Dual-permeability System Research Articles

Introducing a transition domain for describing the solute exchange between macropores/fractures and matrix in dual-permeability system

The dual-permeability model (DPM) is highly efficient for describing the solute transport with multiple flow paths in macroporous/fractured media. However, an accurate and efficient description of the solute exchange process between the macropores/fractures and matrix in the dual-permeability system still remains a challenge. Therefore, a new approach, the dual-permeability model with transition domain (DPMTD), is proposed under saturated conditions. DPMTD characterizes the boundary layer by dividing the part of the matrix blocks in contact with the macropores (or fractures) into the transition domain. This new method takes into account the effect of concentration distribution in the matrix on the solute exchange process without upgrading the dimension of equations. The expressions of the first-order mass transfer coefficient, which is used to describe the interdomain solute exchange in the DPMTD, for four defined aggregate geometries are obtained. A sand column experiment containing an artificial macropore is used to evaluate the performance of the DPMTD and DPM. The simulation results of the DPMTD and DPM reveal that the DPMTD captures the bimodal transport (especially the first peak) more effectively because it calculates the rapid solute exchange in the early time and the slow solute exchange in the later stage more accurately. Subsequently, we studied the effect of η, which indicates the volume proportion of the boundary layer to the dual-permeability media in the DPMTD, on results. In short, this study emphasizes the importance of the boundary layer, and provides a new efficient approach to describe solute exchange process between macropores (or fractures) and matrix in dual-permeability system.

Field Application of a Novel Multiresolution Multiwell Unconventional Reservoir Simulation: History Matching and Parameter Identification

Summary This study focuses on developing an efficient workflow by integrating a multiresolution simulation model and a multiobjective evolutionary algorithm (MOEA) for application to multiwell unconventional reservoirs. In this approach, hydraulic fractures are represented using a dual porosity, dual permeability system facilitated by an embedded discrete fracture model (EDFM). A novel fast-marching simulation method is used to cut down on computational expenses by an order of magnitude, greatly accelerating the history-matching process. A variety of integrated monitoring technologies were implemented to map out the hydraulic fracture network. Insights into hydraulic fracture locations were gleaned from warm-back analysis of distributed temperature sensing data, and these locations were then assimilated into the simulation model as embedded discrete fractures. For the simulation, a fast-marching-based multiresolution model was used to partition the reservoir into local and shared domains guided by the diffusive-time-of-flight (DTOF) principle. The local domain maintained the original 3D grids near the wells while transforming the remaining area into 1D grids to accelerate the simulation process. Before history matching, a thorough sensitivity analysis was conducted to pinpoint the most impactful parameters. Subsequently, the model was fine-tuned using production data through an MOEA. The most sensitive parameters in history matching were identified as fracture geometry and conductivity, fluid saturations, and rock compressibility in the stimulated reservoir volume (SRV) areas. After history matching, there was a noteworthy reduction in the uncertainty of these tuning parameters. The calibrated parameters are valuable to evaluate the effectiveness of the well completion design. Overall, this work emphasizes the innovative combination of techniques applied, the efficiency gains in the history-matching process, and the scalability of the approach to other oilfield applications.

