Recent Publications
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2009
SPE 122456 Conceptualization and Modeling of Flow and Transport Through Fault Zones. Yu-Shu Wu, SPE, Colorado School of Mines, and Kenzi Karasaki, Lawrence Berkeley National Laboratory. Latin American and Caribbean Petroleum Engineering Conference, 31 May-3 June 2009, Cartagena de Indias, Colombia
Abstract: A physically based fault conceptual model is presented for modeling multiphase flow and transport processes in fractured rock of fault zones. In particular, we discuss a general mathematical framework model for dealing with fracture-matrix interactions, which is applicable to both continuum and discrete fracture conceptualization in fault zones. In this conceptual model, faults or fault zones of formations are conceptualized as a multiple-continuum medium, consisting of (1) highly permeable, large-scale and well-connected fractures, (2) low-permeability rock matrix, (3) various-sized vugs or large pore volumes, and (4) surrounding fractured or matrix formations on both sides. Flow through fault zones may be different from that through fractured reservoir rock, because of higher permeabilities and larger pore spaces in fault zones. In addition fault flow may be further complicated by non-Darcy’s and other nonlinear flow behavior because of large pore space. To account for such complicated flow regime, our model formulation includes non-Darcy flow, using the multiphase extension of the Forchheimer equation as well as descriptions for flow in parallel-wall fractures or tubes, based on solutions of flow through a parallel-wall, uniform fracture and Hagen-Poiseuille tube flow. The proposed fault flow model is discretized using an unstructured grid with regular or irregular meshes, followed by time discretization carried out using a backward, first-order, finite-difference method. The final discrete nonlinear equations are handled fully implicitly, using Newton iteration. The numerical scheme proposed is applicable to simulating multiphase fluid and heat flow as well as solute transport through the fractured fault zones and their interaction with surrounding rocks. The conceptual fault model is implemented into a general-purpose reservoir simulator, applicable to 1-D, 2-D, and 3-D simulation of multiphase flow in fault zones. As a demonstration example, we apply the model to simulate pressure and temperature responses in wells for a flow system controlled by faults.
SPE 122972 A Simple Method to Account for Permeability Anisotropy in Reservoir Models and Multi-Well Pressure Interference Tests. C. Yetkin, NITEC LLC; B. Ramirez, Marathon Oil Corporation; and M. Al-Kobaisi, H. Kazemi, and E. Ozkan, Colorado School of Mines, SPE Members. SPE Rocky Mountain Petroleum Technology Conference, 14-16 April 2009, Denver, Colorado.
Abstract: Permeability anisotropy, via full permeability tensor, has not been accurately accounted for in reservoir models because of the implementation complexity. Specifically, numerical implementation of the off-diagonal components of the permeability tensor is inconvenient and cumbersome. This paper shows how directional permeability, calculated from a full permeability tensor, can be used as a simple replacement both in coding numerical models and in day-to-day engineering analysis. For the former, we have implemented the directional permeability for single-phase flow in a 9-point finite-difference formulation, which is easy to code. This formulation, however, is easily applicable to any control-volume formulation including the perpendicular bisector (PEBI) grid. The implementation of this technique has produced excellent numerical results in numerical simulation of multi-phase flow displacement. For routine engineering applications, we have also applied this technique to generate pressure responses for a four-well interference test in a highly anisotropic system. The analysis of the test results by conventional type-curve matching produced the correct reservoir geometric-average permeability and a very good approximation for the direction of the maximum permeability, which is a testimony to the credibility of the formulation. The use of this formulation should be very useful in determining major natural fracture trends in reservoirs undergoing water or gas injection, and in modeling fracture trends in other fractured reservoir situations, such as tight sands.
SPE 122611 Non-Darcy Porous Media Flow According to the Barree and Conway Model: Laboratory and Numerical Modeling Studies. Bitao Lai, Jennifer L. Miskimins, and Yu-Shu Wu, Colorado School of Mines. SPE Rocky Mountain Petroleum Technology Conference, 14-16 April 2009, Denver, Colorado
Abstract: This paper presents supplementary laboratory data to show that a non-Darcy flow model, proposed by Barree and Conway in 2004, is capable of overcoming the limitation with the Forchheimer non-Darcy equation in high flow rates while describing the entire range of relationships between rate and potential gradient from low- to high-flow rates through proppant packs using a single equation or model. To supplement these laboratory findings, a numerical model is developed that incorporates the Barree and Conway model into a general-purpose reservoir simulator for modeling single-phase non-Darcy flow in porous and fractured media. In the numerical approach, flow through fractured rock is handled using a general multi-continuum approach, applicable to both continuum and discrete fracture conceptual models. The numerical formulation is based on a discretization using an unstructured grid of regular or irregular meshes, followed by time discretization carried out with a backward, first-order, finite-difference method. The final discrete nonlinear equations are handled fully implicitly, using Newton iteration. Additionally, an analytical solution under steady-state linear flow condition is derived and used to verify numerical simulation results for the steady-state linear flow case. The numerical model is applied to evaluate the transient flow behavior at an injection well for non-Darcy flow according to the Barree and Conway model. Results show that the parameter of characteristic length, τ, is more sensitive than other parameters; while the impact of the minimum permeability plateau is shown only at extremely large flow rates or pressure gradients. The proposed numerical modeling approach is suitable for modeling various types of multi-dimensional non-Darcy flow through porous and fractured heterogeneous reservoirs.
SPE 124213 A Critical Review for Proper Use of Water/Oil/Gas Transfer Functions in Dual-Porosity Naturally Fractured Reservoirs: Part II. M. Al-Kobaisi , SPE, H. Kazemi, SPE, B. Ramirez, SPE, and E. Ozkan, SPE, Colorado School of Mines; and S. Atan, SPE, Marathon Oil Corporation. SPE Reservoir Evaluation & Engineering, Volume 12, Number 2, April 2009, pp. 211-217.
Abstract: This paper continues the work presented in Ramirez et al. (2009). In Part I, we discussed the viability of the use of simple transfer functions to accurately account for fluid exchange as the result of capillary, gravity, and diffusion mass transfer for immiscible flow between fracture and matrix in dual-porosity numerical models. Here, we show additional information on several relevant topics, which include (1) flow of a low-concentration water-soluble surfactant in the fracture and the extent to which the surfactant is transported into the matrix; (2) an adjustment to the transfer function to account for the early slow mass transfer into the matrix before the invading fluid establishes full connectivity with the matrix; and (3) an analytical approximation to the differential equation of mass transfer from the fracture to the matrix and a method of solution to predict oil-drainage performance. Numerical experiments were performed involving single-porosity, fine-grid simulation of immiscible oil recovery from a typical matrix block by water, gas, or surfactant-augmented water in an adjacent fracture. Results emphasize the viability of the transfer-function formulations and their accuracy in quantifying the interaction of capillary and gravity forces to produce oil depending on the wettability of the matrix. For miscible flow, the fracture/matrix mass transfer is less complicated because the interfacial tension (IFT) between solvent and oil is zero; nevertheless, the gravity contrast between solvent in the fracture and oil in the matrix creates convective mass transfer and drainage of the oil.
SPE 109821 A Critical Review for Proper Use of Water/Oil/Gas Transfer Functions in Dual-Porosity Naturally Fractured Reservoirs: Part I. B. Ramirez, SPE, H. Kazemi, SPE, M. Al-Kobaisi, SPE, and E. Ozkan, SPE, Colorado School of Mines; and S. Atan, SPE, Marathon Oil Corporation. SPE Reservoir Evaluation & Engineering, Volume 12, Number 2, April 2009, pp. 200-210.
