Parallel Iterative Solver for the Dual-Porosity, Dual-Permeability System in Fractured-Reservoir Simulation

Author(s):  
Larry S.K. Fung ◽  
Tareq Mutlaq Al-Shaalan
2009 ◽  
Vol 12 (03) ◽  
pp. 380-389 ◽  
Author(s):  
Juan Ernesto Ladron de Guevara-Torres ◽  
Fernando Rodriguez-de la Garza ◽  
Agustin Galindo-Nava

Summary The gravity-drainage and oil-reinfiltration processes that occur in the gas-cap zone of naturally fractured reservoirs (NFRs) are studied through single porosity refined grid simulations. A stack of initially oil-saturated matrix blocks in the presence of connate water surrounded by gas-saturated fractures is considered; gas is provided at the top of the stack at a constant pressure under gravity-capillary dominated flow conditions. An in-house reservoir simulator, SIMPUMA-FRAC, and two other commercial simulators were used to run the numerical experiments; the three simulators gave basically the same results. Gravity-drainage and oil-reinfiltration rates, along with average fluid saturations, were computed in the stack of matrix blocks through time. Pseudofunctions for oil reinfiltration and gravity drainage were developed and considered in a revised formulation of the dual-porosity flow equations used in the fractured reservoir simulation. The modified dual-porosity equations were implemented in SIMPUMA-FRAC (Galindo-Nava 1998; Galindo-Nava et al. 1998), and solutions were verified with good results against those obtained from the equivalent single porosity refined grid simulations. The same simulations--considering gravity drainage and oil reinfiltration processes--were attempted to run in the two other commercial simulators, in their dual-porosity mode and using available options. Results obtained were different among them and significantly different from those obtained from SIMPUMA-FRAC. Introduction One of the most important aspects in the numerical simulation of fractured reservoirs is the description of the processes that occur during the rock-matrix/fracture fluid exchange and the connection with the fractured network. This description was initially done in a simplified manner and therefore incomplete (Gilman and Kazemi 1988; Saidi and Sakthikumar 1993). Experiments and theoretical and numerical studies (Saidi and Sakthikumar 1993; Horie et al. 1998; Tan and Firoozabadi 1990; Coats 1989) have allowed to understand that there are mechanisms and processes, such as oil reinfiltritation or oil imbibition and capillary continuity between matrix blocks, that were not taken into account with sufficient detail in the original dual-porosity formulations to model them properly and that modify significantly the oil-production forecast and the ultimate recovery in an NFR. The main idea of this paper is to study in further detail the oil reinfiltration process that occurs in the gas invaded zone (gas cap zone) in an NFR and to evaluate its modeling to implement it in a dual-porosity numerical simulator.


2002 ◽  
Vol 5 (02) ◽  
pp. 154-162 ◽  
Author(s):  
S. Sarda ◽  
L. Jeannin ◽  
R. Basquet ◽  
B. Bourbiaux

