Evolution of fracture permeability and its compressibility in proppant-supported shale

Highlights

• Seepage mechanism of shale fractures under proppant compaction and embedding is discussed.

• A shale permeability model considering proppant compaction and embedding is proposed.

• A calculation method of shale fracture compressibility considering proppant compaction and embedding is proposed.

• Evaluated the evolution of fracture compressibility under the combined effects of stress and proppant.

Abstract

Hydraulic fracturing is one of the effective means to increase shale gas production, during which, proppant was widely used to support fractures to form stable seepage channels. Following which changes in permeability are restricted by the compaction and embedding of proppants, so studies on the impact of proppant on the fracture conductivity are highly desirable. In this paper, we discussed first the change mechanism relating to fracture compressibility under the combined effects of proppant compaction and embedding, and, further, proposed a new calculation model denoting fracture compressibility. Moreover, the effect of the number of proppant paving layers was also incorporated in that model. Secondly, based on the exponential relationship between stress and permeability, and by taking fracture compressibility as a bridge, a shale fracture permeability model, that considered the combined effects of proppant compaction and embedment, was constructed. The proposed permeability model was, then, verified through evidence from publicly released test data, and the permeability change law relating to shale fractures. In addition, we focused on the influence of factors: such as, stress, proppant types, rock types, and the number of proppant layers on fracture compressibility. The results revealed that fracture compressibility in its original state was a higher than that of the supporting fracture. The increased stress leads to reduced fracture compressibility It was found that the higher the rock hardness, the smaller the corresponding fracture compressibility, the smaller the elastic modulus of the proppant, and an increase in fracture compressibility. The analysis of these results would help to improve the basic understanding of the key processes affecting proppant performance and permeability alterations.

Introduction

In recent years, due to the huge reserves of shale gas, it has gradually entered the public (Howarth et al., 2011; Alagoz et al., 2021; Lu et al., 2022). However, the exploitation of shale gas is not easy, mainly due to the extremely low reservoir permeability (Wang et al., 2009). Thus, many reservoir (i.g. Coal and shale) permeability enhancement technologies have been proposed, such as hydraulic fracturing, CO2 fracturing, and liquid nitrogen cooling (Zhai et al., 2016; Zou and Lin, 2018; Fan et al., 2021). Wherein, multi-stage hydraulic fracturing technology is mostly used at production sites (Estrada and Bhamidimarri, 2016). The study of the development of hydraulic fracturing and other mining technologies, has led shale gas to achieve, albeit gradually, commercial production (Alramahi and Sundberg, 2012; Gong et al., 2020; Barboza et al., 2021). In the process of implementing hydraulic fracturing technology, the characteristics of shale fractures, such as, the shape and length, would change accordingly, to form a complex network system to increase a reservoir's permeability (Wei and Xia, 2017; Hou et al., 2017). The compaction and embedding of proppants ensured that the formed seepage channels remained open after the pressure was released, and, significantly, improved the conductivity of the reservoir fracture (Brannon et al., 2004). Fracture permeability also plays a critical effect in determining the long term production of shale gas, so it is necessary to understanding combined effect of proppant compaction and embedment on shale fracture permeability and its compressibility.

Reservoir permeability generally has a negative relationship with stress (McKee et al., 1988; Pan et al., 2010; Zhou et al., 2021). The fracture compressibility was widely used as a bridge to describe the relationship between permeability and stress (Zhou et al., 2019, 2021; Yang et al., 2021). The calculation of fracture compressibility can be obtained by theoretical calculation and experimental determination. Wherein, the value of coal fracture compressibility of coal ranged from 0.04 to 0.20 MPa⁻¹, and the fracture compressibility of shale ranged from 0.01 to 0.1 MPa⁻¹ (Tan et al., 2019). For some tight reservoir, it was difficult to determine the volume. Consequently, that was usually obtained by comparing theoretical formulas with experimental data (McKee et al., 1988; Liu et al., 2012, 2020; Chen et al., 2015; Robertson and Christiansen, 2007). Based on the heterogeneous characteristics of shale fractures, fracture compressibility can be estimated by NMR experiments and computational model (Li et al., 2013; Hou et al., 2019). Based on the difference in the fracture interface, the fracture compressibility factor can be expressed as a function of the effective stress (Zhou et al., 2019). In order to further quantify the impact of proppant embedding on fracture compressibility, Xu et al. (2020) proposed a calculation model for fracture compressibility that included proppant embedding and fracture porosity changes, and analyzed changes in compressibility under different conditions. To explore the key factors controlling the permeability evolution of proppant-supported fractures under high stress in shale, Chen et al. (2021) and Tan et al. (2017) obtained fracture compressibility by modeling experimental data using different permeability models. The relationship between stress, proppant layer and compressibility is also described.

