The large number of geological realizations and well trajectory parameters make field development optimization under geological uncertainty a time-consuming task. A novel deep learning-based surrogate model with a novel well trajectory parametrization technique is proposed in this study to optimize the trajectory of wells under geological uncertainty. The proposed model is a deep neural network with ConvLSTM layers to extract the most salient features from highly channelized and layered reservoirs efficiently. ConvLSTM layers are used because they can extract spatiotemporal features simultaneously since layered reservoirs can be regarded as a time series of spatially distributed reservoir properties. The proposed surrogate model could predict the individual objective function with a coefficient of determination of 0.96. After verifying the validity of the surrogate model, four approaches were used to optimize well trajectories. Two of the approaches consumed all available realizations (surrogate model-based and simulation-based approaches), while the remaining two used a subset of realizations. The selection of the subset was based on the cumulative oil production (COP) and the diffusive time of flight (DTOF). Results showed that although the surrogate model used all realizations, it could provide similar results to the simulation-based optimization with only a 5% computational cost of the simulation-based approach. The novelty of this work lies in its proposal of an innovative surrogate model to improve the analysis of channelized and layered reservoirs and its introduction of a novel well trajectory optimization framework that effectively addresses the challenge of optimizing well trajectories in complex three-dimensional spaces, a problem not adequately tackled in previous works.
{"title":"Well Trajectory Optimization under Geological Uncertainties Assisted by a New Deep Learning Technique","authors":"Reza Yousefzadeh, M. Ahmadi","doi":"10.2118/221476-pa","DOIUrl":"https://doi.org/10.2118/221476-pa","url":null,"abstract":"\u0000 The large number of geological realizations and well trajectory parameters make field development optimization under geological uncertainty a time-consuming task. A novel deep learning-based surrogate model with a novel well trajectory parametrization technique is proposed in this study to optimize the trajectory of wells under geological uncertainty. The proposed model is a deep neural network with ConvLSTM layers to extract the most salient features from highly channelized and layered reservoirs efficiently. ConvLSTM layers are used because they can extract spatiotemporal features simultaneously since layered reservoirs can be regarded as a time series of spatially distributed reservoir properties. The proposed surrogate model could predict the individual objective function with a coefficient of determination of 0.96. After verifying the validity of the surrogate model, four approaches were used to optimize well trajectories. Two of the approaches consumed all available realizations (surrogate model-based and simulation-based approaches), while the remaining two used a subset of realizations. The selection of the subset was based on the cumulative oil production (COP) and the diffusive time of flight (DTOF). Results showed that although the surrogate model used all realizations, it could provide similar results to the simulation-based optimization with only a 5% computational cost of the simulation-based approach. The novelty of this work lies in its proposal of an innovative surrogate model to improve the analysis of channelized and layered reservoirs and its introduction of a novel well trajectory optimization framework that effectively addresses the challenge of optimizing well trajectories in complex three-dimensional spaces, a problem not adequately tackled in previous works.","PeriodicalId":510854,"journal":{"name":"SPE Journal","volume":"63 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141705981","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Developing unconventional reservoirs such as shale oil is vital for fulfilling the need for energy consumption in the world. Oil production from shale reservoirs is still the most complicated and uncertain phenomenon because of its complex fracture networking, low matrix porosity, and permeability. Production forecasting is crucial for decision-making and tactical exploitation of subsurface resources during production. Traditional methods, such as the Arps decline model and reservoir simulation methods, face significant challenges in forecasting hydrocarbon production due to the highly nonlinear and heterogeneous nature of rocks and fluids. These methods are prone to substantial deviations in forecasting results and show limited applicability to unconventional reservoirs. Therefore, it is essential to improve the production forecasting capability with the help of a data-driven methodology. The data set for modeling is collected from two prominent shale oil-producing regions, the Eagle Ford and the Bakken. The Bakken data set is used to train and test the models, and the Eagle Ford data set is used to validate the model. The random search method was used to optimize the model parameters, and the window sliding technique was used to find a suitable window size to predict future values efficiently. The combination of different deep learning (DL) methods has designed a total of six hybrid models: gated recurrent unit (GRU), long short-term memory (LSTM), and temporal convolutional network (TCN). These models can capture the spatial and temporal patterns in the oil production data. The results concluded that the TCN-GRU model performed best statistically and computationally compared with other individual and hybrid models. The robust model can accelerate decision-making and reduce the overall forecasting cost.
