Proppant Properties Research Articles

Optimization of ceramic proppant properties through an innovative coating approach

In this current research endeavor, a comprehensive exploration into the properties of ceramic coatings has been undertaken, utilizing bauxite, talc, and kaolin clay. The primary focus lies in the meticulous analysis of the mechanical strength of ceramic proppants. The proppant raw material employed is kaolin clay, treated through a dry coating technique and subsequently sintered at 1300°C. Evaluation of sample performance is based on the establishment of coating and substrate shrinkage. Shrinkage and density assessments are separately conducted for the coating mixtures and substrate. X-ray diffraction (XRD) is employed to discern the crystalline phases within the coatings, while structural characterization is facilitated through scanning electron microscopy (SEM) coupled with energy dispersive X-ray (EDX). Density and mechanical strength of proppants are meticulously investigated using picnometry and crush tests. The performances of the coated and uncoated samples were compared and investigated. Interestingly, the coated proppants demonstrate slightly higher density than their uncoated counterparts. Remarkably, the specimen featuring a coating composition of bauxite (72wt%)+clay (25wt%)+talc (3wt%) yields optimal results for mechanical strength. The sole crystalline phase detected in the coating is mullite, with a minimum coating thickness of 10μm.

Model for fracture conductivity considering particle size redistribution caused by proppant crushing

Clarifying the dynamic evolution and control mechanisms of fracture conductivity is crucial for optimizing hydraulic fracturing design. Previous studies on fracture conductivity mechanisms in deep shale reservoirs have been insufficient, particularly when considering proppant crushing, rendering existing models inapplicable. Therefore, in this study, the coupled effects of particle size redistribution caused by proppant crushing were considered. A particle crushing model based on fractal theory was introduced. It was combined with the Kozeny–Carman equation, and equations were derived for the evolution of the equivalent diameter of the proppant pile gradation curve and permeability, establishing a new model for predicting the fracture conductivity considering the particle size redistribution caused by proppant crushing. Furthermore, it provides an optimized chart of conductivity that matches the supply conductivity of the reservoir. The results of the study reveal that the fracture conductivity decreases owing to proppant rearrangement, compaction, and crushing, with a more significant decline in the initial compression stage, where the rate of conductivity reduction is 2.5 times that of the compaction stage. Proppant crushing shifts the gradation curve leftward, reducing the equivalent particle diameter and, consequently, the fracture conductivity. By adjusting the crushing ratio, apparent Young's modulus, looseness factor, and proportion of large-particle components of the proppant, the fracture conductivity can be controlled. This provides a theoretical basis for the development of proppant properties and fracturing optimization in deep shale reservoirs.

Improving enhanced geothermal systems performance using adaptive fracture conductivity

Maximizing heat extraction from enhanced geothermal systems (EGS) depends heavily on an efficient heat sweeping or basically an effective circulation of water through fracture networks. Fracture hydraulic conductivity can play a critical role in controlling potential thermal breakthroughs; however, the exact geometry and properties of these fractures cannot be determined in practice. Thermal breakthrough remains a main challenge for maintaining efficient heat extraction throughout the lifespan of an EGS project. In this work, we explore the concept of fracture conductivity tuning using temperature-sensitive proppants to extract more heat and delay thermal breakthrough from the particle scale to the reservoir scale. We derive an empirical equation to describe fracture conductivity as a function of proppant properties and in-situ conditions including closure stress and temperature. Sensitivity analysis are performed to determine which parameters are the most crucial in determining the temperature-sensitive proppant permeability. Temperature and thermal expansion coefficient are the main contributing factors to the change in proppant permeability. Poisson’s ratio is found to have negligible impact on the proppant permeability. The derived equation is used to quantify the improvement in heat extraction from EGS at the field scale. The outcome shows that using temperature-sensitive proppant can increase the heat extracted by 47.8% compared to using typical proppant. This work assesses the feasibility of using temperature-sensitive proppants to effectively delay thermal breakthrough and sweep larger amounts of heat from EGS. In addition, this paper provides a quick and robust method to determine the required properties of such temperature-sensitive proppants to achieve uniform thermal gradient along different flow paths in the subsurface autonomously.

