Generally Applicable Method For Calculation Of The Matrix-fracture Fluid Transfer Rates

Abstract The pressure response pattern of a naturally fractured reservoir is considered under the assumption allowing matrix-to-fracture crossflow to result from a diffusion mechanism of fluid transfer through the matrix. The transitional pressure during time-variant crossflow is shown to develop on a semilog plot a linear segment with a slope equal to one-half that of the early- and late-time pressure segments. For a single well, this allows use of a conventional Homer-type analysis. Introduction A naturally fractured formation is generally represented by a tight matrix rock broken up by fractures of secondary origin. The fractures are assumed continuous throughout the formation and to represent the paths of principal permeability. The high diffusivity of a fracture results in a rapid permeability. The high diffusivity of a fracture results in a rapid response along the fracture to any pressure change such as that caused by well production. The rock matrix, having a lower permeability but a relatively higher primary porosity, has a "delayed" response to pressure changes that occur in the surrounding fractures. Such nonconcurrent responses cause pressure depletion of the fracture relative to the matrix, which in turn induces matrix-to-fracture crossflow. This period of transient crossflow takes place immediately after the fracture pressure response and before the matrix and the fracture pressures equilibrate, after which the formation acts as a uniform medium with composite properties. The effect of assumptions made on the nature of matrix and properties. The effect of assumptions made on the nature of matrix and fracture interaction is manifested during this transitional period of matrix-to-fracture fluid transfer. The flux of fluid released by the matrix depends on the matrix size, porosity, permeability, and the matrix/fracture pressure difference. At the matrix/fracture interface, the matrix flux contribution to fracture flow may be assumed proportional to either the pressure difference between matrix and fracture or to the averaged pressure gradient throughout the matrix block. The former assumption, introduced in fractured reservoir description by Barenblatt and Zheltov and Barenblatt et al. and employed by Warren and Root, has an advantage of simplifying the mathematical analysis of the flow problem and a disadvantage of not correctly representing either the mechanism of pressure readjustment between matrix and fracture by time-variant crossflow pressure readjustment between matrix and fracture by time-variant crossflow or the formation pressure response during the transitional time. According to this assumption, the matrix flux is independent of spatial position, which can be true only when pressure is linearly distributed in space-i.e., at a state of pressure equilibrium or at a pseudosteady-state time. This assumption, therefore, is often referred to as a "pseudosteady-state" or "lumped-parameter" flux assumption. It neglects the matrix storage capacitance by allowing an instantaneous pressure drop throughout the matrix as soon as fracture depletion occurs. The pressure response of a medium subject to this assumption has a characteristic S-shape transitional curve with an inflection point. The curve connects the initial pressure segment (the early-time fracture response) to the final pressure segment, representative of the late-time pseudosteady-state flow of an equivalent uniform medium that has fracture permeability and composite (the sum of fracture and matrix) storage. By contrast, the averaged gradient assumption on matrix-to-fracture crossflow, while somewhat complicating a mathematical analysis of the problem, has an advantage of more correctly describing the pressure problem, has an advantage of more correctly describing the pressure equilibration process that occurs during the transitional period. Matrix fluxes arising from fluid expansion forces are subject to Darcy flow and, thus, to diffusivity-type flow constraints. SPEJ p. 769

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The impact of time-dependent matrix-fracture fluid transfer in upscaling match procedures

Journal of Petroleum Science and Engineering ◽

10.1016/j.petrol.2016.07.039 ◽

2016 ◽

Vol 146 ◽

pp. 752-763 ◽

Cited By ~ 8

Author(s):

Manuel Gomes Correia ◽

Célio Maschio ◽

João Carlos von Hohendorff Filho ◽

Denis José Schiozer

Keyword(s):

Time Dependent ◽

Matrix Fracture ◽

Fracture Fluid ◽

Fluid Transfer ◽

The Impact

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An Integrally Embedded Discrete Fracture Model for Flow Simulation in Anisotropic Formations

Energies ◽

10.3390/en13123070 ◽

2020 ◽

Vol 13 (12) ◽

pp. 3070

Author(s):

Renjie Shao ◽

Yuan Di ◽

Dawei Wu ◽

Yu-Shu Wu

Keyword(s):

Flow Simulation ◽

Fracture Model ◽

Fluid Exchange ◽

Two Phase ◽

Fine Grid ◽

Discrete Fracture Model ◽

Matrix Fracture ◽

Discrete Fracture ◽

The Matrix ◽

Anisotropic Formation

The embedded discrete fracture model (EDFM), among different flow simulation models, achieves a good balance between efficiency and accuracy. In the EDFM, micro-scale fractures that cannot be characterized individually need to be homogenized into the matrix, which may bring anisotropy into the matrix. However, the simplified matrix–fracture fluid exchange assumption makes it difficult for EDFM to address the anisotropic flow. In this paper, an integrally embedded discrete fracture model (iEDFM) suitable for anisotropic formations is proposed. Structured mesh is employed for the anisotropic matrix, and the fracture element, which consists of a group of connected fractures, is integrally embedded in the matrix grid. An analytic pressure distribution is derived for the point source in anisotropic formation expressed by permeability tensor, and applied to the matrix–fracture transmissibility calculation. Two case studies were conducted and compared with the analytic solution or fine grid result to demonstrate the advantage and applicability of iEDFM to address anisotropic formation. In addition, a two-phase flow example with a reported dataset was studied to analyze the effect of the matrix anisotropy on the simulation result, which also showed the feasibility of iEDFM to address anisotropic formation with complex fracture networks.

