ANALYTICAL SOLUTIONS FOR PERMEABILITY OF A THREE-DIMENSIONAL FRACTAL-LIKE TREE NETWORK MODEL WITH FRACTURES HAVING VARIABLE WIDTHS

Fractals ◽  
2020 ◽  
Vol 28 (01) ◽  
pp. 2050013
Author(s):  
RICHENG LIU ◽  
LIYUAN YU ◽  
YANG GAO ◽  
MING HE ◽  
YUJING JIANG
Keyword(s):  
Network Model ◽  
Analytical Solutions ◽  
Constant Width ◽  
Fracture Network ◽  
Length Ratio ◽  
Width Ratio ◽  
Fracture Aperture ◽  
Fracture Width ◽  
Fracture Length ◽  
Aperture Ratio

This study proposed analytical solutions for permeability of a fractal-like tree network model with fractures having variable widths, which has not been reported before, if any. This model is more realistic with natural fracture networks than the traditional constant width fracture network models. The results show that considering fracture width variations decreases the permeability. Taking the fracture width ratio that equals to 0.6 and the total number of branching levels that equals to 30 as an example, the permeability decreases by more than three orders of magnitude with respect to that of a constant width fracture network model. The fracture length ratio plays a more significant role in permeability when it is larger than 0.8 than that is less than 0.8. The permeability is more sensitive to the fracture aperture ratio that is less than 0.8. When the total number of branching levels is large (i.e. 30), the permeability changes significantly (i.e. more than three orders of magnitude); whereas when the total number of branching levels is small (i.e. 5), the permeability varies in a small range (i.e. less than one order of magnitude). When taking into account the relationships among fracture length ratio, fracture aperture ratio and fracture width ratio, the parameters can be easily obtained and analytical solutions for permeability can also be easily derived. The empirical function for predicting critical hydraulic gradient is proposed, which can be used to estimate whether the fluid flow is within the linear flow regime and whether the proposed analytical solutions are applicable in the present study.

scholarly journals Study on the effects of fracture on permeability with pore-fracture network model

2018 ◽  
Vol 36 (6) ◽  
pp. 1556-1565 ◽  
Author(s):  
Chunyan Jiao ◽  
Yong Hu ◽  
Xuan Xu ◽  
Xiaobing Lu ◽  
Weijun Shen ◽  
...  
Keyword(s):  
Network Model ◽  
Fracture Network ◽  
Network Control ◽  
Control Mode ◽  
Fractured Reservoir ◽  
Fracture Density ◽  
Gas Reservoirs ◽  
Fracture Length ◽  
Fracture Development ◽  
The Matrix

Reservoir quality and productivity of fractured gas reservoirs depend heavily on the degree of fracture development. The fracture evaluation of such reservoir media is the key to quantify reservoir characterization for the purposes such as well drilling and completion as well as development and simulation of fractured gas reservoirs. In this study, a pore-fracture network model was constructed to understand the effects of fracture on permeability in the reservoir media. The microstructure parameters of fractures including fracture length, fracture density, fracture number, and fracture radius were analyzed. Then two modes and effects of matrix and fracture network control were discussed. The results indicate that the network permeability in the fractured reservoir media will increase linearly with fracture length, fracture density, fracture number, and fracture radius. When the fracture radius exceeds 80 µm, the fracture radius has a little effect on network permeability. Within the fracture density less than 0.55, it belongs to the matrix control mode, while the fracture network control mode is dominant in the fracture density exceeding 0.55. The network permeability in the matrix and fracture network control modes is affected by fracture density and the ratio of fracture radius to pore radius. There is a great change in the critical density for the matrix network control compared with the fracture network control. This work can provide a better understanding of the relationship between matrix and fractures, and the effects of fracture on permeability so as to evaluate the fluid flow in the fractured reservoir media.

Modeling Coupled Fracture-Matrix Fluid Flow in Geomechanically Simulated Fracture Networks

2005 ◽  
Vol 8 (04) ◽  
pp. 300-309 ◽  
Author(s):  
Zeno G. Philip ◽  
James W. Jennings ◽  
Jon E. Olson ◽  
Stephen E. Laubach ◽  
Jon Holder
Keyword(s):  
Fluid Flow ◽  
Finite Difference ◽  
Flow Simulation ◽  
Fracture Network ◽  
Fracture Aperture ◽  
Grid Cells ◽  
Fracture Networks ◽  
Fracture Permeability ◽  
Fracture Length ◽  
Fracture Patterns

