Fracture Intersections Research Articles

Treatments of Fractures Intersection in the Enriched-Embedded Discrete Fracture Model (nEDFM) for Porous Flow

Treatments of Fractures Intersection in the Enriched-Embedded Discrete Fracture Model (nEDFM) for Porous Flow

Topology-based 3-D fractal characterization of fracture complexity in propagation experiment

The complexity of the fracture network, formed by the interaction of hydraulic fractures and natural fractures during hydraulic fracturing, is one of the important criteria for guiding shale gas field production. In this study, we selected the deep shale of the Longmaxi formation as the object of study. Through indoor hydraulic fracturing experiments and fracture 3-D reconstruction technology, we conducted a quantitative study on the complexity of the fracture network created by the influence of hydraulic and natural fractures interacting with each other during hydraulic fracturing. The results show that the fractal dimensions, average connection numbers of topological structure branches, and relative lengths of fracture intersections for hydraulic fractures in 10 groups of specimens are 1.93-2.27, 0-1.143, and 1.02-1.98, respectively.

An Analytical Method for Determining the Bottom‐Hole Pressure of Vertical Well With Multiple Fractures

Hydraulic fracturing has been a common treatment to enhance well productivity, especially in tight oil and gas reservoirs. Studying the pressure response characteristics of fractured reservoir has been a hot topic due to the significant contribution of fractures to conductivity enhancement. Because of the difficulty in describing the flow problems in vertical fractured well and the lack of related literatures, a novel method to determine the bottom‐hole pressure of a vertical well with multiple fractures based on Newman product method is proposed in this paper. First, the physical model and corresponding mathematical model are established. Then, the solution of bottom‐hole pressure can be obtained through Laplace transformation. Sequentially, the validations of computational method and computational codes contain are presented. From the view of curve fitting and interpretation results, the calculations in this paper are in good agreement with the previous numerical results and our computation method is reliable. Next, a group of typical curves are generated to analyze the flow regimes. And a series of curves are generated to demonstrate effects of key parameters on curve shape. The results indicate that increasing the fracture wings, fracture intersection angle, and fracture length uniformity can enhance the well productivity. Lastly, a case study is exhibited to show the application of the proposed method.

Investigation into contributions of fracture geometry characterization and interference to productivity of multi-fractured vertical gas well

Vertically fractured wells have been widely used to develop tight gas reservoirs. Characterizing the geometry of fractures created by hydraulic fracturing is a key factor influencing the productivity of such wells. Appropriately modeling the shapes of actual fractures is thus important for accurately predicting the well productivity. Past research in the area has tended to simplify fractures into straight lines, but this does not adequately represent the complex hydraulic fractures encountered in fractured reservoirs. In this study, we propose a generalized model for the productivity of a vertically fractured well to capture the characteristics of hydraulic fractures in gas fields. The proposed model accounts for several relevant mechanisms, including Knudsen slippage, characteristics of complex fracture geometry, and interference caused by multiple fractures. We validate the proposed model by applying it to a series of cases considered in the literature, and analytically examine key parameters such as the fracture number Nf and characteristics of the fracture geometry, including the length ratio a, width ratio b, branching angle θ and level n, fracture penetration ratio l0re, asymmetry in the length of fracture wing, and fracture intersection angle φ et al. The results show that there is a small drop in pressure between the inlet and outlet of the fracture. The well productivity is found to be positively associated with Nf, l0re, φ, and asymmetry in the length of the fracture wing. Furthermore, the productivity of a well intercepted by tree-shaped fractures primarily depends on a and n, and is almost entirely unaffected by b. By contrast, the well productivity gradually decreases with increasing θ. A tree-shaped fracture significantly enhances the well productivity by 110% (a=0.9, n=3), compared with a straight fracture. Finally, we provide an approach to increase the productivity of vertical wells based on the findings of this study.

Consistent treatment of shear failure in embedded discrete fracture models using XFVM

AbstractUnderstanding deformations and fluid flow in fractured rocks is of central importance for many subsurface flow applications. Thus, numerical frameworks are needed that capture the coupled mechanical and hydraulic behaviour, including scenarios with complex fracture networks. This paper employs the extended finite volume method to represent fracture manifolds in a poroelastic matrix domain and to compute shear and tensile displacements of fracture segments. However, using embedded fractures with non‐conforming grids can lead to severe convergence issues while computing shear slip and tensile opening of intersecting and parallel fractures, particularly if they have similar slopes. Our proposed solution of this problem is to slightly deform the fracture geometry by merging critical segments. We discuss and show examples of which attributes the merged segment has to adopt to ensure the correct slip behaviour at an intersection. Thereby it is crucial that the flow topology remains unaltered. Analysing failures of kinked fractures and fracture intersections show the flexibility of the devised algorithm. Moreover, it is demonstrated that deformation and opening patterns of a natural network with more than 200 fractures are qualitatively predicted very well. This method is a simple solution to treat multiple fracture segments in a grid cell, hence it can be used for any model embedding fractures in non‐conforming grids.