Hydraulic Fracturing Unlocks Potential of Europe’s Largest Reservoir

_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 205250, “Hydraulic Fracturing at Clair: Unlocking the Potential of Europe’s Largest Reservoir,” by Alistair M. Roy, SPE, Graeme H. Allan, SPE, and Corrado Giuliani, SPE, BP, et al. The paper has not been peer reviewed. _ Greater Clair, Europe’s largest oil field, has two existing platforms, Clair Phase 1 and Clair Ridge, on production with the potential for a third platform targeting the undeveloped Lower Clair Group (LCG) to the South of Phase 1. In some areas, however, low matrix quality and lack of natural fractures were the dominant characteristics, resulting in lower production rates. The authors write that fracturing technology brings opportunities to unlock poorer Phase 1 and Ridge reservoir areas. Introduction Reservoir Description. The Clair field is 75 km west of the Shetland Islands on the UK Continental Shelf within the extensional Faroe-Shetland Basin. The Old Red Sandstone reservoir is divided into two lithostratigraphic units, the Upper and LCG. The LCG contains the bulk of the oil in place and underpins the Clair development. The reservoir is characterized by large variations in facies and permeabilities. The LCG is subdivided into six units, I through VI, based on variations in sedimentary facies and heavy mineral assemblages. Development drilling preferentially targets the highest quality reservoirs in Units V and III. The LCG is defined as a dual-permeability system with a variable fracture distribution. Three main scales of fracture features are observed in the core: fault-related, fracture corridors unrelated to large offsets, and lower-density joint-type networks. Open fracture density varies considerably by stratigraphy, with the highest densities in Units V and VI. Field Development Phases. Exploration Well 206/08-1A discovered Clair in 1977. Clair underwent a protracted appraisal program before sanction of the Phase 1 development in 2001. The commercial viability of the reservoir was not confirmed until an extended well test in 1996 proved that oil rates from 15,000 to 20,000 BOPD could be sustained from long horizontal wells targeting high-productivity fracture zones. The scale and complexity of the reservoir drove a phased multiplatform development. Phase 1 began production with 20 producer and injector wells coming online between 2005 and 2011. Five additional wells drilled during 2016–2017 increased platform production by 70%. The second platform, Clair Ridge, came online in 2018, and the development wells drilled to date have encountered varying degrees of natural fractures. Design and Characteristics of Well A23 for Hydraulic Fracturing Candidate Well for Propped Fracturing. Horizontal Well A23 was completed in March 2017. The lateral penetrated the low-permeability unfractured Unit VI of the LCG in the Graben area of Phase 1. It crosses the core/graben fault, which is assumed to act as a baffle to communication between Zones 1 and 2 and Zones 3 and 4. Well A23 was put on gas lift production in 2017, producing approximately 1,300 BOPD. The well trajectory was designed to remain 40 m above the shale layer and to facilitate roughly transverse fractures within Unit VI Upper by drilling perpendicularly to the maximum horizontal stress to overcome vertical drainage issues.

A fully coupled multidomain and multiphysics model considering stimulation patterns and thermal effects for evaluation of coalbed methane (CBM) extraction

A deep understanding of the process of coalbed methane (CBM) extraction is of significance for both the unconventional energy supply and mine safety. The effects of stimulation patterns and thermal effects (including thermal shrinkage, non-isothermal sorption, and gas density change) significantly affect the CBM extraction process. Although thermal effects on CBM extraction have been investigated in previous studies, these effects have not been coupled with stimulation patterns, leading to an insufficient evaluation accuracy of previous models and a limited understanding of gas extraction in stimulated CBM reservoirs. This study developed a multidomain and multiphysics (thermal-hydraulic-mechanical, THM) model to fully couple different physical processes (including gas flow, coal deformation, gas desorption, and heat transfer) within a CBM reservoir framework considering various stimulation patterns to improve the simulation accuracy and obtain insights into CBM extraction. Three domains with distinct properties, i.e., the stimulated reservoir domain (SRD), non-stimulated reservoir domain (NSRD), and radial primary fracture (PF), were integrated into the CBM reservoir model to characterize the stimulation pattern. A group of partial differential equations (PDEs) was derived to characterize CBM transport within each domain and across different domain boundaries. A stimulated coalbed was defined as an assembly of three interacting porous media: coal matrix, continuous fractures (CF), and PF. The matrix and CF constituted a dual-porosity dual-permeability system, while the PF was simplified as a 1-D fractured medium. The finite element method (FEM) was employed to numerically solve the above PDEs. The proposed model was verified against two sets of field-measured CBM production data and compared to three previously published numerical models to reveal its advantage. The verified model was applied to investigate multidomain effects of stimulation treatment and evaluate the thermal effects of gas depletion on gas extraction in stimulated CBM reservoirs. The simulation results suggested (1) that the distinct properties of the different domains result in different permeability evolutions, which in turn influences CBM production; (2) that increasing the fracture complexity, enlarging the SRD size, and improving the SRD permeability with suitable stimulation techniques constitute effective approaches to enhance the CBM recovery; and (3) that ignoring thermal effects in CBM extraction can either overestimate or underestimate production, which mainly depends on the net effects of the thermal shrinkage strain and non-isothermal sorption during different production periods.