Summary In conventional reservoir simulations, gridblock permeabilities are frequently assigned values larger than those observed in core measurements to obtain reasonable history matches. Even then, accuracy with regard to some aspects of the performance such as water or gas cuts, breakthrough times, and sweep efficiencies may be inadequate. In some cases, this could be caused by the presence of substantial flow through natural fractures unaccounted for in the simulation. In this paper, we present a numerical investigation into the effects of coupled fracture-matrix fluid flow on equivalent permeability. A fracture-mechanics-based crack-growth simulator, rather than a purely stochastic method, was used to generate fracture networks with realistic clustering, spacing, and fracture lengths dependent on Young's modulus, the subcritical crack index, the bed thickness, and the tectonic strain. Coupled fracture-matrix fluid-flow simulations of the resulting fracture patterns were performed with a finite-difference simulator to obtain equivalent permeabilities that can be used in a coarse-scale flow simulation. The effects of diagenetic cements completely filling smaller aperture fractures and partially filling larger aperture fractures were also studied. Fractures were represented in finite-difference simulations both explicitly as grid cells and implicitly using nonneighbor connections (NNCs) between grid cells. The results indicate that even though fracture permeability is highly sensitive to fracture aperture, the computed equivalent permeabilities are more sensitive to fracture patterns and connectivity. Introduction High-permeability fracture networks in a matrix system can create high-conductivity channels for the flow of fluids through a reservoir, producing larger flow rates and, therefore, larger apparent permeabilities. The presence of fractures can also cause early breakthrough of the displacing fluid and lead to poorer sweep efficiencies in displacement processes. A better understanding of reservoir performance in such cases may be obtained by including the details of the fluid flow in fractures in a coupled fracture-matrix reservoir flow model. It is very difficult to directly measure interwell fracture-network geometry in sufficient detail to model its effect on reservoir behavior. Thus, most modeling approaches have been statistical, using data from outcrop and wellbore observations to determine distributions of fracture attributes such as fracture length, spacing, and aperture to randomly populate a field. In this paper, we use a mechanistic approach to generate the fracture patterns. Attributes of the fracture network depend on the applied boundary conditions and material properties.

Propagation of a Vertical Hydraulic Fracture

1972 ◽  
Vol 12 (04) ◽  
pp. 306-314 ◽  
Author(s):  
R.P. Nordgren
Keyword(s):  
Cross Section ◽  
Volume Change ◽  
Continuity Equation ◽  
Large Time ◽  
Constant Width ◽  
Approximate Solutions ◽  
Fracture Plane ◽  
Fluid Loss ◽  
Fracture Width ◽  
Fracture Length

Abstract This paper treats the propagation of hydraulic fractures of limited vertical extent and elliptic cross-section with the effect of fluid loss included. Numerical and asymptotic approximate solutions in dimensionless form give the fracture length and width at any value of time or any set of physical parameters. The insight provided by The dimensionless parameters. The insight provided by The dimensionless results and approximate solutions should be useful in the design of fracture treatments. Introduction The theory and practice of hydraulic fracturing has been reviewed by Howard and Fast. Therefore, we confine our discussion of previous investigations to those pertinent to the present study of the propagation of vertical fractures. propagation of vertical fractures. An important theoretical result is Carter's formula for the area of a fracture of constant width formed by injection at constant rate with fluid lost to the formation. For a vertical fracture of constant height, Carter's formula gives fracture length as a function of time. In general, Carter's assumption of constant width is not realistic. However, at large values of time the effect of this assumption becomes insignificant since the effect of fluid loss dominates. The width of a vertical fracture was first investigated by Khristianovic and Zheltov under the assumption that the width does not vary in the vertical direction. Thus, a state of plane strain prevails in horizontal planes and the width can be prevails in horizontal planes and the width can be determined as the solution of a plane elasticity problem. An approximate solution is found in Ref. 3 problem. An approximate solution is found in Ref. 3 upon neglect of fluid loss, fracture volume change, and pressure variation along the fracture. The fracture length is determined by the condition of finite stress at the fracture tip. Baron et al. and Geertsma and de Klerk have included the effect of fluid loss in the approach of Ref. 3. Geertsma and de Klerk give simple approximate formulas for fracture length and width. A different approach to the determination of fracture width was taken by Perkins and Kern. They considered a vertically limited fracture under the assumption of plane strain in vertical planes perpendicular to the fracture plane. The perpendicular to the fracture plane. The cross-section of the fracture is found to be elliptical, and the maximum width decreases along the fracture according to a simple formula that contains the fracture length. In the derivation of this formula, fluid loss and fracture volume change are neglected in the continuity equation and the fracture length is not determined. In a subsequent application, a "reasonable" fracture length was assumed. Carter's formula for length and the width formula of Perkins and Kern are both cited by Howard and Fast, and combined use of the two formulas is believed to be common practice. The present theoretical investigation is concerned with vertically limited fractures of the type studied by Perkins and Kern. However, we include the effects of fluid loss and fracture volume change in the continuity equation. Consequently, fracture length is determined as part of the solution. General results for the variation of fracture width and length with time are obtained in dimensionless form by a numerical method. In addition, asymptotic solutions are derived for large and small values of time. The small-time solution is also the exact solution for the case of no fluid loss to the formation. For large values of time our asymptotic formula for fracture length is identical with Carter's formula at large time. Our large-time formula for fracture width differs from the formula of Perkins and Kern by a numerical factor that varies along the fracture. In comparison with our formula, this formulas overestimates the width by 12 percent at the well and 24 percent at the midlength of the fracture. At early times Perkins and Kern's formulas for width in terms of length is again a fair approximation to our result. However, our formula for length differs from Carter's formula, which is not applicable since the neglected width variation is important at early times. The results for the width of a vertically limited fracture as obtained here and in Ref. 6 differ from the results for vertically constant fractures. SPEJ P. 306