{"title":"Deep Learning–Based Production Forecasting and Data Assimilation in Unconventional Reservoir","authors":"Bineet Kumar Tripathi, Indrajeet Kumar, Sumit Kumar, Anugrah Singh","doi":"10.2118/223074-pa","DOIUrl":"https://doi.org/10.2118/223074-pa","url":null,"abstract":"\u0000 Developing unconventional reservoirs such as shale oil is vital for fulfilling the need for energy consumption in the world. Oil production from shale reservoirs is still the most complicated and uncertain phenomenon because of its complex fracture networking, low matrix porosity, and permeability. Production forecasting is crucial for decision-making and tactical exploitation of subsurface resources during production. Traditional methods, such as the Arps decline model and reservoir simulation methods, face significant challenges in forecasting hydrocarbon production due to the highly nonlinear and heterogeneous nature of rocks and fluids. These methods are prone to substantial deviations in forecasting results and show limited applicability to unconventional reservoirs. Therefore, it is essential to improve the production forecasting capability with the help of a data-driven methodology. The data set for modeling is collected from two prominent shale oil-producing regions, the Eagle Ford and the Bakken. The Bakken data set is used to train and test the models, and the Eagle Ford data set is used to validate the model. The random search method was used to optimize the model parameters, and the window sliding technique was used to find a suitable window size to predict future values efficiently. The combination of different deep learning (DL) methods has designed a total of six hybrid models: gated recurrent unit (GRU), long short-term memory (LSTM), and temporal convolutional network (TCN). These models can capture the spatial and temporal patterns in the oil production data. The results concluded that the TCN-GRU model performed best statistically and computationally compared with other individual and hybrid models. The robust model can accelerate decision-making and reduce the overall forecasting cost.","PeriodicalId":510854,"journal":{"name":"SPE Journal","volume":"16 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141849452","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Supercritical carbon dioxide (scCO2) trapping mechanisms within carbon geostorage (CGS) primarily hinge on the upper caprock system, with shales being favored for their fine-grained nature and geological abundance. Experimental assessments of CO2 reactivity in brine-saturated shales reveal microstructural changes, raising concerns about long-term CO2 leakage risks. Existing models of scCO2 transport through caprocks lack consideration for shale anisotropy. This study addresses these gaps by investigating the diffusive properties and propagation of geochemical reactivity in shaly caprocks, accounting for anisotropy. Horizontal and vertical core samples from three shale formations with varying petrophysical characteristics underwent mineralogical, total organic carbon (TOC), porosity, and velocity measurements. scCO2 treatment for up to 3 weeks at 150°F and 3,000 psi was conducted. The propagation of geochemical reactivity was monitored by multiple surface X-ray fluorescence (XRF) measurements and fine polishing. A nuclear magnetic resonance (NMR)-based H2O-D2O fluid exchange protocol was used to quantify effective diffusivities and tortuosities parallel and perpendicular to bedding. Results indicate preferential surface reactivity toward carbonate minerals; however, the apparent reaction diffusivity of the shaly caprock is notably slow (~10−15 m2/s). This aligns with previous experimental and reactive transport modeling studies, emphasizing long timescales for carbonate dissolution reactions to influence shale caprock properties. Shale-effective diffusivities display anisotropy increasing with clay content, where diffusivities parallel to bedding exceed those perpendicular by at least three times. Faster horizontal diffusion in shaly confining zones should be considered when estimating diffusive leakage along faults penetrating these zones, a significant risk in CGS. Post-scCO2 treatment, diffusivity changes vary among samples, increasing within the same order of magnitude in the clay-rich sample. Nonsteady-state modeling of scCO2 diffusion suggests limited caprock penetration over 100 years, with a minimal increase from 5 m to 7 m post-scCO2 treatment for the clay-rich sample. This study extends existing literature observations on the slow molecular diffusion of scCO2 within shaly caprocks, integrating the roles of geochemical reactions and shale anisotropy under the examined conditions.