Modeling of Crack Development Associated with Proppant Hydraulic Fracturing in a Clay-Carbonate Oil Deposit

Survey and novel research data are used in the present study to classify/identify the lithological type of Verey age reservoirs’ rocks. It is shown how the use of X-ray tomography can clarify the degree of heterogeneity, porosity and permeability of these rocks. These data are then used to elaborate a model of hydraulic fracturing. The resulting software can take into account the properties of proppant and breakdown fluid, thermal reservoir conditions, oil properties, well design data and even the filtration and elastic-mechanical properties of the rocks. Calculations of hydraulic fracturing crack formation are carried out and the results are compared with the data on hydraulic fracturing crack at standard conditions. Significant differences in crack formation in standard and lithotype models are determined. It is shown that the average width of the crack development for the lithotype model is 2.3 times higher than that for the standard model. Moreover, the coverage of crack development in height for the lithotype model is almost 2 times less than that for the standard model. The estimated fracture half-length for the lithotype model is 13.3% less than that of for the standard model. A higher dimensionless fracture conductivity is also obtained for the lithotype model. It is concluded that the proposed approach can increase the reliability of hydraulic fracturing crack models.

Study on the Effect of Acid Corrosion on Proppant Properties

Pre-acid fracturing is an effective technique to improve productivity of tight reservoirs. While acid injection can clean the formation and improve the fracturing performance by reducing the fracture pressure of the reservoir, the chemical reaction of the acid solution with proppant may reduce the compressive strength of the proppant and therefore negatively affect the fracture conductivity. In this study, we experimentally investigated the solubility of the proppant in acid and the effect of acid corrosion on proppant compressive strength and fracture conductivity. The results show that the concentration of the acid solution has the greatest effect on solubility of the proppant, which is followed by the contact reaction time. Though a proppant of larger particle size indicates a lower solubility, the acid corrosion poses a greater damage to its compressive strength and conductivity. The quartz sand proppant exhibits superior stability to ceramic proppant when they are subjected to acid corrosion. The experimental results could serve as reference for selection of proppant and optimization of acid concentration and duration of acid treatment during pre-acid fracturing.

Solidification and utilization of water-based drill cuttings to prepare ceramsite proppant with low-density and high performance

Water-based drill cuttings (WBDC) and bauxite are used as raw materials to prepare proppants with low density and high performance. The effects of sintering temperature, sintering period, mixture ratios of materials, doping with iron oxide, and acid modification of WBDC on the properties of proppants are discussed. The proppant performance is evaluated according to the national standard SY/T5108-2014. The morphology of the proppant is analyzed using scanning electron microscopy (SEM). The crystal phase structure of the proppant is studied using X-ray diffraction (XRD). Thermal analysis of the proppant sintering process is performed using thermogravimetry (TG). Proppant Z-23 completely satisfied the SY/T5108 -2014 standard. This study provides a new perspective for the resource utilization of water-based drill cuttings and preparation of low-density proppants.

Effects of fluid and proppant properties on proppant transport and distribution in horizontal hydraulic fractures of coal under true-triaxial stresses

Proppant distribution and sedimentary area spacing are crucial factors that influence fracture closure, and they directly impact the efficiency and effective utilisation time of unconventional oil and gas. However, the fracture surface roughness of actual hydraulic fractures and the development of microfractures significantly impact proppant transport. Few proppant transport laws for hydraulic fractures under true-triaxial stresses have been proposed. In this study, the effects of fluid and proppant properties on proppant transport and distribution in horizontal coal hydraulic fractures were investigated using a true-triaxial hydraulic fracturing experimental system subjected to high-pressure sand injection. The results show that high-injection-rate fracturing and low-injection-rate sand injection facilitate proppant transport to fracture tip and increase the distribution area of the proppant in fractures. The high viscosity of sand-carrying fluid improves the carrying capacity of the proppant but also increases the transport resistance. The resistance and the buoyancy of the high-viscosity fluid make the proppant transport complex. The higher the proppant concentration, the larger the proppant settlement at the crack entrance, and the closer the proppant-transport distance. During multiple sand injections, the proppant injected previously is pressed into the coal seam under the closure stress. The stress required to migrate the proppant injected subsequently is higher, and the proppant settlement at the crack inlet is larger. The smaller the proppant particle size, the easier the proppant penetrates the microcracks; this is more conducive to reaching the crack tip and promoting the fracture network development.