Abstract: Accurate calculation of multiphase-fluid transfer between the fracture and matrix in naturally fractured reservoirs is a crucial issue. In this paper, we will present the viability of the use of simple transfer functions to account accurately for fluid exchange resulting from capillary, gravity, and diffusion mass transfer for immiscible flow between fracture and matrix in dual-porosity numerical models. The transfer functions are designed for sugar-cube or match-stick idealizations of matrix blocks. The study relies on numerical experiments involving fine-grid simulation of oil recovery from a typical matrix block by water or gas in an adjacent fracture. The fine-grid results for water/oil and gas/oil systems were compared with results obtained with transfer functions. In both water and gas injection, the simulations emphasize the interaction of capillary and gravity forces to produce oil, depending on the wettability of the matrix. In gas injection, the thermodynamic phase equilibrium, aided by gravity/capillary interaction and, to a lesser extent, by molecular diffusion, is a major contributor to interphase mass transfer. For miscible flow, the fracture/matrix mass transfer is less complicated because there are no capillary forces associated with solvent and oil; nevertheless, gravity contrast between solvent in the fracture and oil in the matrix creates convective mass transfer and drainage of oil. Using the transfer functions presented in this paper, fracture- and matrix-flow calculations can be decoupled and solved sequentially--reducing the complexity of the computation. Furthermore, the transfer-function equations can be used independently to calculate oil recovery from a matrix block.
SPE 104580 Verification and Proper Use of Water-Oil Transfer Function for Dual-Porosity and Dual-Permeability Reservoirs. A. Balogun, SPE, Shell E&P, H. Kazemi, SPE, E. Ozkan, SPE, M. Al-Kobaisi, SPE, and B. Ramirez, SPE, Colorado School of Mines. SPE Reservoir Evaluation & Engineering, Volume 12, Number 2, April 2009, pp. 189-199.
Abstract: Accurate calculation of multiphase fluid transfer between the fracture and matrix in naturally fractured reservoirs is a very crucial issue. In this paper, we will present the viability of the use of a simple transfer function to accurately account for fluid exchange resulting from capillary and gravity forces between fracture and matrix in dual-porosity and dual-permeability numerical models. With this approach, fracture- and matrix-flow calculations can be decoupled and solved sequentially, improving the speed and ease of computation. In fact, the transfer-function equations can be used easily to calculate the expected oil recovery from a matrix block of any dimension without the use of a simulator or oil-recovery correlations. The study was accomplished by conducting a 3-D fine-grid simulation of a typical matrix block and comparing the results with those obtained through the use of a single-node simple transfer function for a water-oil system. This study was similar to a previous study (Alkandari 2002) we had conducted for a 1D gas-oil system. The transfer functions of this paper are specifically for the sugar-cube idealization of a matrix block, which can be extended to simulation of a match-stick idealization in reservoir modeling. The basic data required are: matrix capillary-pressure curves, densities of the flowing fluids, and matrix block dimensions.
SPE 121290 Comparison of Fractured Horizontal-Well Performance in Conventional and Unconventional Reservoirs. E. Ozkan, SPE, Colorado School of Mines, M. Brown, SPE, Colorado School of Mines, R. Raghavan, SPE, Phillips Petroleum Co. (Retd.), and H. Kazemi, SPE, Colorado School of Mines. SPE Western Regional Meeting, 24-26 March 2009, San Jose, California.
Abstract: This paper presents a discussion of fractured horizontal-well performance in conventional (milli-Darcy permeability) and unconventional (micro- to nano-Darcy permeability) reservoirs. It provides interpretations of the objective of fracturing horizontal wells in both types of formations. By using a trilinear-flow model, it is shown that the drainage volume of multiply-fractured-horizontal-wells is limited to the inner reservoir between the fractures even for relatively large matrix permeabilities. Unlike conventional reservoirs, favorable productivities are not warranted in unconventional-tight reservoirs because of high reservoir permeability and high hydraulic fracture conductivity. The most efficient mechanism to improve the productivity of unconventional-tight formations is to increase the density of natural fractures. High natural fracture permeabilities may not necessarily contribute to productivity. Decreasing fracture spacing increases the productivity of the well, but the incremental production for each additional fracture decreases. The trilinear-flow model presented in this work can be used to determine optimum hydraulic fracture properties for a multiply-fractured-horizontal-well. The model can also be used as a predictive tool. The information given in this paper should help the design of multiply-fractured-horizontal-wells and predict their performances.
SPE 118233 A Multidomain Approach to Multiscale Compositional Reservoir Simulation. Mohammad F. Al-Matrouk, SPE, Kuwait Institute for Scientific Research, and Mohammed Al-Kobaisi, SPE, Hossein Kazemi, SPE, and Erdal Ozkan, SPE, Colorado School of Mines. SPE Reservoir Simulation Symposium, 2-4 February 2009, The Woodlands, Texas, USA.
Abstract: This paper presents a multidomain (MD) computational approach to multiscale (MS) compositional reservoir simulation amenable to parallel processing. The main objective is to minimize the upscaling process and preserve the pertinent flow characteristics of the fine-scale geological features of the reservoir. The preservation of the fine-scale reservoir characteristics yields higher-accuracy solution compared to an upscaled model. The computing algorithm involves breaking down the fine-grid (FG) computing mesh into an underlying coarse-grid (CG) subdomain. Unlike other MS techniques, the CG subdomain only serves as an assemblage of the FG cells and not as a computational CG overlaying the FG cells. The flow equations are then restructured into a global pressure equation which is solved on the FG using a large time step without solving for the compositions, saturations, etc. The convergence tolerance for the global pressure solution is soft (no iterations) to reduce computing time. The pressure solution is then used to calculate the molar flux of components only at the FG boundaries of the CG subdomain cells. Finally, each CG subdomain subject to its boundary conditions is solved independently using a smaller time step to compute cell pressures, compositions, and phase saturations. This procedure is amenable to parallel processing. This MS scheme was applied to time domain, in which the global pressure solution is obtained with a larger time step than in the local FG solution. This means that the molar flux boundary condition at the CG subdomain boundaries is not updated every time step, thus, buying additional computational advantage. This new technique was tested on several volatile oil and gas-condensate systems and excellent agreement was obtained with FG simulation with about 60% reduction in computing time using a single processor. Much greater time reduction is expected in a multi processing environment.
SPE 118830 Efficient Simulation for Low Salinity Waterflooding in Porous and Fractured Reservoirs. Yu-Shu Wu, SPE, Colorado School of Mines, and Baojun Bai, SPE, Missouri University of Science and Technology. SPE Reservoir Simulation Symposium, 2-4 February 2009, The Woodlands, Texas.