An efficient computational framework for height-contained growing and intersecting hydraulic fracturing simulation via SGBEM–FEM

An efficient computational framework to model the growth of intersecting height-contained hydraulic fractures is proposed. The fracture in solids is modeled by the classical theory of linear elastic fracture mechanics, whereas the injection flow in hydraulic fractures is treated as channel flow. The governing equations of fracture mechanics are formulated in terms of weakly-singular weak-form boundary integral equations, with the knowledge of the fracture surface geometry exploited to reduce the integral dimension. The fluid flow within the fracture is treated using finite element method as one dimensional flow in an arbitrarily curved channel. The symmetric Galerkin boundary element method and finite element method are coupled with the traction continuity condition. The model is then formulated in a variational form and augmented with Lagrange multipliers to prescribe displacement constraints on intersections of hydraulic fractures, while fluid constraints are enforced by a consolidation of associated pressure degrees of freedom. Pertinent numerical implementation techniques, including spatial and temporal discretizations, special crack tip element, crack propagation criteria and remeshing strategy, are presented. The proposed framework is verified by comparing to the numerical results from a three dimensional hydraulic fracturing simulator and then verified by comparing the stress intensity factors to the XFEM and Murakami’s results for both star shaped cracks and symmetric branched cracks. The verification shows the utility properly enforces the physical constraints on the intersections of fractures. Three numerical examples are shown to demonstrate the capability of the proposed computational framework modeling the intersecting hydraulic fracturing process in a single or separated height-contained pay zones.

The Criteria for Transition of Fluid to Nonlinear Flow for Fractured Rocks: The Role of Fracture Intersection and Aperture

Understanding the fluid pattern is of special significance for estimating the hydraulic conductivity of fractured rock masses. The nonlinearity of fluid flow in discrete fracture networks (DFNs) originates from inertial effects and is enhanced by complex geometric topologies, which produces additional viscous friction and is subject to inertia effects, consequently transitioning the fluid to the nonlinear flow regime. Therefore, it is important to obtain the critical conditions for the transition of a fluid from laminar to turbulent flow. To investigate the role of fracture aperture and fracture intersection on the onset of the transition of a fluid to nonlinear flow in fractured rocks, the fluid dynamic computation was performed by solving Navier–Stokes (N–S) equations in DFN models. The results show that the flow flux initially linearly correlates with the hydraulic gradient (J) and the permeability of DFNs initially remains constant. As the hydraulic gradient increases, the flow flux presents a strong nonlinear relationship with the hydraulic gradient, and the permeability decreases dramatically. In particular, significant inertial effects appear earlier with a large fracture aperture or a dense fracture intersection. A critical hydraulic gradient (Jc) is proposed to judge the onset of nonlinear flow. The mathematical expression of Jc and Forchheimer coefficients A and B involving the fracture aperture and fracture intersection density is established through a multiple regression algorithm. Finally, the reliability of the predictive model was verified by comparing the results of the prediction and fluid dynamic computation of a series of DFN models with well-known geometric distributions. The consistency of the fitted equations and a correlation coefficient greater than 0.9 between them indicate that the predictive model proposed in this study is reliable.

Effects of inflection curvature on flow interference at furcating fracture intersections

Effects of inflection curvature on flow interference at furcating fracture intersections

Fracture Network Analysis of Karstified Subis Limestone Build-Up in Niah, Sarawak

