Experimental observations of heterogeneous strains inside a dual porosity sample under the influence of gas-sorption: A case study of fractured coal

Highlights

• The non-monotonic and fracture-scale dependent deformations are firstly measured.

• Before equilibrium, matrix swelling near fractures causes distant matrix shrinkage.

• The time reaching final equilibrium is found to be longer than previously reported.

• Gas adsorption dynamically changes coal strains, then alters its fracture aperture.

Abstract

A “permeability equilibration time” is typically assumed in interpreting permeability measurements – indicating that equilibration has been reached and both sorption-induced changes in deformation and their impact on permeability evolution have ceased. However, for extremely low matrix permeability (tight) dual porosity rocks, this “permeability equilibration time” may easily exceed the time interval between two consecutive permeability measurements – invalidating the interpretation of a steady permeability if the non-steady state conditions are not correctly accommodated. This is especially important where pressure diffusion from fracture to matrix results in a non-monotonic and non-asymptotic approach to a steady permeability, but instead contains multiple stages, plateaus and permeability reversals. We validated this hypothesis through experiments and analysis. Experiments measured the non-monotonic and scale-dependent deformations of fracture and matrix and linked these directly to the dynamic evolution of reservoir permeability. These laboratory strain measurements were integrated with numerical analyses to explore how mass and stresses transferred between matrix and fracture and were coupled under conditions of constant confining pressure. Strain gauges were distributed to directly measure stress transfer between matrix and fracture and interrogated deformation at different scales and at different proximities to control fractures. The prismatic sample of coal was tested under freely expanding boundary conditions. Optical microscopy and X-ray CT imaging were used to define the fracture distribution throughout the sample with mercury intrusion (capillary) porosimetry (MICP) constraining the pore size distribution and enabling independent estimation of matrix permeability. A numerical model was built and verified by matching measured strains and then applying this to model the evolution coal permeability from initial to ultimate equilibrium. Both the experimental and numerical results show that the final equilibrium state (pressure, stress and mass contents) for the matrix system extends to months rather than hours and suggests that some current permeability data may therefore reflect a non-equilibrium permeability state. Results also show that during this non-equilibrium condition, the swelling of the matrix near the fracture will cause not only compaction and narrowing of the fracture, but also shrinkage of the matrix that is distant from the fracture under constant confining pressure condition. Both experimental and numerical results demonstrate that the evolution of non-equilibrium strain/permeability is determined by the matrix-fracture interactions, including sorption-induced swelling/shrinking, through transient stresses in matrix and fractures. And that these non-equilibrium stress transfers determine the dynamic permeability evolution during gas extraction (e.g., CH₄) or injection (e.g., CO₂) at reservoir scale for tight dual porosity rocks (e.g., coal and shale).

Introduction

The boom in unconventional resources (e.g., coalbed methane, shale gas) has substantially reshaped the oil and gas industry over the past two decades. Exploitation of coalbed methane (CBM) from coal seams also benefits mining safety and reduces greenhouse gas emissions (Karacan et al., 2011). Coal and shale reservoirs are generally regarded as dual porosity media that consists of the porous matrix and the surrounding fractures. However, gas adsorption/desorption induces swelling/shrinking of the matrix system (Karacan, 2007; Kiyama et al., 2011; Pan and Connell, 2007), further affecting the permeability evolution. The contrasting permeabilities of the adjoining matrix and fracture systems sustain a pressure difference between the matrix system and fracture system, together with a differential effective stress during non-equilibrium periods of gas extraction/injection. Meanwhile, interaction between matrix and fracture determines the dynamic change of reservoir permeability in dual porosity rocks and exerts a control on gas production during the drainage process (Cui et al., 2018a; Liu et al., 2017; Wang et al., 2016; Wei et al., 2019c). Thus, it is vital to understand modes of stress transfer between matrix and fracture in response to gas flow in dual porosity rocks for geoengineering activities (e.g., coalbed methane production, shale gas extraction).

Coal reservoirs can be represented as a dual porosity/permeability system. The fractures are the primary pathway for rapid fluid flow, while the coal matrix serves as a storage site with gas stored in the various-sized pores (Haenel, 1992; Zheng et al., 2018). It is commonly assumed that Darcy flow predominates in the fracture system but can be neglected in the coal matrix where diffusion dominates (Cui et al., 2018b; Fan et al., 2019; Liu et al., 2019; Palmer, 2009; Pan and Connell, 2012; Purl et al., 1991; Ried et al., 1992; Zhang et al., 2019) – although there are equivalencies between permeability and diffusivity. When gas is injected into coal, gas rapidly invades the fractures due to the relatively high permeability. As a consequence, a pressure difference between the matrix and the fracture is created and this in turn results in the diffusion of gas from the fracture into the matrix. The gas diffuses rapidly from the fractures into the matrix where there is a high matrix permeability/diffusivity (e.g., sandstone) – and the interval time for pressures to stabilize can be neglected (Shi et al., 2018). However, for coal, this may take several days (Harpalani and Chen, 1997) or even several weeks (Gensterblum et al., 2014). When, in addition to diffusion-only, the retarding impact of gas sorption is included, the time for equilibration may extend to a few months (Danesh et al., 2017; Guo et al., 2007). These coupled diffusion/sorption phenomena determine the localized deformation within the ensemble matrix-fracture system and can be investigated through tightly constrained laboratory experiments and numerical models.