Summary Advanced characterization methodology and software are now able to provide realistic pictures of fracture networks. However, these pictures must be validated against dynamic data like flowmeter, well-test, interference-test, or production data and calibrated in terms of hydraulic properties. This calibration and validation step is based on the simulation of those dynamic tests. What has to be overcome is the challenge of both accurately representing large and complex fracture networks and simulating matrix/ fracture exchanges with a minimum number of gridblocks. This paper presents an efficient, patented solution to tackle this problem. First, a method derived from the well-known dual-porosity concept is presented. The approach consists of developing an optimized, explicit representation of the fractured medium and specific treatments of matrix/fracture exchanges and matrix/matrix flows. In this approach, matrix blocks of different volumes and shapes are associated with each fracture cell depending on the local geometry of the surrounding fractures. The matrix-block geometry is determined with a rapid image-processing algorithm. The great advantage of this approach is that it can simulate local matrix/fracture exchanges on large fractured media in a much faster and more appropriate way. Indeed, the simulation can be carried out with a much smaller number of cells compared to a fully explicit discretization of both matrix and fracture media. The proposed approach presents other advantages owing to its great flexibility. Indeed, it accurately handles the cases in which flows are not controlled by fractures alone; either the fracture network may be not hydraulically connected from one well to another, or the matrix may have a high permeability in some places. Finally, well-test cases demonstrate the reliability of the method and its range of application. Introduction In recent years, numerous research programs have been focusing on the topic of fractured reservoirs. Major advances were made, and oil companies now benefit from efficient methodologies, tools, and software for fractured reservoir studies. Nowadays, a study of a fractured reservoir, from fracture detection to full-field simulation, includes the following main steps: geological fracture characterization, hydraulic characterization of fractures, upscaling of fracture properties, and fractured reservoir simulation. Research on fractured reservoir simulation has a long history. In the early 1960s, Barenblatt and Zheltov1 first introduced the dual-porosity concept, followed by Warren and Root,2 who proposed a simplified representation of fracture networks to be used in dual-porosity simulators. Based on this concept, reservoir simulators3 are now able to correctly reproduce the main driving mechanisms occurring in fractured reservoirs, such as water imbibition, gas/oil and water/oil gravity drainage, molecular diffusion, and convection in fractures. Even single-medium simulators can perform fractured reservoir simulation when adequate pseudocapillary pressure curves and pseudorelative permeability curves can be input. Indeed, except for particular cases such as thermal recovery processes, full-field simulation of fractured reservoirs is no longer a problem. Geological characterization of fractures progressed considerably in the 1990s. The challenge was to analyze and integrate all the available fracture data to provide a reliable description of the fracture network both at field scale and at local reservoir cell scale. Tools have been developed for merging seismic, borehole imaging, lithological, and outcrop data together with the help of geological and geomechanical rules.3 These tools benefited from the progress of seismic acquisition and borehole imaging. Indeed, accurate seismic data lead to reliable models of large-scale fracture networks, and borehole imaging gives the actual fracture description along the wells, which enables a reliable statistical determination of fracture attributes. Finally, these tools provide realistic pictures of fracture networks. They are applied successfully in numerous fractured-reservoir studies. The upscaling of fracture properties is the problem of translating the geological description of fracture networks into reservoir simulation parameters. Two approaches are possible. In the first one, the fractured reservoir is considered as a very heterogeneous matrix reservoir; therefore, one applies the classical techniques available for heterogeneous single-medium upscaling. The second approach is based on the dual-porosity concept and consists of upscaling the matrix and the fracture separately. Based on this second approach, methodologies and software were developed in the 1990s to calculate equivalent fracture parameters with respect to the dual-porosity concept (i.e., a fracture-permeability tensor with main flow directions and anisotropy and a shape factor that controls the matrix/fracture exchange kinetics3–5). For a given reservoir grid cell, the upscaling procedures consist of generating the corresponding 3D discrete fracture network and computing the equivalent parameters from this network. In particular, the permeability tensor is computed from the results of steady-state flow simulations in the discrete fracture network alone (without the matrix).


2008 ◽  
Vol 11 (06) ◽  
pp. 1071-1081 ◽  
Author(s):  
Amy Whitaker ◽  
C. Shah Kabir ◽  
Wayne Narr

