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1
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.
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Takbiri-Borujeni, Ali, Vahid Mohammadnia, Mahdi Mansouri-Boroujeni, Hossein Nourozieh, and Payam Kavousi Ghahfarokhi. "Upscaling the Steam-Assisted-Gravity-Drainage Model for Heterogeneous Reservoirs." SPE Journal 24, no. 04 (May 27, 2019): 1681–99. http://dx.doi.org/10.2118/195587-pa.
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Summary The effects of heterogeneities in the rock and fluid properties on the governing equations in modeling the steam-assisted-gravity-drainage (SAGD) process are investigated using a spectrum-based upscaling approach. In this approach, heterogeneity is included by assigning random perturbation fields to permeability and thermal diffusivity that hold the assumption of first and second orders of stationarity. Heat and mass-transport parameters and dependent variables (e.g., temperature and viscosity) that are affected by heterogeneity are represented by their mean and perturbations around the mean values. Substituting the perturbed variables and coefficients into the basic governing equations (heat-diffusion and Darcy equations) results in new sets of stochastic partial-differential equations that include mean and perturbation. Mean equations are essentially upscaled new governing equations that include the autocorrelations and cross correlations between different perturbed quantities. The cross correlations are derived by applying the Fourier-Stieltjes transform. Verification and validation of the developed results for the heat-diffusion equation are performed using numerical simulations with synthetic heterogeneities. The upscaled equations embrace the heterogeneity in permeability and thermal diffusivity and can predict the flow rate and shape of the steam chamber. The upscaled model is compared with the homogeneous model, developed by Butler (1991), to quantify the effects of heterogeneities in permeability and thermal diffusivity on the SAGD efficiency. A case is studied by assigning harmonic distribution to the perturbations of thermal diffusivity and permeability. Different cases with different relationships between permeability and thermal-diffusivity fields are considered to investigate their effects on the oil flow rate. The results show that local perturbations decrease the oil flow rate. Furthermore, steam-chamber growth is retarded in a reservoir with local perturbations compared with homogeneous reservoirs. The developed model can be used in the initial stages of SAGD development projects for long-range planning as a guide to find the upper and lower limits of production in reservoirs with heterogeneities.
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Davydova, Yana, Yulia Volkova, Aleksandr Nikonorov, and Maksim Aleksandrovskiy. "Drainage of Small Volume Reservoirs on the Technogenic Territories." MATEC Web of Conferences 170 (2018): 02025. http://dx.doi.org/10.1051/matecconf/201817002025.
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The development of residential construction on alluvial territories requires high-quality engineering background in the initial stages of development. In the area with high ground moisture, the erection of buildings is difficult and drainage measures are required. The necessity to choose the method of wastewater disposal on alluvial territories has become an urgent problem, because the quality and operational characteristics of the construction depend on the correct engineering preparation of the territory, as well as the stability and capital of the buildings and structures being erected. The purpose of the work was to develop a method for the diversion of water from undesirable small reservoirs of anthropogenic origin. Approbation of method was carried out on the example of a temporary reservoir formed on the territory of a residential complex of the wash-up area of the Vasilievsky Island, St. Petersburg, where engineering training is intensively underway. The implementation of proposed method is stated.
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Fujita, Yusuke, Akhil Datta-Gupta, and Michael J. King. "A Comprehensive Reservoir Simulator for Unconventional Reservoirs That Is Based on the Fast Marching Method and Diffusive Time of Flight." SPE Journal 21, no. 06 (May 5, 2016): 2276–88. http://dx.doi.org/10.2118/173269-pa.
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Summary Modeling of fluid flow in unconventional reservoirs requires accurate characterization of complex flow mechanisms because of the interactions between reservoir rock, microfractures, and hydraulic fractures. The pore-size distribution in shale and tight sand reservoirs typically ranges from nanometers to micrometers, resulting in ultralow permeabilities. In such extremely low-permeability reservoirs, desorption and diffusive processes play important roles in addition to heterogeneity-driven convective flows. For modeling shale and tight oil and gas reservoirs, we can compute the well-drainage volume efficiently with a fast marching method (FMM) and by introducing the concept of “diffusive time of flight” (DTOF). Our proposed simulation approach consists of two decoupled steps—drainage-volume calculation and numerical simulation with DTOF as a spatial coordinate. We first calculate the reservoir drainage volume and the DTOF with the FMM, and then the numerical simulation is conducted along the 1D DTOF coordinate. The approach is analogous to streamline modeling whereby a multidimensional simulation is decoupled to a series of 1D simulations resulting in substantial savings in computation time for high-resolution simulation. However, instead of a “convective time of flight” (CTOF), a DTOF is introduced to model the pressure-front propagation. For modeling physical processes, we propose triple continua whereby the reservoir is divided into three different domains: microscale pores (hydraulic fractures and microfractures), nanoscale pores (nanoporous networks), and organic matter. The hydraulic fractures/microfractures primarily contribute to the well production, and are affected by rock compaction. The nanoporous networks contain adsorbed gas molecules, and gas flows into fractures by convection and Knudsen diffusion processes. The organic matter acts as the source of gas. Our simulation approach enables high-resolution flow characterization of unconventional reservoirs because of its efficiency and versatility. We demonstrate the power and utility of our approach with synthetic and field examples.
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Schoof, Christian. "An analysis of instabilities and limit cycles in glacier-dammed reservoirs." Cryosphere 14, no. 9 (September 18, 2020): 3175–94. http://dx.doi.org/10.5194/tc-14-3175-2020.
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Abstract. Glacier lake outburst floods are common glacial hazards around the world. How big such floods can become (either in terms of peak discharge or in terms of total volume released) depends on how they are initiated: what causes the runaway enlargement of a subglacial or other conduit to start the flood, and how big can the lake get before that point is reached? Here we investigate how the spontaneous channelization of a linked-cavity drainage system can control the onset of floods. In agreement with previous work, we show that floods only occur in a band of water throughput rates in which steady reservoir drainage is unstable, and we identify stabilizing mechanisms that allow steady drainage of an ice-dammed reservoir. We also show how stable limit cycle solutions emerge from the instability and identify parameter regimes in which the resulting floods cause flotation of the ice dam. These floods are likely to be initiated by flotation rather than the unstable enlargement of a distributed drainage system.
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Diachkov, A. A. "APPROACHES TO ESTIMATING OF POTENTIAL PRODUCTIVITY OF TEXTURE-HETEROGENEOUS RESERVOIRS." Oil and Gas Studies, no. 5 (October 30, 2018): 51–57. http://dx.doi.org/10.31660/0445-0108-2018-5-51-57.
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The article analyses reservoir properties of Jurassic sediments, where there is textural non-uniformity, and estimates the role of laminated clay volume in determining the calculation parameters. The forecast of flow rates and comparison with actual data of wells operation are produced with the counting of adjusted values of permeability and thickness. It is recommended to carry out the tuning of the hydrodynamical model taking into account the division of the phase permeability by layered clay. According to the results of the performed work we can expect that complete analysis of well testing data and the core materials will allow increasing technological efficiency.
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Yang, Changdong, Vishal Kumar Sharma, Akhil Datta-Gupta, and Michael J. King. "Novel approach for production transient analysis of shale reservoirs using the drainage volume derivative." Journal of Petroleum Science and Engineering 159 (November 2017): 8–24. http://dx.doi.org/10.1016/j.petrol.2017.09.041.
