A new index used to characterize the near-wellbore fracture network in naturally fractured gas reservoirs

Accepted Manuscript A new index used to characterize the near-wellbore fracture network in naturally fractured gas reservoirs Hucheng Deng, Yan Liu, Xianfeng Peng, Yueliang Liu, Huazhou Andy Li PII:

S1875-5100(18)30174-4

DOI:

10.1016/j.jngse.2018.04.018

Reference:

JNGSE 2540

To appear in:

Journal of Natural Gas Science and Engineering

Received Date: 24 November 2017 Revised Date:

10 March 2018

Accepted Date: 16 April 2018

Please cite this article as: Deng, H., Liu, Y., Peng, X., Liu, Y., Li, H.A., A new index used to characterize the near-wellbore fracture network in naturally fractured gas reservoirs, Journal of Natural Gas Science & Engineering (2018), doi: 10.1016/j.jngse.2018.04.018. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Graphical Abstract

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A New Index Used to Characterize the Near-Wellbore Fracture Network in Naturally Fractured Gas Reservoirs

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College of Energy Resources, Chengdu University of Technology, Chengdu 610059, China State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Chengdu 610059, China 3 School of Mining and Petroleum Engineering, Faculty of Engineering, University of Alberta, Edmonton, T6G 1H9, Canada 2

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Hucheng Deng1,2,3, Yan Liu1*, Xianfeng Peng1,3, Yueliang Liu3, Huazhou Andy Li3*

*Corresponding Authors: Dr. Huazhou Andy Li, PhD Assistant Professor, Petroleum Engineering University of Alberta Phone: 1-780-492-1738 Email: [email protected]

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Dr. Yan Liu, PhD Lecturer, Petroleum Geology Chengdu University of Technology Email: [email protected]

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Abstract

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The effectiveness of the near-wellbore fracture network greatly affects the production potential

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of naturally fractured gas reservoirs. In this work, we develop an index to characterize the near-

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wellbore fracture network in naturally fractured gas reservoirs, which is defined as the fracture-

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network effectiveness index. To build such an index, multiple factors are considered, i.e., the

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fracture aperture distribution, the fracture porosity distribution, the fracture permeability

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distribution, and the fracture coverage ratio in the pay-zone. The new index has been calculated

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based on a variety of relevant field data which include well test analysis results, production test

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data, imaging logs, conventional logs, and three-dimensional (3D) whole-core computerized

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tomography (CT) scans. To validate this newly proposed index, the calculated index is applied to

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correlate with the absolute open flow capacity in a target formation located in the Xinchang gas

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field of China. Test results show that the natural fracture-network effectiveness index strongly

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correlates with the absolute open flow capacity in the selected wells. It indicates that the

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proposed index should be a useful tool for evaluating the production potential of the payzones in

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such naturally fractured gas reservoirs. This index can be also applied to guide the effective

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exploitation of naturally fractured gas reservoirs with multiple payzones.

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Keywords: Fracture-Network Effectiveness Index; Near-Wellbore Fracture Network; Western

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Sichuan Basin; Natural Fractures; Fracture Properties

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1 Introduction

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In reservoir formations, the effective and ineffective fractures generally coexist, which form the

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natural fractures. The effective fractures can improve the permeability and thus facilitate the

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migration of the in-situ gas and oil, enhancing the productivity of reservoirs4-5. The effectiveness

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of natural fractures in reservoir formations can represent the ability of fractures in providing

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effective pathways of fluid-flow under reservoir conditions1-3. As a result, fracture-network

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effectiveness of given payzone is an indicator for assessing the productivity potential of the

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naturally fractured payzone.

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Fracture properties, such as aperture, porosity, and permeability, have been extensively used to

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evaluate the effectiveness of the fracture-network6-8. Fracture aperture is defined as the effective

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distance between the two opposite fracture surfaces, while the fracture porosity is calculated as

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the ratio of the fracture volume over the total volume of rock. Based on the previous studies,

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these two parameters contribute to the effectiveness of fractures6-8. The permeability of fracture

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describes the ability of the fractures allowing fluids to migrate through porous media. Although

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this parameter directly reflects the effectiveness of fractures, it is difficult to be directly

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measured downhole. However, the fracture aperture and porosity are generally considered to

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correlate with the fracture permeability; thereby, based on the relationship between the fracture

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aperture and porosity and the fracture permeability, an index can be developed to evaluate the

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effectiveness of the fracture-network. A variety of tests sources, such as field outcrops, drilled

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cores, conventional logs, production test data, and well test data, can be used to obtain such

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fracture-property parameters.

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During 1960s-70s, attempts have been dedicated to developing effective methods for evaluating

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natural fractures. Murry (1968) correlated the rock deformation curvature and the fracture

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density and proposed a model for quantitatively assessing fracture properties based on

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mechanical properties2,9. By using well test methods, de Swaan10 (1976) evaluated the

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effectiveness of natural fractures in hydrocarbon reservoirs. In 1980s, the improvement of

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geophysical well logging techniques enabled quantitative evaluation and analysis of natural

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fracture properties. For example, some researchers used dual laterologs to estimate the natural

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fracture parameters (e.g., fracture length, fracture aperture, and fracture porosity) in fractured

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reservoirs11,12, while some developed methods that used low-frequency reflected Stoneley-wave

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mode to estimate the locations of permeable fractures as well as their effective apertures13,14.

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Recently, methods such as formation micro-imager logs, circumferential acoustic device logs,

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and dipole-shear sonic imaging instruments have been increasingly applied to the identification

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and evaluation of natural fractures17,18. Kulatilake et al.15 (2006) applied the theory of fractals to

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estimate the aperture properties of natural rock fractures. Grayson et al.16 (2015) applied

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resistivity imaging in conjunction with nuclear magnetic resonance (NMR) technique to compute

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the fracture porosity. In addition, three-dimensional (3D) whole-core computerized tomography

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(CT) scanning combined with mathematical modelling is gaining popularity in characterizing

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rock fractures and assessing the effectiveness of natural fractures19-21.

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Although extensive studies have been conducted, we are still lacking systematic methods or

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straightforward indices that can be used to quantitatively assess the effectiveness of natural

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fractures in hydrocarbon reservoirs. Based on the geometric relationship between the direction of

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the principal stress in shale and the shape of natural fractures22, the fracture density and spatial

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distribution have been used to quantify the effectiveness of natural fractures in reservoirs.

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Moreover, the effectiveness of the natural fractures in hydrocarbon reservoirs has also been

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obtained by correlating the fracture porosity with permeability23. These methods aforementioned

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rely on multiple indicators for the evaluation of the effectiveness of natural fracture-network,

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which, however, can result in inconsistent results. Although such indicators can be potentially

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combined, there is no consensus on how to combine them as well as how to determine the weight

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of each indicator.