{"title":"Diffusive Leakage of scCO2 in Shaly Caprocks: Effect of Geochemical Reactivity and Anisotropy","authors":"Felipe Cruz, S. Dang, Mark Curtis, Chandra Rai","doi":"10.2118/219763-pa","DOIUrl":"https://doi.org/10.2118/219763-pa","url":null,"abstract":"\u0000 Supercritical carbon dioxide (scCO2) trapping mechanisms within carbon geostorage (CGS) primarily hinge on the upper caprock system, with shales being favored for their fine-grained nature and geological abundance. Experimental assessments of CO2 reactivity in brine-saturated shales reveal microstructural changes, raising concerns about long-term CO2 leakage risks. Existing models of scCO2 transport through caprocks lack consideration for shale anisotropy. This study addresses these gaps by investigating the diffusive properties and propagation of geochemical reactivity in shaly caprocks, accounting for anisotropy. Horizontal and vertical core samples from three shale formations with varying petrophysical characteristics underwent mineralogical, total organic carbon (TOC), porosity, and velocity measurements. scCO2 treatment for up to 3 weeks at 150°F and 3,000 psi was conducted. The propagation of geochemical reactivity was monitored by multiple surface X-ray fluorescence (XRF) measurements and fine polishing. A nuclear magnetic resonance (NMR)-based H2O-D2O fluid exchange protocol was used to quantify effective diffusivities and tortuosities parallel and perpendicular to bedding. Results indicate preferential surface reactivity toward carbonate minerals; however, the apparent reaction diffusivity of the shaly caprock is notably slow (~10−15 m2/s). This aligns with previous experimental and reactive transport modeling studies, emphasizing long timescales for carbonate dissolution reactions to influence shale caprock properties. Shale-effective diffusivities display anisotropy increasing with clay content, where diffusivities parallel to bedding exceed those perpendicular by at least three times. Faster horizontal diffusion in shaly confining zones should be considered when estimating diffusive leakage along faults penetrating these zones, a significant risk in CGS. Post-scCO2 treatment, diffusivity changes vary among samples, increasing within the same order of magnitude in the clay-rich sample. Nonsteady-state modeling of scCO2 diffusion suggests limited caprock penetration over 100 years, with a minimal increase from 5 m to 7 m post-scCO2 treatment for the clay-rich sample. This study extends existing literature observations on the slow molecular diffusion of scCO2 within shaly caprocks, integrating the roles of geochemical reactions and shale anisotropy under the examined conditions.","PeriodicalId":510854,"journal":{"name":"SPE Journal","volume":"169 1‐2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141693280","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Nowadays, complex 3D trajectories are executed with a succession of circular arcs (CAs). Although they have constant curvature, their tool face is not constant. Consequently, directional drillers must adjust the tool face regularly to reach the target entry within its tolerances. This paper investigates the use of the constant curvature and constant tool face (CTC in short) curve as an alternative to the CA to assist the directional drilling work to reach the target entry within its boundaries. The problem is addressed by calculating a safe operating envelope (SOE) to reach the boundaries of the target entry and provide a tolerance window for the curvature and tool face to support directional drilling decisions. The target entry tolerance is discretized as a polygon. From the current bit position and its direction, the possible choices of curvatures and tool faces are obtained to reach the edges of the target entry shape. The SOE can be calculated with the CA or with the CTC curve. It is, therefore, possible to compare the advantages and disadvantages of both types of curves to attain the target entry and stay within its boundaries. The CA is shorter than the CTC curve. However, it requires adjusting the tool face during the navigation, which is not the case with the CTC curve. As a result, the directional driller can control the bottomhole assembly (BHA) direction such that the well lands within the target entry limits by using set points for tool face and curvature inside the calculated SOE. Furthermore, a new way to represent the SOE is introduced. It makes use of a 3D cylindrical representation where the curvature is mapped as the height of a cylinder, while the tool face corresponds to the azimuth in the cylindrical coordinate system, and the length is linked to the radial distance. This provides a visual aid to understand the SOE. Moreover, this visualization helps to appreciate the relationship between the initial bit location and direction in the construction of the SOE and how the margins increase in a particular manner as the bit approaches the target entry polygon. The CTC curve is the natural one followed by directional positive displacement motors (PDMs) or rotary steerable systems (RSS). Potentially, the CTC curve may be a more straightforward solution to automated directional drilling control because it is easier to be followed by both PDM and RSS.