Abstract: Low-salinity brine injection has emerged as a promising, cost-effective improved oil recovery (IOR)method for waterflooding reservoirs. Laboratory tests and field applications show that low-salinity waterflooding could lead to significant reduction of residual oil saturation. There has been a growing interest with an increasing number of low-salinity waterflooding studies. However, there are few quantitative studies on flow and transport behavior of low-salinity IOR processes. This paper presents a general mathematic model (1) to incorporate known IOR mechanisms and (2) to quantify low-salinity waterflooding processes. In our mathematical conceptual model, salt is treated as an additional “component” to the aqueous phase, based on the following physical considerations: salt is transported only within the aqueous phase by advection and diffusion, and also subject to adsorption onto rock solids; relative permeability, capillary pressure, and residual oil saturation depend on salinity. Interaction of salt between mobile and immobile water zones is handled rigorously using a multi-domain approach. Fractured rock is handled using the multiple-continuum model or a discrete-fracture modeling approach. The conceptual model is implemented into a general-purpose reservoir simulator for modeling low-salinity IOR processes, using unstructured, regular, and irregular grids, applicable to 1-D, 2-D, and 3-D simulation of low-salinity water injection into porous media and fractured reservoirs. As demonstrated, the model provides a general capability for quantitative evaluation of low-salinity waterflooding in site-specific investigations.
SPE 118944 A Multi-Continuum Model for Gas Production in Tight Fractured Reservoirs. Yu-Shu Wu, SPE, Colorado School of Mines; George Moridis, SPE, Lawrence Berkeley National Laboratory; Baojun Bai, SPE, Missouri University of Science and Technology; and Keni Zhang, SPE, Lawrence Berkeley National Laboratory. SPE Hydraulic Fracturing Technology Conference, 19-21 January 2009, The Woodlands, Texas.
Abstract: Tight gas reservoirs are characterized by single-phase (gas) or two-phase (gas and liquid) flow in extremely low-permeability, highly heterogeneous porous/fractured, and stress-sensitive rock. Gas flow in such tight formations is further complicated by other co-existing processes, such as Klinkenberg effect, non-Newtonian or non-Darcy flow behavior, due to strong interaction between fluid molecules and solid materials within tiny pores, or micro- and macro- fractures. Because of the low permeability in tight rock, the traditional double-porosity model may not be applicable for handling fracture-matrix interaction of gas flow in these reservoirs. In this work, we present a generalized mathematical model for simulating multiphase flow of gas in tight, porous/fractured reservoirs using a more general, multi-continuum modeling approach. The model incorporates the following processes: (1) Klinkenberg effect, (2) non-Newtonian behavior (i.e., threshold pressure gradient for flow to occur); (3) non-Darcy flow with inertial effects; and (4) rock deformation due to changes in the stress field. We propose to explicitly separate effects of rock mechanical deformation and molecular interaction between fluids and rock materials. The former effect is included using the intrinsic permeability and porosity relations, while the latter is accounted for by an apparent viscosity for non-Newtonian, non-Darcy’s behavior, or a modified permeability for Klinkenberg effect The proposed mathematical model has been implemented into a multiphase, multidimensional reservoir simulator. In the numerical model, specifically, a control-volume, integral finite-difference method is used for spatial discretization with an unstructured grid, and a first-order finite-difference scheme is adapted for temporal discretization of governing two-phase flow equations in tight gas reservoirs. The resulting discrete nonlinear equations are solved fully implicitly by Newton iteration. The numerical scheme has been verified against analytical solutions with Klinkenburg effect, non-Newtonian or non-Darcy flow, and flow in deformable fractured rock in our previous studies. The model’s application to actual tight gas reservoirs is an on-going research project.
2008
SPE 117411 Testing and Analysis of Wells Producing Commingled Layers in Priobskoye Field. Alfred Davletbaev, RN-UfaNIPIneft, Erdal Ozkan, SPE, Colorado School of Mines, Andrey Slabetskiy, RNYuganskneftegas, Vyacheslav Nikishov, KNTTz <Rosneft> R&D, and Timur Usmanov, RN-UfaNIPIneft. SPE Russian Oil and Gas Technical Conference and Exhibition, 28-30 October 2008, Moscow, Russia
Abstract: This paper discusses a Downhole Flow Control (DHFC) technology and describes its application for injection and fall-off testing of commingled layered reservoirs. The Simultaneous Separate Injection (SSI) technology has been successfully applied in over 150 injection wells by the Rosneft Oil Company in the Priobskoye Oil Field. The SSI assembly is a cable tool consisting of valves, packers, and pressure transducers and provides the ability to distribute the surface injection rate into individual layers in a controlled manner. The ability to control layer injection rates is intended for effective flooding of poor-injectivity layers. The concurrent measurement of layer pressures also provides the opportunity to simultaneously test multiple layers. Currently, the SSI assembly only regulates the distribution of the layer injection rates but does not measure the bottomhole injection rates. Valves on the SSI assembly are preset at the surface based on the spinner tests to determine the injection profile. The main advantage of this technique is the drastic reduction of test time and cost to obtain estimates of individual layer properties and injectivities. This paper focuses on the use of the SSI assembly in pressure-transient testing of commingled, multi-layer reservoirs. The application of the testing technology and the analysis of measured test responses are demonstrated on examples from the Priobskoye Field. Also presented are the results of the Single-Layer Steady-State Injection Tests. These tests are useful to understand the fracture development during injection and the resulting injectivity increases. This information is used to regulate the layer injection rates with the SSI technology and the in the design of the injection and fall-off tests.
SPE 108110 Productivity and Drainage Area of Fractured Horizontal Wells in Tight Gas Reservoirs. F. Medeiros, SPE, Petrobras, and E. Ozkan, SPE, and H. Kazemi, SPE, Colorado School of Mines. SPE Reservoir Evaluation & Engineering, Vol.11, #5, October 2008, pp. 902-911.
Abstract: This paper discusses the performance and productivity of fractured horizontal wells in heterogeneous, tight-gas formations. Production characteristics and flow regimes of unfractured and fractured horizontal wells are documented. The results show that if hydraulic fracturing affects stress distribution to create or rejuvenate natural fractures around the well, the productivity of the system is significantly increased. Unless there is significant contrast between the conductivities of the hydraulic and natural fractures, hydraulic fractures may not significantly contribute to the productivity. For extremely tight formations, the effective drainage area may be limited to the naturally fractured region around the well and the hydraulic fractures. It is also shown that very long transient flow periods govern the productivity and economics of fractured horizontal wells in tight formations. The results of this study are also applicable to oil production from fractured shale.
SPE 115678 Modeling Particle Gel Propagation in Porous Media. Yu-Shu Wu, SPE, Colorado School of Mines, and Baojun Bai, SPE, Missouri University of Science and Technology. SPE Annual Technical Conference and Exhibition, 21-24 September 2008, Denver, Colorado, USA
Abstract
Gel treatments are a proven cost-effective method to reduce excess water production and improve sweep efficiency in waterflood reservoirs. A newer trend in gel treatments uses particle gel (PG) to overcome some distinct drawbacks inherent in in-situ gelation systems. In this paper, we present a conceptual numerical model, based on laboratory tests and analyses, to simulate PG propagation through porous rock. In particular, we use a continuum modeling approach to simulate PG movement and its impact on isothermal oil and water flow and displacement processes. In this conceptual model, the PG is treated as one additional “component” to the water phase. This simplified treatment is based on the following physical considerations: (1) PG is mobilized only within the aqueous phase by advection in reservoirs; (2) PG, once retained in the porous media, will occupy pore space in pore bodies or pore throats and therefore reduce the permeability to bypassing water or oil; and (3) PG mobilization may not occur through pores or pore throats until some thresholds in pressure and/or pressure gradients are achieved and these threshold conditions are described by analogy to non-Newtonian fluid or non-Darcy flow in porous media, i.e., by a modified Darcy’s law. The model is able to predict and evaluate the effects of PG as a conformance control agent to improve oil production and control excess water production.