Understanding complex carbonate fracture networks and karstification at various geological scales is challenging, especially with limited multi-scale datasets. This paper aims to reduce uncertainty in the fracture architecture of Central Luconia karstified reservoirs by narrowing observational gaps between seismic and well data by using the discrete fracture models of exposed limestone outcrops as analogues for the subsurface carbonate reservoir. An outcrop-based fracture network characterisation of a near-surface paleo-karst at Subis Limestone combined with lineament analysis was conducted to extract fracture parameters. The karst structure was first delineated using a digital elevation map and outcrop examination. Then, topology analysis was performed, following the creation of two-dimensional discrete fracture models. Two main fracture sets oriented northeast–southwest and northwest–southeast and 79 potential dolines were identified. Fracture intersections, northeast–southwest major orientations, and drainage systems highly influenced the karst features. The Subis Limestone fracture model revealed that the highest number of fractures and total length of fractures were concentrated in the northern part of the Subis Limestone build-up (X: 250–350, Y: 150–250) and became denser towards the northwest direction of the outcrop (X: 600–800). The fractures in the Subis paleo-karsts appear isolated, with I-nodes ranging from 0.74 to 0.94. Hence, it is crucial to incorporate matrix porosity into multiple scales of fracture network modelling to improve upscaling and the modelling of fracture–vug networks, as well as to minimise the underestimation of discrete fracture networks in fractured and karstified limestone.

DFNMesh: Finite element meshing for discrete fracture matrix models

This paper presents a novel methodology for robust Finite Element (FE) mesh generation of Discrete Fracture Matrix (DFM) models. The method can handle the complete multi-dimensional domain from the tridimensional porous rock matrix, through fracture surfaces, down to open curves for fracture–fracture intersections. The accompanying open-source code is written in modern C++ with a JSON interface and largely relies on two state-of-the-art FE libraries: NeoPZ and Gmsh. Starting from a user-defined coarse mesh, fractures are sequentially read as convex polygons and introduced without distortions to the coarse geometry. The main steps involve: intersect edges by checking for nodes on opposite sides of the fracture plane, extend intersections from edges to faces, coalesce intersections to closest existing nodes (given a tolerance), refine interface elements to conform to the fracture, identify subsets of fracture surface, mesh the surface, and locate boundaries and intersections where they arise. Finally, the space around fractures is filled with the fine-scale unstructured mesh, which is kept conformal. The robustness of the implementation is derived from the consistent background of well-defined and simple premises like convexity and side-specific element neighborhood. Results show that the proposed technique can construct adequate 3D DFM grids, while still giving users freedom to adjust between geometrical fidelity and mesh quality through more aggressive feature rejection.

Coupled fluid flow, solute transport and dissolution processes in discrete fracture networks: An advanced Discontinuous Galerkin model

Modeling dissolution processes in discrete fracture networks (DFNs) is a challenging task. Challenges are related to the highly nonlinear coupling between flow, mass transport, and reactive processes associated with fracture aperture evolution by dissolution. Further, advection-dominated transport due to fast fluid flow in fractures renders the problem more complex from a computational point of view, as traditional numerical methods may introduce unphysical oscillations or excessive numerical diffusion. The Discontinuous Galerkin (DG) method is known to be suitable for the simulation of advection-dominated transport. In this work, an advanced DG model is developed to model transport with dissolution in DFNs. We propose an upwind formulation to deal with the upstream concentration at the intersection of several fractures. The upstream concentration at an intersection node is calculated based on the average nodal concentrations of all the fractures having an inflow at that node, weighted by the volumetric fluxes of these fractures. The dispersion term is discretized with the Mixed Finite Element (MFE) method, which ensures the continuity of the dispersive flux at the intersection of fractures with different apertures. The obtained nonlinear coupled flow-transport-dissolution equations are discretized in time with a high-order scheme via the method of lines (MOL). Numerical examples and comparisons with standard finite element (FE) and finite volume (FV) solutions are performed to investigate the correctness and efficiency of the developed model. Results show that the new DG-DFN model avoids unphysical oscillations encountered with the standard FE method and strongly reduces the numerical diffusion observed with the upwind FV scheme. The DG-DFN model is then used to investigate the effect of the dissolution rate on the flow, transport, and aperture evolution processes for a single fracture and for a DFN. A quasi-linear evolution of the fracture aperture is observed for low dissolution rates. For high dissolution rates, a funnel-shaped enlargement is observed with a significant widening for the fractures near the inlet and minor effects for those away from the injection location.