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In this work, we develop a quantitative index for measuring the effectiveness of natural fractures

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in hydrocarbon reservoirs. The proposed near-wellbore fracture-network effectiveness index

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incorporates three key fracture parameters, i.e., fracture aperture, fracture porosity, and fracture

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permeability, into a single parameter for straightforward measurement of the fracture-network

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effectiveness. The proposed fracture-network effectiveness index can quantitative assess the

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effectiveness of natural fractures present in a given payzone. The use of such single index avoids

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inconsistent evaluation that would be otherwise resulted due to the use of different indicators.

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This paper describes the proposed fracture-network effectiveness index, the rationale of

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developing such single index, and the procedure for its calculation. A detailed case study is

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followed to validate the proposed fracture-network effectiveness index.

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2. Methodology

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The aperture, porosity and permeability of fractures are the key parameters characterizing fluid

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transportation in fractures. As for the fractures adjacent to the wellbore, these properties can be

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obtained based on the characterization of the core samples retrieved from downhole, well

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logging data, and well test data. In a natural-fracture network, the local fractures do not

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necessarily share similar properties, thereby leading to varied contributions towards the overall

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gas production. The overall gas production in a wellbore is controlled by the effectiveness of the

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whole fracture network surrounding the wellbore. A higher gas production can be expected from

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a fracture network with a higher fracture coverage and favourable fracture properties. Therefore,

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it is of great importance to properly evaluate the effectiveness of the whole fracture network

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surrounding the wellbore, instead of that of a single fracture.

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2.1 Fracture-Network Effectiveness Index

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In this work, a quantitative index is developed to evaluate the effectiveness of the fracture-

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network. To build such an index, some relevant parameters, including the distributions of

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aperture, porosity, and permeability of fractures, and fracture coverage ratio of the payzone, are

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included.

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The effectiveness of a fracture-network mainly depends on: 1) how many fractures are

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surrounding a wellbore in a given formation, which represents the richness of the fractures in a

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given formation; and 2) the effectiveness of individual fractures, which depends on the fracture

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properties. Often, a fracture network tends to be more effective if the number of fractures in the

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fracture network is higher, and the individual fractures have properties favourable for oil/gas

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flow. Therefore, a fair evaluation of effectiveness of a fracture network should take into account

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both the maturity of the fractures in a given formation and the effectiveness of individual

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fractures. On the basis of the production data collected from many naturally fractured reservoirs,

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it is observed that well productivity positively correlates with the fracture aperture, fracture

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porosity, fracture permeability, and fracture density23-27. But majority of the researchers only rely

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on the use of single fracture parameter to evaluate the effectiveness of a fracture network (such

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as fracture porosity, fracture aperture, or fracture permeability)24, 25. In our research, we have

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taken these two factors, i.e., the richness of fractures in a given formation and effectiveness of

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individual fractures in a fracture network, into account to construct a more representative index

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for evaluating the fracture-network effectiveness. In this work, we first determine the richness of

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the fractures in a given formation. Then we collect all the available data for the three

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characteristic parameters of individual fractures (i.e., fracture porosity, fracture aperture, or

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fracture permeability) in a given fracture network; next, we rely on the key statistical indicators

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of the available data for a given characteristic parameter (including maximum, minimum and

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peak values of a given characteristic parameter) to evaluate the overall effectiveness of the

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fracture network. A more reasonable index for quantifying the effectiveness of the fracture-

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network can be hence built by considering both the richness of fractures and the effectiveness of

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individual fractures in a given formation. With the knowledge of the fracture aperture

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distribution, the fracture porosity distribution, the fracture permeability distribution, and the

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fracture coverage ratio (comparable to the concept of fracture density), we propose the following

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index to evaluate the effectiveness of the fracture-network for a given ith payzone out of all the

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payzones:

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(1)

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 Api Z i − ( Ap Z ) min  , if only Ap distribution and Z are available  ( Ap Z ) max − ( Ap Z )min   φ pi Z i − (φ p Z )min E fi =  , if only φ p distribution and Z are available Z − Z φ φ ( ) ( ) p p  max min   k pi Z i − ( k p Z )min , if all the Ap , φ p and k p distributions and Z are available   ( k p Z )max − ( k p Z )min

where Efi is the fracture-network effectiveness index of the ith payzone, Api is the the peak value

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in the fracture aperture distribution for the ith payzone, Zi is the fracture coverage ratio of the ith

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payzone, φpi is the peak value in the fracture porosity distribution for the ith payzone, kpi is the

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peak value in the fracture permeability distribution for the ith payzone, the subscript min stands

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for the minimum value among all payzones, and the subscript max stands for the maximum value

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among all payzones. The calculated result using Equation (1) is a dimensionless number between

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[0, 1]. If the calculated index of the effectiveness of the fracture-network is closer to 1, it

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indicates that the fracture-network is more effective in supplying natural gas production to the

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wellbore. The fracture coverage ratio of the ith payzone is calculated by the following formula,

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n

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j =1

ji

Hi

(2)

where hji is the thickness of the jth fracture network in the ith payzone, n is the number of fracture

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segments, and Hi is the thickness of the ith payzone. The fracture networks can be identified by

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well logging interpretations28. After determining the thicknesses of the individual fracture

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networks (hji) for a given payzone, we can then calculate the total thickness occupied by all the

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fracture networks. Next, based on the conventional well logging methods, we explain how to

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determine the parameters in Equation (1), i.e., the deep and shallow laterologs. The reason why

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we choose these conventional well logs to develop such index is that these conventional logs are

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generally obtained for all the production wells across the field.

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This index can be also potentially used to evaluate the effectiveness of artificially created

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fracture networks in a well. For example, the Longmaxi shale gas reservoir is one of the most

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productive shale gas field in China, and engineers often want to know how effective the artificial

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fracture network in a shale gas well tends to be. Then if re-logging is done after fracturing to

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provide the logging data, we can apply the above method to calculate the fracture-network

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effectiveness index to evaluate the effectiveness of the artificially created fracture network.