SPE 116136 Semianalytical Representation of Wells and Near-Well Flow Convergence in Numerical Reservoir Simulation. B. Kurtoglu, SPE, Colorado School of Mines; F. Medeiros, Jr., SPE, Petrobras; and E. Ozkan, SPE, and H. Kazemi, SPE, Colorado School of Mines. SPE Annual Technical Conference and Exhibition, 21-24 September 2008, Denver, Colorado, USA
Abstract: This paper presents a new approach to compute wellbore pressures and near-well flow convergence in numerical reservoir simulation. In this semi-analytical approach, the solution of the flow problem in porous media is related to the boundary-element formulations. To account for reservoir heterogeneity, solution domain is subdivided into internally homogeneous reservoir blocks, which may include wells, and the solutions are coupled with the requirement of flux and pressure continuity at the block boundaries. Knowing the boundary values of the solution domain, this formulation solves for the flux at the block boundaries and flux and pressure on wells. Knowing the flux boundary condition, this formulation also enables the solution of pressure at any point within the reservoir blocks. This feature of the solution serves the purposes of multiscale simulation of flow and transport in porous media. Although the solution can be applied on field scale, this paper focuses on the applications to near-well flow convergence region. When the solution is used for the near-well flow-convergence region, the required boundary values of the solution domain can be obtained from any standard solution techniques, including finite-difference simulation, by accounting for wells as source terms.
SPE 116255 Numerical Inversion of Laplace Transforms in the Solution of Transient Flow Problems With Discontinuities. N. Al-Ajmi, SPE, Colorado School of Mines; M. Ahmadi, SPE, Norwest Questa Engineering; and E. Ozkan, SPE, and H. Kazemi, SPE, Colorado School of Mines. SPE Annual Technical Conference and Exhibition, 21-24 September 2008, Denver, Colorado, USA
Abstract: Laplace transformation provides advantages in the solution of many pressure-transient analysis problems. Usually, these applications lead to a solution that needs to be inverted numerically to the real-time domain. The algorithm presented by Stehfest in 1970 is the most common tool in petroleum engineering for the numerical inversion of Laplace transforms. This algorithm, however, is only applicable to continuous functions and this limitation precludes its use for a wide variety of problems of practical interest. Other algorithms have also been used, but with limited success or popularity. A recent algorithm presented by Iseger in 2006 removes the restriction of continuity and provides opportunities for many practical applications. This paper exploits the useful features of the Iseger’s algorithm in the inversion of continuous as well as singular and discontinuous functions that arise in the solution of pressure-transient analysis problems. The most remarkable applications are in the problems that require the use of piecewise continuous and piecewise differentiable functions, such as the use of tabulated data in the Laplace transform domain, deconvolution algorithms, and solutions that include step-rate changes as in the mini-DST tests.
SPE 113651 Multiscale Compositional Simulation of Naturally Fractured Resevoirs. B. Ramirez, SPE, Colorado School of Mines; Safian Atan, SPE, Marathon Oil Company; and Hossein Kazemi, SPE, Colorado School of Mines. Europec/EAGE Conference and Exhibition, 9-12 June 2008, Rome, Italy
Abstract: To obtain accurate descriptions of fluid flow in the reservoir, it is necessary to include detailed geological information on the scale of geocellular models. However, computation resources are often overwhelmed by the vast amount of information that geocellular models contain.
The multiscale approach presented in this paper is designed to include the detailed geological information into the flow calculations while making computations less expensive. The distinguishing characteristic of this paper lies on the procedure used to carry out the computations. The procedure splits the computation into pressure solution on a coarser grid and the saturations and compostions calculations on a very fine scale. This is based the physical and theoretical evidence that pressure effects travel at much higher velocities than saturation and composition fronts – thus, different scales on computation. Splitting up the computations through appropriate physical rules, the multiscale approach divides the computation of pressure propagation and convective processes like the saturation and composition fronts. The pressure propagation is diffusive in nature, while the saturation and composition computation being transport processes are convective in nature. These characteristics allow the computation of the solution at different scale levels. The multiscale approach of this paper is a sequential formulation based on a volume balance model using partial molar volumes. It starts with a compositional pressure equation based on the overall components balance. Once the pressure solution is obtained, the total phase and component velocities are calculated on a fine scale to track the saturation and composition fronts. The multiscale method begins with the use of coarse grid blocks, which contain numerous finer grid blocks (the geocellular scale). Flux calculations based on the total face velocities at the boundaries of the coarse grid blocks are used to set up the fine grid calculations for both the pressure and saturations within each coarse grid block for accurate tracking of the displacement fronts. The finer scale solution is subsequently employed to improve the accuracy of the coarse grid block boundary conditions. The scheme is intended to capture the fine scale physics of gravity, capillarity, and phase behavior interactions as well as the global effect of rock heterogeneity (the dual-porosity effects), pore structure, stratigraphy, and reservoir architecture.
ITU Semi-analytical simulation of flow in heterogenous reservoirs: Theory and applications. F. Medeiros, Jr., Petrobras, and E. Ozkan, Colorado School of Mines. 18th ITU Petroleum and Natural Gas Engineering Seminar and Exhibition, June 19-20, 2008, Istanbul, Turkey.
SPE 84294 Estimation of Storativity Ratio in a Layered Reservoir With Crossflow. N.M. Al-Ajmi, SPE, H. Kazemi, SPE, and E. Ozkan, SPE, Colorado School of Mines. N.M. Al-Ajmi, SPE, H. Kazemi, SPE, and E. Ozkan, SPE, Colorado School of Mines, Volume 11, Number 2, April 2008, pp 267-279.
Abstract: This paper presents a practical method to estimate the storativity ratio of a dual-permeability layered reservoir with crossflow from pressure-transient data. The method uses an analytical formula for the storativity ratio in terms of the separation between the two semilog straight lines on the pressure vs. log-time plot, similar to the method used for dual-porosity systems. Knowing the storativity ratio from a well test allows individual-layer properties to be estimated if the layer flow rates are available from production logs. Demonstrations of the method to estimate the storativity ratio and individual-layer properties are presented by examples. Comparison of the results with those obtained from the existing techniques is also provided to highlight the accuracy of the proposed technique.
2007
IPTC 11778: A Critical Review for Proper Use of Water-Oil-Gas Transfer Functions in Dual-Porosity Naturally Fractured Reservoirs – Part II. M. Al-Kobaisi, H. Kazemi, B. Ramirez, E. Ozkan, and S. Atan. This paper was prepared for presentation at the International Petroleum Technology Conference held in Dubai, U.A.E., 4–6 December 2007.
Abstract: This paper is Part II of SPE 109821. In Part I, we discussed the viability of the use of simple transfer functions to accurately account for fluid exchange resulting from capillary, gravity and diffusion mass transfer for immiscible flow between fracture and matrix in dual-porosity numerical models. Here we will show additional information on several relevant topics, which include (1) flow of a low concentration, water-soluble surfactant in the fracture and the extent to which the surfactant is transported into the matrix, (2) an adjustment to the transfer function to account for the early slow mass transfer into matrix before the invading fluid establishes full connectivity with the matrix, and (3) an analytical approximation to the differential equation of mass transfer from a fracture to the matrix and a method of solution to predict oil drainage performance. Numerical experiments involving single-porosity, fine-grid simulation of immiscible oil recovery from a typical matrix block by water, gas, or surfactant-augmented water in an adjacent fracture were performed. Results emphasize the viability of the transfer function formulations and their accuracy in quantifying the interaction of capillary and gravity forces to produce oil depending on the wettability of the matrix. For miscible flow the fracture-matrix mass transfer is less complicated because the interfacial tension between solvent and oil is zero; nevertheless, gravity contrast between solvent in the fracture and oil in the matrix creates convective mass transfer and drainage of the oil.