如今，复杂的三维轨迹是通过连续的圆弧（CA）来实现的。虽然圆弧的曲率是恒定的，但其刀面却不是恒定的。因此，定向钻井人员必须定期调整工具面，以便在公差范围内到达目标入口。本文研究了如何使用恒定曲率和恒定刀面曲线（简称 CTC）来替代 CA，以帮助定向钻井工作在其边界内到达目标入口。该问题通过计算安全作业包络线（SOE）来解决，以达到目标入口的边界，并为曲率和工具面提供一个公差窗口，以支持定向钻井决策。目标入口公差被离散化为一个多边形。从当前钻头位置及其方向出发，可以选择不同的曲率和钻具面，以达到目标入口形状的边缘。SOE 可以用 CA 或 CTC 曲线计算。因此，可以比较这两种曲线的优缺点，以达到目标入口并保持在其边界内。CA 比 CTC 曲线短。但是，它需要在导航过程中调整刀面，而 CTC 曲线则不需要。因此，定向钻井者可以通过在计算出的 SOE 内设置工具面和曲率点来控制井底组件（BHA）的方向，从而使油井在目标入口范围内着陆。此外，还引入了一种表示 SOE 的新方法。它使用三维圆柱表示法，其中曲率映射为圆柱的高度，而工具面对应于圆柱坐标系中的方位角，长度则与径向距离相关联。这为理解 SOE 提供了视觉帮助。此外，这种可视化方法还有助于理解 SOE 构造中初始钻头位置和方向之间的关系，以及当钻头接近目标入口多边形时，余量是如何以特定方式增加的。CTC 曲线是定向容积马达（PDM）或旋转转向系统（RSS）所遵循的自然曲线。由于 CTC 曲线更容易被 PDM 和 RSS 遵循，因此有可能成为自动定向钻井控制的一种更直接的解决方案。
{"title":"Assisting Directional Drilling by Calculating a Safe Operating Envelope","authors":"L. Saavedra Jerez, E. Cayeux, D. Sui","doi":"10.2118/217707-pa","DOIUrl":"https://doi.org/10.2118/217707-pa","url":null,"abstract":"\u0000 Nowadays, complex 3D trajectories are executed with a succession of circular arcs (CAs). Although they have constant curvature, their tool face is not constant. Consequently, directional drillers must adjust the tool face regularly to reach the target entry within its tolerances. This paper investigates the use of the constant curvature and constant tool face (CTC in short) curve as an alternative to the CA to assist the directional drilling work to reach the target entry within its boundaries.\u0000 The problem is addressed by calculating a safe operating envelope (SOE) to reach the boundaries of the target entry and provide a tolerance window for the curvature and tool face to support directional drilling decisions. The target entry tolerance is discretized as a polygon. From the current bit position and its direction, the possible choices of curvatures and tool faces are obtained to reach the edges of the target entry shape. The SOE can be calculated with the CA or with the CTC curve. It is, therefore, possible to compare the advantages and disadvantages of both types of curves to attain the target entry and stay within its boundaries.\u0000 The CA is shorter than the CTC curve. However, it requires adjusting the tool face during the navigation, which is not the case with the CTC curve. As a result, the directional driller can control the bottomhole assembly (BHA) direction such that the well lands within the target entry limits by using set points for tool face and curvature inside the calculated SOE. Furthermore, a new way to represent the SOE is introduced. It makes use of a 3D cylindrical representation where the curvature is mapped as the height of a cylinder, while the tool face corresponds to the azimuth in the cylindrical coordinate system, and the length is linked to the radial distance. This provides a visual aid to understand the SOE. Moreover, this visualization helps to appreciate the relationship between the initial bit location and direction in the construction of the SOE and how the margins increase in a particular manner as the bit approaches the target entry polygon.\u0000 The CTC curve is the natural one followed by directional positive displacement motors (PDMs) or rotary steerable systems (RSS). Potentially, the CTC curve may be a more straightforward solution to automated directional drilling control because it is easier to be followed by both PDM and RSS.","PeriodicalId":510854,"journal":{"name":"SPE Journal","volume":"29 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141853946","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Type curves are a powerful tool in characterizing hydraulic fracture (HF) and reservoir properties based on flowback and production data. We propose a type-curve method to evaluate HF characteristics and their dynamics for multifractured horizontal wells (MFHWs) in hydrocarbon reservoirs using flowback production data. The type curve incorporates the HF damage effect of choked-fracture skin factor in the two-phase flow in HF and matrix domains. The type-curve method can be applied to inversely estimate choked-fracture skin factor, s, HF pore volume (PV), Vfi, and HF initial permeability, kfi, by analyzing two-phase flowback production data. By introducing the new dimensionless parameters, the nonuniqueness problem of the type-curve analysis for two-phase flow is significantly reduced by incorporating the complexity of fracture dynamics into one set of curves. The accuracy of the type curve is examined against the results obtained from numerical simulations of shale gas and oil reservoirs. The validation results demonstrate a good match of analytical type curves and numerical data plots and confirm the accuracy of the proposed method in estimating the static and dynamic fracture properties. The results show that the relative errors in Vfi, kfi, and s estimations are all <10% for the simulated cases that are presented in this work. The flexibility and robustness of the proposed method are illustrated using the field example from a shale oil MFHW. The accuracy and applicability of the proposed type curve are also validated by comparing the calculated fracture properties from the field example using straightline analysis with Vfi and kfi of 705.3 Mcf and 245.2 md, type-curve analysis method (without skin effect) with Vfi and kfi of 751.9 Mcf and 249.8 md, and the type-curve method (with the choked fracture skin considered) with Vfi and kfi of 708.7 Mcf and 252.9 md, which showed that the results of each case are very close to one another. The interpreted results from the flowback analysis of the field example offer quantitative insight into HF properties and dynamics.
