Proppant Distribution Research Articles

Pressure Decline Analysis in Fractured Horizontal Wells: Comparison between Diagnostic Fracture Injection Test, Flowback, and Main Stage Falloff

SummaryThe pressure decline data after the end of a hydraulic fracture stage are sometimes monitored for an extended period of time. However, to the best of our knowledge, these data are not analyzed and are often ignored or underappreciated because of a lack of suitable models for the closure of propped fractures. In this study, we present a new approach to model and analyze pressure decline data that are available in unconventional horizontal wells with multistage, transverse hydraulic fracturing. The methods presented in this study allow us to quantify closure stress and average pore pressure inside the stimulated reservoir volume (SRV) and to infer the uniformity of proppant distribution without additional data acquisition costs. For the first time, field data of diagnostic fracture injection test (DFIT), flowback, and pressure decline of main fracturing stages from the same well are compared and analyzed. We found that the early-time main fracturing stage pressure decline trend is controlled by fracture tip extension, followed by progressive hydraulic fracture closure on the proppant pack, whereas late-time pressure decline reflects linear flow. When DFIT data are not available, pressure decline analysis of a main hydraulic fracturing stage can be a substitution if it can be monitored for an extended period to allow fracture closure on proppants and asperities.

A review on proppant transport modelling

Proppant transport is a critical physical process in hydraulic fracturing which has been extensively used for reservoir stimulation in petroleum engineering. Proppants injected together with fracturing fluid provide structural support to the stimulated fracture network and prevent them from closing after flowback. Hence, the final proppant distribution in fracture networks affects directly the effectiveness of hydraulic fracturing. Owing to the limitation and high cost of well logging, computational modelling has been increasingly used to study proppant transport, where different assumptions and numerical models have been employed often without rigorous validation or justification. This work presents a comprehensive review on proppant transport modelling, from relevant physics to numerical approaches, aiming to provide an unbiased global picture of the-state-of-the-art studies, inspire new insights, and promote the development of innovative and reliable computational models for proppant transport.

XFEM-based numerical modeling of well performance considering proppant transport, embedment, crushing and rock creep in shale gas reservoirs

Predicting the production rate and estimating the ultimate recovery are of great significance for the optimization of shale gas development. One possible reason for production decline is the width reduction of propped fractures caused by proppant deformation, embedment, crushing, and viscoelasticity of the reservoir. In order to obtain more in-depth knowledge of how these factors influence the gas production, a novel approach is proposed to simulate the processes of both hydraulic fracturing and gas production using the extended finite element method (XFEM). On the one hand, a numerical model which involves the coupled processes of deformation of the porous rock medium, fluid flow and leak-off, crack propagation, and proppant transport is proposed to obtain the proppant distribution for the hydraulic fracturing simulation. On the other hand, a coupled rock deformation and two-phase flow model considering stress-dependent fracture conductivity, crushing of proppant grains, creep of surrounding rock, gas diffusion and desorption, and influence of natural fractures is developed for the flowback and gas production simulation. The fracture closure during the shut-in and flowback process of fracturing fluid is considered. In addition, the size effects of proppant grains are investigated by using Weibull theory. After validation of the proposed model through history-matching, the sensitivity analysis of the proposed model on gas production is conducted. This study reveals that the proppant size has a dominant influence. Although proppant with larger grain sizes leads to a more permeable propped fracture, it is found that only proppant grains of proper size, not too large or too small, has the potential to achieve economic gas production due to the combined effects of size effect of the grains and “bridging out” of the proppant. The second influential factor on the gas production is the proppant concentration which is followed by the viscosity of shale formation, the Young's modulus of proppant, and the Young's modulus of shale formation. This study leads to a better understanding of proppant-related mechanisms involved in hydraulic fracturing and gas production and provides an efficient numerical tool for the prediction of well performance in field development planning.