A numerical pressure transient model of fractured well with complex fractures of tight gas reservoirs considering gas-water two phase by EDFM

Tight gas reservoirs considering gas-water two phase is common and show obvious permeability stress sensitivity and non-Darcy seepage characteristic. However, conventional analytical and semi-analytical solving method cannot simulate wellbore pressure response of tight gas reservoirs considering gas-water two phase. Numerical model can overcome the disadvantage of analytical and semi-analytical method and achieve wellbore pressure response simulation of fractured well with complex fracture. Therefore, a gas-water two phase mathematical model of the fractured well is established and solved by embedded discrete-fracture method (EDFM) and finite volume method. Transmissibility corrections is improved on the basis of the framework of Matlab Reservoir Simulation Toolbox (MRST). Result shows that the seven flow regimes can be found according to the pressure drop derivative curves characteristic. When permeability stress sensitivity and non-Darcy is considered, pressure and derivative curve of middle-late stage shows obvious ‘upwarp’ and non-Darcy make reservoirs pressure uneven distribution. Induced fractures parameters have obvious influence on pressure and derivative curves during early and middle flow regime. In addition, fracture intersection and neighbor well production style has obvious influence on pressure curve.

Investigation into a perfect matching between fracture transfer performance and vertical well productivity based on multi-scale and total factor characteristic models

In fractured tight gas reservoirs, complex hydraulically induced fracture networks determine fluid flowing abilities of reservoirs. Thus, characterizing the complex fracture networks and revealing fracture transfer performances become a challenging work because of fracture branching, bending, and reversing in fractured reservoirs. In this paper, a fractal-like tree-shaped fracture model for gas transfer is proposed to optimize flow conductivity, pressure distribution at fracture intersection points, and flow transfer in such a complex fracture network considering the multi-scale effect, and total factor characteristics, including the length ratio, width ratio, branching angle, and branching level. The model is implemented to conduct validation against the experiment data in the literature. Subsequently, applying the proposed fracture model, the productivity equation for a vertical gas well intercepted by the fractal-like tree-shaped fracture network is further formulated. In addition, the good match with productivity simulation validates the accuracy of the developed productivity model for a vertical gas well. As a result, the impacts of the Knudsen number, fracture total factor characteristics, reservoir parameters, etc. on fracture transfer performances and well productivity are examined using the two proposed models. The results demonstrate that optimum fracture transfer performances do not match with the maximum well productivity. In contrast, the well productivity is jointly determined by both inlet flow volume of the fracture network and matrix permeability. Hence, a new formula considering both fracture characteristics and reservoir properties is proposed to match with the optimum fracture total length and maximum well productivity, thereby contributing to high-efficient and economic exploration of tight gas reservoirs.

An inversion for asymmetric hydraulic fracture growth and fracture opening distribution from tilt measurements

The eigenstrain tensor is defined in terms of the unit vector normal to the fracture plane and the dislocation vector to characterize the fracture geometry and to determine the fracture induced deformation field. Compared to the conventional nonlinear fracture model, the forward fracture model provides a linear relationship between fracture geometry parameters (eigenstrain) and the induced deformation. Therefore, a linear inverse problem needs to be tackled in mapping the fracture geometry by inversion of tilt observations. The fracture orientation and opening distribution of a tensile-dominated hydraulic fracture can be mapped iteratively in a coupled way by using the forward model defined in terms of the dislocation vector. The proposed analysis method is applied to field tilt data collected for monitoring the growth of a hydraulic fracture placed in the preconditioning of a roof rock over a coal longwall panel at a test site. Inversion of the tilt data produces a low fracture dip angle of 6.8°, which agrees with a nearly horizontal fracture orientation confirmed by intersection data collected in offset monitoring boreholes. Tikhonov regularization technique is applied to stabilize the discrete ill-posed inverse problem. The regularized solution provides information on the fracture opening distribution and asymmetric fracture growth. The inversion shows that the fracture grows uniformly and roughly in a radial pattern at early injection times, but grows asymmetrically, preferentially, and consistently to the northwest during later times. The predicted fracture growth agrees with the temperature logging to measure fracture intersections with the offset monitoring boreholes.

Effects of intersection geometry on flow velocity interference and flow rate redistribution in furcating fractures