Control of depositional and diagenetic processes on the reservoir properties of the Mishrif Formation in the AD oilfield, Central Mesopotamian Basin, Iraq

The results of a multiproxy study on Mishrif carbonates from the margins of the Central Mesopotamian Basin of Iraq display a wide range of rock fabrics and diagenetic features, all affecting reservoir quality and flow properties in a complex manner. Based on petrographic and facies analyses of the Mishrif Formation in the AD oilfield, the model of a homoclinal ramp geometry with twelve characteristic microfacies types is proposed. A relevant observation is that the ramp, judging from the core data of the AD oilfield studied here, reflects low-energy conditions as documented by an abundancy of fine-grained carbonates in nearly all microfacies types. This notion is perhaps best understood in the context of an intrashelf basin with significant wave-seafloor interaction leading to wave degradation and a shallow effective wave base. In contrast to the rudist bioherms that typify the more basin-marginal settings, we find mainly evidence for small, low-relief buildups characterized by green algae. The Mishrif reservoir properties are shaped by two main diagenetic features: (i) early diagenetic, aquifer-related marine-meteoric mixing zone dissolution inducing abundant fabric selective porosity and (ii) the preferential cementation of Thalassinoides burrows leading to low-porosity concretionary carbonate nodules with reservoir properties that differ significantly from those of the host carbonate. Given the somewhat more distal position of the AD oilfield, the effects of prolonged stages of subaerial exposure related to sea-level fall, as reported from more basin marginal settings, are not recognized. The bending and splaying of seams around nodules and the well-preserved skeletal material within these concretionary carbonates demonstrate that the onset of nodule cementation was early diagenetic/pre-compactional in nature. Based on integrated microfacies and reservoir properties, seven rock types (i.e., Rock Type I-VII) with distinctive reservoir qualities are recognized. Nodular concretions are mainly developed in the Rock Type I lithology and result in distinctive cm-to dm-scale heterogeneity. The contrast between small, poorly-connected pore systems in nodules and medium-sized, well-connected pore systems in the host rock are best described as an inconspicuous, dual permeability system. Data shown here and evidence from other studies dealing with the Mishrif in the Central Mesopotamian Basin are important to understand and predict reservoir properties in other carbonate fields with similar properties.

The Middle Permian Maokou reservoir (southern Sichuan Basin, China): Controls on karst development and distribution

The Middle Permian Maokou limestone is a major natural gas producing reservoir in the southern Sichuan Basin, China. While matrix porosity is low, bit drops, losses while drilling, blowouts, and extremely high well testing flow rates indicate the presence of a dual permeability system in the form of paleocaves, which were formed by karstification in the late Maokouan Age. A combination of geological, paleogeomorphological and karstic analyses reveal that the development and distribution of the karst features within the reservoir are primarily regulated by shoal facies, paleotopography and syndepositional faults. In our conceptual paleogeomorphological model, the potential cave-bearing zones are located along the rim and outer edge of the Luzhou Paleohigh, which was the highland during the karst. Outside the highland were the karst slopes, and the poljes were on the flanks of the study area. Reservoir performance data suggest, there are two types of sweet spots in the study area. The first corresponds to the syndepositional fault zones along the rim of the karst highland and on the karst slope, where the caves appear to distribute along the faults, impacting the reservoir's vertical permeability. The second corresponds to the shoals of the Mao 2 and Mao 3 members on the lower western karst slope and the upper eastern karst slope, where the caves are widespread, enhancing the horizontal permeability and connectivity of the reservoir. However, the caves are rare in the central karst highland, lower karst slopes, and poljes, which is consistent with the limited gas discoveries.