Numerical investigation of fluid flow in fracture junctions with consideration to effect of fracture morphology

AbstractBecause the fracturing fluid flow at fracture junctions directly affects the proppant distribution in fracture networks, it is very important to quantitatively investigate the fluid flow in fracture junctions. In this study, the fluid flow in a laboratory‐size fracture junction was investigated, and equations for calculating the fluid split ratio were established. The correlations between the pressure loss coefficients and the width ratio, approaching angle, and fluid split ratio were obtained by simulation. Using a custom‐made Visual Basic program, the fluid split ratios in an actual‐size fracture or complex fracture networks with several secondary or tertiary fractures were calculated. The results reveal that the fluid split ratio is significantly affected by the approaching angle and width ratio in laboratory‐size fractures. In contrast, in an actual‐size fracture junction, the fluid split ratio is mainly affected by the length of the fracture channel and the width ratio. The split ratios in laboratory‐size and real‐size fracture networks with several secondary or tertiary fractures are quite different, which indicates that the split ratio should be quantitatively estimated when investigating the proppant distribution by experiment or simulation. The findings of this study can be useful in the quantitative investigation of the proppant distribution in fracture networks.

Experimental and Numerical Study on Proppant Transport in a Complex Fracture System

Slickwater fracturing can create complex fracture networks in shale. A uniform proppant distribution in the network is preferred. However, proppant transport mechanism in the fracture network is still uncertain, which restricts the optimization of sand addition schemes. In this study, slot flow experiments are conducted to analyze the proppant placement in the complex fracture system. Dense discrete phase method is used to track the particle trajectories to study the transport mechanism into the branch. The effects of the pumping rate, sand ratio, sand size, and branch angle and location are discussed in detail. Results demonstrate that: (1) under a low pumping rate or coarse proppant conditions, the dune development in the branch depends on the dune geometry in the primary fracture, and a high proportion of sand can transport into the branch; (2) using a high pumping rate or fine proppants is beneficial to the uniform placement in the fracture system; (3) sand ratio dominates the proppant placement in the branch and passing-intersection fraction of a primary fracture; (4) more proppants may settle in the near-inlet and large-angle branch due to the size limit. Decreasing the pumping rate can contribute to a uniform proppant distribution in the secondary fracture. This study provides some guidance for the optimization of proppant addition scheme in the slickwater fracturing in unconventional resources.

Experiments of Sand Distribution among Perforation Clusters in a Horizontal Pipe

ABSTRACT Multistage horizontal fracturing is the key technique in developing shale gas reservoirs. Although the parameters of perforation clusters are almost the same in each stage, production from each perforation cluster is vastly different. One of the factors that influences gas production between perforation clusters is the uneven proppant distribution among perforation clusters. In order to investigate proppant distribution among perforation clusters, the theory on proppant settling along horizontal lateral is presented to calculate the minimal critical velocity. Meanwhile, experiments on 20/40 and 40/70 mesh sand distribution with different concentrations were conducted at different pumping rates utilizing slick water fluids. The experimental parameters of perforation cluster, such as perforation density, length, and distance between clusters are scaled to simulate the actual treatment in shale gas fracturing. Therefore, the experimental results in this study can represent the actual distribution of proppants among perforation clusters. The results are analyzed, and some conclusions are presented. Pumping rate and viscosity are the two important factors that can have a big impact on the sand distribution. At a lower pumping rate, more sand was deposited at the first perforation cluster, whereas at a high pumping rate, more sand was deposited at the third cluster. The viscosity of slick water will also affect sand distribution largely. At a low fluid viscosity, sand distribution was varied much among clusters at the same pumping rate, and sand tended to distribute evenly when the fluid viscosity is increased. Therefore, in order to distribute proppants evenly among perforation clusters, the treatment parameters such as the pumping rate or the viscosity of slick water fluid can be adjusted accordingly.

