Academic literature on the topic 'Drainage Volume in Heterogeneous Reservoirs'
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Journal articles on the topic "Drainage Volume in Heterogeneous Reservoirs"
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Xie, Jiang, Changdong Yang, Neha Gupta, Michael J. King, and Akhil Datta-Gupta. "Depth of Investigation and Depletion in Unconventional Reservoirs With Fast-Marching Methods." SPE Journal 20, no. 04 (August 20, 2015): 831–41. http://dx.doi.org/10.2118/154532-pa.
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Summary The concept of depth of investigation is fundamental to well-test analysis. Much of the current well-test analysis relies on solutions based on homogeneous or layered reservoirs. Well-test analysis in spatially heterogeneous reservoirs is complicated by the fact that Green's function for heterogeneous reservoirs is difficult to obtain analytically. In this paper, we introduce a novel approach for computing the depth of investigation and pressure response in spatially heterogeneous and fractured unconventional reservoirs. In our approach, we first present an asymptotic solution of the diffusion equation in heterogeneous reservoirs. Considering terms of highest frequencies in the solution, we obtain two equations: the Eikonal equation that governs the propagation of a pressure “front” and the transport equation that describes the pressure amplitude as a function of space and time. The Eikonal equation generalizes the depth of investigation for heterogeneous reservoirs and provides a convenient way to calculate drainage volume. From drainage-volume calculations, we estimate a generalized pressure solution on the basis of a geometric approximation of the drainage volume. A major advantage of our approach is that one can solve very efficiently the Eikonal equation with a class of front-tracking methods called the fast-marching methods. Thus, one can obtain transient-pressure response in multimillion-cell geologic models in seconds without resorting to reservoir simulators. We first visualize the depth of investigation and pressure solution for a homogeneous unconventional reservoir with multistage transverse fractures, and identify flow regimes from a pressure-diagnostic plot. And then, we apply the technique to a heterogeneous unconventional reservoir to predict the depth of investigation and pressure behavior. The computation is orders-of-magnitude faster than conventional numerical simulation, and provides a foundation for future work in reservoir characterization and field-development optimization.
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Xue, Xu, Changdong Yang, Jaeyoung Park, Vishal Kumar Sharma, Akhil Datta-Gupta, and Michael J. King. "Reservoir and Fracture-Flow Characterization Using Novel Diagnostic Plots." SPE Journal 24, no. 03 (November 2, 2018): 1248–69. http://dx.doi.org/10.2118/194017-pa.
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Summary Multistage hydraulically fractured horizontal wells provide an effective means to exploit unconventional reservoirs. The current industry practice in the interpretation of field response often uses empirical decline-curve analysis or pressure-transient analysis/rate-transient analysis (PTA/RTA) for characterization of these reservoirs and fractures. These analytical tools depend on simplifying assumptions and do not provide a detailed description of the evolving reservoir-drainage volume accessed from a well. Understanding of the transient-drainage volume is essential for unconventional-reservoir and fracture assessment and optimization. In our previous study (Yang et al. 2015), we developed a “data-driven” methodology for the production rate and pressure analysis of shale-gas and shale-oil reservoirs. There are no underlying assumptions of fracture geometry, reservoir homogeneity, and flow regimes in the method proposed in our previous study. This approach depends on the high-frequency asymptotic solution of the diffusivity equation in heterogeneous reservoirs. It allows us to determine the well-drainage volume and the instantaneous recovery ratio (IRR), which is the ratio of the produced volume to the drainage volume, directly from the production data. In addition, a new w(τ) plot has been proposed to provide better insight into the depletion mechanisms and the fracture geometry. w(τ) is the derivative of pore volume with respect to τ. In this paper, we build upon our previous approach to propose a novel diagnostic tool for the interpretation of the characteristics of (potentially) complex fracture systems and drainage volume. We have used the w(τ) and IRR plots for the identification of characteristic signatures that imply complex fracture geometry, formation linear flow, partial reservoir completions, and fracture-interference/compaction effects during production. The w(τ) analysis gives us the fracture surface area and formation diffusivity, while the IRR analysis provides additional information on fracture conductivity. In addition, quantitative analysis is conducted using the novel w(τ) plot to interpret fracture-interference time, formation permeability, total fracture surface area, and stimulated reservoir volume (SRV). The major advantages of this current approach are the model-free analysis without assuming planar fractures, homogeneous formation properties, and specific flow regimes. In addition, the w(τ) plot captures high-resolution flow patterns not observed in traditional PTA/RTA analysis. The analysis leads to a simple and intuitive understanding of the transient-drainage volume and fracture conductivity. The results of the analysis are useful for hydraulic-fracturing-design optimization and matrix- and fracture-parameter estimation.
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Li, Chen, and Michael J. King. "Integration of Pressure Transient Data into Reservoir Models Using the Fast Marching Method." SPE Journal 25, no. 04 (March 29, 2020): 1557–77. http://dx.doi.org/10.2118/180148-pa.
