A Novel Analytical Fracture-Permeability Model Dependent on Both Fracture Width and Proppant-Pack Properties

Summary For an empty fracture, the fracture permeability (kf) is mainly influenced by the effect of viscous shear from fracture walls and can be analytically estimated if the fracture width (wf) is known a priori (i.e., kf=β2wf2/12, where β2 is the unit-conversion factor). For an adequately propped fracture, the fracture permeability is mainly influenced by the proppant-pack properties and can be approximated with the proppant-pack permeability (kf=kp, where kp is proppant-pack permeability). It can be readily inferred that as the effect of viscous shear fades (or the proppant-pack effect becomes pronounced), there should be a regime within which both the viscous shear and the proppant-pack properties exert significant influences on the fracture permeability. However, the functional relationship between fracture permeability, viscous shear (or fracture width), and proppant-pack properties is still elusive. In this work, we propose a new fracture-permeability model to account for the influences of the proppant-pack permeability, proppant-pack porosity (ϕp), and fracture width on the fracture permeability. This new fracture-permeability model is derived from a modified Brinkman equation. The results calculated with the fracture-permeability model show that with different values of the Darcy parameter, the fluid flow can be divided into viscous-shear-dominated (VSD) regime, transition regime, and Darcy-flow-dominated (DFD) regime. If the Darcy parameter is sufficiently large, the effect of proppant-pack permeability on fracture permeability can be neglected and the fracture permeability can be calculated with the VSD fracture-permeability (FP) (VSD-FP) equation (i.e., kf=β2ϕpwf2/12). If the Darcy parameter is sufficiently small, the effect of viscous shear on fracture permeability can be neglected and the fracture permeability can be calculated with the DFD-FP equation (i.e., kf=kp). Both the VSD-FP and DFD-FP equations are special forms of the proposed fracture-permeability model. For the existing empirical/analytical fracture-conductivity models that neglect the effect of viscous shear, one can multiply these models by the coefficient of viscous shear to make these models capable of estimating the fracture conductivity with large values of Darcy parameter.

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A Semianalytical Model for Production Simulation From Nonplanar Hydraulic-Fracture Geometry in Tight Oil Reservoirs

SPE Journal ◽

10.2118/178440-pa ◽

2016 ◽

Vol 21 (03) ◽

pp. 1028-1040 ◽

Cited By ~ 48

Author(s):

Wei Yu ◽

Kan Wu ◽

Kamy Sepehrnoori

Keyword(s):

Hydraulic Fracture ◽

Transient Flow ◽

Flow Behavior ◽

Tight Oil ◽

Well Performance ◽

Fracture Permeability ◽

Fracture Geometry ◽

Fracture Conductivity ◽

Fracture Width ◽

Stress Dependent

Summary Two key technologies such as horizontal drilling and hydraulic fracturing have led to the economic production of unconventional resources such as shale gas and tight oil. In reality, a nonplanar hydraulic-fracture geometry with varying fracture width and fracture permeability is created during the hydraulic-fracturing process. However, it is challenging to simulate well performance from the nonplanar fracture geometry. For the sake of simplicity, the nonplanar fracture geometry is often represented by ideal planar fracture geometry with constant fracture width, which one can easily handle analytically, semianalytically, and numerically. However, such ideal fracture geometry is inadequate to capture the physics of the transient flow behavior of the nonplanar fracture geometry. Although significant efforts were made in recent years to numerically model well performance from the complex fracture geometry, these approaches are still challenging to model the nonplanar fracture geometry with varying width because of a large considerable fracture-gridding issues and an expensive computation cost. In addition, the effect of nonplanar fracture geometry on well productivity and transient flow behavior was not reported in the literature. Hence, a model to handle the nonplanar fracture geometry by considering varying fracture width and fracture permeability is still lacking in the petroleum industry. Zhou et al. (2014) proposed a semianalytical model to handle the complex fracture geometry with constant fracture width. However, the semianalytical model did not consider the effects of stress-dependent fracture conductivity and the nonplanar fracture geometry as well as planar fracture geometry with varying fracture width along the fracture. In this work, we extended the semianalytical model to simulate production from the nonplanar fracture geometry as well as planar fracture geometry with varying width. In addition, the effect of stress-dependent fracture conductivity was implemented in the model. We verified the semianalytical model against a numerical reservoir simulator for single planar fracture with constant width. We performed two case studies. The first case contains a comparison of two planar fractures, one with constant fracture width and another with varying fracture width. In the second study, we compared two fractures with different fracture geometries such as planar fracture geometry and nonplanar fracture geometry, which were generated from the fracture-propagation model. In addition, transient flow regimes were investigated on the basis of a log-log graph of the dimensionless pressure drop and pressure-drop derivative vs. the dimensionless time. This work can provide critical insights into understanding the well performance from tight oil reservoirs with the nonplanar hydraulic-fracture geometry.