Optimal pumping schedule with high-viscosity gel for uniform distribution of proppant in unconventional reservoirs

Hydrocarbon recovery from a hydraulic-fractured unconventional reservoir can be enhanced by replacing slickwater with non-Newtonian high-viscosity gel as a fracturing fluid. However, in the literature, the role of gel rheology on hydrocarbon production from a fractured reservoir is not very well understood. This lack of understanding makes it difficult for the industry to choose appropriate viscosity parameters of fracturing gels. Motivated by these limitations, first, we have developed a high-fidelity model of non-Newtonian fluid flow to simulate fracture propagation, fluid leak-off, and gel flowback processes to predict the oil production from a hydraulic fractured reservoir. Simulation results of the high-fidelity model show how fracture geometry, formation damage, and gel cleanup process varies with the fracturing fluid rheology. Hence, the developed model is used to understand the effect of gel rheology on hydrocarbon production via a sensitivity analysis, which provides a set of rheological parameters that maximize the cumulative amount of oil production. Finally, utilizing this optimal high-viscosity gel, a model predictive controller is designed to obtain an optimal pumping schedule necessary for producing a target fracture geometry and proppant concentration. The closed-loop simulation results demonstrate that the obtained pumping schedule successfully achieved the desired fracture geometry and proppant concentration at the end of pumping, leading to the maximum oil production from an unconventional reservoir.

Field-Scale Numerical Investigation of Proppant Transport among Multicluster Hydraulic Fractures

Summary Plug-and-perforation (P-n-P) completion has been widely used in horizontal wells for the development of unconventional reservoirs. In the field, uneven proppant distribution among different fractures within a fracturing stage has been frequently observed in P-n-P treatments, leaving a large portion of reservoir volume understimulated. In this paper, an efficient 3D multiphase particle-in-cell (MP-PIC) method has been used to simulate proppant transport among multiple fractures (fracture near the heel, middle fracture, fracture near the toe) at the field scale. This work studies the fundamental physics of the proppant transport process and reveals the mechanisms of uneven proppant placement, giving strategies to improve the proppant placement. Before applying the MP-PIC method to field-scale problems, we conducted indoor experiments to validate the model. The simulation results show an excellent agreement with the vertical slot experimental results. After model validation, we used the MP-PIC method to directly simulate the field process of proppant transport, involving slurry transport from the wellbore through perforation holes and finally into fractures. A base case with three fractures in a stage was first established to calculate the percentage of proppant mass distribution in each fracture. Then, we performed the sensitivity analysis of both proppant size and injection rate to investigate their effects on proppant placement. The results reveal that all the cases tend to have a heel-biased proppant distribution among three fractures, which agrees with the field observations. There are two reasons for the heel-biased proppant distribution. First, at the very beginning of the injection, more proppants tend to flow toward the toe side because of large momentum. As more and more proppants move to the toe side, the concentration near the toe side gradually increases, which adds flow resistance to the newly injected proppants. Therefore, most newly injected proppants will go to the first fracture. The second reason comes from the fracture geometry. Because the first fracture has the largest fracture width among three fractures, it has the smallest flow resistance for proppant transport. More slurry will flow into the first fracture. Apart from giving explanations for the heel-biased distribution, we also suggest some strategies to improve the proppant distribution. The sensitivity analysis shows that the strong heel-biased proppant distribution can be mitigated by optimizing the proppant size and injection rate. Our study for the first time conducts a field-scale numerical investigation of proppant transport in the wellbore-fracture system during P-n-P treatments. The results can provide us with more insights into the optimization of fracture design in field practice.

A generalized analytical model for hydrocarbon production using multi-fractured horizontal well with non-uniform permeability distributions

The multi-fractured horizontal well (MFHW) has significantly facilitated the exploitation of unconventional hydrogen-carbon compound reservoirs, which is an abundant source of fossil hydrogen energy. The composite linear flow models were frequently adopted to analytically evaluate the hydrocarbon production using MFHW. Most of the existing composite linear flow models assume uniform permeability in the primary fractures and the Stimulated Reservoir Volume (SRV) region. However, due to the non-uniform proppant distribution in the primary fractures and the heterogeneity in the density of the secondary fractures in SRV region, the permeability field in both regions are non-uniform. For the first time, a generalized analytical model incorporating continuous permeability heterogeneity in both the primary fractures and SRV region is proposed for the hydrocarbon production of MFHW. Any arbitrary permeability distribution functions can be treated as inputs to the proposed model. The mathematical model is solved using the perturbation technique and the Laplace transform method.The good match with the numerical solution verifies the accuracy of the proposed analytical model. Subsequently, the proposed solution is assigned with different modes of permeability heterogeneity to investigate their impacts on well production performances, i.e., cumulative hydrocarbon production and transient bottom-hole pressure (BHP). The results reveal that the incorporation of permeability heterogeneity will enhance the production rate and lower the BHP drawdown compared to the homogeneous case with the same average permeability. Besides, a field case is presented to demonstrate the applicability of the proposed model.