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Wang, Jingyi, and Ian Gates. "Identifying Reservoir Features via iSOR Response Behaviour." Energies 14, no. 2 (January 14, 2021): 427. http://dx.doi.org/10.3390/en14020427.
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To extract viscous bitumen from oil sands reservoirs, steam is injected into the formation to lower the bitumen’s viscosity enabling sufficient mobility for its production to the surface. Steam-assisted gravity drainage (SAGD) is the preferred process for Athabasca oil sands reservoirs but its performance suffers in heterogeneous reservoirs leading to an elevated steam-to-oil ratio (SOR) above that which would be observed in a clean oil sands reservoir. This implies that the SOR could be used as a signature to understand the nature of heterogeneities or other features in reservoirs. In the research reported here, the use of the SOR as a signal to provide information on the heterogeneity of the reservoir is explored. The analysis conducted on prototypical reservoirs reveals that the instantaneous SOR (iSOR) can be used to identify reservoir features. The results show that the iSOR profile exhibits specific signatures that can be used to identify when the steam chamber reaches the top of the formation, a lean zone, a top gas zone, and shale layers.
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Xin, Xiankang, Gaoming Yu, Zhangxin Chen, Keliu Wu, Xiaohu Dong, and Zhouyuan Zhu. "Effect of Polymer Degradation on Polymer Flooding in Heterogeneous Reservoirs." Polymers 10, no. 8 (August 2, 2018): 857. http://dx.doi.org/10.3390/polym10080857.
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Polymer degradation is critical for polymer flooding because it can significantly influence the viscosity of a polymer solution, which is a dominant property for polymer enhanced oil recovery (EOR). In this work, physical experiments and numerical simulations were both used to study partially hydrolyzed polyacrylamide (HPAM) degradation and its effect on polymer flooding in heterogeneous reservoirs. First, physical experiments were conducted to determine basic physicochemical properties of the polymer, including viscosity and degradation. Notably, a novel polymer dynamic degradation experiment was recommended in the evaluation process. Then, a new mathematical model was proposed and an in-house three-dimensional (3D) two-phase polymer flooding simulator was designed to examine both polymer static and dynamic degradation. The designed simulator was validated by comparison with the simulation results obtained from commercial software and the results from the polymer flooding experiments. This simulator further investigated and validated polymer degradation and its effect. The results of the physical experiments showed that the viscosity of a polymer solution increases with an increase in polymer concentration, demonstrating their underlying power law relationship. Moreover, the viscosity of a polymer solution with the same polymer concentration decreases with an increase in the shear rate, demonstrating shear thinning. Furthermore, the viscosity of a polymer solution decreased with an increase in time due to polymer degradation, exhibiting an exponential relationship. The first-order dynamic degradation rate constant of 0.0022 day−1 was greater than the first-order static degradation rate constant of 0.0017 day−1. According to the simulation results for the designed simulator, a 7.7% decrease in oil recovery, after a cumulative injection volume of 1.67 pore volume (PV) was observed between the first-order dynamic degradation rate constants of 0 and 0.1 day−1, which indicates that polymer degradation has a detrimental effect on polymer flooding efficiency.
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Yuan, Bin, Zhenzihao Zhang, and Christopher R. Clarkson. "Improved Distance-of-Investigation Model for Rate-Transient Analysis in a Heterogeneous Unconventional Reservoir With Nonstatic Properties." SPE Journal 24, no. 05 (July 2, 2019): 2362–77. http://dx.doi.org/10.2118/191698-pa.
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Summary The concept of distance of investigation (DOI) has been widely applied in rate– and pressure–transient analysis for estimating reservoir properties and for optimizing hydraulic fracturing. Despite its successful application in conventional reservoirs, significant errors arise when extending the concept to unconventional reservoirs. This work aims to clearly demonstrate such errors when using the traditional square–root–of–time model for DOI calculations in unconventional reservoirs, and to develop new models to improve the DOI calculations. In this work, the following mechanisms in unconventional reservoirs are first incorporated into the calculation of DOI: (1) pressure–dependency of rock and fluid properties; (2) continuous/discontinuous spatial variation of reservoir properties. To achieve this, pseudopressure, pseudotime, and pseudodistance are introduced to linearize the diffusivity equation. Two novel methods are developed for calculating DOI: one using the concept of continuous succession of steady states, and the other using the concept of dynamic drainage area (DDA). Both models are verified using a series of fine–grid numerical simulations. A production–data–analysis workflow using the new DOI models is proposed to analytically characterize reservoir heterogeneity and fracture properties. The new DOI models compensate for the inability of the traditional square–root–of–time model to capture spatial and temporal variations of reservoir and fluid properties. The pressure–dependency of fluids and reservoirs (i.e., fluid density, fluid viscosity, rock permeability, and rock porosity) and reservoir heterogeneities (i.e., deterioration of reservoir quality from the primary fracture to the reservoir) can significantly retard the propagation of the DOI. Another important outcome of this work is to provide a practical and analytical approach to directly estimate the spatial heterogeneity from the production history of field cases.
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Hird, K. B., and Olivier Dubrule. "Quantification of Reservoir Connectivity for Reservoir Description Applications." SPE Reservoir Evaluation & Engineering 1, no. 01 (February 1, 1998): 12–17. http://dx.doi.org/10.2118/30571-pa.