Single porosity/permeability models (Connell et al., 2010; Cui and Bustin, 2005; McKee et al., 1988; Palmer and Mansoori, 1996; Pan and Connell, 2007; Pini et al., 2009; Robertson and Christiansen, 2006; Seidle et al., 1992; Seidle and Huitt, 1995; Shi and Durucan, 2004) are used under specific conditions (such as uniaxial strain) to explain the experimental observations. However, these models are not applicable in interpreting some experimental observations (Izadi et al., 2011; Liu et al., 2011b; Wang et al., 2011). On the basis of dual poroelasticity theory, dual porosity and dual permeability models have been established (Bai et al., 1993; Lu and Connell, 2007, Lu and Connell, 2011; Pan and Connell, 2007; Peng et al., 2014; Wang et al., 2013; Wu et al., 2011; Wu et al., 2010), which are capable of accommodating the roles of fracture-matrix interaction. Among these models, the interactions between coal matrix and fractures are normally defined by the mass exchange of gas. However, the role of mechanical interaction between matrix and fracture, that can cause the transition of coal matrix swelling, from local swelling to macro-swelling, under differential pressure, together with their impact on the evolution of permeability is not rigorously accommodated (Liu et al., 2011a; Liu et al., 2011b). To address this shortcoming, permeability models have been established with the interaction between matrix and fracture geometry and location suitably accommodated (Liu et al., 2018; Wei et al., 2019a; Zhang et al., 2018). In this, a full set of cross-coupling relations are connected between the matrix and the fracture, including local force balance, local deformation compatibility, and mass exchange (Zhang et al., 2018). The fracture aperture change in coal containing discrete fractures, following gas injection under unconstrained conditions, is consequently rigorously accommodated (Liu et al., 2018). This includes consideration of the non-uniform deformation induced by gas diffusion and described by a strain-rate-based permeability model coupling coal deformation and gas flows in both fractures and matrix (Wei et al., 2019a).

The majority of experimental studies on cleat-matrix interaction have been completed by measuring the correlation between coal permeability and pore pressure – with these experiments divided between displacement-controlled and stress-controlled experiments. For displacement-controlled experiments, uniaxial strain experiments are normally used to study the evolution of coal permeability (Fan and Liu, 2018; Mitra et al., 2012; Wang et al., 2015). As for the stress-controlled experiments, two types of experiments are generally conducted, with one keeping total stress constant (Gensterblum et al., 2014; Harpalani and Schraufnagel, 1989, Harpalani and Schraufnagel, 1990; Harpalani and Zhao, 1989; Kumar et al., 2012; Meng et al., 2015; Pini et al., 2009; Robertson and Christiansen, 2005; Wang et al., 2017b; Wang et al., 2019; Wang et al., 2015), and the other keeping effective stress constant (Al-hawaree, 1999; Anggara et al., 2016; Chen et al., 2011; Feng et al., 2017; Harpalani and Chen, 1997; Li et al., 2015; Li et al., 2013; Lin and Kovscek, 2014; Lin et al., 2008; Meng and Li, 2017; Pan et al., 2010; Seomoon et al., 2015; Xu et al., 2013). Regardless of the choice of boundary conditions, these experiments typically ignore the pressure difference between the matrix and the fracture – and assumes steady condition to interpret the results. In order to study the impact of dynamic deformation between matrix and fracture within the coal sample, a set of experiments have been performed to measure the evolution of dynamic permeability during gas injection/depletion under constant confining pressures (Liu et al., 2016a; Mazumder and Wolf, 2008; Siriwardane et al., 2009; Wei et al., 2019b). Importantly, the evolution of the distribution of strains throughout the entire samples and under different stress conditions were also observed. Helium gas (He) was injected into both jacketed and unjacketed coal samples within a pressurized core holder to investigate coal matrix swelling during the process of gas diffusion from cleats, and the impact on the evolution of strain within the entire sample were observed (Wang et al., 2016). For a constant volume boundary condition (zero displacement), local deformation of the coal sample and its permeability were measured through strain gauges and unsteady flow during helium gas injection (Wang et al., 2017a), respectively. These results demonstrated that gas diffusion from the fracture to the matrix can result in localized swelling of the coal matrix and affect the aperture of the cleat. Under this condition, coal permeability is controlled primarily by the local deformation. Normally it is assumed that 100% of the coal swelling would contribute to the reduction of coal permeability provided that the fractures are much more compliant than the coal matrix (Harpalani and Chen, 1995; Liu et al., 2011b; Ma et al., 2011). However, few direct observations of this have been made, and the distribution of deformations in different parts of the sample has not been clearly explained.

The following study observed the stress transfer between matrix and fracture through the proxy of measured strains. Strain gauges were used to measure the mean strain on different parts of a prismatic coal sample containing a variable density distribution of fractures. The sample was tested under conditions of free expansion (zero stress). Optical microscopy and X-ray CT imaging were used to define the fracture distribution throughout the sample with mercury intrusion (capillary) porosimetry (MICP) constraining the pore size distribution measured and enabling independent estimation of matrix permeability. This work offers a first direct observation into the dynamics of stress transfer between fracture and matrix and a new understanding of permeability evolution in response to the transition in dual porosity rocks. These results and findings are reported in the following sections.