{"title":"A Two-Phase Flowback Type Curve with Fracture Damage Effects for Hydraulically Fractured Reservoirs","authors":"Fengyuan Zhang, Yang Pan, Chuncheng Liu, Chia-Hsin Yang, Hamid Emami‐Meybodi, Zhenhua Rui","doi":"10.2118/215034-pa","DOIUrl":"https://doi.org/10.2118/215034-pa","url":null,"abstract":"\u0000 Type curves are a powerful tool in characterizing hydraulic fracture (HF) and reservoir properties based on flowback and production data. We propose a type-curve method to evaluate HF characteristics and their dynamics for multifractured horizontal wells (MFHWs) in hydrocarbon reservoirs using flowback production data. The type curve incorporates the HF damage effect of choked-fracture skin factor in the two-phase flow in HF and matrix domains. The type-curve method can be applied to inversely estimate choked-fracture skin factor, s, HF pore volume (PV), Vfi, and HF initial permeability, kfi, by analyzing two-phase flowback production data. By introducing the new dimensionless parameters, the nonuniqueness problem of the type-curve analysis for two-phase flow is significantly reduced by incorporating the complexity of fracture dynamics into one set of curves. The accuracy of the type curve is examined against the results obtained from numerical simulations of shale gas and oil reservoirs. The validation results demonstrate a good match of analytical type curves and numerical data plots and confirm the accuracy of the proposed method in estimating the static and dynamic fracture properties. The results show that the relative errors in Vfi, kfi, and s estimations are all <10% for the simulated cases that are presented in this work. The flexibility and robustness of the proposed method are illustrated using the field example from a shale oil MFHW. The accuracy and applicability of the proposed type curve are also validated by comparing the calculated fracture properties from the field example using straightline analysis with Vfi and kfi of 705.3 Mcf and 245.2 md, type-curve analysis method (without skin effect) with Vfi and kfi of 751.9 Mcf and 249.8 md, and the type-curve method (with the choked fracture skin considered) with Vfi and kfi of 708.7 Mcf and 252.9 md, which showed that the results of each case are very close to one another. The interpreted results from the flowback analysis of the field example offer quantitative insight into HF properties and dynamics.","PeriodicalId":510854,"journal":{"name":"SPE Journal","volume":"306 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141691976","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper presents a novel approach to the numerical simulation of fractured reservoirs, called the connection element method (CEM), which differs from traditional grid-based methods. The reservoir computational domain is discretized into a series of nodes, and a system of connection elements is constructed based on the given connection lengths and angles. The pressure diffusion term is approximated using generalized finite difference theory. Meanwhile, the transmissibility and volume of the connection elements are determined, and pressure equations are solved discretely to obtain pressure at nodes to approximate the upstream flux along connection elements. Then, we solve the transport equation to obtain oil saturation profiles with low numerical diffusion, utilizing the discontinuous Galerkin (DG) method. Moreover, the flow path tracking algorithm is introduced to quantify the flow allocation factors between wells. In all, the pressure equation can be solved at a global coarse-scale point cloud and the saturation equation is calculated at a local fine-scale connection element. In other words, CEM is of multiscale characteristics relatively. Finally, several numerical examples are implemented to demonstrate that CEM can achieve a relatively better balance between computational accuracy and efficiency compared with embedded discrete fracture modeling (EDFM). Furthermore, CEM adopts flexible meshless nodes instead of grids with strong topology, making it more practical to handle complex reservoir geometry such as fractured reservoirs.
{"title":"A Novel Connection Element Method for Multiscale Numerical Simulation of Two-Phase Flow in Fractured Reservoirs","authors":"Hui Zhao, Wentao Zhan, Zhiming Chen, Xiang Rao","doi":"10.2118/221481-pa","DOIUrl":"https://doi.org/10.2118/221481-pa","url":null,"abstract":"\u0000 This paper presents a novel approach to the numerical simulation of fractured reservoirs, called the connection element method (CEM), which differs from traditional grid-based methods. The reservoir computational domain is discretized into a series of nodes, and a system of connection elements is constructed based on the given connection lengths and angles. The pressure diffusion term is approximated using generalized finite difference theory. Meanwhile, the transmissibility and volume of the connection elements are determined, and pressure equations are solved discretely to obtain pressure at nodes to approximate the upstream flux along connection elements. Then, we solve the transport equation to obtain oil saturation profiles with low numerical diffusion, utilizing the discontinuous Galerkin (DG) method. Moreover, the flow path tracking algorithm is introduced to quantify the flow allocation factors between wells. In all, the pressure equation can be solved at a global coarse-scale point cloud and the saturation equation is calculated at a local fine-scale connection element. In other words, CEM is of multiscale characteristics relatively. Finally, several numerical examples are implemented to demonstrate that CEM can achieve a relatively better balance between computational accuracy and efficiency compared with embedded discrete fracture modeling (EDFM). Furthermore, CEM adopts flexible meshless nodes instead of grids with strong topology, making it more practical to handle complex reservoir geometry such as fractured reservoirs.","PeriodicalId":510854,"journal":{"name":"SPE Journal","volume":"35 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141702636","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Peng Zong, Hao Xu, D. Tang, Zhenhong Chen, Feiyu Huo