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OPTIMISATION OF HYDRAULIC FRACTURING DESIGN IN LOWER OLIGOCENE RESERVOIR, KINH NGU TRANG OILFIELD

Tạp chí Khoa học và Công nghệ Biển ◽

10.15625/1859-3097/18/3/10678 ◽

2018 ◽

Vol 18 (3) ◽

pp. 323-337

Author(s):

Nguyen Huu Truong

Keyword(s):

Hydraulic Fracturing ◽

Complex Structure ◽

Power Requirement ◽

Fracture Conductivity ◽

Fracture Width ◽

The North ◽

Fracture Closure ◽

Average Water ◽

White Tiger ◽

Fracture Height

Kinh Ngu Trang oilfield is of the block 09-2/09 offshore Vietnam, which is located in the Cuu Long basin, the distance from that field to Port of Vung Tau is around 140 km and it is about 14 km from the north of Rang Dong oilfield of the block 15.2, and around 50 km from the east of White Tiger in the block 09.1. That block accounts for total area of 992 km2 with the average water depth of around 50 m to 70 m. The characteristic of Oligocene E reservoir is tight oil in sandstone, very complicated with complex structure. Therefore, the big challenges in this reservoir are the low permeability and the low porosity of around 0.2 md to less than 1 md and 1% to less than 13%, respectively, leading to very low fracture conductivity among the fractures. Through the Minifrac test for reservoir with reservoir depth from 3,501 mMD to 3,525 mMD, the total leak-off coefficient and fracture closure pressure were determined as 0.005 ft/min0.5 and 9,100 psi, respectively. To create new fracture dimensions, hydraulic fracturing stimulation has been used to stimulate this reservoir, including proppant selection and fluid selection, pump power requirement. In this article, the authors present optimisation of hydraulic fracturing design using unified fracture design, the results show that optimum fracture dimensions include fracture half-length, fracture width and fracture height of 216 m, 0.34 inches and 31 m, respectively when using proppant mass of 150,000 lbs of 20/40 ISP Carbolite Ceramic proppant.

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Application Investigation of Light Proppant in Hydraulic Fracturing of Marcellus Shale

10.2118/201807-ms ◽

2021 ◽

Author(s):

Aymen Alhemdi ◽

Ming Gu

Keyword(s):

History Matching ◽

Marcellus Shale ◽

In Situ Stress ◽

Production Performance ◽

Well Performance ◽

Fracture Permeability ◽

Fracture Conductivity ◽

Stimulated Reservoir Volume ◽

Conductivity Distribution ◽

Cumulative Production

Abstract Slickwater-sand fracturing design is widely employed in Marcellus shale. The slickwater- sand creates long skinny fractures and maximizes the stimulated reservoir volume (SRV). However, due to the fast settling of sand in the water, lots of upper and deeper areas are not sufficiently propped. Reducing sand size can lead to insufficient fracture conductivity. This study proposes to use three candidate ultra-lightweight proppants ULWPs to enhance the fractured well performance in unconventional reservoirs. In step 1, the current sand pumping design is input into an in-house P3D fracture propagation simulator to estimate the fracture geometry and proppant concentrations. Next, the distribution of proppant concentration converts to conductivity and then to fracture permeability. In the third step, the fracture permeability from the second step is input into a reservoir simulator to predict the cumulative production for history matching and calibration. In step 4, the three ULWPs are used to replace the sand in the frac simulator to get new frac geometry and conductivity distribution and then import them in reservoir model for production evaluation. Before this study, the three ULWPs have already been tested in the lab to obtain their long-term conductivities under in-situ stress conditions. The conductivity distribution and production performance are analyzed and investigated. The induced fracture size and location of the produced layer for the current target well play a fundamental effect on ultra-light proppant productivity. The average conductivity of ULWPs with mesh 40/70 is larger and symmetric along the fracture except for a few places. However, ULWPs with mesh 100 generates low average conductivity and create a peak conductivity in limited areas. The ULW-3 tends to have less cumulative production compared with the other ULWPs. For this Marcellus Shale study, the advantages of ultra-lightweight proppant are restricted and reduced because the upward fracture height growth is enormous. And with the presence of the hydrocarbon layer is at the bottom of the fracture, making a large proportion of ULWPs occupies areas that are not productive places. The current study provides a guidance for operators in Marcellus Shale to determine (1) If the ULWP can benefit the current shale well treated by sand, (2) what type of ULWP should be used, and (3) given a certain type of ULWP, what is the optimum pumping schedule and staging/perforating design to maximize the well productivity. The similar workflow can be expanded to evaluate the economic potential of different ULWPs in any other unconventional field.