Application of Flow Diagnostics to Rapid Production Data Integration in Complex Grids and Dual-Permeability Models

SummaryStreamline-based methods, as repeatedly demonstrated in multiple applications, offer a robust and elegant framework for reconciling high-resolution geologic models with observed field responses. However, significant challenges persist with the application of streamline-based methods in complex grids and dual-permeability media due to the difficulty with streamline tracing in these systems. In this work, we propose a novel and efficient framework that circumvents these challenges by avoiding explicit tracing of streamlines but exploits the inherent desirable features of streamline-based production data integration in high-resolution geologic models.Our approach features the application of flow diagnostics to inverse problems involving the integration of multiphase production data in reservoir models. Here, time-of-flight as well as numerical tracer concentrations for each well, on the basis of a defined flux field, are computed on the native finite-volume grid. The information embedded in these metrics are used in the dynamic definition of stream-bundles and, eventually, in the computation of analytical water arrival-time sensitivities with respect to model properties. This calculation mimics the streamline-derived analytical sensitivity computation used in the well-established generalized travel-time inversion (GTTI) technique but precludes explicit streamline tracing. The reservoir model property field is updated iteratively by solving the LSQR (sparse least-squares with QR factorization) system composed of the computed analytical sensitivity and the optimal water travel-time shift, augmented with regularization and smoothness constraints.The power and efficacy of our approach are demonstrated using synthetic model and field applications. We first validate our approach by benchmarking with the streamline-based GTTI algorithm involving a single-permeability medium. The flow-diagnostics-derived analytical sensitivities were observed to show good agreement with the streamline-derived sensitivities in terms of correctly capturing relevant spatiotemporal trends. Furthermore, the desirable quasilinear behavior characteristic of the traditional streamline-based GTTI technique was preserved. The flow-diagnostics-based inversion technique is then applied to a field-scale problem involving the integration of multiphase production data into a dual-permeability model of a large naturally fractured reservoir. The results clearly demonstrate the effectiveness of the proposed approach in overcoming the limitations of classical streamline-based methods with dual-permeability systems. By construction, this approach finds direct application in single/multicontinuum models with generic grid designs, both in structured and fully unstructured formats, thereby aiding well-level history matching and high-resolution updates of modern geologic models.This work presents, for the first time, an application of the GTTI to dual-permeability models of naturally fractured reservoirs. This is facilitated by a simplified, yet effective approach to travel-time sensitivity computations directly on finite-volume grids. The proposed approach can be easily applied to subsurface models at levels of complexity identified as challenging for classical streamline-based methods.

Efficient development strategies for large ultra-deep structural gas fields in China

Through analyzing the development of large ultra-deep structural gas fields in China, strategies for the efficient development of such gas fields are proposed based on their geological characteristics and production performance. According to matrix properties, fracture development degree and configuration between matrix and fractures, the reservoirs are classified into three types: single porosity single permeability system, dual porosity dual permeability system, and dual porosity single permeability system. These three types of gas reservoirs show remarkable differences in different scales of permeability, the ratio of dynamic reserves to volumetric reserves and water invasion risk. It is pointed out that the key factors affecting development efficiency of these gas fields are determination of production scale and rapid identification of water invasion. Figuring out the characteristics of the gas fields and working out pertinent technical policies are the keys to achieve efficient development. The specific strategies include reinforcing early production appraisal before full scale production by deploying high precision development seismic survey, deploying development appraisal wells in batches and scale production test to get a clear understanding on the structure, reservoir type, distribution pattern of gas and water, and recoverable reserves, controlling production construction pace to ensure enough evaluation time and accurate evaluation results in the early stage, in line with the development program made according to the recoverable reserves, working out proper development strategies, optimizing pattern and proration of wells based on water invasion risk and gas supply capacity of matrix, and reinforcing research and development of key technologies.

A Microfluidic Investigation of the Synergistic Effect of Nanoparticles and Surfactants in Macro-Emulsion-Based Enhanced Oil Recovery