Preparing high-strength and low-density proppants with oil-based drilling cuttings pyrolysis residues and red mud: Process optimization and sintering mechanism

This study aimed to assess the feasibility of manufacturing high-strength and low-density proppants from oil-based drilling cuttings pyrolysis residues (ODPR) and red mud (RM). The effects of ODPR and RM content on the performance of the proppants were studied, respectively. The optimum sintering condition was determined by response surface methodology (RSM), and the sintering mechanism was explored based on microstructural analysis of the proppants. The results showed that high-strength and low-density proppants with the breakage ratio of 8.6 % under 52 MPa closed pressure, bulk density of 1.45 g·cm−3, and apparent density of 2.96 g·cm−3 were obtained under the optimum preparation conditions (mass ratio of ODPR: RM: bauxite: MnO2 of 20: 8: 76: 4, sintering temperature of 1342 °C, sintering time of 1.0 h, sintering rate of 4.9 °C·min−1). The performance of the product proppants could meet the requirements of the Chinese Petroleum and Gas Industry Standard “Measurement of properties of proppants used in hydraulic fracturing and gravel-packing operations” (SY/T 5108-2014). ODPR and RM in the raw materials provided the chemical components of Al2O3, SiO2, CaO, BaO, Na2O, and K2O, which were involved in the formation of crystalline phases and molten phases during the sintering process. The performance of high-strength was primarily provided by the framework structure containing the crystalline phases and the dense structure caused by the molten phases. In addition, the Fe2O3 of RM would promote the generation of closed pores and then enhance the lightweight performance of proppants; however, excessive RM incorporation would lead to the formation of connected pores, which had a negative effect on the breakage ratio of proppants. This study not only creates a new pathway for recycling ODPR and RM within the shale gas industry but also provides a novel approach for manufacturing high-strength and low-density proppants.

Optimization of hydraulic fracturing with rod-shaped proppants for improved recovery in tight gas reservoirs

Due to the increasing demand and importance of natural gas in the global energy mix, its expeditious recovery is crucial, especially from large-scale unconventional geo-resources. Hydraulic stimulation is an established means of productivity increase especially from tight gas reservoirs. The fracture conductivity generally depends on proppant properties, particularly the shape. Therefore, in this research, the effect of using rod-shaped proppants was investigated. Using rod-shaped proppants instead of conventional spherically shaped proppants, can make a significant difference. Due to the cylindrical shape, higher porosity and permeability are generated, resulting in better conductivity fractures. Thus, to analyze the effect of different proppant shapes on post-fracture performance, a production model was implemented in the FLAC3Dplus-TMVOC framework. Later, an in-depth sensitivity analysis was performed to investigate the effects of the proppant shape, size, strength, and effective stress on the fracture aperture reduction and conductivity due to proppant deformation and embedment. The application to a generic model revealed that recovery can be increased by about 7% using aspect ratio 1 rod-shaped proppant with the same diameter as the spherical proppant. Then, increasing the rod-shaped proppant size from an aspect ratio of 1–10 can significantly increase the gas recovery by 13% but results in higher proppant deformation. Finally, the application of rod-shaped proppants to fracturing proposals in well x in a tight gas reservoir of Germany showed that the recovery could be significantly improved if spherical proppants are replaced with rod-shaped proppants.

Achieving Near-Uniform Fluid and Proppant Placement in Multistage Fractured Horizontal Wells: A Computational Fluid Dynamics Modeling Approach