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Summary Calibration of reservoir model properties by integration of well-test data remains an important research topic. Well-test data have been recognized as an effective tool to describe transient flow behavior in petroleum reservoirs. It is also closely related to the drainage volume of the well and the pressure-front propagation in the subsurface. Traditional analytic means of estimating reservoir permeability relies on an interpretation of the diagnostic plot of the well pressure and production data, which usually leads to a bulk average estimation of the reservoir permeability. When more detailed characterization is needed, a forward model that is sensitive to the reservoir heterogeneity needs to be established, and a numerical inversion technique is required. We use the concept of the diffusive time of flight (DTOF) to formulate an asymptotic solution of the diffusivity equation that describes transient flow behavior in heterogeneous petroleum reservoirs. The DTOF is obtained from the solution of the Eikonal equation using the fast marching method (FMM). It can be used as a spatial coordinate that reduces the 3D diffusivity equation to an equivalent 1D formulation. We investigate the drainage-volume evolution as a function of time in terms of the DTOF. The drainage volume might be directly related to the well-test derivative, which can be used in an inversion calculation to calibrate reservoir model parameters. The analytic sensitivity coefficients of the well-test derivative with respect to reservoir permeability are derived and incorporated into an objective function to perform model calibration. The key to formulating the sensitivity coefficients is to use the functional derivative of the Eikonal equation to derive the analytic sensitivity of the DTOF to reservoir permeability. Its solution is implemented by tracking the characteristic trajectory of the local Eikonal solver within the FMM. The major advantage of calculating the sensitivity coefficients using the FMM is its significant computational efficiency during the iterative inversion process. This inverse-modeling approach is tested on a 2D synthetic heterogeneous reservoir model and then applied to the 3D Brugge Field, where a single well with constant flow rate is simulated. The well-test derivative is shown to be inversely proportional to the drainage volume and is treated as the objective function for inversion. With an additional constraint to honor the prior model, our inverse-modeling approach will adjust the reservoir model to obtain permeability as a function of distance from the well within the drainage volume. It provides a modification of reservoir permeability both within and beyond the depth of investigation (DOI).
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Zhang, Yanbin, Neha Bansal, Yusuke Fujita, Akhil Datta-Gupta, Michael J. King, and Sathish Sankaran. "From Streamlines to Fast Marching: Rapid Simulation and Performance Assessment of Shale-Gas Reservoirs by Use of Diffusive Time of Flight as a Spatial Coordinate." SPE Journal 21, no. 05 (May 2, 2016): 1883–98. http://dx.doi.org/10.2118/168997-pa.
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Summary Current industry practice for characterization and assessment of unconventional reservoirs mostly uses empirical decline-curve analysis or analytic rate- and pressure-transient analysis. High-resolution numerical simulation with local perpendicular bisector (PEBI) grids and global corner-point grids has also been used to examine complex nonplanar fracture geometry, interaction between hydraulic and natural fractures, and implications for the well performance. Although the analytic tools require many simplified assumptions, numerical-simulation techniques are computationally expensive and do not provide the more-geometric understanding derived from the depth-of-investigation (DOI) and drainage-volume calculations. We propose a novel approach for rapid field-scale performance assessment of shale-gas reservoirs. Our proposed approach is dependent on a high-frequency asymptotic solution of the diffusivity equation in heterogeneous reservoirs and serves as a bridge between simplified analytical tools and complex numerical simulation. The high-frequency solution leads to the Eikonal equation (Paris and Hurd 1969), which is solved for a “diffusive time of flight” (DTOF) that governs the propagation of the “pressure front” in the reservoir. The Eikonal equation can be solved by use of the fast-marching method (FMM) to determine the DTOF, which generalizes the concept of DOI to heterogeneous and fractured reservoirs. It provides an efficient means to calculate drainage volume, pressure depletion, and well performance and can be significantly faster than conventional numerical simulation. More importantly, in a manner analogous to streamline simulation, the DTOF can also be used as a spatial coordinate to reduce the 3D diffusivity equation to a 1D equation, leading to a comprehensive simulator for rapid performance prediction of shale-gas reservoirs. The speed and versatility of our proposed method makes it ideally suited for high-resolution reservoir characterization through integration of static and dynamic data. The major advantages of our proposed approach are its simplicity, intuitive appeal, and computational efficiency. We demonstrate the power and utility of our method by use of a field example that involves history matching, uncertainty analysis, and performance assessment of a shale-gas reservoir in east Texas. A sensitivity study is first performed to systematically identify the “heavy hitters” affecting the well performance. This is followed by history matching and an uncertainty analysis to identify the fracture parameters and the stimulated-reservoir volume. A comparison of model predictions with the actual well performance shows that our approach is able to reliably predict the pressure depletion and rate decline.
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Chen, Hongquan, Tsubasa Onishi, Jaeyoung Park, and Akhil Datta-Gupta. "Computing Pressure Front Propagation Using the Diffusive-Time-of-Flight in Structured and Unstructured Grid Systems via the Fast-Marching Method." SPE Journal 26, no. 03 (January 14, 2021): 1366–86. http://dx.doi.org/10.2118/201771-pa.
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Summary Diffusive-time-of-flight (DTOF), representing the travel time of pressure front propagation, has found many applications in unconventional reservoir performance analysis. The computation of DTOF typically involves upwind finite difference of the Eikonal equation and solution using the fast-marching method (FMM). However, the application of the finite difference-based FMM to irregular grid systems remains a challenge. In this paper, we present a novel and robust method for solving the Eikonal equation using finite volume discretization and the FMM. The implementation is first validated with analytical solutions using isotropic and anisotropic models with homogeneous reservoir properties. Consistent DTOF distributions are obtained between the proposed approach and the analytical solutions. Next, the implementation is applied to unconventional reservoirs with hydraulic and natural fractures. Our approach relies on cell volumes and connections (transmissibilities) rather than the grid geometry, and thus can be easily applied to complex grid systems. For illustrative purposes, we present applications of the proposed method to embedded discrete fracture models (EDFMs), dual-porosity dual-permeability models (DPDK), and unstructured perpendicular-bisectional (PEBI) grids with heterogeneous reservoir properties. Visualization of the DTOF provides flow diagnostics, such as evolution of the drainage volume of the wells and well interactions. The novelty of the proposed approach is its broad applicability to arbitrary grid systems and ease of implementation in commercial reservoir simulators. This makes the approach well-suited for field applications with complex grid geometry and complex well architecture.