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2.2 Determination of the Fracture Aperture

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Fracture aperture can be readily obtained from the dual laterologs. According to Luo29 (1990),

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the aperture of vertical/inclined fractures can be calculated as per:

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A=

Rm ( RLLD − RLLS )

1 ×103 RLLD RLLS 1.5 (1 + cos α ) − cos α  g s − gd gs − gd =

r  ln ( D S / r ) ln ( D D / r )  −   2 H  DS − r DD − r 

(4)

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(3)

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where A is the fracture aperture in µm, Rm is the mud resistivity in ohm-m, RLLD and RLLS are the

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deep-laterolog resistivity and shallow-laterolog resistivity in ohm-m, respectively,

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inclination angle of the fracture with respect to the horizontal direction, r is the wellbore radius

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in mm that can be obtained from the caliper log, DD and DS are the probe depths of the deep

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laterolog and the shallow laterolog in mm, respectively, which depend on the specifications of

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the logging tool, and H is the thickness of the focused current in mm. It is noted that if A is

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negative, its absolute value should be used instead. To improve the accuracy of the calculated

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fracture aperture, well test and production test data are further used in conjunction with the dual

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laterologs if they are available.

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2.2 Determination of the Fracture Porosity

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Fracture porosity can be determined based on the dual laterologs11,30 :

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is the

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  1 1 φ f =  Rm  −   RLLS RLLD

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α

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mf

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where φf is the fracture porosity in percentage and m f is the fracture porosity index (1.5 used for

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normally fractured reservoirs). The fracture porosity obtained from the dual laterologs can be

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further amended by the 3D-CT scans of rock samples if these scans are available.

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2.3 Determination of the Fracture Permeability

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Fracture permeability represents the capability of fracture in transporting fluids. With the

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knowledge of the fracture aperture and fracture porosity, the fracture permeability31 can be given

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as,

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k f = 8.333 ×10−4 φ f A2

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where k f is the fracture permeability in µm2. It is noted that the fracture aperture and fracture

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porosity can be directly inferred from the dual laterologs, while the fracture permeability can be

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calculated based on the fracture aperture and fracture porosity. Depending on the availability of

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fracture aperture and fracture porosity, we can apply Equation (1) to figure out the effectiveness

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of the fracture-network.

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3. Application of the Fracture-Network Effectiveness Index

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To demonstrate how to use the proposed the index of the effectiveness of the fracture-network,

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we conduct a case study on a naturally fractured gas reservoir, i.e., the Xinchang X2 gas

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reservoir located in the west depression of Sichuan basin of China; this gas reservoir is

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characterized as a sandstone matrix with ultralow-permeability that is abundant in natural

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fractures. The Xinchang Xujiahe formation has an estimated volume of 1211.2×108 m3, where

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possesses high-quality H2S-free natural gas with a gas-bearing area of 157.69 km2.32 The

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Xinchang X2 gas reservoir is one of the major producing pools in the Xinchang Xujiahe

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formation. The highly productive wells are found to be the ones that have effective natural

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fracture networks.

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3.1 Geological Settings

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Fig. 1 shows the geographic location of the Xinchang X2 gas reservoir. The Xinchang X2 gas

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reservoir is located approximately 20 km north of Deyang City, Sichuan Province, China. It is

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located in the middle of the large-scale uplift belt in the central part of the West Depression of

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the Sichuan basin. The X2 formation is composed of continental clastic rocks, and its structure

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was originally formed in the early Middle Jurassic. It underwent significant development in the

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Late Jurassic and was further modified through the Early Quaternary by the Himalayan

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deformation to reach its present form33. Field surveys and relevant publications show that the gas

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reservoir contains several northeast-east trending compound anticlines. Faults are well developed

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in the north-south direction and in the northeast direction. The Xinchang X2 gas reservoir was

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formed from the deposition of estuary sand dams on the front edge of a delta and underwater

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channels, with the partial development of distal sand dams32. The sediment primarily consists of

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relatively pure sandstones in thick layers to blocks that form a blanket-like sand body, enabling

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the formation of reservoirs32. Based on surveys and sample tests, the main rock type of the

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sandstones in the gas reservoir is debris sandstone, accounting for 45% of the sandstones,

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followed by feldspar debris sandstone (21%), debris feldspar sandstone (13%), and debris quartz

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sandstone (11%)

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low-porosity/low-permeability layers with well-developed natural fractures 34.

. This reservoir is a typical fracture-porosity-type gas reservoir that contains

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Figure 1. Geographical location of the Xinchang gas field.

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In our study, we have collected the following data to support the development of our new

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fracture-network effectiveness index: outcrop surveys, well logging data, core samples retrieved

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from production wells, and production test data. Fig. 2 shows the geographical locations where

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we have made the 63 outcrop-survey visits; these outcrop locations are around 129 km southwest

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of the Xinchang gas field. At the outcrop locations, we were able to measure and record the

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fracture dip angles, fracture apertures, fracture density, as well as the relationship between fault

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and fractures. The well logging data are available in 25 gas wells, the core samples are available

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in 14 gas wells, and the production test data are available in 15 wells.

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Figure 2. Locations where the outcrop surveys were conducted and the survey routes that were followed to conduct these outcrop surveys.

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3.2 Fracture Characteristics in the Xinchang X2 Gas Reservoir

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This reservoir experienced strong structural movements during the Yanshan and Himalayan

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periods, which led to the generation of vast faults and natural fractures along the northeast-

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southwest direction and the west-east direction. Fig. 3 is a rose diagram showing the directions

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of the natural fractures, which is drawn based on the statistical analysis of all the outcrop survey

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data and imaging logs. Based on the imaging logs results and the measurements conducted on the

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core samples retrieved from the gas wells, we observe that three major types of natural fractures

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as illustrated in Fig. 4: vertical fractures (Fig. 4a), fractures with high inclination angles larger

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than 75o (Fig. 4b and Fig. 4c), and fractures with medium inclination angles between 45o and 75o

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(Fig. 4d and Fig. 4e). To take a quantitative look at the fracture density in the Xingchang X2

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reservoir, we have cored in total 403.42 m of core sections from 14 wells in this reservoir. Fig. 5

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summarizes the fracture density obtained for the 14 wells; herein, the fracture density refers to

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the number of observable fractures with naked eyes per 1 m of core section. It can be seen from

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Fig. 5 that the fracture density varies significantly from well to well: the maximum fracture

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density is 0.87 fractures per meter, while the minimum fracture density is only 0.10 fractures per

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meter. Fig. 6 shows the characteristics of fractures near the small faults at the outcrop position

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No. 2. It can be seen from Fig. 6 that more fractures are present in the locations close to the fault.

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As the distance from the fault increases, we can observe fewer fractures.

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Figure 3. Rose diagram of the fracture orientations in the Xinchang X2 gas reservoir.