Numerical Investigation of the Effect of Partially Propped Fracture Closure on Gas Production in Fractured Shale Reservoirs

Nonuniform proppant distribution is fairly common in hydraulic fractures, and different closure behaviors of the propped and unpropped fractures have been observed in lots of physical experiments. However, the modeling of partially propped fracture closure is rarely performed, and its effect on gas production is not well understood as a result of previous studies. In this paper, a fully coupled fluid flow and geomechanics model is developed to simulate partially propped fracture closure, and to examine its effect on gas production in fractured shale reservoirs. Specifically, an efficient hybrid model, which consists of a single porosity model, a multiple porosity model and the embedded discrete fracture model (EDFM), is adopted to model the hydro-mechanical coupling process in fractured shale reservoirs. In flow equations, the Klinkenberg effect is considered in gas apparent permeability, and adsorption/desorption is treated as an additional source term. In the geomechanical domain, the closure behaviors of propped and unpropped fractures are described through two different constitutive models. Then, a stabilized extended finite element method (XFEM) iterative formulation, which is based on the polynomial pressure projection (PPP) technique, is developed to simulate a partially propped fracture closure with the consideration of displacement discontinuity at the fracture interfaces. After that, the sequential implicit method is applied to solve the coupled problem, in which the finite volume method (FVM) and stabilized XFEM are applied to discretize the flow and geomechanics equations, respectively. Finally, the proposed method is validated through some numerical examples, and then it is further used to study the effect of partially propped fracture closures on gas production in 3D fractured shale reservoir simulation models. This work will contribute to a better understanding of the dynamic behaviors of fractured shale reservoirs during gas production, and will provide more realistic production forecasts.

Biomimicry Surface-Coated Proppant with Self-Suspending and Targeted Adsorption Ability.

Proppant is a key material, which can increase the production of unconventional petroleum and gas. Excellent proppants with a long migration distance are required in the fracture network. Resin-coated proppants have been confirmed as a good choice because of the long migration and the self-suspending ability in fracturing fluids. However, the distribution of the resin-coated proppants in fracture networks is random. The design of proppants with targeted adsorption is urgently needed. In this study, a novel proppant coated with a phenolic resin shell doped with Fe3O4 nanoparticles on ceramic (coated proppant) was designed and investigated. Based on the results, the coated proppant was adsorbed on the magnetic component’s parts of the fracture network surface, which helps in enhancing the uniform distribution of the proppant in the fracture rock cracks. Meanwhile, the self-suspending ability of the coated proppant is five times higher than that of the uncoated proppant and can migrate a longer distance in the fracture network. Moreover, the liquid conductivity of the coated proppant is 30% higher than that of the uncoated ones at a closure pressure of 6.9 MPa. In summary, new insights into the design of functional proppants and further guidelines on the production of unconventional petroleum and gas have been provided in this study.