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Cao, Fei, Haishan Luo, and Larry W. Lake. "Oil-Rate Forecast by Inferring Fractional-Flow Models From Field Data With Koval Method Combined With the Capacitance/Resistance Model." SPE Reservoir Evaluation & Engineering 18, no. 04 (November 25, 2015): 534–53. http://dx.doi.org/10.2118/173315-pa.
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Summary Many empirical and analytical models were developed to forecast oil production. Empirical models (including data-driven models) can, for example, find correlations between oil cut and production, but they lack explicit knowledge of the physical behavior. Classic analytical models are loyal to reservoir physics. Nevertheless, they often require estimation of water saturation as a function of time, which is difficult to obtain for multiwell reservoirs. It is desirable to combine advantages of both empirical and analytical models and develop a physical-model-based method that uses field data to infer oil rate. In this paper, we propose to infer fractional-flow models from field data by use of the Koval (1963) theory. We inversely solved the Koval fractional-flow equation to obtain a relationship between water cut and dimensionless time. By history matching field water-cut data, two model parameters, the Koval factor and the producer-drainage volume, are estimated. Nevertheless, it is challenging to use the Koval approach as a predictive model directly because the injection contribution into each producer in a future-time horizon must be evaluated first. To address this issue, we combine the Koval approach with the capacitance/resistance model (CRM), which characterizes the injector/producer connectivities and response time. The material balance of fluids is established in a producer-based drainage volume to consider the contributions from nearby injectors and the time lag in production caused by reservoir/fluids compressibility. A regression approach is simultaneously advanced to minimize the model error. Because of robustly integrating the reservoir physical behavior and the data-driven approach, the combination of the Koval theory and the CRM can result in a synergy that leads to accurate oil-rate predictions. We validated this integrated method in synthetic homogeneous and heterogeneous reservoirs to test its reliability, and further applied it to a field case in western Venezuela. Case studies demonstrate that one can use this integrated model as a real-time tool to characterize interwell connection and to predict future oil production accurately.
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Gates, Ian Donald, Joseph Kenny, Ivan Lazaro Hernandez-Hdez, and Gary L. Bunio. "Steam Injection Strategy and Energetics of Steam-Assisted Gravity Drainage." SPE Reservoir Evaluation & Engineering 10, no. 01 (February 1, 2007): 19–34. http://dx.doi.org/10.2118/97742-pa.
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Summary Steam-assisted gravity drainage (SAGD) is being operated by several operators in Athabasca and Cold Lake reservoirs in Central and Northern Alberta, Canada. In this process, steam, injected into a horizontal well, flows outward, then contacts and loses its latent heat to bitumen at the edge of a depletion chamber. As a consequence, the viscosity of bitumen falls, its mobility rises, and it flows under gravity toward a horizontal production well located several meters below and parallel to the injection well. Despite many pilots and commercial operations, it remains unclear how to optimally operate SAGD. This is especially the case in reservoirs with a top-gas zone in which pilot data are nearly nonexistent. In this study, a steam-chamber operating strategy is determined that leads to optimum oil recovery for a minimum cumulative steam-to-oil ratio (SOR) in a top-gas reservoir. These findings were established from extensive reservoir-simulation runs that were based on a detailed geostatistically generated static reservoir model. The strategy devised uses a high initial chamber injection rate and pressure prior to chamber contact with the top gas. Subsequent to breakthrough of the chamber into the gas-cap zone, the chamber injection rates are lowered to balance pressures with the top gas and avoid (or at least minimize) convective heat losses of steam to the top-gas zone. The results are also analyzed by examining the energetics of SAGD. Introduction A cross-section of the SAGD process is displayed in Fig. 1. Steam is injected into the formation through a horizontal well. In Fig. 1, the wells are portrayed as points that extend into the page. Around and above the injection well, a steam-depletion chamber grows. At the edge of the chamber, heated bitumen and (steam) condensate flow under the action of gravity to a production well typically placed between 5 and 10 m below and substantially parallel to the injection well. Usually, the production well is located several meters above the base of pay. In industrial practice (Singhal et al. 1998; Komery et al. 1999), injection and production well lengths are typically between 500 and 1000 m. Because the steam chamber operates at saturation conditions, the injection pressure controls the operating temperature of SAGD. SAGD has been piloted extensively in Athabasca and Cold Lake reservoirs in Alberta (Komery et al. 1999; Butler 1997; Kisman and Yeung 1995; Ito and Suzuki 1999; Ito et al. 2004; Edmunds and Chhina 2001; Suggett et al. 2000; Siu et al. 1991; AED 2004) and is being used as a commercial technology to recover bitumen in several Athabasca reservoirs (Yee and Stroich 2004). These pilots and commercial operations have demonstrated that SAGD is technically effective, but it has not been fully established whether its operating conditions are at optimum values. This is especially the case in reservoirs in contact with gas or water zones where the optimum operating strategy remains unclear. The variability of the cumulative injected-steam (expressed in cold water equivalents, or CWE) to produced-oil ratio (cSOR) shows that some SAGD well pairs operate fairly efficiently (with cSOR between 2 and 3), whereas others operate at much greater cSOR (up to 10 and higher) (Yee and Stroich 2004). Higher cSOR means that more steam is being used per unit volume bitumen produced. The higher the steam usage, the greater the amount of natural gas combusted, and the less economic the process. One key control variable in SAGD is the temperature difference between the injected steam and the produced fluids. This value, known as the subcool, is typically maintained in a form of steamtrap control between 15 and 30°C (Ito and Suzuki 1999). The subcool is being used as a surrogate variable instead of the height of liquid above the production well. The liquid pool above the production well prevents flow of injected steam directly from the injection well to the production well, thus promoting injected steam to the outer regions of the depletion chamber and enabling delivery of its latent heat to the bitumen. The value of the optimum steamtrap subcool temperature difference and how the operating pressure impacts the optimum subcool value remains unclear. It also remains unclear how the subcool should be controlled in heterogeneous reservoirs that have top gas.