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A new fracture permeability model: Influence of surrounding rocks and matrix pressure

Journal of Petroleum Science and Engineering ◽

10.1016/j.petrol.2020.107320 ◽

2020 ◽

Vol 193 ◽

pp. 107320 ◽

Cited By ~ 1

Author(s):

Peng Yu ◽

Yuetian Liu ◽

Jun Wang ◽

Chuixian Kong ◽

Wenhuan Gu ◽

...

Keyword(s):

Fracture Permeability ◽

Permeability Model

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Estimating Unpropped-Fracture Conductivity and Fracture Compliance From Diagnostic Fracture-Injection Tests

SPE Journal ◽

10.2118/189844-pa ◽

2018 ◽

Vol 23 (05) ◽

pp. 1648-1668 ◽

Cited By ~ 13

Author(s):

HanYi Wang ◽

Mukul M. Sharma

Keyword(s):

Earth Science ◽

Mathematical Framework ◽

Field Scale ◽

Time Data ◽

Fracture Conductivity ◽

Reliable Technique ◽

Fracture Width ◽

In Situ Conditions ◽

Fracture Closure

Summary A new method is proposed to estimate the compliance and conductivity of induced unpropped fractures as a function of the effective stress acting on the fracture from diagnostic-fracture-injection-test (DFIT) data. A hydraulic-fracture resistance to displacement and closure is described by its compliance (or stiffness). Fracture compliance is closely related to the elastic, failure, and hydraulic properties of the rock. Quantifying fracture compliance and fracture conductivity under in-situ conditions is crucial in many Earth-science and engineering applications but is very difficult to achieve. Even though laboratory experiments are used often to measure fracture compliance and conductivity, the measurement results are influenced strongly by how the fracture is created, the specific rock sample obtained, and the degree to which it is preserved. As such, the results may not be representative of field-scale fractures. During the past 2 decades, the DFIT has evolved into a commonly used and reliable technique to obtain in-situ stresses, fluid-leakoff parameters, and formation permeability. The pressure-decline response across the entire duration of a DFIT reflects the process of fracture closure and reservoir-flow capacity. As such, it is possible to use these data to quantify changes in fracture conductivity as a function of stress. In this paper, we present a single, coherent mathematical framework to accomplish this. We show how each factor affects the pressure-decline response, and the effects of previously overlooked coupled mechanisms are examined and discussed. Synthetic and field-case studies are presented to illustrate the method. Most importantly, a new specialized plot (normalized system-stiffness plot) is proposed, which not only provides clear evidence of the existence of a residual fracture width as a fracture is closing during a DFIT, but also allows us to estimate fracture-compliance (or stiffness) evolution, and infer unpropped fracture conductivity using only DFIT pressure and time data alone. It is recommended that the normalized system-stiffness plot (NS plot) be used as a standard practice to complement the G-function or square-root-of-time plot and log-log plot because it provides very valuable information on fracture-closure behavior and the properties of fracture-surface roughness at a field-scale, information that cannot be obtained by any other means.

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Impact of Various Parameters on the Production of Coalbed Methane

SPE Journal ◽

10.2118/162722-pa ◽

2013 ◽

Vol 18 (05) ◽

pp. 910-923 ◽

Cited By ~ 17

Author(s):

Zhongwei Chen ◽

Jishan Liu ◽

Akim Kabir ◽

Jianguo Wang ◽

Zhejun Pan

Keyword(s):