Numerical simulation and evaluation of the fracturing and tight gas production with a new dimensionless fracture conductivity (FCD) model

Hydraulic fracturing is an essential technology for the development of unconventional resources such as tight gas. The evaluation of the fracture performance and productivity is important for the design of fracturing operations. However, the traditional dimensionless fracture conductivity is too simple to be applied in real fracturing operations. In this work, we proposed a new model of dimensionless fracture conductivity (FCD), which considers the irregular fracture geometry, proppant position and concentration. It was based on the numerical study of the multistage hydraulic fracturing and production in a tight gas horizontal well of the North German Basin. A self-developed full 3D hydraulic fracturing model, FLAC3Dplus, was combined with a sensitive/reliability analysis and robust design optimization tool optiSLang and reservoir simulator TMVOCMP to achieve an automatic history matching as well as simulation of the gas production. With this tool chain, the four fracturing stages were history matched. The simulation results show that all four fractures have different geometry and proppant distribution, which is mainly due to different stress states and injection schedule. The position and concentration of the proppant play important roles for the later production, which is not considered in the traditional dimensionless fracture conductivity FCD. In comparison, the newly proposed formulation of FCD could predict the productivity more accurately and is better for the posttreatment evaluation.

Experimental study on proppant diversion transportation and multi-size proppant distribution in complex fracture networks

Proppant transportation in fracture networks is significant for hydraulic fracture design and evaluation. Previous studies on proppant placement in complex fracture networks had shortcomings in terms of proppant diversion transportation, proppant distribution in a secondary fracture, and proppant distribution with different particle sizes. This experimental study was conducted on proppant diversion transportation and distribution in complex fracture networks based on the visualization proppant placement model. The findings revealed that the critical proppant diversion time rapidly decreased with the increase in the pumping rate. When the pumping rate was lower than 2.5 m3/h, no proppant diversion transportation was found in the second- and third-branch fractures. The smaller-sized proppant particles (100 mesh) were distributed mainly in the fracture located far away from the wellbore or the major fracture. More smaller-sized proppant particles were distributed in the deeper fracture when the difference between the proppant particle sizes was large. Increasing the pumping times increased the transport of proppant particles to deeper fractures. However, the increase in the amplitude was larger in 100-mesh proppant particles than in 30/50-mesh proppant particles. Smaller-sized proppant particles were more easily transported to branch fractures, thus increasing the proppant placement efficiency. The experimental findings can be used to optimize the parameters of the stimulated reservoir volume fracturing to improve the effectiveness of fracture networks.

Experimental Study of Sand Distribution among Perforation Clusters in Horizontal Wellbore of Shale Gas Reservoir

Multistage horizontal fracturing is the key technique in developing shale gas reservoirs. In each stage, several perforation clusters will be placed to create complex fractures, and the parameters of perforation clusters are almost the same, so the production from each perforation cluster should be similar. However, in fact, production from each perforation cluster is different vastly. If the characteristics of the shale gas reservoir where the horizontal wellbore oriented through are similar, the cause that resulted in production difference may be uneven proppant distribution among perforation clusters. In order to investigate proppant distribution through perforation clusters, the theory about proppant settling along horizontal lateral is analyzed, which can provide a proper pumping rate for future experiments. Then, an experimental model to simulate horizontal lateral and perforated clusters is designed. Fresh water was pumped to transport proppant flowing into different clusters, the volume of water and proppant through each cluster was qualified. Some parameters, such as proppant concentration, sizes, flow rate, and perforation parameters, are changed in lab tests; the simulation results will be helpful in understanding the phenomenon of uneven proppant distribution in perforation clusters. There are some conclusions from the experimental results. First, proppant settling at different positions along horizontal lateral is different when the slurry is mixed by proppant and water is pumped at different rates. Meanwhile, proppants concentration also has an influence on proppants settling. The settling of proppants will impact proppants distribution among perforation clusters. Second, at a low pumping rate, uneven proppants distribution was observed mostly. When the pumping rate was increased, the phenomenon of uneven proppants distribution was decreasing. Thus, the pumping rate is the main influential factor. Third, uneven proppants distribution can be improved or even avoided by adjusting perforation parameters, such as perforation numbers and diameter.