IPTC 11781: Pressure-Transient Performances of Hydraulically Fractured Horizontal Wells in Locally and Globally Naturally Fractured Formations. F. Medeiros, B. Kurtoglu, E. Ozkan, and H. Kazemi. This paper was prepared for presentation at the International Petroleum Technology Conference held in Dubai, U.A.E., 4–6 December 2007.
Abstract: This paper presents a discussion of diagnostic pressure and pressure-derivative plots for hydraulically fractured horizontal wells in locally and globally fractured formations. The discussions are based on pressure-transient responses generated by using a semi-analytical, heterogeneous reservoir simulator. Pressure-transient characteristics are discussed and documented. Performances of horizontal wells with longitudinal and transverse fractures are compared. It is shown that global and local natural fractures display distinct pressure transient characteristics and, hence, significantly influence well performance. In general, conductive, interconnected natural fractures dominate the pressure-transient characteristics of horizontal wells in tight formations even in the presence of hydraulic fractures. Furthermore, the results also indicate that if the reservoir is naturally fractured, hydraulic fracturing might not improve productivity significantly, unless large hydraulic fracture conductivities can be achieved. Finally, if there is a significant contrast between the effective permeabilities of local natural fractures and surrounding homogeneous reservoir, it might be possible to estimate the volume of the naturally fractured region.
SPE 110848: Analysis of Production Data From Hydraulically Fractured Horizontal Wells in Tight, Heterogeneous Formations. F. Medeiros, B. Kurtoglu, E. Ozkan, and H. Kazemi. Presented at the SPE Annual Technical Conference and Exhibition in Anaheim California, 11-14 November 2007
Abstract: This paper discusses the analysis of production data from hydraulically fractured horizontal wells in tight, heterogeneous formations. We consider horizontal wells with longitudinal and transverse hydraulic fractures, which might be surrounded by a region with natural fractures. These well-reservoir configurations are of interest in many unconventional reservoirs, including tight-gas sands and shale-oil or gas formations. A semi-analytical model that can incorporate the key features of reservoir heterogeneity and the details of hydraulic fracture and wellbore flow is used to compute production decline. Production decline characteristics are presented in terms of transient productivity index. Computation of transient productivity index from field data and the analysis of production decline by transient productivity index are explained. Example applications of production data analysis for fractured horizontal wells in tight, heterogeneous formations are presented.
SPE 109821: A Critical Review for Proper Use of Water/Oil/Gas Transfer Functions in Dual-Porosity Naturally Fractured Reservoirs—Part I. B. Ramirez, H. Kazemi, M. Al-Kobaisi, E. Ozkan, and S. Atan. Presented at the SPE Annual Technical Conference and Exhibition in Anaheim California, 11-14 November 2007
Abstract: Accurate calculation of multi-phase fluid transfer between the fracture and matrix in naturally fractured reservoirs is a crucial issue. In this paper, we will present the viability of the use of simple transfer functions to accurately account for fluid exchange resulting from capillary, gravity and diffusion mass transfer for immiscible flow between fracture and matrix in dual-porosity numerical models. The transfer functions are designed for sugar-cube or match-stick idealizations of matrix blocks.
The study relies on numerical experiments involving fine-grid simulation of oil recovery from a typical matrix block by water or gas in an adjacent fracture. The fine-grid results for water-oil and gas-oil systems were compared with results obtained with transfer functions. Both in water and gas injection, the simulations emphasize the interaction of capillary and gravity forces to produce oil depending on the wettability of the matrix.
In gas injection, the thermodynamic phase-equilibrium, aided by gravity-capillary interaction and to a lesser extent by molecular diffusion, is a major contributor to interphase mass transfer. For miscible flow the fracture-matrix mass transfer is less complicated because there is no capillary forces associated with solvent and oil; nevertheless, gravity contrast between solvent in the fracture and oil in the matrix creates convective mass transfer and drainage of oil.
Using the transfer functions presented in this paper, fracture and matrix flow calculations can be decoupled and solved sequentially–reducing the complexity of the computation. Furthermore, the transfer function equations can be used independently to calculate oil recovery from a matrix block.
SPE 109295: Non-Darcy Flow Effects in Dual-Porosity, Dual-Permeability, Naturally Fractured Gas Condensate Reservoirs. B. Ramirez, H. Kazemi, E. Ozkan, and M. Al-Matrook. Presented at the SPE Annual Technical Conference and Exhibition in Anaheim California, 11-14 November 2007
Abstract: This paper addresses the retrograde condensation behavior in natural fractures and in the near wellbore region of a naturally fractured reservoir (NFR). The study includes the combined effect of non-Darcy flow in presence of retrograde condensation and wellbore damage on pressure transient analysis of naturally fractured reservoirs. A single well compositional model was constructed and used to evaluate both the early-time and late-time characteristics of the pressure transient data.
In naturally fractured reservoirs the high velocity region could be substantially beyond the near wellbore region because of the narrowness of the fractures. To assess this situation, draw-down, build-up and multi-rate tests were simulated in rich gas and lean gas condensate reservoirs. It was concluded that the gas condensation in the near wellbore region significantly increases the calculated skin factor beyond the physical damage.
SPE 108110: Productivity and Drainage Area of Fractured Horizontal Wells in Tight Gas Reservoirs. F. Medeiros, E Ozkan, and H. Kazemi. Presented at the 2007 Rocky Mountain Oil & Gas Technology Symposium in Denver, CO, 16-18 April 2007.
Abstract: This paper discusses the performance and productivity of fractured horizontal wells in heterogeneous, tight-gas formations. Production characteristics and flow regimes of unfractured and fractured horizontal wells are documented. The results show that if hydraulic fracturing affects stress distribution to create or rejuvenate natural fractures around the well, productivity of the system is significantly increased. Unless there is significant contrast between the conductivities of the hydraulic and natural fractures, hydraulic fractures may not significantly contribute to the productivity. For extremely tight formations, effective drainage area may be limited to the naturally fractured region around the well and the hydraulic fractures. It is also shown that very long transient flow periods govern the productivity and economics of fractured horizontal wells in tight formations. The results of this study are also applicable to oil production from fractured shale.
SPE 104581: Transient Behavior of Multilateral Wells in Numerical Models: A Hybrid Analytical-Numerical Approach. C. Aguilar, E. Ozkan, H. Kazemi, M. Al-Kobaisi, and B. Ramirez. Presented at the 15th SPE Middle East Oil & Gas Show and Conference held in Bahrain International Exhibition Centre, Kingdom of Bahrain, 11-14 March 2007.
Abstract: This paper presents an extension of transient well index approach to simulate pressure transient behavior of multilateral wells. This approach uses an analytical solution for the well index at early times and switches to the numerical well index at late times. The use of the transient well index eliminates the need for excessive grid refinement around the well. In this paper, we have improved the accuracy of the transient well index approach and have provided for a flexible and easily implementable approach to place multilaterals in conventional, Cartesian-grid reservoir models.