Fracture intersections are an essential element of fracture networks in energy extraction. The accurate evaluation of the flow behavior at intersections in the furcating fracture is the key to describing the flow behavior of fractured reservoirs, yet fracture intersections are often oversimplified or even ignored. To fill this knowledge gap, the effect of geometric characteristics internal to the intersection was investigated based on direct numerical simulation by solving Navier-Stokes equations. Two parameters, θ1 and θ2, which are the angles between the normal inlet branch direction and the two sides of a closed triangle, are introduced to characterize the geometry of the intersection in a furcating fracture, and the role of geometrical parameters θ1 and θ2 in the interference effect and flow rate distribution is investigated. The results demonstrate that intersection geometry interferes with the fluid flow passing through the intersection to a certain range. With an increasing hydraulic gradient J and θ, the flow interference range increases. Under the conditions of these simulations (J = 10−3 – 10−2, Re = 101–102), J is linearly correlated with flow rate q, but with an increasing J and θ, the area and percentage of the low-velocity zone caused by an intersection increases leading to the enhancement of nonlinear flow. Furthermore, based on the simulation results, an empirical formula for quantifying the flow redistribution at intersections is proposed, contributing to the effectiveness and accuracy of modeling seepage in the fracture networks. Finally, the physical meanings of geometric parameters θ1 and θ2 are determined. This study advances the understanding of flow behavior at intersections commonly observed in discrete fracture networks from a fresh perspective, despite the difficulty of monitoring.

Coronal translation of the forearm, proximal capitate, and ulnar styloid predict radial inclination in distal radius fractures in older female patients.

The aims of this study were to identify means to quantify coronal plane displacement associated with distal radius fractures (DRFs), and to understand their relationship to radial inclination (RI). From posteroanterior digital radiographs of healed DRFs in 398 female patients aged 70 years or older, and 32 unfractured control wrists, the relationships of RI, quantifiably, to four linear measurements made perpendicular to reference distal radial shaft (DRS) and ulnar shaft (DUS) axes were analyzed: 1) DRS to radial aspect of ulnar head (DRS-U); 2) DUS to volar-ulnar corner of distal radius (DUS-R); 3) DRS to proximal capitate (DRS-PC); and 4) DRS to DUS (interaxis distance, IAD); and, qualitatively, to the distal ulnar fracture, and its intersection with the DUS axis. In the study (fracture) and control groups, respectively, the mean values were: RI, 17.2° (SD 7.2°; -7° to 35°) and 25.6° (SD 2.6°; 21° to 30°); DRS-U, 13.5 mm (SD 1.7; 4.9 to 20.8) and 15.3 mm (SD 0.72; 13.8 to 16.3); DUS-R, 13.4 mm (SD 2.1; 4.8 to 18.5) and 12.0 mm (SD 0.99; 9.7 to 13.9); DRS-PC (positive value radial to DRS, negative value ulnar), 0.14 mm (SD 5.4; -10.9 to 22.7) and -6.1 mm (SD 1.6; -10.6 to -2.3); and IAD, 25.3 mm (SD 2.5; 17.6 to 31.1) and 27.1 mm (SD 1.5; 24.5 to 31.0). All means were significantly different between the study and control groups. RI correlated strongly with DRS-PC. Ulnar styloid fracture intersection with the DUS axis, reflective of ulnar translation of both radial and ulnar shafts, was associated with significantly lower RI. After DRF, the relationship of the proximal capitate to the DRS axis in the coronal plane correlates with the final radial inclination. Additionally, ulnar styloid intersection with the DUS axis is associated with even lower radial inclination. DRF reduction should seek to restore the normal coronal relationship of both radial and ulnar shafts to their distal counterparts.

Flow of non-Newtonian fluids in single fractures and fracture networks: Current status, challenges, and knowledge gaps

Flow of non-Newtonian fluids in rock fractures is ubiquitous in engineering practice and involves e.g. cement flow in tunnel grouting, drilling fluid flow when a fracture is met during drilling, and flow of fracturing fluids in hydraulic fracturing. In this review article, basic information about rheological behavior of non-Newtonian fluids is provided in Section 1. In Section 2, a summary of equations for the flow of non-Newtonian fluids between smooth parallel plates is provided, and knowledge gaps are identified, including those in two-phase flow. In Section 3, non-Newtonian fluid flow in fracture networks is reviewed, and outstanding research tasks are identified. The article concludes with a summary of current challenges in Section 4. Amongst the main knowledge gaps and challenges identified in the review and relevant for engineering geological practice are fracture flow of thixotropic fluids; two-phase flow regimes and instabilities associated with it; flow of non-Newtonian fluids through (and their mixing with Newtonian fluids at) fracture intersections; efficient algorithms for network flow at arbitrary pressure gradients; leak-off of non-Newtonian fluids through fracture walls; modelling of non-Newtonian fluids that include environmental effects and the resulting multiple couplings and multiphysics.