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Lu, Cheng, Ling Chen, Xiaodong Wang, Wanjing Luo, Yue Peng, Yudong Cui, Lin Wang, and Bailu Teng. "A New Approach for Determining the Control Volumes of Production Wells considering Irregular Well Distribution and Heterogeneous Reservoir Properties." Geofluids 2021 (May 20, 2021): 1–13. http://dx.doi.org/10.1155/2021/6666831.
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The oil and gas fields are commonly developed with a group of production wells. Therefore, it can be essential for the industries to predict the performance of the production wells in order to optimize the development strategies. In practice, it frequently happens that we only hope to study the performance of a single production well. In such cases, it can be time consuming to run the reservoir simulation with the entire reservoir model to study the well performance. Hence, it can be preferred to determine the control volume (or drainage volume) of the target well from the entire reservoir and run the simulation with the small control volume to reduce the simulation cost. However, an irregular layout of the production wells and the heterogeneity of reservoir properties, which can be commonly observed in real field cases, can induce a stringent barrier for one to determine the control volumes. At present, we are still lacking a method to determine the control volumes of the production wells considering well distribution and reservoir heterogeneities. In order to overcome such a barrier, the authors proposed a new approach to divide the entire reservoir into small control volumes on the basis of the fast marching method (FMM). This approach is validated by comparing the simulation outputs of the target well calculated only with the determined control volume to those calculated with the entire reservoir model. The calculated results show that using the control volume that is determined with the proposed method to calculate the well performance can yield results that agree well with the results that are calculated with the entire reservoir model. This indicates that this proposed method is reliable to determine the control volume of the production wells. In addition, the calculated results in this work show that changing fracture length exerts a slight influence on the control volumes if the length of all fractures is increased, whereas, if only one of the fracture lengths is increased, the control volume of the corresponding well will be significantly increased. The number of the production wells and the distribution of the production well can noticeably influence the control volumes of the production wells. The findings of this study can help for optimizing the well spacing, estimating the ultimate recovery, and reducing the computational cost.
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Sarda, S., L. Jeannin, R. Basquet, and B. Bourbiaux. "Hydraulic Characterization of Fractured Reservoirs: Simulation on Discrete Fracture Models." SPE Reservoir Evaluation & Engineering 5, no. 02 (April 1, 2002): 154–62. http://dx.doi.org/10.2118/77300-pa.
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Summary Advanced characterization methodology and software are now able to provide realistic pictures of fracture networks. However, these pictures must be validated against dynamic data like flowmeter, well-test, interference-test, or production data and calibrated in terms of hydraulic properties. This calibration and validation step is based on the simulation of those dynamic tests. What has to be overcome is the challenge of both accurately representing large and complex fracture networks and simulating matrix/ fracture exchanges with a minimum number of gridblocks. This paper presents an efficient, patented solution to tackle this problem. First, a method derived from the well-known dual-porosity concept is presented. The approach consists of developing an optimized, explicit representation of the fractured medium and specific treatments of matrix/fracture exchanges and matrix/matrix flows. In this approach, matrix blocks of different volumes and shapes are associated with each fracture cell depending on the local geometry of the surrounding fractures. The matrix-block geometry is determined with a rapid image-processing algorithm. The great advantage of this approach is that it can simulate local matrix/fracture exchanges on large fractured media in a much faster and more appropriate way. Indeed, the simulation can be carried out with a much smaller number of cells compared to a fully explicit discretization of both matrix and fracture media. The proposed approach presents other advantages owing to its great flexibility. Indeed, it accurately handles the cases in which flows are not controlled by fractures alone; either the fracture network may be not hydraulically connected from one well to another, or the matrix may have a high permeability in some places. Finally, well-test cases demonstrate the reliability of the method and its range of application. Introduction In recent years, numerous research programs have been focusing on the topic of fractured reservoirs. Major advances were made, and oil companies now benefit from efficient methodologies, tools, and software for fractured reservoir studies. Nowadays, a study of a fractured reservoir, from fracture detection to full-field simulation, includes the following main steps: geological fracture characterization, hydraulic characterization of fractures, upscaling of fracture properties, and fractured reservoir simulation. Research on fractured reservoir simulation has a long history. In the early 1960s, Barenblatt and Zheltov1 first introduced the dual-porosity concept, followed by Warren and Root,2 who proposed a simplified representation of fracture networks to be used in dual-porosity simulators. Based on this concept, reservoir simulators3 are now able to correctly reproduce the main driving mechanisms occurring in fractured reservoirs, such as water imbibition, gas/oil and water/oil gravity drainage, molecular diffusion, and convection in fractures. Even