SPE 104580: Verification and Proper Use of Water/Oil Transfer Function for Dual-Porosity and Dual-Permeability Reservoirs. A. Balogun, H. Kazemi, E. Ozkan, M. Al-Kobaisi, and B. Ramirez Presented at the 15th SPE Middle East Oil & Gas Show and Conference held in Bahrain International Exhibition Centre, Kingdom of Bahrain, 11-14 March 2007.
Abstract: Accurate calculation of multi-phase fluid transfer between the fracture and matrix in naturally fractured reservoirs is a very crucial issue. In this paper, we will present the viability of the use of a simple transfer function to accurately account for fluid exchange resulting from capillary and gravity forces between fracture and matrix in dual-porosity and dual-permeability numerical models. With this approach, fracture and matrix flow calculations can be decoupled and solved sequentially, improving the speed and ease of computation. In fact, the transfer function equations can be easily used to calculate the expected oil recovery from a matrix block of any dimension without the use of a simulator or oil recovery correlations.
The study was accomplished by conducting fine-grid simulation of a typical matrix block and comparing the results with those obtained with the use of a simple transfer function for a water-oil system. This study was similar to a previous study (Alkandari, 2002) we had conducted for a gas-oil system.
The transfer functions of this paper are specifically for the sugar-cube idealization of a matrix block, which can be extended to simulation of a match-stick idealization in reservoir modeling. The basic data required are: matrix capillary pressure curves, densities of the flowing fluids, and matrix block dimensions.
2006
SPE 101987: Effects of Formation Damage and High-Velocity Flow on the Productivity of Slotted-Liner Completed Horizontal Wells. Y. Tang, T. Yildiz, E. Ozkan, and M. Kelkar. Presented at the 2006 International Oil & Gas Conference and Exhibition in China held in Beijing, China, 5-7 December 2006.
Abstract: Slotted-liner is a relatively simple and cost-effective well completion technique for horizontal wells. However, fluid flow into a slotted-liner completion is quite complicated due to three dimensional flow convergence around slots and limited open-to-flow areas. Furthermore, the compounded effects of formation damage and non-Darcy flow on the fluid flow towards slotted-liners must be considered in well completion design process.
This paper presents a comprehensive semi-analytical model for estimating the productivity of horizontal wells completed with slotted liners. The semi-analytical model is obtained by coupling the reservoir flow and wellbore flow equations. The model includes the additional pressure drops due to mechanical skin and non-Darcy effect. Additionally, the model could handle non-uniform flux, non-uniform skin distribution, and selective completion with blank pipes. Both oil well and gas wells are evaluated. For gas wells, the standard pseudo-functions are used. Detailed discussion of the effects of formation damage and non-Darcy flow is provided.
Results indicate that the productivity reduction because of formation damage is more significant for slotted-liner completion than the openhole completion due to increased pressure drop with flow convergence in the region with reduced permeability. Control of drilling damage ratio is more important than control of drilling damage radius. High slot density with low phasing angle helps to reduce the non-Darcy flow effect.
SPE 84378: Pressure-Transient Responses of Horizontal and Curved Wells in Anticlines and Domes. N. Al-Mohannadi, E. Ozkan, and H. Kazemi. Presented at the 2003 SPE Annual Technical Conference and Exhibition, Denver, 5-8 October, and revised for publication. Paper peer approved 5 November 2006.
Abstract: This paper presents a discussion of the pressure-transient responses of horizontal wells in anticlinal structures and curved and undulating wells in slab reservoirs. It confirms that, in the absence of a gas cap, conventional horizontal-well models may be used to approximate the flow characteristics of the systems in which the trajectory of the well does not conform to the curvature of the producing structure. If a gas cap is present, however, the unconformity of the well trajectory and producing layer manifests itself, especially on derivative characteristics when the gas saturation increases around the well. In general, the most significant deviations from the conventional horizontal-well behavior are observed during the buildup periods following long drawdowns. In these cases, the pressure-transient analysis is complicated and requires detailed numerical modeling of the well trajectory and reservoir geometry in the vertical plane.
SPE 102834: A Semianalytical, Pressure-Transient Model for Horizontal and Multilateral Wells in Composite, Layered, and Compartmentalized Reservoirs. F. Medeiros Jr., E. Ozkan, and H. Kazemi. Presented at the SPE Annual Technical Conference and Exhibition, 24-27 September 2006, San Antonio, Texas, USA
Abstract: This paper presents a semianalytical model for the pressure-transient analysis of horizontal wells in composite, layered, and compartmentalized reservoirs. The model divides the reservoir into blocks that represent locally homogeneous substructures of the reservoir and couples the analytical, pressure-transient solutions at the block boundaries. This approach is consistent with the averaging effect of pressure transients and provides an alternative to full numerical modeling of horizontal-well pressure-transient responses in heterogeneous formations. The model can also be generalized for multiple wells of different geometry including multiple laterals.
SPE 90623: Combined Effect of Non-Darcy Flow and Formation Damage on Gas-Well Performance of Dual-Porosity and Dual-Permeability Reservoirs. C. Pereira Tavares, H. Kazemi, and E. Ozkan. Presented at the 2004 Annual Technical Conference and Exhibition, Houston, TX, 26-29 September, and revised for publication. Paper peer approved 31 July 2006.
Abstract: This paper addresses the combined effect of formation damage and non-Darcy flow in naturally fractured reservoirs using simplified analytical solutions and a 2D numerical simulator. Pressure drawdown, buildup, and isochronal tests simulated in this work indicate that, despite high fracture permeability, skin damage may accentuate the non-Darcy flow effect and drastically influence pressure-transient characteristics of low-pressure, naturally fractured reservoirs. In high-pressure reservoirs, this effect is significant only at high rates. Non-Darcy flow does not usually mask the typical pressure-transient characteristics of dual-porosity and dual-permeability reservoirs, but the conventional interpretation of the early-time data may lead to erroneous results. If the exponent, n, of the isochronal tests approaches 0.5 while the matrix permeability is low and flow rate is rather high, this would indicate the predominance of fracture flow. Under these conditions, small contributions from skin damage may greatly reduce gas-well performance in naturally fractured reservoirs.
Paper 2006-162: Pressure-Transient-Analysis of Horizontal Wells with Transverse, Finite-Conductivity Fractures. M. Al-Kobaisi, E. Ozkan, H. Kazemi, and B. Ramirz. Presented at the Petroleum Society’s 7th Canadian International Petroleum Conference (57th Annual Technical Meeting) Calgary, Alberta Canada, 13-15 June 2006.
Abstract: This paper discusses the analysis of pressure-transient responses of horizontal wells intercepting finite-conductivity transverse fractures. We use a hybrid, numerical-analytical model to simulate the impact of the fracture properties on the early-time flow regimes and pressure transient characteristics of fractured horizontal wells. It is shown that the fractured geometry and well location strongly influence the flow convergence in a horizontal-well fracture and lead to early-time flow regimes different from vertical-well fractures. Accordingly, appropriate pressure-transient models and analysis procedures should be used to determine fracture properties. We present straight-line analysis equations for radial-linear and pseudo-bilinear flow regimes for circular and rectangular fractures, respectively. We also bring the conventional fracture half-length and conductivity concepts into perspective and question the assumption that the properties estimated from pressure transient test of horizontal-well may be taken as effective properties when fractures are not rectangular. We show that flow convergence toward the wellbore may increase non-Darcy flow within the fracture. If the additional pressure drop because of flow choking and non-Darcy flow is not taken into account, pressure-transient test indicate smaller effective conductivity or fracture size. Because this additional pressure-drop is flow rate dependent, the estimated effective fracture properties are not useful for performance prediction purposes.