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Summary This study investigates means for efficiently estimating reservoir performance characteristics of heterogeneous reservoir descriptions with reservoir connectivity parameters. We use simulated primary and waterflood performance for two-dimensional (2D) vertical, two- and three-phase, black oil reservoir systems to identify and quantify spatial characteristics that control well performance. The reservoir connectivity parameters were found to correlate strongly with secondary recovery efficiency and drainable hydrocarbon pore volume. We developed methods for estimating primary recovery and water breakthrough time for a waterflood. We can achieve this estimation with three to five orders of magnitude less computational time than required for comparable flow simulations. Introduction Several geostatistical methods have been developed over the past decade for generating fine-scale, heterogeneous reservoir descriptions. These methods have become popular because of their ability to model heterogeneities, quantify uncertainties, and integrate various data types. However, the quality of results obtained with these stochastic methods is strongly dependent on the underlying assumed model. Reservoir heterogeneities will not be modeled correctly if the appropriate scales of heterogeneities are not considered. Uncertainties in future reservoir performance will not be quantified if the entire range of critical spatial characteristics are not explored. Simulated reservoir performance will not match historical performance if the appropriate data constraints are not imposed. The likelihood of using an inappropriate model can be greatly reduced if production data is integrated into the reservoir description process. This is because production data is influenced by those heterogeneities that impact future rates and recoveries. This paper investigates the applicability of using reservoir connectivity characteristics based on static reservoir properties as predictors of reservoir performance. We investigate two types of reservoir connectivity-based parameters. These connectivity parameters were developed to estimate secondary recovery efficiency and drainable hydrocarbon pore volume (HCPV). We use 2D vertical cross sections in the study. Previous work1–3 investigated the correlation of spatial reservoir parameters on reservoir performance for 2D areal reservoir descriptions. We first describe the general procedure. We then follow with definitions, more specific procedure details, and a discussion of the results for the two reservoir characteristics investigated. General Method We generated sets of permeability realizations, each set honoring at least the "conventional" geostatistical constraints (i.e., the univariate permeability distribution, the permeability variogram, and the wellblock permeabilities). We used simulated annealing4–6 to generate the permeability realizations and a linear porosity vs. log (permeability) relationship to obtain porosity values at each gridblock location. Porosity and permeability were the only heterogeneous reservoir properties considered during the study; reservoir thickness was assumed to be a constant. We performed all the flow simulations at the same scale as the permeability conditional simulations. The two- and three-phase black oil flow simulations were run with Amoco's in-house flow simulator, GCOMP,7 on a Sun SPARC 10 workstation.8 We used flow simulation results and analytical calculations to determine water breakthrough time (tBt) and ultimate primary oil recovery. The results for each flow simulation were plotted vs. values of various spatial permeability and porosity-based parameters. We identified the spatial parameter having the strongest correlation with each simulated performance data type. Recovery Efficiency Definitions. Secondary recovery efficiency is considered to be impacted by interwell reservoir connectivity characteristics. However, reservoir connectivity can be defined many different ways. A method has been reported that uses horizontal and vertical permeability thresholds to transform permeabilities to binary values.9 The least resistive paths are determined by finding the minimum distance required to move from one surface (i.e., a set of adjacent gridblocks) to another, for example, from an injector to a producer. We used a binary indicator approach to simplify the computations, thus resulting in an extremely fast connectivity algorithm. However, the success of the method is dependent on the applicability of the designated cutoff values. Such an approach would be most successful for systems comprised of two rock types (e.g., clean sand and shale), each having a small variance but significantly different means. The permeability distributions used in the present study do not fit in this category. Thus, attempts to correlate secondary recovery efficiency variables with the indicator-based connectivity parameters were unsuccessful. We concluded that a more sophisticated connectivity definition, accounting for actual permeability values, was needed to better quantify interwell reservoir connectivity. As a result of further investigation, the following connectivity parameter was developed for 2D cross sections: where IRe(i, k) is the secondary recovery efficiency "resistivity index" at gridblock (i, k), ?L is the distance between the centers of adjacent gridblocks, ka is the average absolute directional permeability between two adjacent gridblocks, krw(i) is the estimated relative permeability to water for the ith column, and A is the cross-sectional area perpendicular to the direction of movement. For a horizontal step, ?L/A=?Lx/?Lz, whereas for a vertical step, ?L/A=?Lz/?Lx . The resistivity index parameter is derived from the analogy between Darcy's law for linear, single-phase fluid flow, and Ohm's law for linear electric current where I is the electrical current, ?E is the voltage drop, and R is the electrical resistance. Inspection of Eqs. 2 and 3 shows that the permeance of the fluid system, kA/µL, is analogous to the reciprocal of the electrical resistance. Eq. 1 is the multiphase flow equivalent of the reciprocal of the permeance, dropping the viscosity constant µ.
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Guérillot, Dominique, and Jérémie Bruyelle. "Transmissibility Upscaling on Unstructured Grids for Highly Heterogeneous Reservoirs." Water 11, no. 12 (December 15, 2019): 2647. http://dx.doi.org/10.3390/w11122647.
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One critical point of modeling of flow in porous media is the capacity to consider parameters that are highly variable in space. It is then very challenging to simulate numerically fluid flow on such heterogeneous porous media. The continuous increase in computing power makes it possible to integrate smaller and smaller heterogeneities into geological models of up to tens of millions of cells. On such meshes, despite computer performance, multi-phase flow equations cannot be solved in an acceptable time for hydrogeologists and reservoir engineers, especially when the modeling considers several components in each fluid and when taking into account rock-fluid interactions. Taking average reservoir properties is a common approach to reducing mesh size. During the last decades, many authors studied the upscaling topic. Two different ways have been investigated to upscale the absolute permeability: (1) an average of the permeability for each cell, which is then used for standard transmissibility calculation, or (2) computing directly the upscaled transmissibility values using the high-resolution permeability values. This paper is related to the second approach. The proposed method uses the half-block approach and combines the finite volume principles with algebraic methods to provide an upper and a lower bound of the upscaled transmissibility values. An application on an extracted map of the SPE10 model shows that this approach is more accurate and faster than the classical transmissibility upscaling method based on flow simulation. This approach keeps the contrast of transmissibility values observed at the high-resolution geological scale and improves the accuracy of field-scale flow simulation for highly heterogeneous reservoirs. Moreover, the upper and lower bounds delivered by the algebraic method allow checking the quality of the upscaling and the gridding.
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Xie, Jiang, Changdong Yang, Neha Gupta, Michael J. King, and Akhil Datta-Gupta. "Integration of Shale-Gas-Production Data and Microseismic for Fracture and Reservoir Properties With the Fast Marching Method." SPE Journal 20, no. 02 (July 23, 2014): 347–59. http://dx.doi.org/10.2118/161357-pa.
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Summary We present a novel approach to calculate drainage volume and well performance in shale gas reservoirs by use of the fast marching method (FMM) combined with a geometric pressure approximation. Our approach can fully account for complex fracture-network geometries associated with multistage hydraulic fractures and their impact on the well pressure and rates. The major advantages of our proposed approach are its simplicity, intuitive appeal, and computational efficiency. For example, we can compute and visualize the time evolution of the well-drainage volume for multimillion-cell geologic models in seconds without resorting to reservoir simulation. A geometric approximation of the drainage volume is then used to compute the well rates and the reservoir pressure. The speed and versatility of our proposed approach make it ideally suited for parameter estimation by means of the inverse modeling of shale-gas performance data. We use experimental design to perform the sensitivity analysis to identify the “heavy hitters” and a genetic algorithm (GA) to calibrate the relevant fracture and matrix parameters in shale-gas reservoirs by history matching of production data. In addition to the production data, microseismic information is used to help us constrain the fracture extent and orientation and to estimate the stimulated reservoir volume (SRV). The proposed approach is applied to a fractured shale-gas well. The results clearly show reduced ranges in the estimated fracture parameters and SRV, leading to improved forecasting and reserves estimation.
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Amirian, Ehsan, Juliana Y. Leung, Stefan Zanon, and Peter Dzurman. "Integrated cluster analysis and artificial neural network modeling for steam-assisted gravity drainage performance prediction in heterogeneous reservoirs." Expert Systems with Applications 42, no. 2 (February 2015): 723–40. http://dx.doi.org/10.1016/j.eswa.2014.08.034.
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Kang, SukSang, Akhil Datta-Gupta, and W. John Lee. "Impact of natural fractures in drainage volume calculations and optimal well placement in tight gas reservoirs." Journal of Petroleum Science and Engineering 109 (September 2013): 206–16. http://dx.doi.org/10.1016/j.petrol.2013.08.024.
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Wang, Zhenzhen, Andrew Malone, and Michael J. King. "Quantitative production analysis and EUR prediction from unconventional reservoirs using a data-driven drainage volume formulation." Computational Geosciences 24, no. 2 (July 17, 2019): 853–70. http://dx.doi.org/10.1007/s10596-019-09833-8.
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Fu, Suotang, Wenxiong Wang, Xianwen Li, Shengli Xi, Xifeng Hu, and Yanming Zhang. "Volume fracturing and drainage technologies for low-pressure marine shale gas reservoirs in the Ordos Basin." Natural Gas Industry B 8, no. 4 (August 2021): 317–24. http://dx.doi.org/10.1016/j.ngib.2021.07.001.
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Zhao, Lisha, Li Li, Zhongbao Wu, and Chenshuo Zhang. "Analytical Model of Waterflood Sweep Efficiency in Vertical Heterogeneous Reservoirs under Constant Pressure." Mathematical Problems in Engineering 2016 (2016): 1–9. http://dx.doi.org/10.1155/2016/6273492.