single-medium simulators can perform fractured reservoir simulation when adequate pseudocapillary pressure curves and pseudorelative permeability curves can be input. Indeed, except for particular cases such as thermal recovery processes, full-field simulation of fractured reservoirs is no longer a problem. Geological characterization of fractures progressed considerably in the 1990s. The challenge was to analyze and integrate all the available fracture data to provide a reliable description of the fracture network both at field scale and at local reservoir cell scale. Tools have been developed for merging seismic, borehole imaging, lithological, and outcrop data together with the help of geological and geomechanical rules.3 These tools benefited from the progress of seismic acquisition and borehole imaging. Indeed, accurate seismic data lead to reliable models of large-scale fracture networks, and borehole imaging gives the actual fracture description along the wells, which enables a reliable statistical determination of fracture attributes. Finally, these tools provide realistic pictures of fracture networks. They are applied successfully in numerous fractured-reservoir studies. The upscaling of fracture properties is the problem of translating the geological description of fracture networks into reservoir simulation parameters. Two approaches are possible. In the first one, the fractured reservoir is considered as a very heterogeneous matrix reservoir; therefore, one applies the classical techniques available for heterogeneous single-medium upscaling. The second approach is based on the dual-porosity concept and consists of upscaling the matrix and the fracture separately. Based on this second approach, methodologies and software were developed in the 1990s to calculate equivalent fracture parameters with respect to the dual-porosity concept (i.e., a fracture-permeability tensor with main flow directions and anisotropy and a shape factor that controls the matrix/fracture exchange kinetics3–5). For a given reservoir grid cell, the upscaling procedures consist of generating the corresponding 3D discrete fracture network and computing the equivalent parameters from this network. In particular, the permeability tensor is computed from the results of steady-state flow simulations in the discrete fracture network alone (without the matrix).
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Cui, Jingyuan, Changdong Yang, Ding Zhu, and Akhil Datta-Gupta. "Fracture Diagnosis in Multiple-Stage-Stimulated Horizontal Well by Temperature Measurements With Fast Marching Method." SPE Journal 21, no. 06 (August 3, 2016): 2289–300. http://dx.doi.org/10.2118/174880-pa.
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Summary Downhole-temperature measurement is one of the solutions to understanding downhole-flow conditions, especially in complex well/reservoir domains such as multistage-fractured horizontal wells. In the past, models and methodologies have been developed for fracture diagnosis for multiple-stage-fractured horizontal wells. They are based either on a semianalytical approach for simplicity or on reservoir simulation for generality. The challenges are that semianalytical models are not robust enough to describe complex fracture systems, whereas numerical simulation is computationally expensive and impractical for inversion. To develop a comprehensive approach to translate temperature to flow profile, we adopted the fast marching method (FMM) in simulating both heat transfer and the velocity/pressure field in the interested domain (heterogeneous reservoir with multiple-fractured horizontal wells). FMM is a new approach that is efficient in front tracking. Previous studies show a significant success in the investigation of pressure-depletion behavior and shale-gas production-history match. By the nature of heat transfer in porous media, the thermal-front propagation would lag behind pressure, and the noticeable temperature change in the reservoir only happens near hydraulic/natural fractures. FMM can be used to efficiently track the heat front that is associated with the flow field. In this study, we solve the thermal model in porous media by transforming the general energy-balance equation into a 1D equation, with the diffusive time of flight (DTOF) as the spatial coordinate system. Besides the diffusive heat conduction, the convection, Joule-Thomson effect, and viscous dissipation are considered in the model. The inner boundary of the model is carefully handled, and the drainage volume of each fracture is calculated to identify different inflow temperature related to flow rate at perforation locations. The model was validated by the finite-difference approach. Examples are presented in the paper to illustrate the application of the new method. The approach can be used to quantitatively interpret temperature measurements to fracture profiles in horizontal wells.
Dissertations / Theses on the topic "Drainage Volume in Heterogeneous Reservoirs"
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Kang, Suk Sang 1975. "Model Calibration, Drainage Volume Calculation and Optimization in Heterogeneous Fractured Reservoirs." Thesis, 2012. http://hdl.handle.net/1969.1/148064.
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We propose a rigorous approach for well drainage volume calculations in gas reservoirs based on the flux field derived from dual porosity finite-difference simulation and demonstrate its application to optimize well placement. Our approach relies on a high frequency asymptotic solution of the diffusivity equation and emulates the propagation of a 'pressure front' in the reservoir along gas streamlines. The proposed approach is a generalization of the radius of drainage concept in well test analysis (Lee 1982), which allows us not only to compute rigorously the well drainage volumes as a function of time but also to examine the potential impact of infill wells on the drainage volumes of existing producers. Using these results, we present a systematic approach to optimize well placement to maximize the Estimated Ultimate Recovery.