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(a)

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(c)

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(d) (e) Figure 4. Digital images of core samples with fractures: (a) Vertical fracture with partial feldspar filling (Sampled at 4901.46-4902.06 m from well YZ565); (b) Two parallel fractures with a high inclination angle (Sampled at 4844.5-4844.85 m from well Z201); (c) Joint fracture with a high inclination angle (Sampled at 4802-4802.16 m from well YZ560); (d) Joint fracture with low inclination angle (Sampled at 5052.98-5053.19 m from well YZ565); (e) Feldsparfilling fracture with a high inclination angle (sampled at 4895.84-4896.44 m from well Z501).

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Figure 5. The measured fracture density in 14 wells. The fracture density is defined as the number of fractures per 1-meter wellbore.

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Figure 6. Characteristics of fractures near the small faults at the outcrop position No. 2 as marked in Figure 2.

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We also took microscopic images of the micro-fractures present in the core samples retrieved

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from the gas wells in the Xinchang X2 gas reservoir. Fig. 7 shows the casting section images

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detailing the configurations of the micro-fractures present in the core samples. Both Fig. 7a and

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Fig. 7b present that dense micro-fracture networks are distributing in the core samples retrieved

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from the gas wells of the Xinchang X2 gas reservoir. These fracture networks are usually well

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connected to the effective pores, providing excellent flow path enabling the migration of natural

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gas in the porous media. Based on the macroscopic and microscope investigations with regard to

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the fracture morphologies, we observed that the functional fractures mainly include the open

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fractures as observed in Fig. 4b and Fig. 7, and the partially filled fractures as shown in Fig. 4a,

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while the non-functional fractures mainly include the joint fractures as shown in Fig. 4c and the

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completely filled fractures as shown in Fig. 4e.

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(a)

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Figure 7. Casting thin-section images taken on typical core samples: (a) Open micro-fractures that are connected to the effective pores and also penetrate the quartz grain (Sampled at 4935.04 m from well Z10); (b) Open micro-fractures that are forming a network structure (Sampled at 5022.52 m from well Z11).

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3.3 Evaluation of Fracture-Network Effectiveness of the Xinchang X2 Gas Reservoir

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In this case, we have chosen fifteen vertical wells without hydraulic fracturing treatment to

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illustrate how to calculate the effectiveness index of natural fracture networks. Because the gas

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reservoir in which these wells are located is naturally fractured gas reservoir, and these wells are

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not hydraulically fractured, it is appropriate to use these wells as a case study to demonstrate

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how to evaluate the effectiveness of natural fracture networks by using the proposed index.

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3.3.1 Calculation of the Fracture Coverage Ratio

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Taking the well Z11 for instance, we demonstrate how to use the conventional well logging data

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to identify the presence of fractures along the wellbore. Fig. 8 shows the conventional logging

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results. First of all, we need to identify the fractures surrounding the wellbore by interpreting the

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well logging curves. In our previous research, we developed a series of interpretation models that

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can be effectively applied to identify the presence of fractures for a given zone; the detailed

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fracture-identification methodology was elaborated in Deng et al.28 (2009). As can be seen from

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Fig. 8, seven fracture segments can be identified in the payzone. After summing up the

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thicknesses of individual fracture segments, we can use Equation (2) to calculate the fracture

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coverage ratio. Table 1 summaries the computed fracture coverage ratios for the 15 gas wells.

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The fracture coverage ratios for the 15 wells fall in the range of 0.0323-0.1917.

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Table 1 Key parameters used for assessing the fracture-network effectiveness index of the selected wells in the Xinchang X2 gas reservoir.

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Frequency

ϕP

0.08 0.08 0.08 0.11 0.10 0.10 0.08 0.12 0.09 0.10 0.10 0.10 0.08 0.10 0.08

1546 2551 3324 496 1946 1013 2560 1582 1365 2071 398 2128 2724 904 1963

1.01 1.02 1.09 1.23 0.81 1.02 1.01 0.86 1.02 1.00 1.01 1.04 1.02 1.01 0.90

Frequency

kP

Frequency

2073 2002 1479 727 1675 1533 3128 914 2158 3037 626 2173 3187 1434 648

2.01 2.23 2.14 1.96 1.62 1.84 1.86 1.64 2.02 1.84 1.84 2.52 2.01 1.98 1.52

1651 1403 1306 464 1133 1024 1735 746 1182 2061 352 2000 2625 1002 328

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AP

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L150 YK1 YZ560 YZ565 Z101 Z11 Z201 Z202 Z203 Z206 Z3 Z5 Z501 Z851 Z856

kf (µm2)

ϕf (%)

A (mm)

Well ID

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0.0387 0.1917 0.0323 0.1323 0.1122 0.1313 0.0658 0.1847 0.0779 0.0364 0.1402 0.1178 0.0431 0.1094 0.0803

0.03 1.00 0.01 0.54 0.32 0.49 0.16 0.67 0.25 0.00 0.54 0.64 0.05 0.42 0.16

AOF (104 m3/d) 8 135 7 80 30 30 17 54 23 12 58 45 28 40 20

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Figure 8. Identification of the fracture segments in Well Z11 based on the well logging data. The last column shows the thicknesses of the fracture networks interpreted using the well logging data. GR refers to the gamma ray logging, SP refers to the spontaneous potential logging, AC refers to the acoustic logging, DEN refers to the density logging, CNL refers to compensated neutron logging, RLLD refers to the deep laterolog, RLLS refers to the shallow laterolog, and Rxo refers to the flushed-zone resistivity logging.

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3.3.2 Determination of the Fracture Aperture

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The fracture apertures can be calculated using Equations (3) and (4) with the knowledge of the

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deep and shallow laterologs. As for the Xingchang X2 gas reservoir, the following equation

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parameters are found to be appropriate and thereby used in the fracture-aperture calculation:

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DD=2.63 m, DS=0.80 m, H=600 mm (based on the specifications of the logging tool), and α=65o

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(average inclination angle of the fracture). The wellbore radius is directly obtained based on the

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caliper logging results. In particular, the following formula is used to calculate the mud

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resistivity at different temperatures based on the mud resistivity at 18o 29:

Rmo 1 + 0.026 (T − 18)

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(7)

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where Rmo is the mud resistivity at 18o (1.13 ohm-m in our study), and T is the in-situ

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temperature as calculated according to the local geothermal gradient, T = 14 + 0.034 L

where L is the well depth in m.

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It should be noted that the fracture apertures calculated from the dual laterologs are sometimes

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biased and should be corrected using the actual well test data. A regression analysis of the

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fracture apertures calculated from the dual laterolog versus those based on the well test data from

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four wells suggests that a fairly good logarithmic relationship exists between them (See Fig. 9):

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AWell −test = 0.0362 ln ( ALogging ) + 0.3073

(9)

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where AWell-test is the fracture aperture that is obtained from the well test data (mm), ALogging the

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fracture aperture that is interpreted by the dual laterologs (mm). Based on this relationship, we

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are able to correct the fracture apertures obtained from the dual laterologs for all the 15 wells in

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the Xinchang X2 gas reservoir (See Table 1). The corrected fracture apertures fall within the

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range of 0.01-0.56 mm. 21

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Figure 9. Regression analysis of fracture apertures calculated from the dual laterologs versus those based on the well test data from four wells.