Summary Injecting oil-in-water (O/W) emulsions stabilized with nanoparticles (NPs) or surfactants is a promising option for enhanced oil recovery (EOR) in harsh-condition reservoirs. Stability and rheology of the flowing emulsion in porous media are key factors for the effectiveness of the EOR method. The objective of this study is to use microfluidics to (1) quantitatively evaluate the synergistic effect of surfactants and NPs on emulsion dynamic stability and how NPs affect the emulsion properties, and to (2) investigate how emulsion properties affect the sweep performance in emulsion flooding. A microfluidic device with well-defined channel geometry of a high-permeability pathway and multiple parallel low-permeability pathways was created to represent a fracture/matrix dual-permeability system. Measurement of droplet coalescence frequency during flow is used to quantify the dynamic stability of emulsions. An NP aqueous suspension (2 wt%) shows excellent ability to stabilize the macro-emulsion when mixed with a trace amount of surfactant (0.05 wt%), revealing a synergistic effect between NPs and surfactant. For a stable emulsion, when a pore throat is present in the high-permeability pathway, it was observed that flowing emulsion droplets compress each other and then block the high-permeability pathway at a throat structure, which forces the wetting phase into low-permeability pathways. Droplet size shows little correlation with this blocking effect. Water content was observed to be much higher in the low-permeability pathways than in the high-permeability pathways, indicating different emulsion texture and viscosity in channels of different sizes. Consequently, the assumption of bulk emulsion viscosity in the porous medium is not applicable in the description and modeling of the emulsion-flooding process. Flow of emulsions stabilized by an NP/surfactant mixture shows droplet packing in high-permeability regions that is denser than those stabilized by surfactant only, at high-permeability regions, which is attributed to the enhanced interaction between droplets caused by NPs in the thin liquid film between neighboring oil/water (O/W) interfaces. This effect is shown to enhance the performance of emulsion-blockage effect for sweep-efficiency improvement, showing the advantage of NPs as an emulsion stabilizer during an emulsion-based EOR process.

Effect of Matrix-Wellbore Flow and Porosity on Pressure Transient Response in Shale Formation Modeling by Dual Porosity and Dual Permeability System

A mathematical dual porosity and dual permeability numerical model based on perpendicular bisection (PEBI) grid is developed to describe gas flow behaviors in shale-gas reservoirs by incorporating slippage corrected permeability and adsorbed gas effect. Parametric studies are conducted for a horizontal well with multiple infinite conductivity hydraulic fractures in shale-gas reservoir to investigate effect of matrix-wellbore flow, natural fracture porosity, and matrix porosity. We find that the ratio of fracture permeability to matrix permeability approximately decides the bottom hole pressure (BHP) error caused by omitting the flow between matrix and wellbore and that the effect of matrix porosity on BHP is related to adsorption gas content. When adsorbed gas accounts for large proportion of the total gas storage in shale formation, matrix porosity only has a very small effect on BHP. Otherwise, it has obvious influence. This paper can help us understand the complex pressure transient response due to existence of the adsorbed gas and help petroleum engineers to interpret the field data better.

A New Method of Optimization Design of Hydraulic Fracture Parameters in Low Porosity and Fractured Gas Reservoir

A new composite reservoir simulation model of lower computation cost was used to optimize hydraulic fracture length and fracture conductivity during performing a hydraulic fracturing. The simulation model is divided into inner part and outer part. The inner part is dual-porosity and dual-permeability system, and the other is single porosity system. The research shows that the natural fracture permeability and density are the most influential parameters; a relative long fracture with high hydraulic fracture conductivity is required for a high production rate due to non-Darcy flow effects. A shorter primary fracture is better in a gas reservoir of high natural density. The composite model represents the flow characteristic more accurately and provides the optimal design of fracturing treatments to obtain an economic gas production.

A Combination Method of Mixed Multiscale Finite-Element and Laplace Transform for Flow in a Dual-Permeability System

An efficient combination method of Laplace transform and mixed multiscale finite-element method for coupling partial differential equations of flow in a dual-permeability system is present. First, the time terms of parabolic equation with unknown pressure term are removed by the Laplace transform. Then the transformed equations are solved by mixed FEMs which can provide the numerical approximation formulas for pressure and velocity at the same time. With some assumptions, the multiscale basis functions are constructed by utilizing the effects of fine-scale heterogeneities through basis functions formulation computed from local flow problems. Without time step in discrete process, the present method is efficient when solving spatial discrete problems. At last, the associated pressure transform is inverted by the method of numerical inversion of the Laplace transform.

Development of a multi-mechanistic, dual-porosity, dual-permeability, numerical flow model for coalbed methane reservoirs

Most existing coalbed methane (CBM) simulators usually treat coal seams as dual-porosity, single-permeability systems ignoring the effects of water presence in the coal matrix. In this study, a compositional dual-porosity, dual-permeability CBM simulator has been developed. The CBM reservoir is treated as a dual-porosity, dual-permeability system consisting of coal matrix and fracture network. The development of the proposed numerical model incorporates the effects of water presence in the coal matrix and the phenomena of coal shrinkage and swelling. The transport of gas follows a multi-mechanistic flow mechanism triggered by pressure and concentration gradients. In addition, the proposed simulator is able to collapse to simpler coal seam representations and was successfully tested against the existing commercial and research CBM simulators for CO2-enhanced CBM recovery process. Successful history matching exercises were performed on pure CO2 injection and flue gas injection tests using the actual field data.

