersect (2012). The results in terms of Field gas-oil ratio (FGOR ) vs total pore volume injected are shown in Figure 2 for the various models.

Figure 2 FGOR vs pore volume injected for a first contact miscible gas injection in a fractured carbonate reservoir sector, for different models: fully unstructured grid (red line), EDFM with grid size equal to 258x258 ft (blue line), EDFM with grid size equal to 388x388 ft (green line), EDFM with grid size equal to 775x775 ft (orange line). The gas breakthrough and GOR development is comparable for all the considered cases. EDFM models with higher grid resolution gave results closer to the fully unstructured solution. A comparison between fully unstructured model and 258x258ft EDFM in terms of gas saturation at 0.5 pore volume injected is shown in Figure 3. It may be emphasized that EDFM is able to honour the back ground fracture distribution and reproduce the gas flow-path along fracture corridors in a way comparable to the one obtained with the more complex unstructured approach.

Figure 3 Gas saturation distribution at 0.5 pore volume injected for a first contact miscible gas injection in a fractured carbonate reservoir sector at a fixed depth: fully unstructured grid (left), EDFM with grid size equal to 258x258 ft (right). This proved the effectiveness of EDFMs in capturing the real physic fluid behaviour inside a DFN without the need for complexity required by the use of an unstructured grid framework .


Conclusions This work documented the implementation of EDFM using standard simulation technology giving a chance to efficiently model complex fractured reservoirs characterized by a DFN. The workflow and the methodology have been briefly summarized, then two cases were presented to highlight the capability to account for different grid/fracture orientation and the possibility to use EDFM for simulating challenging multi-phase flow problem, like FCM gas injection in highly fractured reservoirs. Our results confirmed the possibility to use EDFM as a cost-efficient alternative to unstructured gridding for modelling reservoir characterized by means of a DFN. References Dershowitz, B., LaPointe, P., Eiben, T. and Wei, L. [2000] Integration of discrete feature network methods with conventional simulator approaches. SPE Reservoir Evaluation & Engineering, 3(2), 165-170. Eclipse [2012] 2011.2 Technical Description. Schlumberger Information Solutions. Karimi-fard, M., Durlofsky, L.J. and Aziz, K., [2004] An efficient discrete-fracture model applicable for general purpose reservoir simulators. SPE Journal, 9, 227-236. Intersect [2012] 2012.2 Reservoir Simulation Software Technical Description. Schlumberger Information Solutions. Li, L. and Lee, S.H. [2008] Efficient field scale simulation of black oil in a naturally fractured reservoir through discrete fracture networks and homogenized media. SPEREE, 11(4), 750-758. Raghavan, R., Chen, C.C. and Agarwal, B. [1997] An analysis of horizontal wells intercepted by multiple fractures. SPE Journal, 9, 235-245. Warren, J.E. and Root, P.J. [1963] The behavior of naturally fractured reservoirs. SPE Journal, 9, 245-255.
