**1. Introduction**

The purpose of injecting proppants in shale reservoirs is to maintain the fracture conductivity for a longer period and to prevent the fracture from closure due to subsurface stresses. On the other hand, the proppants themselves can be a problem in the case where they develop surface penetration in the formation. As a result, the proppant is embedded into the formation and decreases the fracture conductivity of the reservoir as shown in **Figure 1**. Due to inhomogeneous stress distributions between quartz grains and proppants, high tensile stress concentrations beneath the area of contact between quartz grains and proppants are observed even at small external stress applied to the rock-proppant system. These high-stress concentrations are responsible for the early onset of damage at the fracture face and determine the type of proppant failure [1].

Water imbibition and some other tests on saturated shale were carried out to observe the crack generation process and compare the failure patterns as well as damage resistance of saturated shale kernels and unsaturated shale kernels. The average damage resistance of saturated kernel water is found to be around 11.69 MPa compared to 30.57 MPa of unsaturated shale kernels, which implies that water can decrease the resistance to shale damage and helps in generating

**Figure 1.** *Propped hydraulic fracture conductivity [2].*

fractures [3]. Fracture networks created during the process of hydraulic fracturing usually have a complex pattern. Most of these fractures are kept open by the incorporation of proppants in the form of proppant packs, as shown in **Figure 1**. In the case of secondary fractures, other than bi-wing fractures, proppants are unable to enter into the fractured surface due to narrow apertures and thus, these fractures cannot maintain conductivity for a longer period. The effective vertical and horizontal stresses are responsible for the decrease in hydraulic fracture conductivity and an estimated 60% decrease in propped fracture conductivity occurs by increasing effective stress from 6.2 to 34.48 MPa [4].

Considering the narrow apertures of secondary hydraulic fractures, a partial monolayer of proppant, that is, a single layer of proppant having uneven distribution of proppants over the fracture surface, can be introduced instead of multilayer proppant to maintain the maximum possible conductivity for production improvement [5]. The variation in the aperture and surface roughness of the hydraulic fractures are considered as main reasons for the uneven distribution of proppants. In this regard, the study of the conductivity of fractures with narrow apertures, filled with a monolayer of proppant, can be used for the optimization of hydraulic fracturing and the analysis of production in shale reservoirs. In the past, various types of compression, such as long-term and short-term compression on a single proppant, have been studied in-depth by diametric compression tests and DEM/ FEM simulations. Most proppants have shown creep behavior under long-term compression [6]. **Figure 2** shows that the embedment potential is related to many factors especially the proppant material, shape, concentration, and ability of the proppant to resist sinking in the fracture zone [9]. During hydraulic fracturing treatment, high fluid velocities in the fracture are generated by the small contact area between the wellbore and fracture, which results in the erosion of the proppant and fracture connectivity [10].

A computational fluid dynamics study with Eulerian granular modeling (EGM) that is based on solid pressure model and kinetic theory indicates that the transport of the proppant in complex fracture geometries is significantly affected by the dynamics of the fracturing fluids and the properties of the proppant [11]. According to parametric studies, a higher injection rate and lightweight proppants are beneficial for the transport of the proppant through the fracture junctions and to carry proppant in hydraulic fractures and natural fractures [11]. A DEM-CFD (discrete element method–computational fluid dynamics) and the experimental study indicate that during the closure period, the height of the proppants pillar decreases and diameter increases [12]. The proppant flowback could occur easily with a large proppant pillar height or a large fluid pressure gradient. However, the higher bonding strength of the fibers results to improve the stability of the proppant pillar [12].

*Hydraulic Fracture Conductivity in Shale Reservoirs DOI: http://dx.doi.org/10.5772/intechopen.100473*

**Figure 2.** *Flowchart showing factors responsible for embedment [7, 8].*

Proppant pillar is defined as concentrations of proppant in the form of pillars that maintain the aperture of the hydraulic fractures. The change in the optimum distance which is defined as the distance between proppant packs that has the potential to maintain the maximum conductivity after proppant embedment under a sparse distribution condition is primarily controlled by closure pressure, the rock's elastic modulus, and the proppant elastic modulus. It also states that the proppant concentrations and the poroelastic effect do not influence this optimum distance [13]. Studies based on analytical and discrete element method (DEM) have led to the understanding of the effects of various factors such as proppant size combination, concentration, time ratio, elastic modulus-to-stress ratio, and looseness coefficient [14, 15]. In these studies, deformation was considered elastic; however, actual phenomena can be captured by considering the intermediate states of elasticity and plasticity such as elastoplastic behavior of rock as well as proppant. In the case of monolayer proppant distribution, the embedment depth and contact stress decrease with the increase in proppant concentration [16]. In the past, machine learning and computational fluid dynamics approaches have been used to explore the well operation and the transport of sand particles by the injection of foam [17–23].

The production performance of fractured wells depends on two factors, that is, formation parameters and fracture parameters [24]. Formation parameters include porosity, permeability, and geo-mechanical properties of the formation, while the fracture parameters comprise a length, aperture, and conductivity of fractures [25, 26]. Hydraulic fracture conductivity reflects the transport capacity of the permeable channel through the reservoir and any alteration to this permeable channel will directly impact the stimulation achieved from the fracturing treatment [27]. The experimental study performed on shale samples with fluids shows that the reduction in the elastic modulus can lead to a significant reduction in the effective fracture conductivity [28]. Zhang et al. reported an 88% reduction in fracture conductivity by injecting water at 27.58 MPa closure stress [29]. In this study, water as a fracturing fluid has been injected to find the excessive proppant embedment caused by the interaction of water with shale matrix, altering the hydraulic fracture conductivity. Water injection increased of local pore pressure and reduction of bonding strength of mineral in clay-rich shale that led to the softening of shale.

The effects of rock stiffness, the roundness of proppant, and the effective stresses on the conductivity of the fracture were studied by a geomechanics-fluid mechanics-coupled numerical workflow considering the interaction between rock matrix and proppant as well as fluid flow in a hydraulic fracture during the process of the reservoir depletion [30]. Compared to the weak shale, less embedment of proppant is observed in sandstone, having high stiffness, which indicates that the rock matrix with higher stiffness is helpful in maintaining the fracture aperture and conductivity [30]. The correlation between the fracture conductivity and the corresponding production performance was quantitatively analyzed using the finite element method [31]. The proposed research can provide valuable information on the unconventional maximization of resource recovery [31]. For future extensions, a network of fractal fractures with a stochastic-based fractal fracture network combined with micro-seismic events can be coupled to quantify the complex fractures of the network to improve fracture conductivity and production performance [31].

The hydraulic fracturing process is a costly job; therefore, improving the reservoir quality evaluation mechanism and optimization of the technical parameters are important. As the low-quality hydrocarbon (HC) shale reservoirs are also gaining increasing attention, to this end, optimization of the hydraulic fracture conductivity is of utmost importance to make the job profitable. To estimate the actual hydraulic fracture conductivity in shale reservoirs, the computational contact analysis of proppant between fracture surfaces has been carried out in this study. In the numerical analysis, a material property of proppant and formation characteristics is introduced from the experimental analysis. The influence of formation load and resulting deformation of formation is calculated by the total penetration of proppant. The deformation mechanism and proppant embedment in shale rocks, saturated with fracking fluid, are then simulated. The finite element code in ANSYS is used to simulate the shale reservoir/proppant contact-impact behavior in the fracture surface. The embedment depth of the shale samples was obtained by numerical as well as experimental methods and the permeability was calculated by the Kozeny–Carman correlation.