Role of Diffusion in Chemical Oxidation of PCE in a Dual Permeability System

The effect of in situ chemical oxidation (ISCO) with permanganate (MnO4-) on tetrachloroethene (PCE) in a dual permeability system consisting of low permeability clay with high permeability sand lenses was investigated by two-dimensional laboratory experiments. The experiments imitate a field remediation at a former dry cleaning facility in Denmark. Results from laboratory experiments and field observations both show that after an application of MnO4- in the sand layer, the diffusion rate into the matrix is decreased due to reaction with PCE and the natural oxidant demand (NOD) related to the clayey till. A narrow but very efficient reaction zone is created in the clayey till. Initiallythe zone developed rapidlyfollowed by a slower expansion with time. PCE will counter diffuse into the reaction zone, where it will be degraded as long as MnO4- is present. A mass balance for the laboratory experiment revealed that the reaction between MnO4- and the clayey till was responsible for up to 90% of the total MnO4- consumption. Based on laboratory experiments, the high MnO4- consumption from reaction with clayey till appears to have been the limiting factor for the oxidation of PCE at the field site and is thus impairing the efficiency of ISCO as a remedy.

Fossilized worm burrows influence the resource quality of porous media

Burrow-associated, selective dolomitization in the Yeoman Formation limestone (Ordovician, Williston basin) is characterized by distinct textural heterogeneity. Physical parameters such as permeability, porosity, tortuosity, and dispersivity are therefore difficult to assess. This study compares the relative dispersivities of three geologic media: homogeneous sandstone, fractured limestone, and burrowed dolomitic limestone. Results show that the flow paths present in burrow-associated dolomite are tortuous, and that the interaction between the flow paths and the matrix is extensive. Such rocks act as dual-permeability systems in the subsurface. Hydrocarbon production from such deposits will be strongly influenced by burrow-related heterogeneity, and its influence should be carefully considered before secondary recovery schemes are implemented.

Streamline simulation of counter-current imbibition in naturally fractured reservoirs

Describing fluid transport in naturally fractured reservoirs entails additional challenge because of the complicated physics arising from matrix–fracture interactions. In this paper, the streamline-based simulation is generalized to describe fluid transport in naturally fractured reservoirs through a dual-media approach. The fractures and matrix are treated as separate continua that are connected through a transfer function, as in conventional finite difference simulators for modeling fractured systems. The transfer functions that describe fluid exchange between the fracture and matrix system can be implemented easily within the framework of the current single-porosity streamline models. In particular, the streamline time of flight concept is utilized to develop a general dual-porosity, dual-permeability system of equations for water injection in naturally fractured reservoirs. The saturations equations are solved using an operator splitting approach that involves ‘convection’ along streamline followed ‘matrix–fracture’ exchange calculations on the grid. The proposed formulation reduces to the commonly used dual-porosity model when the flow in the matrix is considered negligible. For modeling matrix–fracture interactions, two different transfer functions are examined: an empirical transfer function (ETF) and a conventional transfer function (CTF). The ETF allows for analytical solution of the saturation equation for dual porosity systems and is used to validate numerical implementation. Results obtained using the CTF are compared with a commercial finite-difference simulator (ECLIPSE) for waterflooding in five-spot and nine-spot patterns. The streamline approach shows close agreement in terms of recovery histories and saturation profiles with a marked reduction in numerical dispersion and grid orientation effects. Finally, an examination of the scaling behavior of the computation time indicates that the streamline approach is likely to result in significant savings for large-scale field applications.