Numerical simulation of fractured vertical well in low-permeable oil reservoir with proppant distribution in hydraulic fracture

In this paper, numerical simulations of fractured vertical well in low-permeable oil reservoir are carried out and two issues: threshold pressure gradient (TPG) in reservoir matrix and proppant distribution in hydraulic fractures are focused on. A physical definition of effective fracture length (EFL) is presented to evaluate the fracture effectiveness due to uneven proppant distribution. In terms of numerical processing for TPG, based on the subsurface Darcy's flow module in COMSOL Multiphysics, an effective numerical simulation method is adopted by substituting the gravitational acceleration vector in Darcy's law (Liu et al., 2019b). The simulation results show that, proppant distribution has great influence on fracture effectiveness. Unappealing proppant distribution can reduce effective fracture length by 49.6%, which is negative for low-permeable oil reservoir development. TPG in reservoir matrix mainly affects the moving boundary and pressure-disturbed area in reservoir. When TPG in matrix reduces from 0.02 MPa/m to 0 MPa/m, the distance of moving boundary at 300 days could increase for almost double and pressure-disturbed area enlarged drastically for around 74%. Furthermore, a heterogenous low-permeable oil with secondary fracture networks is designed to study the joint effect of TPG and proppant distribution. If we neglect these two factors, cumulative oil rate will be greatly overestimated by 38.6% at 1000 days. At the same time, the existence of natural fractures could also affect the streamline distribution in low-permeable oil reservoir and contribute to fluid flow in reservoir.

Effect of fracture roughness on the hydrodynamics of proppant transport in hydraulic fractures

The effect of fracture roughness is investigated on proppant transport in hydraulic fractures using Joint Roughness Coefficient and a three-dimensional multiphase modelling approach. The equations governing the proppant transport physics in the fracturing fluid is solved using the hybrid computational fluid dynamics model. The reported proppant transport models in the literature are limited to the assumption of a smooth fracture domain with no fluid leak-off or fluid flow from fracture to rock matrix interface. In this paper, a proppant transport model is proposed that accounts for the proppant distribution in rough fracture geometry with fluid leak-off effect to surrounding porous rock. The hydrodynamic and mechanical behaviour of proppant transport was found directly related to the fracture roughness and flow regime especially under the influence of low viscosity fracturing fluid typically used in shale gas reservoirs. For the proppant transport in smooth fractures, the fracture walls employ mechanical retardation effects and reduce the proppant horizontal velocity resulting in more significant proppant deposition. On the contrary, for the proppant transport in rough fractures, the inter-proppant and proppant wall interactions become dominant that adds turbulence to the flow. It results in mechanical interaction flow effects becoming dominant and consequently higher proppants suspended in the slurry and greater horizontal transport velocity. Furthermore, the mechanical interaction flow effects were found to be principally dependant on the proppant transport regime and become significant at higher proppant Reynolds number.

Coupled Hydraulic Fracture and Proppant Transport Simulation

This paper focuses on the study of proppant transport mechanisms in fractures during frac-packing operation. A multi-module, numerical proppant, reservoir and geomechanics simulator has been developed, which improves the current numerical modeling techniques for proppant transport. The modules are linked together and tailored to capture the processes and mechanisms that are significant in frac-pack operations. The proposed approach takes advantage of a robust and sophisticated numerical smeared fracture simulator and incorporates an in-house proppant transport module to calculate propped fracture dimensions and concentration distribution. In the development of software capability, the propped fracture geometry and proppant concentration, which are the output of the proppant module, are imported to the hydraulic fracture simulator through mobility modification. Complex issues of proppant transport in fractures that are addressed in the literature and captured by the current model are: hindered settling velocity (terminal velocity of proppant in the injection fluid), the effect of fracture walls, proppant concentration and inertia on settling (due to extra drag forces applied on particles, compared to single-particle motion in Stokes regime in unbounded medium), possible propped fracture porosity and also mobility change due to the presence of proppant, and fracture closure or extension during proppant injection. A sensitivity analysis is conducted using realistic parameters to provide guidelines that allow more accurate predictions of the proppant concentration and fluid flow. The main objective of this study is to link a numerical hydraulic fracture model to a proppant transport model to study the fracturing response and proppant distribution and to investigate the effect of proppant injection on fracture propagation and fracture dimensions.