The Hydraulic Connection Analysis of Dongying Geothermal Fluid Using Hydrochemical Information and Isotope Data in Tianjin Coastal Regions

Dongying’s Paleogene geothermal resources are an important part of the geothermal resources of the Tianjin coastal region. The extent of the geothermal fluid resources and the supply relationship have become increasingly important, and will determine whether demand targets can be met. Dongying’s Paleogene formation in the Tianjin coastal regions is widely distributed to the east of the Cangdong fracture, but it is absent west of the Cangdong fracture. On the basis of introducing the geological characteristics and depositional characteristics of the Dongying formation, we analyzed the hydraulic conductivity of the Cangdong fracture to the Dongying formation geothermal reservoir from the aspects of geological condition, dynamic of groundwater level and hydrologic geochemistry. Based on the hydrochemical information and the isotope data gained during the water quality evaluation and isotope data analysis process, we discovered the main chemical composition, hydrogen and oxygen isotope data and geothermal fluid age are significantly different between the Dongying formation geothermal reservoir and the overlying and underlying geothermal reservoirs. It is inferred that the hydraulic conductivity of the Cangdong fracture to the Dongying formation geothermal reservoir in this area is weak, and along the Haihe fracture, where the Haihe fracture intersects with the Cangdong fracture, there is a certain hydraulic conductivity. In addition, there is no obvious hydraulic connection between the Dongying formation and the upper and lower geothermal reservoirs.

Simulation study of micro-proppant carrying capacity of supercritical CO2 (Sc-CO2) in secondary fractures of shale gas reservoirs

Micro-proppants with stronger portability have more potential to migrate to the massive micro-sized secondary fractures (SFs) or natural fractures activated by supercritical CO2 (Sc-CO2) fracturing in shale gas reservoirs. However, the transportation behaviour of micro-proppants in massive SFs has been scarcely studied to date. In this study, we report the simulation of micro-proppant migration across a fracture intersection during Sc-CO2 fracturing based on a combination of computational fluid dynamics and the discrete element method. A straight fracture intersection model was first validated against experimental data from an earlier study. Next, the influential factors, including fluid viscosity, cross angle, proppant diameter, fluid velocity and the ratio of proppant diameter to SF, were examined in the transportation behaviour of micro-proppants in Sc-CO2 fracturing. The results show that the poor proppant distribution in SFs is dominated by the ultralow viscosity of Sc-CO2, but the decrease of proppant diameter to 25 μm presents slurry flow behaviour, resulting in a migration distance around 8 times longer than that of 200 μm and much stronger proppant-carrying capacity into SFs. The transportation behaviour of micro-proppants into SFs depends on the suspended proppants concentration and the rolling proppants from the proppant embankment in the primary fracture (PF), determined by the combined effects of different factors. Fast fluid velocity of 0.2 m/s increases the priority of the proppant embankment formation in SFs. Cross angles greater than 45° limit the suspended proppants in SF, and the proppant embankment in the SF dominantly depends on rolling proppants from PF. Greater SF aperture facilitates proppants transportation into the SF due to the reduced bridging effect, but not into the PF. The key findings are optimized proppant-carrying capacity into SFs and improved stimulated volume during Sc-CO2 fracturing in shale reservoirs.

Closed‐form solution of fluid flow in and around a crack disk embedded in a 3D porous medium

AbstractThis paper considers the fluid flow through a porous medium containing intersecting fractures and presents three main analytical findings, namely: (1) mass exchange between fractures and surrounding matrix at the fracture intersection; (2) fluid potential solution (pressure field) within the whole domain under the form of a single singular integral equation; and (3) closed‐form solutions of fluid flow in and around a crack disc under a far field pressure gradient. The crack is represented mathematically by a 2D smooth surface (i.e., zero thickness) within a 3D porous medium, while physically by a constant aperture. The fluid flow within the crack obeys Poisseuille's law, while Darcy's law is used to represent the fluid flow in the surrounding matrix. The general solution of pressure field for the general case of multiple intersecting cracks is firstly derived under a singular integral equation form. The mass exchange between the porous matrix and the crack, as well as the mass conservation at the intersection between cracks are the keys to obtaining this general solution. Then, the general solution is written for the case of a single crack. Rigorous derivation of the latter equation allows obtaining a closed‐form solution of flow through a single crack. Introducing this solution of flow into the general equation gives the pressure field around the crack. The solution derived in this paper for a crack disk with Poisseuille's flow is slightly different from the well‐known Eshelby's solution for the case of flattened inclusion in which the flow obeys Darcy's law.