In fractured reservoirs, the fracture system is considered to be the main channel for fluid flow. To better investigate the impacts of fracture morphology (tortuosity and roughness) and spatial distribution on the flow capacity, a fractal model of fracture permeability was developed. Based on micro-computed tomography (CT) images, the 3D structure of the fracture was reconstructed, and the fractal characteristics were systematically analyzed. Finally, the control of permeability by fracture morphology and spatial distribution in different fractured reservoirs was identified. The results demonstrate that the complexity of the fracture distribution in 2D slices can represent the nature of the fracture distribution in 3D space. The permeability fractal prediction model was developed based on porosity (φ), spatial distribution fractal dimension (Df), tortuosity fractal dimension (DT), and opening fractal dimension of the maximum width fracture (Db). The permeability prediction results of the fractal model for Samples L-01 (limestone), BD-01 (coal), BD-02 (coal), S-01 (sandstone), M-01 (mudstone), and C-01 (coal) are 0.011 md, 0.239 md, 0.134 md, 0.119 md, 1.429 md, and 27.444 md, respectively. For different types of rocks, the results predicted by the model show good agreement with numerical simulations (with an average relative error of 2.51%). The factors controlling the permeability of fractured reservoirs were analyzed through the application of the mathematical model. The permeability is positively exponentially correlated with the fractal dimension of spatial distribution and negatively exponentially correlated with the fractal dimension of morphology. When Df < 2.25, the fracture spatial structure is simple, and the morphology and spatial distribution jointly control the seepage capacity of fractured reservoirs. When Df > 2.25, the fracture spatial structure is complex, and the impact of morphology on seepage capacity can be disregarded. This work can effectively lay the foundation for the study of fluid permeability in fractured reservoirs by investigating the effects of fracture morphology (tortuosity and roughness) and spatial distribution on flow capacity.
{"title":"A Fractal Model of Fracture Permeability Considering Morphology and Spatial Distribution","authors":"Peng Zong, Hao Xu, D. Tang, Zhenhong Chen, Feiyu Huo","doi":"10.2118/221488-pa","DOIUrl":"https://doi.org/10.2118/221488-pa","url":null,"abstract":"\u0000 In fractured reservoirs, the fracture system is considered to be the main channel for fluid flow. To better investigate the impacts of fracture morphology (tortuosity and roughness) and spatial distribution on the flow capacity, a fractal model of fracture permeability was developed. Based on micro-computed tomography (CT) images, the 3D structure of the fracture was reconstructed, and the fractal characteristics were systematically analyzed. Finally, the control of permeability by fracture morphology and spatial distribution in different fractured reservoirs was identified. The results demonstrate that the complexity of the fracture distribution in 2D slices can represent the nature of the fracture distribution in 3D space. The permeability fractal prediction model was developed based on porosity (φ), spatial distribution fractal dimension (Df), tortuosity fractal dimension (DT), and opening fractal dimension of the maximum width fracture (Db). The permeability prediction results of the fractal model for Samples L-01 (limestone), BD-01 (coal), BD-02 (coal), S-01 (sandstone), M-01 (mudstone), and C-01 (coal) are 0.011 md, 0.239 md, 0.134 md, 0.119 md, 1.429 md, and 27.444 md, respectively. For different types of rocks, the results predicted by the model show good agreement with numerical simulations (with an average relative error of 2.51%). The factors controlling the permeability of fractured reservoirs were analyzed through the application of the mathematical model. The permeability is positively exponentially correlated with the fractal dimension of spatial distribution and negatively exponentially correlated with the fractal dimension of morphology. When Df < 2.25, the fracture spatial structure is simple, and the morphology and spatial distribution jointly control the seepage capacity of fractured reservoirs. When Df > 2.25, the fracture spatial structure is complex, and the impact of morphology on seepage capacity can be disregarded. This work can effectively lay the foundation for the study of fluid permeability in fractured reservoirs by investigating the effects of fracture morphology (tortuosity and roughness) and spatial distribution on flow capacity.","PeriodicalId":510854,"journal":{"name":"SPE Journal","volume":"255 1‐2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141708433","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In response to the constraint on model size imposed by computational capabilities and the inability to capture the heterogeneity within the core and its dynamic oil displacement characteristics, this paper proposes two novel methods for cost-effectively modeling heterogeneous core models based on scale changes of nuclear magnetic resonance (NMR) and X-ray computed tomography (X-CT) data, respectively. By utilizing NMR and X-CT techniques to characterize information at the subcore scale, we establish a more realistic model at the core scale. First, by using a method of setting up inactive grids, a homogeneous model is established to better represent the actual cross-section of the core. By fitting the core water displacement experimental data, a random heterogeneous core model based on the NMR-T2 spectrum is established by using the modified Schlumberger-Doll Research (SDR) model and complementarity principle. The numerical simulation results show that the random heterogeneous core model partially reflect the heterogeneity of the core, but the simulation results are unstable. Building on this, a deterministic homogeneous core model is established based on X-CT scan data by using the modified Kozeny-Carman model and pore extraction method. Sensitivity analysis results suggest that higher grid accuracy leads to a better fitting effect, with the axial plane grid accuracy impacting the model water-drive process more significantly than that of the end plane. The study paves the way for the rapid and accurate establishment of core models.