A history matching algorithm is proposed that sequentially calibrates reservoir parameters from the global-to-local scale considering parameter uncertainty and the resolution of the data. Parameter updates are constrained to the prior geologic heterogeneity and performed parsimoniously to the smallest spatial scales at which they can be resolved by the available data. In the first step of the workflow, Genetic Algorithm is used to assess the uncertainty in global parameters that influence field-scale flow behavior, specifically reservoir energy. To identify the reservoir volume over which each regional multiplier is applied, we have developed a novel approach to heterogeneity segmentation from spectral clustering theory. The proposed clustering can capture main feature of prior model by using second eigenvector of graph affinity matrix.
In the second stage of the workflow, we parameterize the high-resolution heterogeneity in the spectral domain using the Grid Connectivity based Transform to severely compress the dimension of the calibration parameter set. The GCT implicitly imposes geological continuity and promotes minimal changes to each prior model in the ensemble during the calibration process. The field scale utility of the workflow is then demonstrated with the calibration of a model characterizing a structurally complex and highly fractured reservoir.
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Gupta, Neha 1986. "A Novel Approach for the Rapid Estimation of Drainage Volume, Pressure and Well Rates." Thesis, 2012. http://hdl.handle.net/1969.1/148380.
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For effective reservoir management and production optimization, it is important to understand drained volumes, pressure depletion and reservoir well rates at all flow times. For conventional reservoirs, this behavior is based on the concepts of reservoir pressure and energy and convective flow. But, with the development of unconventional reservoirs, there is increased focus on the unsteady state transient flow behavior. For analyzing such flow behaviors, well test analysis concepts are commonly applied, based on the analytical solutions of the diffusivity equation. In this thesis, we have proposed a novel methodology for estimating the drainage volumes and utilizing it to obtain the pressure and flux at any location in the reservoir.
The result is a semi-analytic calculation only, with close to the simplicity of an analytic approach, but with significantly more generality. The approach is significantly faster than a conventional finite difference solution, although with some simplifying assumptions. The proposed solution is generalized to handle heterogeneous reservoirs, complex well geometries and bounded and semi-bounded reservoirs. Therefore, this approach is particularly beneficial for unconventional reservoir development with multiple transverse fractured horizontal wells, where limited analytical solutions are available.
To estimate the drainage volume, we have applied an asymptotic solution to the diffusivity equation and determined the diffusive time of flight distribution. For the pressure solution, a geometric approximation has been applied within the drainage volume to reduce the full solution of the diffusivity equation to a system of decoupled ordinary differential equations. Besides, this asymptotic expression can also be extended to obtain the well rates, producing under constant bottomhole pressure constraint.
In this thesis, we have described the detailed methodology and its validation through various case studies. We have also studied the limits of validity of the approximation to better understand the general applicability. We expect that this approach will enable the inversion of field performance data for improved well and/or fracture characterization, and similarly, the optimization of well trajectories and fracture design, in an analogous manner to how rapid but approximate streamline techniques have been used for improved conventional reservoir management.
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Kumar, Dhananjay. "Modeling steam assisted gravity drainage in heterogeneous reservoirs using different upscaling techniques." Thesis, 2014. http://hdl.handle.net/2152/26441.
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This thesis presents different methods that improve the ability to relate the flow properties of heterogeneous reservoirs to equivalent anisotropic flow properties in order to predict the performance of the Steam Assisted Gravity Drainage (SAGD) process. Process simulation using full scale heterogeneous reservoirs are inefficient and so the need arises to develop equivalent anisotropic reservoirs that can capture the effect of reservoir heterogeneity. Since SAGD is highly governed by permeability in the reservoir, effective permeability values were determined using different upscaling techniques. First, a flow-based upscaling technique was employed and a semi-analytical model, derived by Azom and Srinivasan, was used to determine the accuracy of the upscaling. The results indicated inadequacy of flow-based upscaling schemes to derive effective direction permeabilities consistent with the unique flow geometry during the SAGD process. Subsequently, statistical upscaling was employed using full 3D models to determine relationships between the heterogeneity variables: k[subscript italic v]⁄k[subscript italic h] , correlation length and shale proportion. An iterative procedure coupled with an optimization algorithm was deployed to determine optimal k[subscript italic v] and k[subscript italic k] values. Further regression analysis was performed to explore the relationship between the variables of shale heterogeneity in a reservoir and the corresponding effective properties. It was observed that increased correlation lengths and shale proportions both decrease the dimensionless flow rates at given dimensionless times and that the semi-analytical model was more accurate for cases that contained lower shale proportions. Upscaled heterogeneous values inputted into the semi-analytical model resulted in underestimation of oil flow rate due to the inability to fully account for the impact of reservoir barriers and the configuration of flow streamlines during the SAGD process. Statistical upscaling using geometric averaging as the initial guess was used as the basis for developing a relationship between correlation length, shale proportion and k[subscript italic v]⁄k[subscript italic h]. The initial regression models did not accurately predict the anisotropic ratio because of insufficient data points along the regression surface. Subsequently a non-linear regression model that was 2nd order in both length and shale proportion was calibrated by executing more cases with varying levels of heterogeneity and the regression model revealed excellent matches to heterogeneous models for the prediction cases.text
Book chapters on the topic "Drainage Volume in Heterogeneous Reservoirs"
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Da Silva, J. "Optimization of concrete gravity dams foundation drainage systems." In Dams and Reservoirs, Societies and Environment in the 21st Century, Two Volume Set, 633–39. CRC Press, 2006. http://dx.doi.org/10.1201/b16818-100.