Streamline simulation of counter-current imbibition in naturally fractured reservoirs

Describing fluid transport in naturally fractured reservoirs entails additional challenge because of the complicated physics arising from matrix–fracture interactions. In this paper, the streamline-based simulation is generalized to describe fluid transport in naturally fractured reservoirs through a dual-media approach. The fractures and matrix are treated as separate continua that are connected through a transfer function, as in conventional finite difference simulators for modeling fractured systems. The transfer functions that describe fluid exchange between the fracture and matrix system can be implemented easily within the framework of the current single-porosity streamline models. In particular, the streamline time of flight concept is utilized to develop a general dual-porosity, dual-permeability system of equations for water injection in naturally fractured reservoirs. The saturations equations are solved using an operator splitting approach that involves ‘convection’ along streamline followed ‘matrix–fracture’ exchange calculations on the grid. The proposed formulation reduces to the commonly used dual-porosity model when the flow in the matrix is considered negligible. For modeling matrix–fracture interactions, two different transfer functions are examined: an empirical transfer function (ETF) and a conventional transfer function (CTF). The ETF allows for analytical solution of the saturation equation for dual porosity systems and is used to validate numerical implementation. Results obtained using the CTF are compared with a commercial finite-difference simulator (ECLIPSE) for waterflooding in five-spot and nine-spot patterns. The streamline approach shows close agreement in terms of recovery histories and saturation profiles with a marked reduction in numerical dispersion and grid orientation effects. Finally, an examination of the scaling behavior of the computation time indicates that the streamline approach is likely to result in significant savings for large-scale field applications.

Taking into account the complexity of natural fracture systems in reservoir single-phase flow modelling

In order to develop a methodology for reservoir flow modelling that takes into account the complexity of natural fracture systems, high-quality fracture datasets were collected at different scales in a well-exposed clastic formation at Tayma, Saudi Arabia, and used to design a multiscale fracture model incorporating both large-scale faults and medium- to small-scale fractures (joints) for numerical simulation. Flow modelling was then conducted, taking into account three scales of permeability to represent the matrix, joints, and faults. Actually, the most severe situation was considered, where the permeability of the joints dominates strongly the one of the matrix. The results obtained with this model show that, on a local scale, the maximum directional flow is always horizontal along the direction of a systematic joint set—in this case NW–SE. Vertical flow is only possible where joints j and bedding planes b have conductivity ratios C j/ C b between 0.1 and 10. The flow properties of the model were then upscaled to simulate the entire reservoir through combining the flow properties of the jointed matrix (represented by an equivalent permeability tensor) with those of the large-scale fault system (which was modelled explicitly) in a dual-permeability system. Simulation of a pumping well to illustrate the hydraulic response of the multiscale fracture system according to different permeability ratios between the faults and the jointed rock matrix, i.e. K f/ K m, showed that the influence of the fault system begins to be visible at a permeability ratio of 100. At a ratio of 10,000, the hydraulic potential field is controlled completely by the fault system, the fault planes becoming isopotential lines of the hydraulic field. This multiscale fracture flow simulation procedure, which combines the hydraulic effects of small- to medium-scale fractures and large-scale faults, could be very helpful in predicting flow responses in dual-permeability reservoirs.

Modeling flow and transport in a two-dimensional dual-permeability system with spatially variable hydraulic properties

Most field soils exhibit soil spatial variability as well as soil structure. The challenge is to account adequately for both types of spatial heterogeneity in simulation models. A numerical finite element code was used to compare single- and dual-permeability approaches for modeling variably saturated flow and transport in two-dimensional heterogeneous soil systems. The code was based on the Richards' equation for water flow and the advection-dispersion equation for solute transport. Spatial variability in the soil hydraulic properties was accounted for by randomly generating a hydraulic conductivity field using a one-dimensional first-order Markov process. Soil structural effects were modeled with a two-domain concept in which a first-order kinetic expression is used to describe the transfer of water and solute between the two domains. Numerical experiments were carried out for the case of furrow irrigation, including the breakthrough of a conservative solute to the groundwater table. We compared five different scenarios: a single domain having uniform hydraulic properties (SU), a single domain with a randomly distributed hydraulic conductivity (SR), a dual-permeability system with uniform hydraulic properties (DU), a dual-permeability system with a randomly distributed fracture hydraulic conductivity (DRF), and a dual-permeability system having a randomly distributed matrix hydraulic conductivity (DRM). All scenarios started with pressure heads in equilibrium with a constant groundwater table 150 cm below the soil surface and zero initial solute concentrations. The simulated two-dimensional (2D) vertical concentration profiles showed preferential pathways resulting from both the spatial variability (SR) and soil structure (DRF) scenarios. As expected, drainage of water from the bottom of the profile occurred significantly earlier for dual-than for single-permeability scenarios. The combination of having spatial variability in the hydraulic properties and invoking the dual-permeability approach yielded the quickest and largest leaching of solute. The 2D dual-permeability approach should considerably improve the simulation of water and solute movement in naturally heterogeneous field soils.