Although widely studied, it is difficult to reveal the mechanisms that are associated with the performance of proppants and permeability evolution. When performing hydraulic fracturing, proppants are easily embedded in the reservoir, that cause changes in fracture seepage characteristics (Wei and Xia, 2017; Ahamed et al., 2021a, Ahamed et al., 2021b; Li et al., 2021). Wherein, reservoir type and proppant properties both affect the permeability of proppant-supported rock fractures (Shamsi et al., 2016; Hou et al., 2017). Furthermore, proppants in the shale reservoir will confront adjustments in the form of: aggregation, rearrangement and fragmentation, which will undoubtedly result in changes in permeability (Xu et al., 2020; Zheng et al., 2018). It is worth noting that a multi-layer proppant arrangement can effectively resist stress, reduce proppant fracture caused by stress, and ensure the smallest loss of conductivity in the proppant-filled layer (Elsarawy and Nasr-El-Din, 2018). In addition, the amount of proppant packing, the rock reservoir type, and fracture roughness will affect the fluid flow capacity in the propped fracture (Hari et al., 2021; Liu et al., 2021; Ahamed et al., 2021a, Ahamed et al., 2021b). Wherein, proppants tend to accumulate at the boundary of low to high surface roughness area, that result in greater embedding in those areas (Ahamed et al., 2021a, Ahamed et al., 2021b). Rock reservoirs with lower hardness will facilitate the embedding of proppants, while rock reservoirs with high hardness will promote the fracture of proppants under the action of stress (Xu et al., 2020). Any increase in the number of proppant layers will lead to an increase in its stacked porosity, which may reduce permeability (Man and Wong, 2017).

Permeability is an important parameter in unconventional oil/gas exploration, and theoretical modeling was essential to improve fundamental understanding (Chen et al., 2012; Liu et al., 2017; Zhou et al., 2019). For adsorptive porous rocks, the construction of permeability models is usually referenced to changes in stress and strain (Fan and Liu, 2019; Xie et al., 2020; Zeng et al., 2021). But after proppant injection, the modeling of permeability change in the rock reservoir becomes very complicated, because permeability change is not only affected by effective stress, but also by proppant embedding caused by contact stress (Chen et al., 2017). At this point, it is first necessary to understand the proppants’ embedding depth. Li et al. (2015) respectively assumed that the reservoir and proppant were elastic, and further proposed methods for calculating the embedding depth of single-layer and multi-layer proppants. Based on the theory of contact mechanics and elasticity, Guo et al. (2017) proposed a method for calculating the embedding depth of proppants in a uniform and uneven distribution. Based on the Hertz contact theory, Chen et al. (2017) proposed an exponential calculation model that conformed to the relationship between proppant embedding depth and stress. Second, the previous summary revealed that a permeability modeling usually relied on analysis of fracture width. Thus, the construction of the propped fracture permeability model should consider the effect of proppant compaction and embedding on the fracture width. (Chen et al., 2017; Jia et al., 2019; Xu et al., 2020).

Factors such as the type of proppant and proppant packing format, all determine permeability behavior and compressibility. Considering the combined effects of proppant compaction and embedding, we propose a computational model of fracture compressibility to analyze the microscopic evolution of fractures for proppant-supported shale. Wherein, the model includes the effects of layers of proppant placement, proppant compaction, and proppant embedding. On this basis, a permeability model of proppant-supported shale was established. The proposed permeability model is suitable for describing the permeability change of shale fractures under the combined effects of proppant compaction and embedding. In particular, it is used to analyze the effect of stress and number of proppant layers on fracture permeability. Then, the proposed fracture compressibility calculation model is used to describe the compressibility for proppant-supported shale under stress. The proposed model is validated by data matching of fracture permeability of proppant-supported shale, and analyzed the key processes that affected proppant performance and permeability change. In addition, we also discussed the evolution law of the fracture compressibility factor considering the proppant type, the number of layers of proppant laid and the packing format. This study aims to obtain a better understanding of the relationships between stress, proppant layers and compressibility in the hydraulic fracture for shale.

This paper is organized as follows: First, a calculation model of fracture compressibility for proppant-supported shale is constructed, so as to quantitatively analyze the influence of proppant compaction and embedment on shale fracture compressibility. Based on the relationship between fracture compressibility and permeability, a permeability model considering proppant compaction and embedding is constructed to describe the permeability evolution mechanism of proppant-supported shale (Section 2). Second, the model is validated by matching the permeability data of proppant-supported shale, and the fracture permeability behavior of proppant-supported shale is analyzed through the model. On this basis, combined with the relevant physical parameters of shale and proppant in that study, the law of fracture compressibility of proppant-supported shale was analyzed (Section 3). Third, the effects of proppant properties and packing format on fracture compressibility are discussed (Section 4).