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Román, A., and A. Gonzalo. "New technologies in the rehabilitation of the drainage network in dams." In Dams and Reservoirs, Societies and Environment in the 21st Century, Two Volume Set, 545–51. CRC Press, 2006. http://dx.doi.org/10.1201/b16818-87.
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Wilson, Edith Newton, W. Lynn Watney, and G. Michael Grammer. "An Overview of the Giant Heterogeneous Mississippian Carbonate System of the Midcontinent: Ancient Structure, Complex Stratigraphy, Conventional Traps, and Unconventional Technology in a High Fluid Volume World." In Mississippian Reservoirs of the Midcontinent, 1–23. The American Association of Petroleum Geologists, 2019. http://dx.doi.org/10.1306/13632140m1163784.
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Van Rompaey, A., and G. Govers. "Assessing the Impacts of Land Use Policy on Soil Erosion Risk." In Environmental Information Systems in Industry and Public Administration, 146–56. IGI Global, 2001. http://dx.doi.org/10.4018/978-1-930708-02-0.ch008.
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Soil erosion is regarded as a major and widespread soil degradation process. The consequences of soil erosion occur both on- and off-site. On-site consequences are particularly important on agricultural land where the redistribution of soil within a field, the loss of soil from a field, the breakdown of soil structure and the decline in organic matter and nutrients result in a reduction of the cultivable soil depth and a decline in soil fertility (Morgan, 1996). Off-site problems result from sedimentation downstream which reduces the capacity of rivers and drainage ditches, enhances the risk of flooding, blocks irrigation canals and shortens the design life of reservoirs (Verstraeten and Poesen, 1999). Sediment is also a pollutant in its own right, and through the chemicals absorbed it can increase the levels of nitrogen and phosphorus in water bodies and result in eutrophication (Steegen et al., subm.). The rate of soil loss is normally expressed in units of mass or volume per unit area per unit time. Young (1969) quotes annual rates of the order of 0.0045 Mg ha-1 for areas of moderate relief and 0.45 Mg ha-1 for steep relief. For comparison, rates from agricultural land are in the range of 5 to 500 Mg ha-1 (Morgan, 1996; Van Rompaey et al., 2000).
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Ortloff, Charles R. "Ancient South-East Asia." In Water Engineering in the Ancient World. Oxford University Press, 2009. http://dx.doi.org/10.1093/oso/9780199239092.003.0006.
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Cambodia is situated in southeast Asia on the coast of the Gulf of Thailand and shares borders with Vietnam to the east, Thailand to the west, and Laos to the north. Lake Tonle Sap occupies ~2.5% of Cambodia’s land area and plays a vital role in the rice agriculture of the country. The total cultivatable area is about 2.1 million hectares, of which 1.8 million is devoted to rice agriculture. The growing season is largely coupled to the monsoon cycles: the bimodal wet season starts in May and ends in October with peaks in June and September/ October resulting from diVerent rainfall origins. Rainfall levels vary around the country: although average levels are about 1.5 m, amounts vary from about 1.0m at Svay Check in the western province of Banteay Meanchey to nearly 4.7m in the southern province of Kampot. The Tonle Sap River reverses flow twice each year: from July to October, water flows into Tonle Sap Lake from branches of the Mekong River, swelling its area from 2,600 to 10,500 km<sup>2</sup>; in November when the flow rate of the Mekong River decreases, the Tonle Sap River reverses flow and water flows into the Mekong once again. Since 85% of Cambodia’s land area is included in the Mekong River basin, river water levels coupled to groundwater levels play a role in agricultural systems. The dry season from November to April requires irrigation to support rice agriculture making water storage and high groundwater levels important. Based on recent research (FAO 2005), the net renewable water balance (volume in flows minus volume) is equal to about 120km<sup>3</sup> with about 18 km<sup>3</sup> stored in groundwater reduced by 13 km<sup>3</sup> per year by river drainage. Of the total amount of water withdrawal per year (520_10<sup>6</sup>m<sup>3</sup>), about 94% is devoted to agriculture; given the dependence on rice farming through the ages, it is likely that a similar percentage was used for agriculture in ancient times as now to support like-sized agrarian populations. In the 10th to 14th centuries ce, Angkor’s water supply system was based on four (baray) reservoirs (not all functioning simultaneously) with a total capacity of 100–150_10<sup>6</sup>m<sup>3</sup>.
Conference papers on the topic "Drainage Volume in Heterogeneous Reservoirs"
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Faerstein, Marcos, Paulo Couto, and José Alves. "A Comprehensive Approach for Assessing the Impacts of Wettability on Oil Production in Carbonate Reservoirs." In ASME 2012 31st International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/omae2012-84219.
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This paper discusses the impacts that rock wettability may have upon the production and recovery of oil with waterflooding in carbonate reservoirs and how it should be modeled. A broad review of the state of the art has been conducted surveying existing disagreements and knowledge gaps, basic definitions, as well as the correct understanding of the physical phenomena and identification of the characteristics of the various wettability scenarios. Case studies conducted with a black oil reservoir simulator evaluated the impact of different wettability scenarios on oil production and recovery. A comprehensive approach considering all the parameters involved in the wettability modeling was applied to the case studies, showing how the behavior of the reservoir varies as a function of their wettability. This paper shows how relative permeability and capillary pressure should be varied to correctly represent different wettability scenarios and consequently assess its impacts on oil production and recovery. The case studies show that the evaluation of the volume of oil in the reservoir is impacted by wettability through the irreducible water saturation and primary drainage capillary pressure and must be considered in the analyses. In long term analyses, mixed-wet scenarios have a higher oil production and recovery. In medium and short term, the water-wet scenarios have the higher recovery, but in relation to oil production, these scenarios are negatively influenced by the smaller volume of oil in place. The main contribution of this paper is the simultaneous analyses of all the parameters involved in the modeling of wettability showing how they impact the behavior of a reservoir. It shows how the parameters must be varied in a heterogeneous reservoir and how heterogeneity impacts the relevance of wettability in the studies.