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An analytical model has been developed for quantitative evaluation of vertical sweep efficiency based on heterogeneous multilayer reservoirs. By applying the Buckley-Leverett displacement mechanism, a theoretical relationship is deduced to describe dynamic changes of the front of water injection, water saturation of producing well, and swept volume during waterflooding under the condition of constant pressure, which substitutes for the condition of constant rate in the traditional way. Then, this method of calculating sweep efficiency is applied from single layer to multilayers, which can be used to accurately calculate the sweep efficiency of heterogeneous reservoirs and evaluate the degree of waterflooding in multilayer reservoirs. In the case study, the water frontal position, water cut, volumetric sweep efficiency, and oil recovery are compared between commingled injection and zonal injection by applying the derived equations. The results are verified by numerical simulators, respectively. It is shown that zonal injection works better than commingled injection in respect of sweep efficiency and oil recovery and has a longer period of water free production.
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Logan, W. D., J. P. Horkowitz, Robert Laronga, and D. W. Cromwell. "Practical Application of NMR Logging in Carbonate Reservoirs." SPE Reservoir Evaluation & Engineering 1, no. 05 (October 1, 1998): 438–48. http://dx.doi.org/10.2118/51329-pa.
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This paper (SPE 51329) was revised for publication from paper SPE 38740, first presented at the 1997 SPE Annual Technical Conference & Exhibition, San Antonio, Texas, 5-8 October. Original manuscript received for review 7 October 1997. Revised manuscript received 1 June 1998. Paper peer approved 15 June 1998. Summary Nuclear magnetic resonance (NMR) data acquisition and interpretation in carbonate reservoirs is much more challenging than in sandstones, where it is a well-established technology. Heterogeneous porosity distribution, a broad range of pore sizes, a wide variety of complex textures, and low surface relaxivity combine to complicate the picture considerably. The successful practical application of NMR in these reservoirs requires the development of acquisition and interpretation techniques specifically suited to the task. In carbonate reservoirs dominated by intercrystalline or intergranular porosity, NMR can deliver accurate estimates of porosity, permeability, bound fluid volume, and residual oil saturation (ROS). In heterogeneous carbonate reservoirs more complex interpretation models are required, normally based on the integration of whole core and log data. NMR answer products, based on these new techniques, are presented and validated with core data and by comparison with other logging measurements. P. 438
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Medeiros, Flavio, Erdal Ozkan, and Hossein Kazemi. "Productivity and Drainage Area of Fractured Horizontal Wells in Tight Gas Reservoirs." SPE Reservoir Evaluation & Engineering 11, no. 05 (October 1, 2008): 902–11. http://dx.doi.org/10.2118/108110-pa.
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Summary 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. Introduction Economic gas and oil production from low permeability reservoirs has been a challenge for the oil and gas industry. Because most of the high permeability reservoirs have been exploited and many low permeability reservoirs remain undeveloped, the latter have taken the industry attention recently. Particular attention has been given to tight-gas reservoirs with permeability in the range of micro-Darcies or below and to oil accumulation in fractured shale. Hydraulically fractured horizontal wells are the proven technology to produce oil and gas from tight formations. Hydraulic fractures reduce well drawndown, increase the productivity of horizontal wells by increasing the surface area in contact with formation, and provide high conductivity paths to the wellbore. Depending on in-situ stress orientation, hydraulic fractures can be parallel (longitudinal) or perpendicular (transverse) to horizontal well axis. Project economics in tight formations, however, depends strongly on well spacing and the number of hydraulic fractures required to drain the reservoir efficiently. Field evidence indicates that the drainage areas of fractured horizontal wells in tight formations may be limited to a rectangular region confining the horizontal well and the transverse hydraulic fractures. Also, there has been evidence that hydraulic fracturing in tight formations changes stresses in fracture drainage area, which could create or rejuvenate natural fractures in the near-vicinity of the horizontal well. This fracture network, which may be characterized as a dual-porosity system, may contribute significantly to improve productivity of the fractured horizontal well. Much work has been done (Soliman et al. 1990; Larsen and Hegre 1994; Temeng and Horne 1995; Raghavan et al. 1997; Wan and Aziz 1999; Al-Kobaisi et al. 2006) to investigate pressure-transient analysis and short- and long-term productivity of horizontal wells with single or multiple hydraulic fractures. The effect of a dual-porosity zone surrounding hydraulic fractures, however, has not been considered in the previous studies. The main objective of this study is to investigate the combined effects of a dual-porosity region and hydraulic fractures on the productivity of horizontal wells. The results presented in this work are based on a semianalytical model developed by Medeiros et al. (2006). The model was derived from the Green's function formulation of the solution for the diffusivity equation (Gringarten and Ramey, 1974, Ozkan and Raghavan, 1991a, 1991b) and has the capability to incorporate local heterogeneities. In this work, we use the semianalytical model to incorporate induced finite-conductivity fractures (transverse and longitudinal) along the horizontal well and naturally fractured zones around the hydraulically fractured horizontal well by using the dual-porosity idealization. We use the example data sets given in Tables 1 through 3 to consider different cases of horizontal wells with and without induced and natural fractures.
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Shapiro, Serge A., Elmar Rothert, Volker Rath, and Jan Rindschwentner. "Characterization of fluid transport properties of reservoirs using induced microseismicity." GEOPHYSICS 67, no. 1 (January 2002): 212–20. http://dx.doi.org/10.1190/1.1451597.
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We systematically describe an approach to estimate the large‐scale permeability of reservoirs using seismic emission (microseismicity) induced by fluid injection. We call this approach seismicity‐based reservoir characterization (SBRC). A simple variant of the approach is based on the hypothesis that the triggering front of hydraulically‐induced microseismicity propagates like a diffusive process (pore pressure relaxation) in an effective homogeneous anisotropic poroelastic fluid‐saturated medium. The permeability tensor of this effective medium is the permeability tensor upscaled to the characteristic size of the seismically active heterogeneous rock volume. We show that in a homogeneous medium the surface of the seismicity triggering front has the same form as the group‐velocity surface of thelow‐frequency anisotropic, second‐type Biots wave describing kinematic aspects of triggering‐front propagation in a way similar to the eikonal equation for seismic wavefronts. In the case of isotropic heterogeneous media, the inversion for the hydraulic properties of rocks follows from a direct application of this equation. In the case of an anisotropic heterogeneous medium, only the magnitude of a global effective permeability tensor can be mapped in a 3‐D spatial domain. We demonstrate the method on several field examples and also test the eikonal equation‐based inversion.
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Lee, Eui Hoon, Young Hwan Choi, and Joong Hoon Kim. "Real-Time Integrated Operation for Urban Streams with Centralized and Decentralized Reservoirs to Improve System Resilience." Water 11, no. 1 (January 2, 2019): 69. http://dx.doi.org/10.3390/w11010069.