{"title":"Novel Methods for Cost-Effectively Generating a Heterogeneous Core Model Based on Scale Change of Nuclear Magnetic Resonance and X-ray Computed Tomography Data","authors":"Zili Zhou, Hu Jia, Rui Zhang","doi":"10.2118/221490-pa","DOIUrl":"https://doi.org/10.2118/221490-pa","url":null,"abstract":"\u0000 In response to the constraint on model size imposed by computational capabilities and the inability to capture the heterogeneity within the core and its dynamic oil displacement characteristics, this paper proposes two novel methods for cost-effectively modeling heterogeneous core models based on scale changes of nuclear magnetic resonance (NMR) and X-ray computed tomography (X-CT) data, respectively. By utilizing NMR and X-CT techniques to characterize information at the subcore scale, we establish a more realistic model at the core scale. First, by using a method of setting up inactive grids, a homogeneous model is established to better represent the actual cross-section of the core. By fitting the core water displacement experimental data, a random heterogeneous core model based on the NMR-T2 spectrum is established by using the modified Schlumberger-Doll Research (SDR) model and complementarity principle. The numerical simulation results show that the random heterogeneous core model partially reflect the heterogeneity of the core, but the simulation results are unstable. Building on this, a deterministic homogeneous core model is established based on X-CT scan data by using the modified Kozeny-Carman model and pore extraction method. Sensitivity analysis results suggest that higher grid accuracy leads to a better fitting effect, with the axial plane grid accuracy impacting the model water-drive process more significantly than that of the end plane. The study paves the way for the rapid and accurate establishment of core models.","PeriodicalId":510854,"journal":{"name":"SPE Journal","volume":"96 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141713611","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The distribution of proppant within hydraulic fractures significantly influences fracture conductivity, thus playing an essential role in oil and gas production. Currently, small-scale and static fracture problems have been successfully simulated with high accuracy using Lagrangian proppant transport models. Field-scale problems are often simulated with the mixture model, the accuracy of which still requires improvement. In this work, a novel model that couples fracture propagation and proppant transport using an Eulerian-Lagrangian framework is proposed. The displacement discontinuity method (DDM), the extended Poiseuille’s equation, and the multiphase particle-in-cell (MP-PIC) method are used for fracture deformation and propagation, fluid flow, and proppant transport simulations, respectively. The fluid flow is fully coupled with the fracture equations and then coupled with the Lagrangian proppant model using a two-way coupling strategy. The proposed model is carefully validated against published numerical and experimental results. Then, we use the model to investigate the fracturing process in a layered reservoir. The impacts of fluid leakoff and proppant injection order are discussed. Special phenomena such as proppant bridging and tip screenout are captured. This study provides a novel and reliable way for simulating proppant transport in practical problems, which is of great importance to fracturing designs.