SPE 92040: A Hybrid Numerical/Analytical Model of a Finite-Conductivity Vertical Fracture Intercepted by a Horizontal Well. M. Al-Kobaisi, E. Ozkan, and H. Kazemi. Presented at the 2004 SPE international Petroleum Conference in Puebla, Mexico, 7-9 November, and revised for publication. Paper peer approved 17 May 2006.
Abstract: This paper presents a hybrid numerical/analytical model for the pressure-transient response of a finite-conductivity fracture intercepted by a horizontal well. The model dynamically couples a numerical fracture model with an analytical reservoir model. This approach allows us to include finer details of the fracture characteristics while keeping the computational work manageable. For example, the fracture may have irregular shape, nonuniform width, and variable conductivity, and the well may not intersect the fracture at its geometric center.
In this paper, we use the hybrid model to investigate the effects of fracture properties on the pressure-transient characteristics of a single, finite-conductivity horizontal-well fracture. The single horizontal-well-fracture model can be extended easily to multiply fractured horizontal wells by superposition. The model also can be used to compute the pseudoskin caused by the effects of nonideal fracture geometry, variable conductivity, and flow choking around the wellbore and to investigate the influence of fracture properties on the performance of horizontal wells.
2005
SPE 77534: Effects of Formation Damage and High-Velocity Flow on the Productivity of Perforated Horizontal Wells. Y. Tang, T. Yildiz, E. Ozkan, and M. Kelkar. Presented at the 202 SPE Annual Technical Conference and Exhibition, San Antonio, TX, 29 September – 2 October and revised for publication. Paper peer approved 24 May 2005.
Abstract: A comprehensive semianalytical model has been built to investigate the effects of drilling and perforating damage and high-velocity flow on the performance of perforated horizontal wells. The model incorporates the additional pressure drop caused by formation damage and high-velocity flow into a semianalytical coupled wellbore/reservoir model. The reservoir model considers the details of flow in the vicinity of the wellbore, including 3D convergent flow into individual perforations, flow through the damaged zone around the wellbore and the crushed zone around the perforation tunnels, and non-Darcy flow in the near-wellbore region. The wellbore flow model includes the effect of frictional pressure drop. Both oil and gas wells are considered.
The expressions provided in this paper for additional pressure losses caused by perforating damage, drilling damage, and high-velocity flow can be used to optimize perforating parameters and decompose the total skin into its components (perforation pseudoskin, damage skin, and non-Darcy skin).
SPE 84292: Analysis of Interference Tests with Horizontal Wells. M. Al-Khamis, E. Ozkan, and R. Raghavan. Presented at the 2003 SPE Annual Technical Conference and Exhibition, Denver, 5-8 October, and revised for publication. Paper peer approved 24 May 2005.
Abstract: One of the common assumptions in horizontal-well interference-test analysis is to ignore fluid flow in and out of the horizontal observation well and represent it by a point. In some cases, the active well is also approximated by a vertical line source. Using a semianalytical model, this paper answers three fundamental questions:
• What is the critical distance between the wells to represent the horizontal observation well by an observation point?
• Where should the observation point be placed along the horizontal well?
• Under what conditions may the active well be approximated by a vertical line source and the exponential integral solution be used to analyze observation-well responses?
Two correlations are presented to simplify the analysis of horizontal-well interference tests. Example applications are presented, and error bounds are documented.
SPE 93296: Interpretation of Skin Effect from Pressure Transient Tests in Horizontal Wells. A.M. Al-Otaibi, and E. Ozkan. Presented at the 14th SPE Middle East Oil & Gas Show and Conference in Bahrain International Exhibition Centre, Bahrain, 12-15 March 2005.
Abstract: Most horizontal wells have non-uniform distribution of skin along their lengths and this creates a challenging problem in the interpretation of their pressure-transient responses. The theory indicates that the rigorous incorporation of non-uniform skin distribution into horizontal well pressure-transient models requires the knowledge of not only the skin distribution but also the flow rate distribution into the horizontal well from the reservoir. Because this information is not normally available to the analyst, standard pressure interpretation techniques and tools assume uniform distribution of skin with the expectation that the estimates would correspond to some average of the skin distribution. The question that has not been adequately addressed in the literature is the physical meaning of the skin estimates from different pressure-transient analysis tools in common use. Because this question has not been adequately addressed, purely geometrical interpretations of the skin estimates have been proposed to calculate horizontal well productivities and develop flow models.
In this paper, we generate synthetic pressure-transient responses for different non-uniform skin distributions along a horizontal well and analyze these responses by using the conventional tools that assume uniform distribution of skin. Skin estimates from well-test interpretation are then compared with the known skin distributions.
The findings of this study are practical and important. First, the pressure drop caused by skin depends on the flow regimes if the skin distribution is non-uniform. Because the models used in commercial software assume the same additional pressure drop due to skin, the regression analysis can only match one of the flow periods for a constant skin value. To interpret the meaning of this skin estimate, we used the semi-log analysis techniques and demonstrated what type of average the estimated skin represents for different flow regimes and different skin distributions. For most cases, the estimates of skin from early-time radial flow analysis represent the arithmetic average of the skin distribution which may be useful for stimulation decisions. The skin estimate from the pseudo-radial flow period corresponds to the skin pressure drop at the heel of the horizontal well, which represents the additional pressure drop to be considered in the productivity calculations. We demonstrate that the geometric interpretation of the non-uniform skin effect proposed in the literature is inaccurate and leads to significant errors in the calculation of horizontal well productivity.
S. Atan, E. Ozkan, and H. Kazemi. Numerical Simulation of Multiphase Flow in Multiscale Heterogeneous Reservoirs Using Multimesh Computing Methodology. 2005.
Abstract: Despite the improvements in recovery from complex reservoirs, on the average, two-thirds of the original oil in place will be left behind. To improve the recovery further, successful reservoir monitoring and accurate modeling of fluid movement are essential. Reservoir monitoring requires building reservoir models that integrate various scales of data; typically geostatistical, seismic, saturation, and pressure/rate measurements. The common simulation approach is to treat all physical processes governing the fluid motion on the same spatial and temporal scale. This requires rescaling of the data to a convenient scale for simulation purposes. However, the upscaled properties, whether it is based on geostatistics or dynamic measurements from flow test, in general, do not provide satisfactory answers for simulation of complex, heterogeneous reservoirs. To accurately account for heterogeneity, multimillion grid simulators may be required, but this brings us to the question of practicality and may not be the correct recourse to deal with data-scale problems. An alternative is to develop reservoir models that use the natural scales of convective flow and pressure diffusion in an integrated computational scheme, known as multimesh computing methodology. In multimesh computation, the first step is to solve the pressure equation on the coarse grid, which is composed of several fine-grid cells per coarse grid cell. The second step is to compute the flow velocities at the boundaries of the coarse grid cells based on the pressure solution and interpolated onto the fine grid cells. Finally, the phase saturation is computed for each fine grid. In general, we solve the convective component flow problem on a fine-grid scale, as small as what geocellular models are. Consequently, we can obtain very accurate tracking of fluid movement in the reservoir reflecting the heterogeneity of the reservoir accurately.
