A corrected cubic law for single-phase laminar flow through rough-walled fractures

He, Xupeng; Sinan, Marwa; Kwak, Hyung; Hoteit, Hussein

doi:10.1016/j.advwatres.2021.103984

Cited by 67 publications

(25 citation statements)

References 45 publications

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“…High-resolution Navier-Stokes (NS) equations accurately describe flow within fractures, including fracture upscaling, and its solutions will be considered as the ground truth. (Brush & Thomson, 2003;He, Sinan, et al, 2021;Robert W Zimmerman & Yeo, 2000). The superiority of the proposed model will be illustrated in the following two aspects.…”

Section: Comparison With High-resolution Ns Solutionsmentioning

confidence: 99%

“…Many efforts, including machine learning, have been proposed in the literature to improve the accuracy and applicability of cubic law. Examples include 1) modification of the definition of the aperture used in cubic law, such as arithmetic average (Brown, 1987), geometric average (Renshaw, 1995), averages proposed by others (e.g., Neuzil & Tracy, 1981;Zimmerman et al, 1991); 2) inclusion of correction factors that account for roughness influence (e.g., Louis, 1969;Patir & Cheng, 1978), tortuosity influence (e.g., Brown, 1987;Waite et al, 1999), combined roughness-tortuosity influence (e.g., He, Sinan, et al, 2021;Xiao et al, 2013); 3) implementation of machine learning techniques Sun et al, 2020). All above modifications, however, are designed for 2D rock fractures or 3D fullyopen fracture cases (e.g., no contact areas).…”

Section: Introductionmentioning

confidence: 99%

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Analytical and Numerical Assessment of Hydraulic Properties of 3D Partially-Open Rock Fractures

Alsinan

Kwak

et al. 2022

Day 3 Wed, February 23, 2022

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Modeling fractured reservoirs requires an accurate assessment of the hydraulic properties of discrete fractures. High-resolution Navier-Stokes simulations provide an accurate description of the flow within the fractures, including fracture upscaling. However, its excessive computational requirements make it impractical. The traditionally used cubic law for fracture upscaling is known for its poor accuracy. This work introduces a new analytical model based on cubic law to estimate hydraulic properties of 3D rock fractures with the irregular contact-area distribution. We first briefly review the applicability of the existing models in the literature. Most of the current models exhibit major limitations related to prediction accuracy and practicality. For instance, most models neglect the effect of contact-area distribution. As a result, they fail to capture properly the heterogeneous and anisotropic flow behaviors caused by irregular contact-area distribution. In addition, some models work well only for idealized cases, such as parallel-smooth fractures with specific shapes of contact areas. Others are only valid for cases with fractional contact area and relative roughness less than certain values. Alternatively, we propose a dynamic indicator using a particle-percolation approach to quantify the effect of the contact-area distribution. We then introduce a more general modified cubic law, which accounts for different factors, including variable aperture, roughness, flow tortuosity, and contact-area distribution. The proposed model predictions are then compared with the solutions of the 3D high-resolution Navier-Stokes simulations and experimental measurements collected from public resources. We assess the predictability of our model and benchmark it with other existing models from the literature with dozens of fracture cases. We show significant superiority of our model compared with other existing models, especially for cases with pronounced fracture anisotropy where the impact of the fracture contact area is dominant. Moreover, results show that the hydraulic aperture decreases with the increase of frictional contact area almost linearly. The contact-area distribution shows a significant impact on hydraulic properties even with the same size of contact regions. We introduce a new analytical model to estimate the hydraulic properties of 3D partially-open rock fractures. Based on our benchmark that included dozens of fractures, our model is superior to commonly used models in the literature. The proposed model also retains the simplicity and efficiency of the cubic law, and can be easily implemented in workflows for reservoir characterization and modeling.