Fracturing Gels as Analogs to Understand Fracture Behavior in Shale Gas Reservoirs

Hydraulic fracturing is widely used in the exploitation of unconventional reservoirs, such as shale gas and tight gas. However, a full understanding of the activation of natural fractures, prediction of fracture growth, distribution of proppant, and network fracture system effectiveness remain unresolved. The onset of fracturing in the media requires energy and this is due to the buildup of pressure within the rock due to continuous injection of fluid. In other words, when the energy associated with the injection fluid reaches the fracture strength of the rock, the fracture initiates and propagates into the formation. Here, we use gelatin in hydraulic fracturing laboratory tests and compare the results to a modified radial hydraulic fracturing theory. The mechanics of the gelatin, procedures to make a testing gelatin block, and procedures to conduct the test are described. The results show that the fracture evolving behaviours from experiments are well matched by the theory. The results are then scaled up to understand fracture growth behaviour in a tight rock reservoir.

Modeling Fracture Closure with Proppant Settling and Embedment during Shut-In and Production

Summary Fracture closure and proppant settling are two fully coupled processes during both shut-in and production. Proppant distribution greatly affects the residual fracture width and conductivity evolution, whereas fracture closure might limit proppant settling and force the proppant to crush or embed into the rock. Modeling fracture closure with proppant settling and embedment is challenging because of the multiple coupled physical processes involved, large time-scale differences, and extreme nonlinearity in the coupling of the processes. Conventional fracture-closure models either use simplified analytical estimates of the stress-dependent permeability of the reservoir or explicitly calculate the fracture width using empirical relationships, without considering the effect of fluid leakoff and dynamic changes in the proppant distribution in the fracture. In this work, we use a novel fully implicitly coupled fracturing/reservoir simulator to study fracture closure and proppant-settling/embedment processes during shut-in and production. This simulator implicitly couples the reservoir (rock deformation and porous flow), fracture (fracturing-fluid flow, proppant transport), and wellbore (slurry distribution, production) domains. During shut-in, a modified Barton-Bandis (Bandis et al. 1983) formula is used to describe the nonlinear relationship between the contact force and the residual fracture aperture considering the dynamic proppant spatial distribution and rock heterogeneity. During production, fracture conductivity is evaluated according to proppant distribution and further fracture closure caused by proppant crushing and embedment. A Newton-Raphson method is applied to solve the coupled system of equations. Results from the simulations clearly show that typical periods of shut-in after fracturing lead to the formation of proppant banks at the bottom of the fracture in low-permeability, low-leakoff formations. This can lead to near-wellbore tortuosity and poor connectivity between the wellbore and the hydraulic-fracture network. Stress-dependent permeability, likely induced by induced unpropped fractures, is shown to be essential to obtain reasonable values of leakoff and to history match production trends. Proppant embedment is shown to be an important factor controlling production-decline rates in clay-rich shales.

Proppant transport in dynamically propagating hydraulic fractures using CFD-XFEM approach

Numerically modelling the fluid flow with proppant transport and fracture propagation together are one of the significant technical challenges in hydraulic fracturing of unconventional hydrocarbon reservoirs. The existing models either model the proppant transport physics in static predefined fracture geometry or account for the analytical models for defining the fracture propagation. Furthermore, the fluid leak-off effects are usually neglected in the hydrodynamics of proppant transport in the existing models. In the present paper, a dynamic and integrated numerical model is determined that uses computational fluid dynamics (CFD) technique to model the fluid flow with proppant transport and Extended finite element method (XFEM) to model the fracture propagation. The results of fracture propagation were validated with the real field results and analytical models, and the results of proppant transport are validated with the experimental results. The integrated model is then used to comprehensively investigate the hydrodynamical properties that directly affect the near-wellbore stress and proppant distribution inside the fracture. The model can accurately model the proppant physics and also propose a solution to a frequent challenge faced in the petroleum industry of fracture tip screen out. Thus, using the current model allows the petroleum engineers to design the hydraulic fracturing operation successfully, model simultaneously fracture propagation and fluid flow with proppant transport and gain confidence by tracking the distribution of proppants inside the fracture accurately.