Time Constant ◽

Coalbed Methane ◽

Dominant Role ◽

Gas Production ◽

Fracture Permeability ◽

Permeability Model ◽

Gas Desorption ◽

Desorption Time ◽

Matrix Blocks ◽

Cbm Production

Summary Coalbed-methane (CBM) reservoirs are naturally fractured formations, comprising both permeable fractures and matrix blocks. The interaction between fractures and matrix presents a great challenge for the forecast of CBM reservoir performance. In this work, a dual-permeability model was applied to study the parameter sensitivity on the CBM production, because the dual-permeability model incorporates not only the influence from matrix and fractures but also that between adjacent matrix blocks. The mass exchange between two systems is defined as a function of desorption time constant at the standard condition, coal matrix porosity, and the difference of gas pressure between two systems. Correspondingly, gas diffusivity in matrix is considered as a variable and represented by a function of shape factor, gas desorption time, and reservoir pressure. These relations are integrated into a fully coupled numerical model of coal geomechanical deformation and gas desorption/gas flow in both systems. This numerical approach demonstrates the important nonlinear effects of the complex interaction between matrix and fractures on CBM production behaviors that cannot be recovered without rigorously incorporating geomechanical influences. This model was then used to investigate the sensitivity of CBM extraction behavior to different controlling factors, including gas desorption time constant, initial fracture permeability, fracture spacing, swelling capacity, desorption capacity, production pressure, and fracture and matrix porosities. Modeling results show that the peak magnitudes of gas-production rate increase with initial fracture permeability, sorption and swelling capacities, and matrix porosity, and decrease with gas desorption time constant and production pressure. These results also show dramatic increase in gas-production efficiency with decreasing magnitudes of fracture spacing. The comparison of the transient contributions of the desorbed gas and the free phase gas from the matrix system to gas production shows that the free phase gas plays the dominant role at the early stage, but diminishes when the adsorption phase gas takes over the dominant role, indicating the necessity of incorporating free phase gas impact in simulation models. The numerical model was also applied to match the history data from a gas-production well. A better matching result than that for the single-permeability model demonstrates the potential capability of the dual-permeability model for the forecast of CBM production.

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Approximate Analytical-Pressure Studies on Dual-Porosity Reservoirs With Stress-Sensitive Permeability

SPE Reservoir Evaluation & Engineering ◽

10.2118/174299-pa ◽

2015 ◽

Vol 18 (04) ◽

pp. 523-533 ◽

Cited By ~ 8

Author(s):

Shuhua Wang ◽

Mingxu Ma ◽

Wei Ding ◽

Menglu Lin ◽

Shengnan Chen

Keyword(s):

Production Rate ◽

Flow Rate ◽

Fractured Reservoirs ◽

Naturally Fractured Reservoirs ◽

Dual Porosity ◽

Fracture Permeability ◽

Permeability Model ◽

Pressure Behavior ◽

Naturally Fractured ◽

Permeability Modulus

Summary Pressure-transient analysis in dual-porosity media is commonly studied by assuming a constant reservoir permeability. Such an assumption can result in significant errors when estimating pressure behavior and production rate of naturally fractured reservoirs as fracture permeability decreases during the production. At present, there is still a lack of analytical pressure-transient studies in naturally fractured reservoirs while taking stress-sensitive fracture permeability into account. In this study, an approximate analytical model is proposed to investigate the pressure behavior and production rate in the naturally fractured reservoirs. This model assumes that fracture permeability is a function of both permeability modulus and pressure difference. The pressure-dependent fracture system is coupled with matrix system with an unsteady-state exchange flow rate. A nonlinear diffusivity equation in fracture system is developed and solved by Pedrosa's transformation and a perturbation technique with zero-order approximation. A total of six solutions in the Laplace space are presented for two inner-boundary conditions and three outer-boundary conditions. Finally, pressure behavior and production rate are studied for both infinite and finite reservoirs. Pressure behavior and production rate from the models with and without stress-sensitive permeability are compared. It is found that, for an infinite reservoir with a constant-flow-rate boundary condition, if permeability modulus is 0.1, dimensionless pressure difference at the well bottom from the model with fracture-permeability sensitivity is 80% higher than that of the constant fracture-permeability model at a dimensionless time of 106. Such difference can be as high as 216% if permeability modulus increases to 0.15. On the contrary, for the infinite reservoirs with a constant-pressure boundary, the constant fracture-permeability model tends to overestimate the flow rate at wellbore and cumulative production. The proposed model not only provides an analytical and quantitative method to investigate the effects of fracture-permeability sensitivity on reservoir-pressure distribution and production, but it also can be applied to build up analysis of well test data from stress-sensitive formations.

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AREAL SURFACE CHARACTERIZATION OF ACID-FRACTURES IN CARBONATE ROCKS

Brazilian Journal of Geophysics ◽

10.22564/rbgf.v30i2.107 ◽

2012 ◽

Vol 30 (2) ◽

Author(s):

Rodrigues Valdo Ferreira ◽

Victor Rodolfo Araujo ◽

Campos Wellington ◽

Ana Catarina da Rocha Medeiros

Keyword(s):