SPE 93294: Dual-Mesh Simulation of Reservoir Heterogeneity in Single- and Dual- Porosity Problems. S. Atan, M. Al-Matrook, H. Kazemi, E. Ozkan, and M. Gardner. Presented at the 2005 Reservoir Simulation Symposium in Houston, TX, 31 January – 2 February 2005.
Abstract: This paper presents dual-mesh computing in simulation of reservoir heterogeneities in single- and dual-porosity reservoirs. The dual-mesh approach provides a great tool for computing displacement processes and saturation distribution on the same fine-grid as the underlying geological models and is also extremely powerful in simulation of naturally fractured, dual-porosity reservoirs. This approach may even be used for the fine-scale computations in compositional modeling of petroleum reservoirs. In principle, the dual-mesh computing surpasses the benefits of streamline simulation both in single and dual-porosity problems. Several convincing examples are presented to illustrate the broad applications. The reasons for the accuracy and efficacy of the dual-mesh computing are also explained.
SPE 93053: Multilevel Fracture Network Modeling of Naturally Fractured Reservoirs. H. Kazemi, S. Atan, M. Al-Matrook, J. Dreier, and E. Ozkan. Presented at the 2005 Reservoir Simulation Symposium in Houston, TX, 21 January 2005 – 2 February 2005
Abstract: This paper provides a review of common approaches for simulation of naturally fractured reservoirs and a new model formulation that is more amenable to the utilization of detailed geologic information from deterministic models, multipoint statistical simulations (MPS), and discrete fracture network (DFN) models. Unlike the common dual-porosity and dual-permeability models, the new model considers flow in several sets of fractures (that is, micro, macro, and mega fracture levels) and the wells can intercept any class of fractures. Matrix flow is also included in the formulation. A dual-mesh-computing algorithm is used to capture the major orientation of fractures in the flow network. The algorithm consists of the conventional five-point discretization for the coarse grid and a special nine-point discretization scheme for the fine grid. The size of the coefficient matrix for the discretization scheme can be reduced because of the dominance of vertical flow drainage in fractured reservoirs.
2004
SPE 91940: Dynamic Behavior of Discrete Fracture Network (DFN) Models. H. Araujo, P. Lacentre, T. Zapata, A. Del Monte, F. Dzelalija, J. Gilman, H. Meng, H. Kazemi, and E. Ozkan. Presented at the 2004 SPE international Petroleum Conference in Puebla, Mexico, 8-9 November 2004
Abstract: This work shows that discrete fracture network modeling is very desirable for the characterization of naturally fractured reservoirs but it is only a highly subjective starting point. Thus, calibration against short and long term pressure transient tests is most crucial. This paper shows how the dynamic behavior of a discrete fracture network model of Margarita gas field compared against pressure transient measurements in a sidetrack delineation-well. The performance comparison of a very fine-grid reservoir model, which included the discrete fracture network information, versus a much coarser upscaled grid model is also documented.
SPE 92039: New Analytical Pressure-Transient Models to Detect and Characterize Reservoirs with Multiple Fracture Systems. J. Dreier, E. Ozkan, and H. Kazemi. Presented at the SPE international Petroleum Conference Held in Puebla, Mexico, 7-9 November 2004.
Abstract: This paper presents two new pressure-transient models for naturally fractured reservoirs. The analytical models consider flow in a quadruple-porosity system that consists of a triple-fracture network with a single-matrix system. The models are used to investigate the pressure-transient characteristics of quadruple-porosity systems. They can also be used to detect, characterize, and simulate naturally fractured reservoirs with quadruple-porosity characteristics. It is shown that the fracture interconnectivity can be determined from pressure-transient tests if the combined fracture storativity is sufficiently large and the matrix contribution can be unambiguously isolated. Regression analysis of pressure-transient tests in naturally fractured reservoir with quadruple-porosity behavior is also discussed. It is demonstrated that the standard regression techniques are very sensitive to the scatter of the pressure vs. time data.
SPE 89880: Streamline Simulation of Countercurrent Water-Oil and Gas-Oil Flow in Naturally Fractured Dual-Porosity Reservoirs. J. Moreno, H. Kazemi, and J. R. Gilman. Presented at the SPE Annual Technical Conference and Exhibition in Houston, TX, 26-29 September 2004.
Abstract: The flow of hydrocarbons in naturally fractured reservoirs is a very complex process involving the interaction of reservoir fluids with two distinct porous media. Accurate simulation of the physics of flow and fast execution of the resulting complex numerical code is fundamental in developing a viable tool for reservoir development and management. This paper addresses this issue by developing and evaluating a basic 3-D streamline reservoir simulator for counter-current water-oil flow in naturally fractured dual-porosity reservoirs. The concept is readily extended to counter-current gas-oil gravity drainage in such reservoirs.
In the water-oil case, the counter-current flow of water and oil between the fracture and matrix media is generally attributed to water imbibition process. However, in oil-wet or mixed-wet rocks, the water imbibition could be non-existent, small, or strongly saturation-dependent. In these cases, given the right conditions, gravity potential can enhance oil drainage. These physical concepts are included in the simulator.
In the gas-oil case, the capillary forces generally resist the gravity potential; thus, preventing counter-current flow of oil and gas. With proper placement of gas-oil contact in the fractures, the gravity potential can overcome the capillary resistance to invoke gas-oil gravity drainage. We will demonstrate how such a formulation can be included a dual-porosity streamline simulator.
In the simulator, we apply an incompressible flow assumption to the fracture network in order to solve the 3-D water-oil displacement problem using a set of 1-D streamlines. Simple, but realistic, transfer functions, handle the matrix-fracture counter-current flow. These transfer functions depend on fracture-matrix relative permeability and capillary pressure functions, as well as the local gravity potential. A simpler, but perhaps more realistic, form of the transfer function is determined experimentally as a scaleable fractional oil recovery curve versus an appropriate dimensionless time. The transfer functions include other conventional reservoir properties such as permeability, porosity, and shape factor.
The simulator was used to model several water-oil displacement test cases and the results were compared with Eclipse 100 dual-porosity model results. The comparisons were favorable and the differences in results were consistent with the difference in the simulation approach.
We believe the streamline simulation of dual-porosity reservoirs could become an important tool for evaluating and managing fractured dual-porosity reservoirs. Because of the efficiency of the formulation, larger, more realistic geologic models can be modeled as compared to conventional simulators. For instance, simulating the frontal advance of the gas-oil contact in fractures, to invoke gravity drainage without gas breakthrough, can be accurately and efficiently handled using the formulation described here. Similarly, the breakthrough of water in fracture channels can be accurately simulated for very complex geologic models.
2003
SPE 84294: Estimation of Storativity Ratio in a Layered Reservoir with Crossflow. N. M. Al-Ajmi, H. Kazemi, and E. Ozkan. Presented at the SPE Annual Technical Conference and Exhibition held in Denver, CO, 5-8 October 2003.
Abstract: This paper presents a practical method to estimate the storativity ratio of a layered reservoir with cross-flow from pressure transient data. The method uses an analytically derived formula for the storativity ratio in terms of the separation between the two semi-log straight lines on pressure versus log-time plot. Knowing the storativity ratio from a well test, individual layer properties may be estimated if the layer flow rates are available from production logs. Demonstrations of the method to estimate the storativity ratio and individual layer properties are presented by examples. Comparison of the results with those obtained from the existing techniques is also provided to highlight the accuracy of the proposed technique.