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Section: Comparison With High-resolution Ns Solutionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analytical and Numerical Assessment of Hydraulic Properties of 3D Partially-Open Rock Fractures

Alsinan

Kwak

et al. 2022

Day 3 Wed, February 23, 2022

Self Cite

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“…However, the actual apertures of rock fractures are usually larger than 2 × 10 −4 mm, especially in carbonate rocks. According to He et al [19], the cubic law often leads to significant errors in the estimated flow conductivity. Various methods have been proposed in the literature to modify the cubic law to consider the deviation caused by the non-ideality of the fracture's geometric properties [20][21][22].…”

Section: Prediction Model Of Transmissivitymentioning

confidence: 99%

“…Various methods have been proposed in the literature to modify the cubic law to consider the deviation caused by the non-ideality of the fracture's geometric properties [20][21][22]. He et al [19] summarized dozens of modified cubic law-based models from the literature, by which correction factors related to the fracture aperture, surface roughness, and flow tortuosity are considered. In addition, DNAPLs exhibit high viscosity and may not fulfill the cubic law assumptions.…”

Section: Prediction Model Of Transmissivitymentioning

confidence: 99%

Evaluating the Hydraulic Conductivity of Dense Nonaqueous Phase Liquid in a Single Fracture of Rock-like Material

et al. 2022

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To investigate the seepage characteristics of dense nonaqueous phase liquids (DNAPLs) in rock fractures, two types of NAPLs (paint and creosote) were used in triaxial permeability tests conducted on single-fracture samples. The hydraulic conductivity of rock fractures with different apertures, confining pressures, and fluid properties was measured, and the influence of various physical factors on transmissivity was explored. The results demonstrated the following: (1) Fracture aperture and fluid viscosity are the main factors influencing transmissivity; (2) The widely used cubic law fails to effectively predict the transmissivity of high-viscosity liquids in a fracture, and the influence of liquid viscosity is considerably higher than that predicted by the cubic law; and (3) This study proposed a transmissivity prediction model of DNAPLs in a rock fracture based on multivariate regression analysis. The proposed model provides more accurate prediction results than those predicted by the cubic law, and is applicable to fracture apertures ranging from 5 × 10−4 to 2.5 × 10−3 m as well as to every kind of fluid used in this study.

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“…Evaluation of rock properties and fluid flow behaviors in rock samples provides valuable information to set up parameters for large-scale reservoir simulation (Geiger et al, 2010;He, Sinan, et al, 2021;Hoteit & Firoozabadi, 2008a, 2008b. However, apart from prohibitive acquisition cost, physical rock samples are risky to be damaged during core flooding experiments.…”

Section: Introductionmentioning

confidence: 99%

Digital Rock Reconstruction Using Wasserstein GANs with Gradient Penalty

Zhu

et al. 2022

Day 1 Mon, February 21, 2022

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Due to the scarcity and vulnerability of physical rock samples, digital rock reconstruction plays an important role in the numerical study of reservoir rock properties and fluid flow behaviors. With the rapid development of deep learning technologies, generative adversarial networks (GANs) have become a promising alternative to reconstruct complex pore structures. Numerous GAN models have been applied in this field, but many of them suffer the unstable training issue. In this study, we apply the Wasserstin GAN with gradient penalty, also known as the WGAN-GP network, to reconstruct Berea sandstone and Ketton limestone. Unlike many other GANs using the Jesnen-Shannon divergence, the WGAN-GP network exhibits a stable training performance by using the Wasserstin distance to measure the difference between generated and real data distributions. Moreover, the generated image quality correlates with the discriminator loss. This provides us an indicator of the training state instead of frequently subjective assessments in the training of deep convolutional GAN (DCGAN) based models. An integrated framework is presented to automate the entire workflow, including training set generation, network setup, model training and synthetic rock validation. Numerical results show that the WGAN-GP network accurately reconstructs both Berea sandstone and Ketton limestone in terms of two-point correlation and morphological properties.

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A corrected cubic law for single-phase laminar flow through rough-walled fractures

Cited by 67 publications

References 45 publications

Analytical and Numerical Assessment of Hydraulic Properties of 3D Partially-Open Rock Fractures

Analytical and Numerical Assessment of Hydraulic Properties of 3D Partially-Open Rock Fractures

Evaluating the Hydraulic Conductivity of Dense Nonaqueous Phase Liquid in a Single Fracture of Rock-like Material

Digital Rock Reconstruction Using Wasserstein GANs with Gradient Penalty

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