Pressure Transients Characterize Fractured Midale Unit

Summary The Midale Unit is a naturally fractured carbonate reservoir in the Williston basin of southeastern Saskatchewan. Recently, the Midale working-interest owners initiated a CO2-flood pilot project with several closely spaced wells. A comprehensive interwell pressure-transient test program was conducted for reservoir-characterization purposes before pilot program was conducted for reservoir-characterization purposes before pilot operations began. The combination of conventional, pulse, and interference tests resulted in a detailed local description of this naturally fractured reservoir. Selected pressure-transient data from the reservoir-characterization program are presented. The data dramatically illustrate the program are presented. The data dramatically illustrate the pressure-transient characteristics of an anisotropic, naturally fractured pressure-transient characteristics of an anisotropic, naturally fractured reservoir. Analytical techniques are reviewed briefly, and an interpretation technique for multiwell pressure-transient tests in wells with negative skins is included. A discussion of the pressure-transient behavior that is observed in wells with typical field spacing is also included. Introduction A significant proportion of the world's oil reserves exists in naturally fractured rocks. As a result, the pressure-transient behavior of naturally fractured reservoirs has been studied widely. These reservoirs, referred to as dual-porosity or dual-permeability systems, can be modeled with matrix blocks of various shapes separated by continuous fracture networks. Typically, the system permeability is largely associated with the fractures, while the tighter matrix contains most of the reservoir-storage volume and acts as a fluid source for the fracture network. Initial production from dual-porosity reservoirs is from the more permeable fracture network, which results permeable fracture network, which results in pressure decline in the fractures. Depletion of the fracture system causes pressure gradients to develop between the matrix blocks and the fractures, which results in fluid flow from the blocks into the fractures. This transitional flow period controls the reservoir-pressure behavior until the matrix fracture pressure regime equilibrates, after which the reservoir acts as a uniform system with composite properties. Pressure-transient testing is an important technique used to describe naturally fractured reservoirs. Each flow period (fractures, transitional, and composite) has distinctive pressure-transient characteristics. Pressure-transient behavior in real Pressure-transient behavior in real dual-porosity reservoirs, however, can be subtle and ambiguous, especially in normal situations with typical well spacing. For example, pressure transients controlled by depletion of the fracture network are rarely seen in the field because of the fast onset of the transitional flow period. Transitional- and composite-system pressure transients can be attributed to such other causes as layers, skin, faults, or boundaries. Wellbore storage can obscure key parts of the pressure-transient curve. For these and other pressure-transient curve. For these and other reasons, few comprehensive pressure-transient data bases exist for naturally fractured reservoirs. The scarcity of good data impedes refinement and validation of precise pressure-transient models. The Midale field (Fig. 1) produces oil from relatively tight, naturally fractured carbonates. The field was discovered in 1953 and produced competitively under primary depletion until unitization for waterflooding in 1962. Secondary performance is dominated fieldwide by the oriented-fracture system, which causes a permeability anisotropy of about 25:1. Recent implementation of a tertiary miscible CO2-flood pilot project in the Midale Unit, with 10 wells on 4.4 acres [1.8 ha], has allowed for very detailed reservoir characterization. Conditions in the Midale CO2-flood pilot are amenable to both single- and multiwell pressure-transient programs. An extensive, precise pressure programs. An extensive, precise pressure transient data base was acquired during pilot-testing operations. The reservoir pilot-testing operations. The reservoir model that was obtained from pressure-transient analyses is consistent with geological, petrophysical, and operational data, and it petrophysical, and operational data, and it provides significant refinement over earlier provides significant refinement over earlier reservoir models.