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Recently, the number of extreme rainfall events has increased because of climate change. The ever-widening impervious area in urban watersheds also continuously augments runoff volume. Most measures to prevent urban inundation are structural, such as the construction, rehabilitation, and replacement of urban drainage facilities. Because structural measures require time and money, nonstructural measures are also required for the efficient prevention of urban inundation. Current operations in Korea focus on the individual operation of urban drainage facilities while neglecting the status of effluent streams. A study on urban drainage facilities that considers the status of urban streams is necessary to improve the operation of drainage facilities in urban areas. A revised resilience index is suggested to evaluate measures. For the historical rainfall event in 2010, the system resilience for current and integrated operations was 0.199 and 0.238, respectively. For the 2011 event, the system resilience for current and integrated operations was 0.064 and 0.235, respectively. The integrated operation exhibited good performance for the 2010 and 2011 events. Based on the results of this study, an operation as a nonstructural measure for the total management of urban areas is proposed. The revised resilience index could support decision-making processes for flood-management plans.
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Zheng, Da, Bin Yuan, and Rouzbeh G. Moghanloo. "Analytical modeling dynamic drainage volume for transient flow towards multi-stage fractured wells in composite shale reservoirs." Journal of Petroleum Science and Engineering 149 (January 2017): 756–64. http://dx.doi.org/10.1016/j.petrol.2016.11.023.
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Shan, Xiaocai, Fei Tian, Fuqi Cheng, Changchun Yang, and Wei Xin. "Spectral Decomposition and a Waveform Cluster to Characterize Strongly Heterogeneous Paleokarst Reservoirs in the Tarim Basin, China." Water 11, no. 2 (February 1, 2019): 256. http://dx.doi.org/10.3390/w11020256.
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The main components of the Ordovician carbonate reservoirs in the Tahe Oilfield are paleokarst fracture-cavity paleo-channel systems formed by karstification. Detailed characterization of these paleokarst reservoirs is challenging because of heterogeneities in characteristics and strong vertical and lateral non-uniformities. Traditional seismic analysis methods are not able to solve the identification problem of such strongly heterogeneous reservoirs. Recent developments in seismic interpretation have heightened the need to describe the fracture-cavity structure of a paleo-channel with more accuracy. We propose a new prediction model for fracture-cavity carbonate reservoirs based on spectral decomposition and a waveform cluster. By the Matching Pursuit decomposition algorithm, the single-frequency data volumes are obtained. The specific frequency data volume that is the most sensitive to the reservoir is chosen based on seismic synthesis traces of well-logging data and geological interpretability. The waveform cluster is then applied to delineate the complex paleokarst systems, particularly the fracture-caves in the runoff zone. This method was applied to the area around Well T615 in the Tahe oilfield, and a paleokarst fracture-cavity system with strong heterogeneity in the runoff zone was delineated and characterized. The findings of this research provide insights for predicting other similar karst systems, such as karstic groundwater and karst hydrogeological systems.
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Bhagwat, Tejas, Igor Klein, Juliane Huth, and Patrick Leinenkugel. "Volumetric Analysis of Reservoirs in Drought-Prone Areas Using Remote Sensing Products." Remote Sensing 11, no. 17 (August 22, 2019): 1974. http://dx.doi.org/10.3390/rs11171974.
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Globally, the number of dams increased dramatically during the 20th century. As a result, monitoring water levels and storage volume of dam-reservoirs has become essential in order to understand water resource availability amid changing climate and drought patterns. Recent advancements in remote sensing data show great potential for studies pertaining to long-term monitoring of reservoir water volume variations. In this study, we used freely available remote sensing products to assess volume variations for Lake Mead, Lake Powell and reservoirs in California between 1984 and 2015. Additionally, we provided insights on reservoir water volume fluctuations and hydrological drought patterns in the region. We based our volumetric estimations on the area–elevation hypsometry relationship, by combining water areas from the Global Surface Water (GSW) monthly water history (MWH) product with corresponding water surface median elevation values from three different digital elevation models (DEM) into a regression analysis. Using Lake Mead and Lake Powell as our validation reservoirs, we calculated a volumetric time series for the GSWMWH–DEMmedian elevation combinations that showed a strong linear ‘area (WA) – elevation (WH)’ (R2 > 0.75) hypsometry. Based on ‘WA-WH’ linearity and correlation analysis between the estimated and in situ volumetric time series, the methodology was expanded to reservoirs in California. Our volumetric results detected four distinct periods of water volume declines: 1987–1992, 2000–2004, 2007–2009 and 2012–2015 for Lake Mead, Lake Powell and in 40 reservoirs in California. We also used multiscalar Standardized Precipitation Evapotranspiration Index (SPEI) for San Joaquin drainage in California to assess regional links between the drought indicators and reservoir volume fluctuations. We found highest correlations between reservoir volume variations and the SPEI at medium time scales (12–18–24–36 months). Our work demonstrates the potential of processed, open source remote sensing products for reservoir water volume variations and provides insights on usability of these variations in hydrological drought monitoring. Furthermore, the spatial coverage and long-term temporal availability of our data presents an opportunity to transfer these methods for volumetric analyses on a global scale.
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Jain, Tarang, Rajan G. Patel, and Japan Trivedi. "Application of polynomial chaos theory as an accurate and computationally efficient proxy model for heterogeneous steam-assisted gravity drainage reservoirs." Energy Science & Engineering 5, no. 5 (October 2017): 270–89. http://dx.doi.org/10.1002/ese3.177.
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Gallardo, Enrique, and Clayton V. Deutsch. "Approximate Physics-Discrete Simulation of the Steam-Chamber Evolution in Steam-Assisted Gravity Drainage." SPE Journal 24, no. 02 (December 31, 2018): 477–91. http://dx.doi.org/10.2118/194016-pa.
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Summary Steam-assisted gravity drainage (SAGD) is a thermal-recovery process to produce bitumen from oil sands. In this technology, steam injected in the reservoir creates a constantly evolving steam chamber while heated bitumen drains to a production well. Understanding the geometry and the rate of growth of the steam chamber is necessary to manage an economically successful SAGD project. This work introduces an approximate physics-discrete simulator (APDS) to model the steam-chamber evolution. The algorithm is formulated and implemented using graph theory, simplified porous-media flow equations, heat-transfer concepts, and ideas from discrete simulation. The APDS predicts the steam-chamber evolution in heterogeneous reservoirs and is computationally efficient enough to be applied over multiple geostatistical realizations to support decisions in the presence of geological uncertainty. The APDS is expected to be useful for selecting well-pair locations and operational strategies, 4D-seismic integration in SAGD-reservoir characterization, and caprock-integrity assessment.
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Leung, Juliana Y., and Sanjay Srinivasan. "Analysis of Uncertainty Introduced by Scaleup of Reservoir Attributes and Flow Response in Heterogeneous Reservoirs." SPE Journal 16, no. 03 (June 16, 2011): 713–24. http://dx.doi.org/10.2118/145678-pa.
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Summary Reservoir heterogeneities occur over a wide range of length scales, and their interaction with various transport mechanisms controls the performance of subsurface flow and transport processes. Modeling these processes at large scales requires proper scaleup of petrophysical properties that are autocorrelated or heterogeneously distributed in space, and analyzing their interaction with underlying transport mechanisms. A method is proposed to investigate and quantify the uncertainty in reservoir models introduced by scaleup. It is demonstrated that when the volume support of the measurement is smaller than the representative elementary volume (REV) scale of the attribute to be modeled, there is uncertainty in the conditioning data because of scaleup and that uncertainty has to be propagated to spatial models for the attribute. This important consideration is demonstrated for mapping total porosity for a carbonate reservoir in the Gulf of Mexico. The results demonstrate that in most cases, the uncertainty distributions obtained by accounting for the scaleup procedure successfully characterize the variability in the actual core and log data observed along new wells. Conventional reservoir models considering the well data as "hard" conditioning data fail to predict the "true" values. Following this discussion on scaling of reservoir attributes, a conceptual understanding of the scaling characteristics of flow responses such as recovery factor (RF) is provided, in terms of the mean and variance of RF at different length scales. Finally, a new technique is presented to systematically quantify the scaling characteristics of transport processes by accounting for subscale heterogeneities and their interaction with various transport mechanisms based on the volume averaging approach. The objective is to provide a tool for understanding the scaling relationships for RF using detailed fine-scale compositional reservoir simulations over a subdomain of the reservoir.