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3.3.2 Determination of the Fracture Porosity

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From this case study, we conducted 3D whole-core CT scans on five core samples obtained from

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three wells, i.e., Z3, Z5, and Z201. Fig. 10 presents a 3D CT scan image; it illustrates the fracture

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morphology in a core sample retrieved from the Well Z5 at the depth of 5024.32m. A fracture

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penetrating the center of the core is observed from Fig. 10. The fracture porosities of the five

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rock cores range between 0.11%-1.13%. Analysis of these scan results reveals a positive

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correlation between the fracture porosity values derived from the CT scans and those from the

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dual laterologs (R2=0.7133; See Fig. 11):

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φCT

φCT = 1.2777φLogging + 0.1134

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is the fracture porosity derived from the 3D whole-core CT scans (%), and φLogging is

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where

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the fracture porosity derived from the dual laterologs (%). Using this correlation, we are able to

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correct the fracture porosity values obtained from the dual laterologs for the 15 wells in the

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Xinchang X2 gas reservoir. We find that the corrected porosities are ranging from 0.21% to

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3.54%.

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Figure 10. Example 3D-CT-scan image of the fracture morphology. The core sample is retrieved from the Z5 well at 5024.32 m. The yellow sections correspond to the fracture space detected by CT.

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Figure 11. Regression analysis of the fracture porosity values derived from the dual laterologs and those obtained by CT scans. 23

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3.3.3 Determination of the Fracture Permeability

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After obtaining the fracture porosity, it is straightforward to calculate the fracture permeability

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using Equation (6). We have calculated the fracture permeability for the 15 wells. The calculated

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fracture permeability ranges from 0.90 to 12.00 µm2.

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3.3.4 Determination of the Fracture-Network Effectiveness Index

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Next, we explain how to evaluate the fracture-network effectiveness indices for the 15 gas wells

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in the Xinchang X2 gas reservoir. Taking well Z11 as an example, Fig. 12 illustrates the

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statistical distribution of fracture apertures measured for this well, Fig. 13 illustrates the

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statistical distribution of fracture porosity measured for this well, and Fig. 14 illustrates the

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statistical distribution of the fracture permeability calculated for this well. As for this well Z11,

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the peak value of the fracture aperture, peak value of fracture porosity, and peak value of the

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fracture permeability are found to be 0.10 mm, 1.02%, and 1.84 µm2, respectively (See Table 1).

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The fracture coverage ratio of this well is found to be 0.1313. Eventually, based on the input

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values, the fracture-network effectiveness index is calculated to be 0.49, which indicates a

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medium level of fracture-network effectiveness. In a similar manner, we can figure out all the

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fracture-network effectiveness indices for the remaining 14 wells in the Xinchang X2 gas

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reservoir (See Table 1). By pinpointing the geographical locations of the 15 wells, Fig. 15 shows

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the fracture-network effectiveness indices of the selected wells in the Xinchang X2 gas reservoir

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that have been determined based on the new methodology.

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Figure 12. Statistical distribution of the fracture apertures in the Z11 well.

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Figure 13. Statistical distribution of the fracture porosity in Z11 well.

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Figure 14. Statistical distribution of the fracture permeability in Z11 well.

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Figure 15. Fracture-network effectiveness indices of the selected wells in the Xinchang X2 gas reservoir that have been determined based on the newly developed methodology.

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3.4 Validation of the Calculated Fracture-Network Effectiveness Index

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In order to validate the soundness of the proposed fracture-network effectiveness index, we are

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attempting to examine if the open absolute flows (AOF) of the 15 gas wells can be correlated

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well with the calculated fracture-network effectiveness values for the same 15 wells. AOF is the

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production rate corresponding to the condition where the bottom hole flow pressure is controlled

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at the atmospheric pressure. Fig. 16 presents the fracture-network effectiveness values against

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AOFs of these 15 wells. It is noted that all the 15 wells were not hydraulically fractured when we

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were measuring the AOFs of these wells, such that the AOF was mainly controlled by the

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effectiveness of the natural fracture-network in the payzone. A regression analysis shows that an

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exponential relationship can be used to describe the dependence of the AOF on the fracture-

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network effectiveness index. The resulting equations is given as follows (R2=0.8777),

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AOF = 14.4045 exp ( 2.2289 E f

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Figure 16. Relationship between fracture-network effectiveness indices and absolute open flows (AOF) for the 15 gas wells in the Xinchang X2 gas reservoir.

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As can be seen from Fig. 16, an increase in the fracture-network effectiveness leads to an

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approximately exponential increase in the AOF, indicating that our new fracture-network

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effectiveness index can be used to capture the production potential of the fracture-network in the

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payzone.

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4. Conclusions

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In this work, we develop a new index, the so-called fracture-network effectiveness index, which

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can be used to quantify the effectiveness of the natural fracture-network surrounding a wellbore.

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Such effectiveness honours the capability of the natural fracture-network in delivering natural

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gas production. The quantitative fracture-network effectiveness index is comprehensive in that it

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takes into consideration the fracture coverage ratio, fracture aperture distribution, fracture

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porosity distribution, and fracture permeability distribution. It can be used to rank the production

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potentials of any gas well in a naturally fractured gas reservoir. To demonstrate its application

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and validate its soundness, we carry out a detailed case study that focuses on a typical naturally

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fractured gas reservoir in China, i.e., the Xinchang X2 gas reservoir in the western Sichuan basin.

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It is found that the fracture-network effectiveness index proposed in this research is indeed an

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excellent indicator of the production potential of naturally fractured gas wells since a good

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correlation has been found between the measured AOF and the calculated fracture-network

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effectiveness index. Note that the proposed fracture-network effectiveness index can be also

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potentially applied to naturally fractured oil reservoirs. This index can be also applied to guide

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the effective exploitation of naturally fractured gas reservoirs with multiple payzones. For

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example, if a naturally fractured gas reservoir has several payzones, we can use this index to

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evaluate the effectiveness of the near-wellbore fracture network in each payzone. Based on the

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index values obtained, reservoir engineers can decide which payzones’ production should be

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prioritized or which payzones should be produced in a commingled manner. In addition, the

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proposed index can also help to guide how to properly determine the locations of new wells to be

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drilled. If we have a sufficient number of drilled wells in a naturally fractured gas reservoir, we

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can evaluate the effectiveness indices of all the available wells. Based on the indices obtained,

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we can draw a contour map showing the distribution of the effectiveness indices across the field.