Dynamic imbibition with aid of surfactant in tight oil fracture network model

2020 ◽  
Vol 193 ◽  
pp. 107393
Author(s):  
Yongpeng Sun ◽  
Kai Gao ◽  
Zhihao Yu ◽  
Yanchao Fang ◽  
Yilin Chang ◽  
...  
Keyword(s):  
Network Model ◽  
Fracture Network ◽  
Tight Oil

scholarly journals A New Approach for Automatic Optimization of Complex Fracture Network in Shale Reservoirs

Lithosphere ◽  
2021 ◽  
Vol 2021 (Special 1) ◽  
Author(s):  
Haibo Wang ◽  
Tong Zhou ◽  
Fengxia Li
Keyword(s):  
Shale Gas ◽  
Flow Model ◽  
Optimization Method ◽  
Fracture Network ◽  
Gas Reservoirs ◽  
Fracture Length ◽  
Complex Fracture ◽  
Shale Gas Reservoirs ◽  
Automatic Optimization ◽  
Complex Fracture Network

Abstract Shale gas reservoirs have gradually become the main source for oil and gas production. The automatic optimization technology of complex fracture network in fractured horizontal wells is the key technology to realize the efficient development of shale gas reservoirs. In this paper, based on the flow model of shale gas reservoirs, the porosity/permeability of the matrix system and natural fracture system is characterized. The fracture network morphology is finely characterized by the fracture network expansion calculation method, and the flow model was proposed and solved. On this basis, the influence of matrix permeability, matrix porosity, fracture permeability, fracture porosity, and fracture length on the production of shale gas reservoirs is studied. The optimal design of fracture length and fracture location was carried, and the automatic optimization method of complex fracture network parameters based on simultaneous perturbation stochastic approximation (SPSA) was proposed. The method was applied in a shale gas reservoir, and the results showed that the proposed automatic optimization method of the complex fracture network in shale gas reservoirs can automatically optimize the parameters such as fracture location and fracture length and obtain the optimal fracture network distribution matching with geological conditions.

scholarly journals Flow characteristics of fractal fracture with different fractal dimension and different fracture width

2021 ◽  
Vol 25 (6 Part B) ◽  
pp. 4477-4484
Author(s):  
Jun-Jun Liu ◽  
Jing Xie ◽  
Yi-Ting Liu ◽  
Gui-Kang Liu ◽  
Rui-Feng Tang ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Rock Mass ◽  
Flow Characteristics ◽  
Fracture Network ◽  
Basic Element ◽  
Single Fracture ◽  
Flow State ◽  
Complex Flow ◽  
Fracture Width ◽  
Fracture Models

Single fracture is the most basic element in complex fracture network of rock mass. Therefore, the study of flow characteristics of single fracture is an important way to reasonably predict the complex flow state in engineering rock mass. In order to study the flow characteristics of fractal single fracture, fracture models with dif?ferent fractal dimension and different fracture width are established in this paper. The results show that: the blocking effect of rough structure on fluid is obviously enhanced under high pressure. In addition, it is weakened and reaches a steady-state with the increase of fracture fractal dimension. The larger the fracture width is, the more obvious the phenomenon is. The hydraulic gradient index tends to 0.5 with the increase of fracture width when fractal dimension is greater than 1.3. It also could tend to 0.5 with the increase of fractal dimension when fracture width is greater than 1 mm.

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