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Ozkan, E., M. Brown, R. Raghavan, and H. Kazemi. "Comparison of Fractured-Horizontal-Well Performance in Tight Sand and Shale Reservoirs." SPE Reservoir Evaluation & Engineering 14, no. 02 (March 29, 2011): 248–59. http://dx.doi.org/10.2118/121290-pa.
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Summary This paper presents a discussion of fractured-horizontal-well performance in millidarcy permeability (conventional) and micro- to nanodarcy permeability (unconventional) reservoirs. It provides interpretations of the reasons to fracture horizontal wells in both types of formations. The objective of the paper is to highlight the special productivity features of unconventional shale reservoirs. By using a trilinear-flow model, it is shown that the drainage volume of a multiple-fractured horizontal well in a shale reservoir is limited to the inner reservoir between the fractures. Unlike conventional reservoirs, high reservoir permeability and high hydraulic-fracture conductivity may not warrant favorable productivity in shale reservoirs. An efficient way to improve the productivity of ultratight shale formations is to increase the density of natural fractures. High natural-fracture conductivities may not necessarily contribute to productivity either. Decreasing hydraulic-fracture spacing increases the productivity of the well, but the incremental production gain for each additional hydraulic fracture decreases. The trilinear-flow model presented in this work and the information derived from it should help the design and performance prediction of multiple-fractured horizontal wells in shale reservoirs.
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Nouri, H., S. Beecham, A. M. Hassanli, and G. Ingleton. "Variability of drainage and solute leaching in heterogeneous urban vegetation environs." Hydrology and Earth System Sciences 17, no. 11 (November 1, 2013): 4339–47. http://dx.doi.org/10.5194/hess-17-4339-2013.
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Abstract. Deep percolation enhancement from recycled wastewater irrigation may contribute to salt accumulation and water table elevation that can ultimately cause soil and ground water degradation. Variation of drainage rate and solute leaching were investigated in an urban park containing heterogeneous landscape plants that were irrigated with recycled wastewater. Field monitoring was undertaken at Veale Gardens in the Adelaide Parklands, Australia. Based on landscape variation in Veale Gardens, two landscape zones were defined: one being largely covered with turf grasses with few trees and shrubs (MG) with the second zone being mostly trees and shrubs with intermittent turf grasses (MT). Experiments were performed on two zero-tension lysimeters placed horizontally 100 cm below ground to monitor the variation of volume and quality indicators of drained water for four seasons. The outcomes showed a significant variation of drainage quantity and quality in the MT and MG zones. The low vegetation cover in the MG zone resulted in more drained water than in the high vegetation cover (MT zone). In both zones, more drainage water was collected in winter than in other seasons. This is in spite of the input water showing a maximum rate in summer. The seasonal salinities measured in the two lysimeters showed very similar trends with the lowest salinity rate in autumn with the levels increasing through winter and spring. Chemical analyses of leachate solute and salt loading indicated no impact from using recycled wastewater.
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Ma, Hongfei, Wenqi Zhao, Meng Sun, Xiaodong Wang, Lun Zhao, Chunmei Zou, and Bo Wang. "Productivity Analysis of Volume Fractured Wells under Different Working Systems." Geofluids 2021 (April 22, 2021): 1–21. http://dx.doi.org/10.1155/2021/5593663.
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The volume fracturing technique has been widely used to improve the productivity of ultralow-permeability reservoirs. This paper presents a new semianalytical model to simulate the pressure transient and production behaviour of finite conductivity vertical fractured wells with stimulated reservoir volume (SRV) in heterogeneous reservoirs. The model is based on the five-linear flow model, the Warren-Root model, and fracture conductivity influence function. The model is validated by comparing its results with a numerical model. One novelty of this model is its consideration of three different kinds of production prediction models. Constant rate, constant pressure, and compound working systems are taken into account. This paper illustrates the effects of the SRV size and shape, mobility ratio, initial flow rate, limiting wellbore pressure, and hydraulic fracture parameters under different working systems. Results show that the SRV and parameters of fractures have a significant influence on long-term well performance. Moreover, the initial rate can extend the constant rate period by 418%, and limiting wellbore pressure can effectively improve the cumulative recovery rate by 23%. Therefore, this model can predict long-term wells’ behaviour and provide practical guiding significance for hydraulic fracturing design.
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Irrgang, H. R. "EVALUATION AND MANAGEMENT OF THIN OIL COLUMN RESERVOIRS IN AUSTRALIA." APPEA Journal 34, no. 1 (1994): 64. http://dx.doi.org/10.1071/aj93005.
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Thin oil columns represent a common and important class of hydrocarbon reserve which are notoriously difficult to evaluate and produce. This paper provides case studies of examples of these reservoirs in Australia and summarises the production methods, well performance and recovery efficiencies.Thin oil column reservoirs are defined here as reservoirs which will cone both water and gas when produced at commercial rates. The oil zone can have a pancake or rim geometry. Examples within Australia include Bream and Snapper (Gippsland Basin), South Pepper and Chervil (Carnarvon Basin), Chookoo (Eromanga Basin) and Taylor (Surat Basin).Parameters which are particularly important in defining the performance of these reservoirs are: horizontal and vertical permeability, column height, stratigraphie dip, well spacing, and oil viscosity. High horizontal permeability is more critical than in other reservoir types as it controls the effectiveness of gravitational forces in opposing coning and other unwanted flows by reducing pressure gradients. Low vertical permeability mitigates coning but can limit across strike drainage in dipping strata. Oil viscosity is also particularly important, even when the mobility ratio is favourable, as it controls the gas/oil ratio and water cut during coning.As coning (by definition) is inevitable the key production issue is gas cap management. The main options are:Limit gas coning by controlling completion depth and production rates.Allow gas cap shrinkage and 'chase' the oil column upwards via recompletions.Reinject gas to control gas-oil contact position.For the latter two options in particular, ultimate reserves are a strong function of the capacity of the installed production facilities, especially offshore, where fixed operating costs are high. When gas cap management is not compromised, reserves increase with higher total fluid withdrawal rates. Examples of the various gas cap management and production strategies are included.Both horizontal (South Pepper, Bream) and conventional (Chookoo, Taylor) completion techniques have been applied to thin oil column reservoirs in Australia. Horizontal completions can increase productivity, mitigate coning and increase the well drainage areas (particularly if drilled across dip in heterogeneous reservoirs). However, horizontal completions are particularly vulnerable to poor cement jobs, natural fractures and undesirable fluid contact movements.A variety of other completion techniques have been tried worldwide in thin oil columns with mixed success. These include multiple completions in the water, oil and/or gas to allow separate production, and injection of fluids to make permeability barriers or alter relative permeability.A number of scaling rules are included to assist in using offset field data for evaluation of thin oil column reservoirs. Improved understanding of these complex reservoirs will maximise their economic potential.