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As a result, we can place new wells in the locations which have high effectiveness-index values.

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Acknowledgments

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The first author greatly acknowledges the financial supports provided by the National Natural

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Science Foundation of China Grant (41672133) and the National Strategic Research Program

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(2016ZX05048-001-04-LH). The fourth author greatly acknowledge China Scholarship Council

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(CSC) for financial support to Y. Liu (201406450028). The fifth author acknowledges a

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Discovery Grant by Natural Sciences and Engineering Research Council (NSERC) of Canada

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(NSERC RGPIN 05394) and an Open Science Research Fund of State Key Laboratory of Oil

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and Gas Reservoir Geology and Exploitation, China (PLC201606).

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References 1. Prats, M. Effect of vertical fractures on reservoir behavior-incompressible fluid case. SPE J. 1, 105-118 (1961). 2. Murry, G.H. Quantitative fracture study; Sanish Pool, Mckenzie County, North Dakota. AAPG Bull. 52, 57-65 (1968). 3. Eaton, B.A. Fracture gradient prediction and its application in oilfield operations. J. Pet. Tech. 21, 1353-1360 (1969). 4. Paillet, F.L., Hess, A.E., Cheng, C.H. & Hardin, E. Characterization of fracture permeability with high resolution vertical flow measurements during borehole pumping. Ground Water. 25, 28-40 (1987). 5. Connolly P. & Cosgrove J. Prediction of fracture-induced permeability and fluid flow in the crust using experimental stress data. AAPG Bull. 83, 757-777 (1999). 6. Gringarten, A.C., Ramey, Jr., H.J. & Raghavan, R. Applied pressure analysis for fractured wells. J. Pet. Tech. 27, 887-892 (1975). 7. Agarwal, R.G., Carter, R.D. & Pollock, C.B. Evaluation and performance prediction of lowpermeability gas wells stimulated by massive hydraulic fracturing. J. Pet. Tech. 31, 362-372 (1979).

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8. Cinco-Ley, H. Transient pressure analysis for fractured wells. J. Pet. Tech. 33, 1749-1766 (1981). 9. Stearns, D.W. & Friedman, M. Reservoirs in fractured rock: Geologic exploration methods, in King, R.E., ed., Stratigraphic oil and gas fields – classification, exploration methods and case histories. AAPG Memo. 16, 82-106 (1981). 10. de Swaan O.A. Analytic solutions for determining naturally fractured reservoir properties by well testing. SPE J. 16, 117-122 (1976). 11. Sibbit, A.M. & Faivre, O. The dual laterolog response in fractured rocks. Paper presented at the SPWLA 26th Annual Logging Symposium, 17-20 June, Dallas, Texas (1985). 12. Vasvari, V. On the applicability of dual laterolog for the deter-mination of fracture parameters in hard rock aquifers. Austrian J. Earth Sci. 104, 80-89 (2011). 13. Hornby, B.E., Johnson, D.L., Winkler, K.W. & Plumb, R.A. Fracture evaluation using reflected Stoneley-wave arrivals. Geophysics, 54, 1274-1288 (1989). 14. Hornby, B.E., Luthi, S.M. & Plumb, R.A. Comparison of fracture apertures computed from electirical borehole scans and reflected Stoneley waves: An integrated interpretation. Log Analyst. 33, 50-66 (1992). 15. Kulatilake, P.H.S.W., Park, J., Balasingam, P. & Morgan, R. Natural rock fracture aperture properties through fractals. Paper ARMA/USRMS 06-936 presented at Golden Rocks 2006, The 41st U.S. Symposium on Rock Mechanics (USRMS): "50 Years of Rock Mechanics Landmarks and Future Challenges.", held in Golden, Colorado, June 17-21 (2006). 16. Grayson, S., Kamberling, M., Pirie, I & Swager, L. NMR-enhanced natural fracture evaluation in the Monterey shale. Paper SPWLA-2015-MMM presented at the SPWLA 56th Annual Logging Symposium, July 18-22 (2015). 17. Brie, A. et al. New directions in sonic logging. Oilfield Review. 10, 40-55 (1998). 18. Lovell, M.A., Williamson, G. & Harvey, P.K. Borehole imaging: applications and case histories. Geological Society Special Publication No. 159. The Geological Society, London, (1999). 19. Muralidharan, V., Chakravarthy, D., Putra, E. & Schechter, D.S. Investigating fracture aperture distributions under various stress conditions using X-Ray CT scanner. Paper PETSOC-2004-230 presented at the Canadian International Petroleum Conference, Calgary, 8-10 June (2004). 20. Kim, T., Putra, E. & Schechter, D. Analyzing Tensleep natural fracture properties using Xray CT scanner. Arch. Mining Sci. 52, 3-20 (2007). 21. Kishida, K., Ishikawa, T, Higo, Y. Sawada, A. & Yasuhara, H. Measurements of fracture aperture in granite core using microfocus X-ray CT and fluid flow simulation. Paper ARMA 15-0485 presented at the 49th US Rock Mechanics / Geomechanics Symposium held in San Francisco, CA, USA, 28 June - 1 July (2015). 22. Zhou, X., Zhang, L., Huang, C. & Wan, X.L. Distraction network conceptual model and validity of fractures in Chang 6-3 low permeable reservoir in Huaqing area. J. Jilin Univ. (Earth Sci. Ed.), 43, 689-697 (2012). (In Chinese) 23. Deng, H., Zhou, W. & Zhou, Q. Quantification characterization of the valid natural fractures in the 2nd Xu member, Xinchang gas field. Acta Petrologica Sinica, 29, 1087-1097(2013). (In Chinese) 24. Lopez, B.A., Gonzalez, L., Aguilera, R. & Garcia-Hernandez, F. Effect of natural fracture properties on production variability of individual wells in multiphase oil reservoirs. Paper