Summary The extent to which fractures affect fluid pathways is a vital component of understanding and modeling fluid flow in any reservoir. We examined the Wafra Ratawi grainstone for which production extending for 50 years, including recent horizontal drilling, has provided some clues about fractures, but their exact locations, intensity, and overall effect have been elusive. In this study, we find that a limited number of total fractures affect production characteristics of the Ratawi reservoir. Although fractures occur throughout the Wafra field, fracture-influenced reservoir behavior is confined to the periphery of the field where the matrix permeability is low. This work suggests that for the largest part of the field, explicit fractures are not necessary in the next-generation Earth and flow-simulation models. The geologic fracture assessment included seismic fault mapping and fracture interpretation of image logs and cores. Fracture trends are in the northeast and southwest quadrants, and fractures are mineralized toward the south and west of the field. Pressure-falloff tests on some peripheral injectors indicate partial barriers, and most of these wells lie on seismic-scale faults in the reservoir, suggesting partial sealing. A few wells show fractured-reservoir production characteristics, and rate-transient analysis on a few producers indicates localized dual-porosity behavior. Producers proximal to dual-porosity wells display single-porosity behavior, however, to attest to the notion of localized fracture response. The spatially restricted fracture-flow characteristics appear to correlate with fracture or vug zones in a low-permeability reservoir. Presence of fracture-flow behavior was tested by constructing the so-called flow-capacity index (FCI), the ratio of khwell (well test-derived value) to khmatrix (core-derived property). Data from 80 wells showed khmatrix to be consistently higher than khwell, a relationship that suggests insignificant fracture production in these wells. Introduction The Wafra field is in the Partitioned Neutral Zone (PNZ) between Kuwait and Saudi Arabia, as shown in Fig. 1. The field has been producing since the 1950s and has seen renewed drilling activity since the late 1990s, including horizontal drilling and implementation of peripheral water injection (Davis and Habib 1999). The Lower Cretaceous Ratawi formation contains the most reserves of the producing intervals at Wafra. The Ratawi oolite (a misnomer--it is a grainstone) reservoir has variable porosity (5 to 35%) and permeability that ranges from tens to hundreds of md (Longacre and Ginger 1988). The main Wafra structure is a gentle (i.e., interlimb angle >170°), doubly plunging anticline trending north-northwest to south-southeast, which culminates near its northern end. The East Wafra spur is a north-trending branch that extends from the center of the main Wafra structure. As seen in Fig. 1, relief on the Main Wafra structure exceeds that on East Wafra. The Ratawi oolite in the Wafra field has been studied at length, and various authors have reported geologic and engineering elements, leading to reservoir characterization and understanding of reservoir performance. Geologic studies are those of Waite et al. (2000) and Sibley et al. (1997). In contrast, Davis and Habib (1999) presented implementation of peripheral water injection, whereas Chawathé et al. (2006) discussed realignment of injection pattern owing to lack of pressure support in the reservoir interior. Previous studies considered the reservoir to behave like a single-porosity system. But recent image-log fracture interpretations indicate high fracture densities, suggesting that the implementation of a dual-porosity model may be necessary because the high impact of fractures during field development has been recognized in some Middle East reservoirs for more than 50 years (Daniel 1954). Static and dynamic data are required to characterize fracture reservoir behavior accurately (Narr et al. 2006). Geologic description of the fracture system, by use of cores, borehole images, seismic data, and well logs, does not in itself determine whether fractures affect reservoir behavior. While seismic and some image logs were available to locate fractures in the Wafra Ratawi reservoir, no dynamic testing with the specific objective of understanding fracture impact has occurred. So, to determine whether fractures influence oil productivity significantly, we used diagnostic analyses of production data and well tests of available injectors. The assessment of fracture effects in the Ratawi reservoir will be used to guide the next generation of geologic and flow-simulation models. Dynamic data involving pressure and rate have the potential to reveal the influence of open fractures in production performance. Unfortunately, pressure-transient testing on single wells does not always provide conclusive evidence about the presence of fractures with the characteristic dual-porosity dip on the pressure-derivative signature (Bourdet et al. 1989). That is because a correct mixture of matrix/fracture storativity must be present for the characteristic signature to appear (Serra et al. 1983). In practice, interference testing (Beliveau 1989) between wells appears to provide more-definitive clues about interwell connectivity, leading to inference about fractures. In contrast to pressure-transient testing, rate-transient analysis offers the potential to provide the same information without dedicated testing. In this field, all wells are currently on submersible pumps. Consequently, the pump-intake pressure and measured rate provided the necessary data for pressure/rate convolution or rate-transient analysis. We provide the Ratawi-reservoir case study primarily as an example of the integration of diverse geologic and engineering data to develop an assessment of fracture influence on reservoir behavior. It illustrates the use of production-data diagnostic tests to determine fracture influence in the absence of targeted fracture-analysis testing. The workflow can be applied to similar static/dynamic problems, such as fault-transmissivity determination. Secondly, this analysis illustrates the process of deciding that fractures, although present throughout the reservoir, may not lead to widespread fractured-reservoir characteristics (e.g., Allan and Sun 2003).


2015 ◽  
Vol 18 (02) ◽  
pp. 187-204 ◽  
Author(s):  
Fikri Kuchuk ◽  
Denis Biryukov

Summary Fractures are common features in many well-known reservoirs. Naturally fractured reservoirs include fractured igneous, metamorphic, and sedimentary rocks (matrix). Faults in many naturally fractured carbonate reservoirs often have high-permeability zones, and are connected to numerous fractures that have varying conductivities. Furthermore, in many naturally fractured reservoirs, faults and fractures can be discrete (rather than connected-network dual-porosity systems). In this paper, we investigate the pressure-transient behavior of continuously and discretely naturally fractured reservoirs with semianalytical solutions. These fractured reservoirs can contain periodically or arbitrarily distributed finite- and/or infinite-conductivity fractures with different lengths and orientations. Unlike the single-derivative shape of the Warren and Root (1963) model, fractured reservoirs exhibit diverse pressure behaviors as well as more than 10 flow regimes. There are seven important factors that dominate the pressure-transient test as well as flow-regime behaviors of fractured reservoirs: (1) fractures intersect the wellbore parallel to its axis, with a dipping angle of 90° (vertical fractures), including hydraulic fractures; (2) fractures intersect the wellbore with dipping angles from 0° to less than 90°; (3) fractures are in the vicinity of the wellbore; (4) fractures have extremely high or low fracture and fault conductivities; (5) fractures have various sizes and distributions; (6) fractures have high and low matrix block permeabilities; and (7) fractures are damaged (skin zone) as a result of drilling and completion operations and fluids. All flow regimes associated with these factors are shown for a number of continuously and discretely fractured reservoirs with different well and fracture configurations. For a few cases, these flow regimes were compared with those from the field data. We performed history matching of the pressure-transient data generated from our discretely and continuously fractured reservoir models with the Warren and Root (1963) dual-porosity-type models, and it is shown that they yield incorrect reservoir parameters.


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