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Tao, Honghua, Liehui Zhang, Qiguo Liu, Qi Deng, Man Luo, and Yulong Zhao. "An Analytical Flow Model for Heterogeneous Multi-Fractured Systems in Shale Gas Reservoirs." Energies 11, no. 12 (December 6, 2018): 3422. http://dx.doi.org/10.3390/en11123422.
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The use of multiple hydraulically fractured horizontal wells has been proven to be an efficient and effective way to enable shale gas production. Meanwhile, analytical models represent a rapid evaluation method that has been developed to investigate the pressure-transient behaviors in shale gas reservoirs. Furthermore, fractal-anomalous diffusion, which describes a sub-diffusion process by a non-linear relationship with time and cannot be represented by Darcy’s law, has been noticed in heterogeneous porous media. In order to describe the pressure-transient behaviors in shale gas reservoirs more accurately, an improved analytical model based on the fractal-anomalous diffusion is established. Various diffusions in the shale matrix, pressure-dependent permeability, fractal geometry features, and anomalous diffusion in the stimulated reservoir volume region are considered. Type curves of pressure and pressure derivatives are plotted, and the effects of anomalous diffusion and mass fractal dimension are investigated in a sensitivity analysis. The impact of anomalous diffusion is recognized as two opposite aspects in the early linear flow regime and after that period, when it changes from 1 to 0.75. The smaller mass fractal dimension, which changes from 2 to 1.8, results in more pressure and a drop in the pressure derivative.
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Lee. "Advanced Operating Technique for Centralized and Decentralized Reservoirs Based on Flood Forecasting to Increase System Resilience in Urban Watersheds." Water 11, no. 8 (July 24, 2019): 1533. http://dx.doi.org/10.3390/w11081533.
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The frequency of inundation in urban watersheds has increased, and structural measures have been conducted to prevent flood damage. The current non-structural measures for complementing structural measures are mostly independent non-structural measures. Unlike the current non-structural measures, the new operating technique based on flood forecasting is a real-time mixed measure, which means the combination of different non-structural measures. Artificial rainfall events based on the Huff distribution were used to generate preliminary and dangerous thresholds of flood forecasting. The new operation for centralized and decentralized reservoirs was conducted by two thresholds. The new operation showed good performance in terms of flooding and resilience based on historical rainfall events in 2010 and 2011. The flooding volume in the new operation decreased from 6617 to 3368 m3 compared to the current operation in 2010, and the flooding volume in 2011 decreased from 664 to 490 m3. In the 2010 event, the results of resilience were 0.831835 and 0.866566 in current and new operations, respectively. The result of resilience increased from 0.988823 to 0.993029 in the 2011 event. This suggestion can be applied to operating facilities in urban drainage systems and might provide a standard for the design process of urban drainage facilities.
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Charles, D. D., H. H. Rieke, and R. Purushothaman. "Well-Test Characterization of Wedge-Shaped, Faulted Reservoirs." SPE Reservoir Evaluation & Engineering 4, no. 03 (June 1, 2001): 221–30. http://dx.doi.org/10.2118/72098-pa.
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Summary Two offshore, wedge-shaped reservoirs in south Louisiana were interpreted with pressure-buildup responses by comparing the results from simulated finite-element model studies. The importance of knowing the correct reservoir shape, and how it is used to interpret the generated boundary-pressure responses, is briefly discussed. Two different 3D computer models incorporating different wedge-shaped geometries simulated the test pressure-buildup response patterns. Variations in the two configurations are topologically expressed as a constant thickness and a nonconstant thickness, with smooth-surface, wedged-shaped reservoir models. The variable-thickness models are pinched-out updip at one end and faulted at the other end. Numerical well-test results demonstrated changes in the relationships between the pressure-derivative profile, the wellbore location, and the extent of partial penetration in the reservoir models. The wells were placed along the perpendicular bisector (top view) at distances starting from the apex at 5, 10, 20, 40, 50, 60, 80, and 90% of the reservoir length. Results demonstrate that boundary distance identification (such as distance, number, and type) based solely on the log-log derivative profile in rectangular and triangular wedge-shaped reservoirs should be strongly discouraged. Partial-penetration effects (PPE's) in wedge-shaped reservoirs are highly dependent on the wellbore location relative to the wedge, and the well-test-data analysis becomes more complex. Introduction The interpretation of the effect of reservoir shape on pressure-transient well-test data needs improvement. It is economically imperative to be able to generate an accurate estimate of reserves and producing potential. This is especially critical for independent operators who wish to participate in deepwater opportunities in the Gulf of Mexico. Proper interpretation of data extracted from cost-effective well tests is an integral part of describing, evaluating, and managing such reservoirs. Well-test information such as average reservoir pressure, transmissivity, pore volume, storativity, formation damage, deliverability, distance to the boundary, and completion efficiency are some of the technical inputs into economic and operational decisions. Several key economic decisions that operators have to make are:Should the reservoir be exploited?How many wells are needed to develop the reservoir?Is artificial lift necessary (and if so, when)? The identification of morphological demarcation components such as impermeable barriers (faults, intersecting faults, facies changes, erosional unconformities, and structural generated depositional pinchouts) and constant-pressure boundaries (aquifer or gas-cap) from well testing help to establish the reservoir boundaries, shape, and volume. One must remember that the geological entrapment structure or sedimentological body does not always define the reservoir's limits. Our present study provides insight into wedge-shaped reservoirs in the Gulf of Mexico. Seismic exploration can define geological shapes in either two or three dimensions in the subsurface. These shapes are expressions of the preserved structural history and depositional environments and are verified by observations of such structures in outcrops and present-day depositional environments. From a sedimentological viewpoint, the following sedimentary deposits can exhibit wedge-shaped geometries. Preserved barchan sand dunes, reworked transgressive sands, barrier-island sands, offshore bars, alluvial fan deposits, delta-front sheet sands, and lenticular channel sands form the more plausible pinchout, wedge-shaped geological models recognized in the Gulf of Mexico sedimentary sequence. Wedge-Shaped Reservoirs Reviewing the petroleum engineering literature, we found very few technical papers addressing wedge-shaped reservoir geometries and their effects on reservoir performance. Their detailed analytical results are discussed and applied to the interpretations of our model results. An overview of the conceptual models is presented as a quick orientation to emphasize some model issues. Horne and Temeng1 were the first to address the problem of recognizing, discriminating, and locating reservoir pinchouts with the Green's functions method proposed by Gringarten and Ramey2 in pressure-transient analysis. The analytical solution considered a dimensionless penetration depth of the well. Their results showed that pinchout boundaries appear similar to constant-pressure boundaries with respect to pressure-drawdown behavior and not as a perpendicular sealing boundary. Yaxley3 presented a set of simple equations for calculating the stabilized inflow performance of a well in infinite rectangular and wedge-shaped drainage systems. The basis for Yaxley's mathematical model is the application of transient linear flow (as opposed to radial flow conditions assumed for the reservoir) and the mathematical difference between a plane source and a line source in linear-flow drainage systems for various rectangular drainage shapes. The equations were derived from transient linear-flow relationships for a well located between parallel no-flow boundaries. This concept was applied to intersecting no-flow boundaries and an outer circular, no-flow, constant-pressure boundary. His approach involved a constant ßr that is interpreted as an extra pressure drop relative to a well of radius ro (radial distance to the well location), which is a result of the distortion of the radial streamline pattern. Chen and Raghavan4 developed a solution to compute pressure distributions in wedge-shaped drainage systems using Laplace transforms. Their mathematical approach overcame existing limitations in some of the previous solutions, which were mentioned earlier. By applying the inversion theorem to the Laplace transformation, they verified that the slope of the pressure profile is inversely proportional to the wedge angle of the drainage system. An examination of their results is important to the interpretation of our own simulated pressure-response issues. Generally, their model solutions showed three radial-flow periods in the absence of wellbore-storage effects. The radial-flow periods showed that:During an initial radial-flow period, neither of the impermeable boundaries registered either singly or jointly.In the second phase, one or two boundaries became evident on the pressure signature.A third radial-flow period exhibited a semi logarithmic slope proportional to p/?o, where ?o=the angle of the wedge.