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SPE 153741 presented at the SPE Latin America and Caribbean Petroleum Engineering Conference, Mexico City, Mexico, 16-18 April (2012). 25. Gonzalez, L. & Aguilera, R. Effect of natural-fracture density on production variability of individual wells in the Nikanassin tight gas formation. J. Can. Pet. Tech. 52, 131-143 (2013). 26. Deng, H., Zhou, W. & Liu, Y. Evaluation technique of multi-origin and multi-period natural fracture system in hydrocarbon reservoir. China Science Press, (2016). (In Chinese) 27. Liu, Y., Wang, G. & Cheng, Z. Fractures development characteristics and their effect on productivity in tight sandstone reservoirs, Keshen gas field, Kuqa depression. Paper presented at the AAPG/SEG International Conference & Exhibition, Cancun, Mexico, September 7 (2016). 28. Deng, H., Zhou, W. & Liang, F. Fracture identification based on conventional logging-case of Yanchang and Yanan formation Mahuangshan area in Ordos basin. Pet. Geol. Oilfield Deve. Daqing. 28, 315-319 (2009). (In Chinese) 29. Luo, Z. Preliminary study on the calculation of fracture aperture using laterologs. Geophys. Well Log. 14, 83-92(1990). (In Chinese) 30. Boyeldieu, C. & Winchester, A. Use of the dual laterolog for the evaluation of the fracture porosity in hard carbonate formations. Paper SPE 10464 presented at the SPE Offshore South East Asia Show, Singapore, February 9-12 (1982). 31. Tiab, D. & Donaldson, E.C. Petrophysics: theory and practice of measuring reservoir rock and fluid transport properties. Gulf Professional Publishing (2015). 32. Dai, J. Giant coal-derived gas fields and their gas sources in China. China Science Press. (2016). 33. Ye, J. & Chen, Z.G. Geological characteristics of large Xinchang gas field in western Sichuan depression and key predication technongies. Oil Gas Geol. 27, 384-391 (2006). (In Chinese) 34. Deng, S., Ye, T., Lu, Z. & Zhang, H. Characteristics of gas pool in the second member of Xujiahe formation in Xin-chang structure, west Sichuan basin. Nat. Gas Ind., 28, 42-45164(2008).

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Highlights •

We develop a new fracture-network effectiveness index

•

This index measures the capability of the natural fracture-networks in delivering natural

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A case study in a gas reservoir in China validates the soundness of the new index

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gas production

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Re: Itemized Response to Reviewers’ Comments Made by Three Reviewers

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Journal: Journal of Natural Gas Science and Engineering Manuscript ID: JNGSE-D-17-02169 Paper Title: A New Index Used to Characterize the Near-Wellbore Fracture Network in Naturally Fractured Gas Reservoirs Authors: H. Deng, Y. Liu*, X. Peng, Y. Liu, H. Li*

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Reviewer #1 Comment #1: Overall the paper is well organized and well written but it fails to answer some key questions which are very necessary to understand this work correctly, check its applicability in naturally fractured gas fields and weigh its importance with regard to decision making for development of field. Response: The authors thank the reviewer for the valuable comments. We have incorporated the reviewer’s comments when revising the manuscript.

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Comment #2: In section 2.1 where the natural factor effective index if mentioned through equation 1, it is not mentioned how this equation was reached. Was it through curve fitting on the data where its validated? or there is any physics behind representing the fracture aperture, porosity and permeability in a certain way to give us the fracture effectiveness index. This is the most crucial element to understanding this work successfully which is not mentioned in the paper. Response: It is an excellent comment. We have elaborated on how the effectiveness index is proposed. The effectiveness of a fracture-network mainly depends on: 1) how many fractures are surrounding a wellbore in a given formation, which represents the richness of the fractures in a given formation; and 2) the effectiveness of individual fractures, which depends on the fracture properties. Often, a fracture network tends to be more effective if the number of fractures in the fracture network is higher, and the individual fractures have properties favourable for oil/gas flow. Therefore, a fair evaluation of effectiveness of a fracture network should take into account both the maturity of the fractures in a given formation and the effectiveness of individual fractures. On the basis of the production data collected from many naturally fractured reservoirs, it is observed that well productivity positively correlates with the fracture aperture, fracture porosity, fracture permeability, and fracture density23-27. But majority of the researchers only rely on the use of single fracture parameter to evaluate the effectiveness of a fracture network (such as fracture porosity, fracture aperture, or fracture permeability)24, 25. In our research, we have taken these two factors, i.e., the richness of fractures in a given formation and effectiveness of individual fractures in a fracture-network, into account to construct a more representative index for evaluating the fracture-network effectiveness. In this work, we first determine the richness of the fractures in a given formation. Then we collect all the available data for the three characteristic parameters of individual fractures (i.e., fracture porosity, fracture aperture, or fracture permeability) in a given fracture network; next, we rely on the key statistical indicators of the available data for a given characteristic parameter (including maximum, minimum and peak values of a given characteristic parameter) to evaluate the overall effectiveness of the fracture network. Eventually, we build a more reasonable index for quantifying the effectiveness of the

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fracture-network by considering both the richness of fractures and the effectiveness of individual fractures in a given formation. Changes: Please see Lines #132-154.

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Comment #3: In figure 11, a straight line correlation is obtained with few scattered data points. This is a big generalization and more data should be obtained to obtain the correct relationship. Response: It should be noted that it is both difficult and expensive to conduct the CT scans on the core samples with fractures. By talking to the collaborators at the Southeast Oil & Gas Company, we have obtained two new data from them and added them to Fig. 11. These new two data are (0.086%, 0.070%) and (0.890%, 1.260%). Changes: Please see the revised Figure 11.

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Comment #4: Can this be applied on hydraulically fractured gas wells in shale formations ? Given the importance of the shale gas reservoirs across the world, can you please add a comment in the paper about the applicability of the natural fracture effectiveness index for these reservoirs? Response: This is an excellent comment. As mentioned by the reviewer, this index can be also potentially used to evaluate the effectiveness of artificially created fracture networks in a well. For example, the Longmaxi shale gas reservoir is one of the most productive shale gas field in China, and engineers often want to know how effective the artificial fracture network in a shale gas well tends to be. Then if re-logging is done after fracturing to provide the logging data, we can apply the above method to calculate the fracture-network effectiveness index to evaluate the effectiveness of the artificially created fracture network. We have added these comments into the revised manuscript. Changes: Please see Lines #177-182.

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Comment #5: Can you please write more on the validation section, describe whether the gas wells used for validation were horizontal or vertical, when were they hydraulically fractured (as mentioned in the text)? What does the AOF represents physically and how was it calculated? Response: This is an excellent comment. The wells we have selected are naturally producing wells without hydraulic fracturing treatment. In our study, we have chosen fifteen vertical wells without hydraulic fracturing treatment to illustrate how to calculate the effectiveness index of natural fracture networks. Because the gas reservoir in which these wells are located is naturally fractured gas reservoir, and these wells are not hydraulically fractured, it is appropriate to use these wells as a case study to demonstrate how to evaluate the effectiveness of natural fracture networks by using the proposed index. Absolute open flow (AOF) corresponds to the gas flow rate that occurs when the bottomhole pressure is zero, as seen from the figure below. It can be obtained by conducting production test on the production well. After the inflow performance relationship curve is obtained, AOF can be determined as the production rate at the zero bottomhole pressure. We have added this clarification in the revised manuscript.