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Hassan, Amro, Ahmed Abd ElMeguid, Arshad Waheed, Mohamed Salah, and Essam Abd ElKarim. "Multistage Horizontal Well Hydraulic Fracturing Stimulation Using Coiled Tubing to Produce Marginal Reserves from Brownfield: Case Histories and Lessons Learned." In SPE Middle East Unconventional Resources Conference and Exhibition. SPE, 2015. http://dx.doi.org/10.2118/spe-172933-ms.
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Abstract The Baharyia formation is a common reservoir in the Western Desert of Egypt. It is characterized as a heterogeneous reservoir with low sand quality. It is comprised of fine-grained sandstone, thin, laminated, sand-poor parasequences with shale interbeds. The heterogeneity and low permeability of the Upper Baharyia reservoirs are the primary challenges to maintaining economic well productivity. The interest in developing low permeability reservoirs stems from favorable economics attributed to advancements in horizontal well drilling and hydraulic fracturing technology, offering methods to increase production by increasing the contact area of the producing interval. Subsequently, it became apparent that wellbore contact alone was not always sufficient for providing production increases expected, thus requiring multistage hydraulic fracturing (MSHF) stimulation treatments to achieve production targets. Primary well production analysis revealed that the cumulative production from the horizontal well discussed was enhanced from 37 to 70% of recoverable reserve and the recovery factor was doubled. From a production analogy standpoint, these resulted in reduced drilling of three vertical wells and had direct economic benefits by reducing the installed artificial lift strings, related expensive artificial lift equipment repairs, and the number of necessary workovers. This paper takes a multidisciplinary approach to help understand productivity enhancement of low permeability reservoirs in the Western Desert of Egypt, through a detailed analysis of well performance and successful implementation of MSHF in horizontal wells to maximize drainage volume around the well. It is intended to serve as guidelines to help operators facing similar challenges.
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Moshir Farahi, M. M., and A. Mamghaderi. "Sensitivity Analysis of Immiscible Forced Gravity Drainage Process in Heterogeneous Reservoirs." In 79th EAGE Conference and Exhibition 2017. Netherlands: EAGE Publications BV, 2017. http://dx.doi.org/10.3997/2214-4609.201701350.
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Sunde, Arild, Her-Yuan Chen, and Lawrence W. Teufel. "Producing Characteristics and Drainage Volume of Dakota Reservoirs, San Juan Basin, New Mexico." In SPE Rocky Mountain Regional/Low-Permeability Reservoirs Symposium and Exhibition. Society of Petroleum Engineers, 2000. http://dx.doi.org/10.2118/60288-ms.
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Tchelepi, H. A., P. Jenny, S. H. Lee, and C. Wolfsteiner. "An Adaptive Multiphase Multiscale Finite Volume Simulator for Heterogeneous Reservoirs." In SPE Reservoir Simulation Symposium. Society of Petroleum Engineers, 2005. http://dx.doi.org/10.2118/93395-ms.
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Yang, Changdong, Xu Xue, Jixiang Huang, Akhil Datta-Gupta, and Michael J. King. "Rapid Refracturing Candidate Selection in Shale Reservoirs Using Drainage Volume and Instantaneous Recovery Ratio." In Unconventional Resources Technology Conference. Tulsa, OK, USA: American Association of Petroleum Geologists, 2016. http://dx.doi.org/10.15530/urtec-2016-2459368.
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Martey, Amarquaye, and Joseph Otevwemerhuere. "Optimizing Hydrocarbon Volume Analysis in Heterogeneous Reservoirs in the Niger Delta." In Nigeria Annual International Conference and Exhibition. Society of Petroleum Engineers, 2009. http://dx.doi.org/10.2118/129578-ms.
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Al-Mudhafar, Watheq J., and Dandina N. Rao. "Proxy-Based Metamodeling Optimization of the Gas-Assisted Gravity Drainage GAGD Process in Heterogeneous Sandstone Reservoirs." In SPE Western Regional Meeting. Society of Petroleum Engineers, 2017. http://dx.doi.org/10.2118/185701-ms.
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Kang, Suksang, Akhil Datta-Gupta, and William John Lee. "Impact of Natural Fractures in Drainage Volume Calculations and Optimal Well Placement in Tight Gas Reservoirs." In North American Unconventional Gas Conference and Exhibition. Society of Petroleum Engineers, 2011. http://dx.doi.org/10.2118/144338-ms.
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Sehbi, Baljit S., Suksang Kang, Akhil Datta-Gupta, and W. John Lee. "Optimizing Fracture Stages and Completions in Horizontal Wells in Tight Gas Reservoirs Using Drainage Volume Calculations." In North American Unconventional Gas Conference and Exhibition. Society of Petroleum Engineers, 2011. http://dx.doi.org/10.2118/144365-ms.
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