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Zhang, Wenjuan, and Mohammed Al Kobaisi. "A two-step finite volume method for the simulation of multiphase fluid flow in heterogeneous and anisotropic reservoirs." Journal of Petroleum Science and Engineering 156 (July 2017): 282–98. http://dx.doi.org/10.1016/j.petrol.2017.06.003.
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Abushaikha, Ahmad S., Martin J. Blunt, Olivier R. Gosselin, Christopher C. Pain, and Matthew D. Jackson. "Interface control volume finite element method for modelling multi-phase fluid flow in highly heterogeneous and fractured reservoirs." Journal of Computational Physics 298 (October 2015): 41–61. http://dx.doi.org/10.1016/j.jcp.2015.05.024.
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Lozynskyi, O. Ye, and V. O. Lozynskyi. "Geological-Field Simulation of the "Well – Formation" System for Low-permeable Reservoirs." Prospecting and Development of Oil and Gas Fields, no. 3(72) (September 30, 2019): 51–57. http://dx.doi.org/10.31471/1993-9973-2019-3(72)-51-57.
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The aim of the research is the creation of an algorithm and a computer program to study the feasibility of poor wells developing. The research method is hydrodynamic simulation of the “well – formation” system by studying the behavior of low-permeable oil-filled reservoirs in the process of creating rising overburdens on the formation (abnormal formation pressures). Geological factors limiting the productivity of an oil well are analyzed. The degree of the decrease of the negative effect of these factors on oil influx to the bottomhole is predicted. The authors have studied the possibility of creating supplementary filtering channels in the bottomhole zone and the possibility of increasing hydroconductivity of the exposed reservoirs within the maximum possible drainage area. The authors also suggest the method to study poor wells using multiple injection of fluid into the reservoir and a gradual increase of the injection pressure and the overburden on the formation. In order to simulate the bottomhole pressure drop in a multi-cycle study, the authors make an algorithm based on an equation linking the pressure at a certain time point after the well shut-in to record the pressure decline curve with an integrated indicator. This indicator takes into account the volume of injection of fluid into the reservoirs before the well shut-in, the total duration of the injection of fluid into the reservoirs, the duration of time from the beginning of the injection of fluid into the reservoirs till the end of the process and the coefficient of the reservoir conductivity at each research cycle. The developed algorithm and computer technology provide the accumulation, storage, processing and reproduction of objective geological-field information. This will give a possibility to make a grounded decision about taking measures to increase the influx of production to the wells. The final result of these measures will be the transfer of out-balance reserves in the drainage areas of the wells to balance reserves and an increase in the total oil production at the field.
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Belila, Aline Maria Poças, Michelle Chaves Kuroda, João Paulo Da Ponte Souza, Alexandre Campane Vidal, and Osvair Vidal Trevisan. "Petrophysical characterization of coquinas from Morro do Chaves Formation (Sergipe-Alagoas Basin) by x-ray computed tomography." Geologia USP. Série Científica 18, no. 3 (September 10, 2018): 3–13. http://dx.doi.org/10.11606/issn.2316-9095.v18-124101.
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Carbonate rocks constitute a large number of petroleum reservoirs worldwide. Notwithstanding, the characterization of these rocks is still a challenge due to their high complexity and pore space variability, indicating the importance of further studies to reduce uncertainty in reservoir interpretation and characterization. This work was performed for coquina samples from Morro do Chaves Formation (Sergipe-Alagoas Basin), analogous to important Brazilian reservoirs. Computed tomography (CT) was used for three-dimensional characterization of rock structure. The neural network named Self-Organizing Maps (SOM) was used for CT images segmentation. According to our tests, CT demonstrated to be a consistent tool for quantitative and qualitative analysis of heterogeneous pore space, by the evaluation of porosity, connectivity and the representative elementary volume.
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Osterloh, W. Terry, Don S. Mims, and W. Scott Meddaugh. "Probabilistic Forecasting and Model Validation for the First-Eocene Large-Scale Pilot Steamflood, Partitioned Zone, Saudi Arabia and Kuwait." SPE Reservoir Evaluation & Engineering 16, no. 01 (January 31, 2013): 97–116. http://dx.doi.org/10.2118/150580-pa.
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Summary The First-Eocene heavy-oil reservoir (1E) in the Wafra field is a candidate for steamflooding because of its world-class resource base and low-estimated primary recovery. However, industry has little experience in steamflooding carbonate reservoirs, which has prompted the staging of several 1E steamflooding tests, the latest of which is the large-scale pilot (LSP) started in 2009. To assist in facilities design, to help understand expected performance in a very heterogeneous reservoir, and to provide input to early-decision analyses, numerical thermal simulation was used to generate probabilistic forecasts. When adequate pilot history was available, the model was validated with probabilistic methods. The LSP model contained 1.5 million cells, which allowed the maintenance of adequate resolution and proper boundary conditions in the pilot area. Parallel computation enabled a probabilistic workflow to be implemented with this large thermal model. In this paper, we highlight the methodologies and inputs used to generate the probabilistic forecasts and validate the model. Major results of this work include the following: In contrast to many greenfield forecasts, the LSP forecasts were conservative, likely because of the unique aspects of the forecasting methodology, proper selection of uncertainty ranges, and the relatively high density of input data for model construction; wide variations in production metrics were forecast, indicative of a highly heterogeneous reservoir; results indicated that the validated model adequately captured the global or statistical pilot heterogeneity, enabling proper capture of steamflood flow/drainage mechanisms; and despite this heterogeneity, forecast oil-recovery levels were comparable with those observed in steamfloods in sandstone reservoirs.
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Qianhua, Xiao, Wang Zhiyuan, Yang Zhengming, Liu Xuewei, and Wei Yunyun. "Porous flow characteristics of solution-gas drive in tight oil reservoirs." Open Physics 16, no. 1 (July 19, 2018): 412–18. http://dx.doi.org/10.1515/phys-2018-0056.
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Abstract The variation of porous flow resistance of solution-gas drive for tight oil reservoirs has been studied by designing new experimental equipment. The results show that the relation between the porous flow resistance gradient and pressure is the exponential function. The solution-gas driving resistance is determined by a combination of factors, such as the gas-oil ratio, density, viscosity, permeability, porosity and the Jamin effect. Based on the material balance and the flow resistance gradient equation, a new governing equation for solution-gas drive is established. After coupling with the nonlinear equation of elastic drive, the drainage radius of solution-gas drive is found to be very small and decreases rapidly when the bottom-hole pressure approaches the bubble-point value. Pressure distribution of the solution-gas drive is non-linear, and the values decrease sharply as it approaches the well bore. The productivity is rather low despite being strongly influenced by permeability. Therefore, stimulated reservoir volume (SRV) is the essential measure taken for effective development for tight oil reservoirs.