{"title":"Coupled Simulation of Fracture Propagation and Lagrangian Proppant Transport","authors":"Zhicheng Wen, Huiying Tang, Liehui Zhang, Shengnan Chen, Junsheng Zeng, Jianhua Qin, Linsheng Wang, Yulong Zhao","doi":"10.2118/221483-pa","DOIUrl":"https://doi.org/10.2118/221483-pa","url":null,"abstract":"\u0000 The distribution of proppant within hydraulic fractures significantly influences fracture conductivity, thus playing an essential role in oil and gas production. Currently, small-scale and static fracture problems have been successfully simulated with high accuracy using Lagrangian proppant transport models. Field-scale problems are often simulated with the mixture model, the accuracy of which still requires improvement. In this work, a novel model that couples fracture propagation and proppant transport using an Eulerian-Lagrangian framework is proposed. The displacement discontinuity method (DDM), the extended Poiseuille’s equation, and the multiphase particle-in-cell (MP-PIC) method are used for fracture deformation and propagation, fluid flow, and proppant transport simulations, respectively. The fluid flow is fully coupled with the fracture equations and then coupled with the Lagrangian proppant model using a two-way coupling strategy. The proposed model is carefully validated against published numerical and experimental results. Then, we use the model to investigate the fracturing process in a layered reservoir. The impacts of fluid leakoff and proppant injection order are discussed. Special phenomena such as proppant bridging and tip screenout are captured. This study provides a novel and reliable way for simulating proppant transport in practical problems, which is of great importance to fracturing designs.","PeriodicalId":510854,"journal":{"name":"SPE Journal","volume":"7 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141694702","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
One of the core assumptions of most deep-learning-based data-driven models is that samples are independent. However, this assumption poses a key challenge in production forecasting—performance is influenced by well interference and reservoir connectivity. Most shale gas wells are hydraulically fractured and exist in complex fracture systems, and the neighboring well characteristics should also be considered when constructing data-driven forecast models. Researchers have explored using the graph convolutional network (GCN) to address this issue by incorporating neighboring well characteristics into production forecasting models. However, applying GCN to field-scale studies is problematic, as it requires training on a full batch, leading to gigantic cache allocation. In addition, the transductive nature of GCN poses challenges for direct generalization to unseen nodes. To overcome these limitations, we adopt the graph sampling and aggregation (GraphSAGE) network architecture, which allows training large graphs with batches and generalizing predictions for previously unseen nodes. By utilizing the gated recurrent unit (GRU) network, the proposed spatial-temporal (ST)-GraphSAGE model can capture cross-time relationships between the target and the neighboring wells and generate promising prediction time series for the target wells, even if they are newly drilled wells. The proposed approach is validated and tested using the field data from 2,240 Montney shale gas wells, including formation properties, hydraulic fracture parameters, production history, and operational data. The algorithm aggregates the first-hop information to the target node for each timestep. The encoder-decoder (ED) architecture is used to generate forecasts for the subsequent 3-year production rate by using the 1-year production history of the wells. The trained model enables the evaluation of production predictions for newly developed wells at any location. We evaluate the model’s performance using P10, P50, and P90 of the test data set’s root mean square error (RMSE). Our method preserves the topological characteristics of wells and generalizes the prediction to unseen nodes while significantly reducing training complexity, making it applicable to larger data sets. By incorporating information from adjacent wells and integrating ST data, our ST-GraphSAGE model outperforms the traditional GRU-ED model and shows enhanced interpretability.
{"title":"Shale Gas Production Forecasting with Well Interference Based on Spatial-Temporal Graph Convolutional Network","authors":"Ziming Xu, Juliana Y. Leung","doi":"10.2118/215056-pa","DOIUrl":"https://doi.org/10.2118/215056-pa","url":null,"abstract":"\u0000 One of the core assumptions of most deep-learning-based data-driven models is that samples are independent. However, this assumption poses a key challenge in production forecasting—performance is influenced by well interference and reservoir connectivity. Most shale gas wells are hydraulically fractured and exist in complex fracture systems, and the neighboring well characteristics should also be considered when constructing data-driven forecast models. Researchers have explored using the graph convolutional network (GCN) to address this issue by incorporating neighboring well characteristics into production forecasting models. However, applying GCN to field-scale studies is problematic, as it requires training on a full batch, leading to gigantic cache allocation. In addition, the transductive nature of GCN poses challenges for direct generalization to unseen nodes. To overcome these limitations, we adopt the graph sampling and aggregation (GraphSAGE) network architecture, which allows training large graphs with batches and generalizing predictions for previously unseen nodes. By utilizing the gated recurrent unit (GRU) network, the proposed spatial-temporal (ST)-GraphSAGE model can capture cross-time relationships between the target and the neighboring wells and generate promising prediction time series for the target wells, even if they are newly drilled wells.\u0000 The proposed approach is validated and tested using the field data from 2,240 Montney shale gas wells, including formation properties, hydraulic fracture parameters, production history, and operational data. The algorithm aggregates the first-hop information to the target node for each timestep. The encoder-decoder (ED) architecture is used to generate forecasts for the subsequent 3-year production rate by using the 1-year production history of the wells. The trained model enables the evaluation of production predictions for newly developed wells at any location. We evaluate the model’s performance using P10, P50, and P90 of the test data set’s root mean square error (RMSE). Our method preserves the topological characteristics of wells and generalizes the prediction to unseen nodes while significantly reducing training complexity, making it applicable to larger data sets. By incorporating information from adjacent wells and integrating ST data, our ST-GraphSAGE model outperforms the traditional GRU-ED model and shows enhanced interpretability.","PeriodicalId":510854,"journal":{"name":"SPE Journal","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141850416","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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