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Changes: Please see Lines #315-319 and #431-434.

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Comment #6: How this natural fracture effective index will be used to make field development decisions or well placement decisions in general? What is the impact of this work is not evident in the whole paper. This should be mentioned in the abstract and conclusions to support the value of this work. Please highlight the value it brings with regard to future development of the field where there is no well data. Response: The authors thank again the reviewer for the excellent comment. As inspired by the reviewer, we have added the following statements in the revised manuscript. This index can be also applied to guide the effective exploitation of naturally fractured gas reservoirs with multiple payzones. For example, if a naturally fractured gas reservoir has several payzones, we can use this index to evaluate the effectiveness of the near-wellbore fracture network in each payzone. Based on the index values obtained, reservoir engineers can decide which payzones’s production should be prioritized or which payzones should be produced in a commingled manner. In addition, the proposed index can also help to guide how to properly determine the locations of new wells to be drilled. If we have a sufficient number of drilled wells in a naturally fractured gas reservoir, we can evaluate the effectiveness indices of all the available wells. Based on the indices obtained, we can draw a contour map showing the distribution of the effectiveness indices across the field. As a result, we can place new wells in the locations which have high effectiveness-index values. Changes: Please see Lines #461-471. Reviewer #3 Comment #1: Good paper, please see attached recommendations and suggestions. Additionally, I would recommend bringing some of the figures and charts to the main body of the paper, making it easier for the reader to reference the figures nad charts while he is reading vs. having to go down to the end of the paper every single time - it is not practical.

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Response: The authors thank the reviewer for the positive comments. We have embedded all the tables and figures into the main body of the paper, making it easier for the reviewers to go through the manuscript.

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Comment #2: Can you please elaborate on this? What does variety of field data mean? Response: We have rephrased the sentence to make it more understandable. The sentence has been changed to “The new index has been calculated based on a variety of relevant field data which include well test analysis results, production test data, imaging logs, conventional logs, and three-dimensional (3D) whole-core computerized tomography (CT) scans.” Changes: Please see Lines #43-46.

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Comment #3: You personally configured an index via calculations? Response: We have added more explanations with regard to how we have proposed this index in the revised manuscript. Please also see the response to the comment #2 made by the first reviewer. Changes: Please see Lines #132-154. Comment #4: I would mention this part in the beginning...it seem to be your objective = > create an index for evaluating production potential in natural fractures. Response: The authors thank the reviewer for the suggestion. We have implemented this suggestion in the abstract. Changes: Please see Lines #38-39.

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Reviewer #4 Comment #1: This manuscript established a new fracture network effectiveness index to help the evaluation of well productivity in the fractured gas reservoirs. The paper is well organized, and the illustration of the content supports the conclusions. Here are my main comments that might be helpful to improve it. In the example case, the fracture apertures seem to have a relative broad range between 0.01-0.56 mm, how to consider and deal with this kind of issue in the index calculation? Response: In the example case, because the well sections we have examined are very long and exhibit high degrees of fracture heterogeneity, the fracture apertures exhibits a broad range of values. As mentioned in the manuscript, we basically use the statistical indicators, such as maximum, minimum and peak values in fracture-aperture distribution (See Figure 12), to define the effectiveness index of fracture networks in a given formation. Changes: Please see Lines #132-154. Comment #2: Have the author done some sensitivity study on the factors which influencing the index? Such as a tornado plot. Response: This comment is well taken by the authors. But due to the fact that our new index is a statistical parameter, rather than a mechanistic parameter, it is not useful to perform sensitivity analysis on the factors affecting the index.

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Comment #3: What is the advantage of this proposed index compared to previous researches? From my point of view, the similar assessment of the fracture network efficiency has been studied by many researchers, and the applications of these methods all have some limitation and uncertainty (sometimes might be considerably big). Then what is the superior aspect of the method proposed in this paper? Response: This comment is well taken by the authors. We have provided more explanations about the motivation as well as the justification of proposing the new effectiveness index. As seen from the following paragraph that has been added to the revised manuscript, we have added more literature review to elaborate on the limitations of existing methodologies and how we have proposed the new index.

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The effectiveness of a fracture-network mainly depends on: 1) how many fractures are surrounding a wellbore in a given formation, which represents the richness of the fractures in a given formation; and 2) the effectiveness of individual fractures, which depends on the fracture properties. Often, a fracture network tends to be more effective if the number of fractures in the fracture network is higher, and the individual fractures have properties favourable for oil/gas flow. Therefore, a fair evaluation of effectiveness of a fracture network should take into account both the maturity of the fractures in a given formation and the effectiveness of individual fractures. On the basis of the production data collected from many naturally fractured reservoirs, it is observed that well productivity positively correlates with the fracture aperture, fracture porosity, fracture permeability, and fracture density23-27. But majority of the researchers only rely on the use of single fracture parameter to evaluate the effectiveness of a fracture network (such as fracture porosity, fracture aperture, or fracture permeability)24, 25. In our research, we have taken these two factors, i.e., the richness of fractures in a given formation and effectiveness of individual fractures in a fracture-network, into account to construct a more representative index for evaluating the fracture-network effectiveness. In this work, we first determine the richness of the fractures in a given formation. Then we collect all the available data for the three characteristic parameters of individual fractures (i.e., fracture porosity, fracture aperture, or fracture permeability) in a given fracture network; next, we rely on the key statistical indicators of the available data for a given characteristic parameter (including maximum, minimum and peak values of a given characteristic parameter) to evaluate the overall effectiveness of the fracture network. Eventually, we build a more reasonable index for quantifying the effectiveness of the fracture-network by considering both the richness of fractures and the effectiveness of individual fractures in a given formation. Changes: Please see Lines #132-154. Comment #4: Overall, the article established a new fracture network effectiveness index to help the evaluation of well productivity in the fractured gas reservoirs. The paper need some clarification before the publication. Response: By incorporating the comments made by the reviewer, we have revised our manuscript accordingly. Also, it should be noted that the original Figure 16 was not drawn correctly. We should have used 15 data points (as listed in Table 1) to draw this figure, rather than 16 data

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points in the original plot. We have corrected this in the revised manuscript; please see the revised Figure 16.

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Yours sincerely, Huazhou Andy Li Assistant Professor, University of Alberta On behalf of coauthors

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Again, we appreciate the valuable comments and suggestions made by the associate editor and two reviewers. These comments and suggestions help us to further solidify the technical quality of our manuscript.