Hydraulic Conductivity ◽

Surface Characterization ◽

Oil And Gas ◽

Fine Particles ◽

Surface Characteristics ◽

Abnormal Behavior ◽

Fracture Conductivity ◽

Surface Parameters ◽

Fracture Width ◽

3D Surface

Fracture surface characteristics have significant effect on fracture hydraulic conductivity. The available acid-fracture conductivity correlations do notconsider surface characteristics or make an incipient use of it. A proper description of the acid-fracture surfaces is the initial step towards the right consideration of surface roughness in hydraulic conductivity. This paper presents an areal (3D) surface evaluation of acid-etched fractures, simulated in samples taken from whole cores of an oil producer limestone. The topography of acid-fractured surfaces was assessed using a laser profilometer. The surfaces were evaluated with a set of 3D surface parameters. The results showed that the main features of acid-etched surfaces are large roughness, negative skewness, high kurtosis, and intermediate isotropy, mostly random, but with some spatial orientation. The acid-fractured surfaces can be represented by the rms height, which showed great linear correlation with most of the surface parameters. The parameters texture aspect ratio, bearing index, valley retention index, and density of summits showed low correlation with rms height. A method to calculate fracture width from surface topography was developed. An attempt to explain abnormal behavior in initial conductivity tests revealed the potential use of surface characterization for management of fine particles in oil and gas reservoirs. It is suggested to search improved fracture conductivity correlation through the relationship between lab measured conductivities and surface characterization parameters.

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Monolayer Microproppant-Placement Quality Using Split-Core-Plug Permeability Measurements Under Stress

SPE Journal ◽

10.2118/189832-pa ◽

2019 ◽

Vol 24 (04) ◽

pp. 1790-1808 ◽

Cited By ~ 1

Author(s):

Brice Y. Kim ◽

I. Yucel Akkutlu ◽

Vladimir Martysevich ◽

Ronald G. Dusterhoft

Keyword(s):

Pressure Pulse ◽

Fracture Permeability ◽

Permeability Model ◽

Eagle Ford ◽

Areal Distribution ◽

Stimulation Experiments ◽

Stress Dependent

Summary The stress-dependent permeabilities of split shale core plugs from Eagle Ford, Bakken, and Barnett Formation samples are investigated in the presence of microproppants. An analytical permeability model is developed for the investigation, including the interactions between the fracture walls and monolayer microproppants under stress. The model is then used to analyze a series of pressure-pulse-decay measurements of the propped shale samples in the laboratory. The analysis provides the propped-fracture permeability of the samples and predicts a parameter related to the quality of the proppant areal distribution in the fracture. The proppant-placement quality can be used as a measure of success of the delivery of proppants into microfractures and to design stimulation experiments in the laboratory.

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A new fracture permeability model of CBM reservoir with high-dip angle in the southern Junggar Basin, NW China

Energy Exploration & Exploitation ◽

10.1177/0144598718807552 ◽

2018 ◽

Vol 37 (1) ◽

pp. 125-143 ◽

Cited By ~ 2

Author(s):

Shiyu Yang ◽

Yidong Cai ◽

Ren Wei ◽

Yingfang Zhou

Keyword(s):

Coalbed Methane ◽

Junggar Basin ◽

Well Testing ◽

Well Test ◽

Fracture Permeability ◽

Permeability Model ◽

Fracture Porosity ◽

Nw China ◽

Coalbed Methane Reservoir ◽

Dip Angle

Predicting the permeability of coalbed methane (CBM) reservoirs is significant for coalbed methane exploration and coalbed methane development. In this work, a new fracture permeability model of coalbed methane reservoir with high-dip angle in the southern Junggar Basin, NW China is established based on the Poiseuille and Darcy laws. The fracture porosity in coalbed methane reservoir is calculated by applying 3D finite element method. The formation cementing index m was calculated by combining fractal theory and the data of acoustic logging, compensated neutron logging, and density logging with the space method. Based on Poiseuille and Darcy laws, the curvature τ is introduced to derive this new method for obtaining the permeability of the original fractures in coalbed methane reservoirs. Moreover, this newly established permeability model is compared with the permeability from the well testing, which shows a very good correlation between them. This model comprehensively includes the effects of fracture porosity, reservoir pore structure, and development conditions on fracture permeability. Finally, the permeability prediction of coalbed methane reservoir with high-dip angle in the southern Junggar Basin, NW China is conducted, which correlates very well with the well test permeability ( R2 = 0.83). Therefore, this model can be used to accurately predict the coalbed methane reservoir permeability of low rank coals in the southern Junggar Basin. The permeability of the No.43 coalbed methane reservoir for the coalbed methane wells without well testing data is evaluated, which ranges from 0.000251 to 0.379632 mD. This significant change in permeability may indicate a complex coalbed methane reservoir structure in the southern Junggar Basin, NW China.

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