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Well Test Analysis of Multiple Matrix - To -Fracture Fluid Transfer in Fractured - Vuggy Reservoir

10.2118/130557-ms ◽

2010 ◽

Cited By ~ 4

Author(s):

Wahyu Djatmiko ◽

V. Hansamuit

Keyword(s):

Well Test ◽

Well Test Analysis ◽

Test Analysis ◽

Fracture Fluid ◽

Fluid Transfer

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Using Green Supplementary Materials to Achieve More Ductile ECC

Materials ◽

10.3390/ma12060858 ◽

2019 ◽

Vol 12 (6) ◽

pp. 858 ◽

Cited By ~ 8

Author(s):

Yichao Wang ◽

Zhigang Zhang ◽

Jiangtao Yu ◽

Jianzhuang Xiao ◽

Qingfeng Xu

Keyword(s):

Fracture Toughness ◽

Tensile Strain ◽

Tension Test ◽

Construction And Demolition Waste ◽

Demolition Waste ◽

Strain Capacity ◽

Fiber Bridging ◽

Matrix Fracture ◽

The Matrix ◽

Tensile Strain Capacity

To improve the greenness and deformability of engineered cementitious composites (ECC), recycled powder (RP) from construction and demolition waste with an average size of 45 μm and crumb rubber (CR) of two particle sizes (40CR and 80CR) were used as supplements in the mix. In the present study, fly ash and silica sand used in ECC were replaced by RP (50% and 100% by weight) and CR (13% and 30% by weight), respectively. The tension test and compression test demonstrated that RP and CR incorporation has a positive effect on the deformability of ECC, especially on the tensile strain capacity. The highest tensile strain capacity was up to 12%, which is almost 3 times that of the average ECC. The fiber bridging capacity obtained from a single crack tension test and the matrix fracture toughness obtained from 3-point bending were used to analyze the influence of RP and CR at the meso-scale. It is indicated that the replacement of sand by CR lowers the matrix fracture toughness without decreasing the fiber bridging capacity. Accordingly, an explanation was achieved for the exceeding deformability of ECC incorporated with RP and CR based on the pseudo-strain hardening (PSH) index.

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Modeling of Matrix/Fracture Transfer with Nonuniform-Block Distributions in Low-Permeability Fractured Reservoirs

SPE Journal ◽

10.2118/191811-pa ◽

2019 ◽

Vol 24 (06) ◽

pp. 2653-2670 ◽

Cited By ~ 1

Author(s):

Didier–Yu Ding

Keyword(s):

Shale Gas ◽

Shape Factor ◽

Oil Reservoirs ◽

Dual Porosity ◽

Tight Oil ◽

Fracture Networks ◽

Matrix Block ◽

Matrix Fracture ◽

Discrete Fracture ◽

The Matrix

Summary Unconventional shale–gas and tight oil reservoirs are commonly naturally fractured, and developing these kinds of reservoirs requires stimulation by means of hydraulic fracturing to create conductive fluid–flow paths through open–fracture networks for practical exploitation. The presence of the multiscale–fracture network, including hydraulic fractures, stimulated and nonstimulated natural fractures, and microfractures, increases the complexity of the reservoir simulation. The matrix–block sizes are not uniform and can vary in a very wide range, from several tens of centimeters to meters. In such a reservoir, the matrix provides most of the pore volume for storage but makes only a small contribution to the global flow; the fracture supplies the flow, but with negligible contributions to reservoir porosity. The hydrocarbon is mainly produced from matrix/fracture interaction. So, it is essential to accurately model the matrix/fracture transfers with a reservoir simulator. For the fluid–flow simulation in shale–gas and tight oil reservoirs, dual–porosity models are widely used. In a commonly used dual–porosity–reservoir simulator, fractures are homogenized from a discrete–fracture network, and a shape factor based on the homogenized–matrix–block size is applied to model the matrix/fracture transfer. Even for the embedded discrete–fracture model (EDFM), the matrix/fracture interaction is also commonly modeled using the dual–porosity concept with a constant shape factor (or matrix/fracture transmissibility). However, in real cases, the discrete–fracture networks are very complex and nonuniformly distributed. It is difficult to determine an equivalent shape factor to compute matrix/fracture transfer in a multiple–block system. So, a dual–porosity approach might not be accurate for the simulation of shale-gas and tight oil reservoirs because of the presence of complex multiscale–fracture networks. In this paper, we study the multiple–interacting–continua (MINC) method for flow modeling in fractured reservoirs. MINC is commonly considered as an improvement of the dual–porosity model. However, a standard MINC approach, using transmissibilities derived from the MINC proximity function, cannot always correctly handle the matrix/fracture transfers when the matrix–block sizes are not uniformly distributed. To overcome this insufficiency, some new approaches for the MINC subdivision and the transmissibility computations are presented in this paper. Several examples are presented to show that using the new approaches significantly improves the dual–porosity model and the standard MINC method for nonuniform–block–size distributions.

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