SummaryMultistage plug-and-perforate fracturing of horizontal wells has proved to be an effective method to develop unconventional reservoirs. Various studies have shown uneven fluid and proppant distributions across all perforation clusters. It is commonly believed that both fracturing fluid and proppant contribute to unconventional well performance. Achieving uniform fluid and proppant placement in all perforation clusters is an important step toward optimal stimulation. This paper discusses how to achieve such uniform placement in each fracturing stage by means of a computational fluid dynamics (CFD) modeling approach.A laboratory-scale CFD model was built and calibrated using experimental data of proppant transport through horizontal pipes available from several laboratory configurations. A field-scale model was then built and validated using perforation erosion data from downhole camera observations. With the field-scale model validated, CFD simulations were performed to evaluate the impact of key parameters on fluid and proppant placement in individual perforations and clusters. Some key parameters investigated in this study included perforation variables (orientation, size, and number), cluster variables (count and spacing), fluid properties, proppant properties, pumping rates, and stress shadow effects.Both laboratory and CFD results show that bottom-side perforations receive significantly more proppant than top-side perforations because of gravitational effects. Laboratory and CFD results also show that proppant distribution is increasingly toe-biased at higher rates. Proppant concentration along the wellbore from heel to toe varies significantly. Gravity, momentum, viscous drag, and turbulent dispersion are key factors affecting proppant transport in horizontal wellbores. This study demonstrates that near-uniform fluid and proppant placement across all clusters in each stage is achievable by optimizing perforation/cluster variables and other treatment design factors. CFD modeling plays an important role in this design-optimization process.

Experimental investigation of long-term fracture conductivity filled with quartz sand: Mixing proppants and closing pressure

With the rapid technological advances in hydraulic fracturing, the economic development of ultra-tight gas/oil reservoirs becomes feasible, altering current energy image between demand and supply. The key parameter evaluating the artificial hydraulic fracture is the long-term conductivity, manifesting the transport capacity for reservoir fluids. The majority of previous contributions focused on the impacts of inherent proppant properties on long-term fracture conductivity, while the influence induced by mixture proppants with a wide range of particle size has not received due attention. In particular, as for the realistic field case, multiple types of proppants with diverse particle sizes are utilized to reach desirable conductivity. At the same time, the stress conditions inevitably change within the depressurization development process, leading to the evident enhancement of closing pressure towards artificial fracture, acting as the detrimental role for long-term fracture conductivity. As a result, it is dramatically necessary and urgent to reveal the mutual influence arising from mixture proppants as well as closing pressure. In order to address this issue, series of laboratory experiments are implemented, and comprehensive theoretical analysis in terms of experimental data is performed. Results show that (a) reduction of particle size is observed with increasing closing pressure, the average decreasing rate approaches 19.3%; (b) Closing pressure acts as a detrimental role impairing conductivity, the amplitude is able to reach 42.1% as for the mixture case with a relatively high proportion of mesh-20/40 particles; (c) Mixing proppants uniformly fails to enhance fracture conductivity effectively, and the forward segmentation is demonstrated as the suitable strategy and beneficial for fluid transport capacity. The contribution expects to advance current understanding regarding the impact of mixture proppants on long-term fracture conductivity.

Numerical Investigation on Proppant–Water Mixture Transport in Slot under High Reynolds Number Conditions

Water hydraulic fracturing involves pumping low viscosity fluid and proppant mixture into the artificial fracture under a high pumping rate. In that high Reynolds number conditions (HRNCs, Re > 2000), the turbulence effect is one of the key factors affecting proppant transportation and placement. In this paper, a Eulerian multiphase model was used to simulate the proppant particle transport in a parallel slot under HRNCs. Turbulence effects in high pumping rates and frictional stress among the proppant particles were taken into consideration, and the Johnson-Jackson wall boundary conditions were used to describe the particle-wall interaction. The numerical simulation result was validated with laboratory-scale slot experiment results. The simulation results demonstrate that the pattern of the proppant bank is significantly affected by the vortex near the wellbore, and the whole proppant transport process can be divided into four stages under HRNCs. Furthermore, the proppant placement structure and the equilibrium height of proppant dune under HRNCs are comprehensively discussed by a parametrical study, including injection position, velocity, proppant density, concentration, and diameter. As the injection position changes from the lower one to the top one, the unpropped area near the entrance decrease by 7.1 times, and the equilibrium height for the primary dune increase by 5.3%. As the velocity of the slurry jet increases from 2 m/s to 5 m/s (Re = 2000–5000), the vortex becomes stronger, so the non-propped area near the inlet increase by 5.3 times, and the equilibrium height decrease by 5.2%. The change of proppant properties does not significantly change the vortex; however, the equilibrium height is affected by the high-speed flush. Thus, the conventional equilibrium height prediction correlation is not suitable for the HRNCs. Therefore, a modified bi-power law prediction correlation was proposed based on the simulation data, which can be used to accurately predict the equilibrium height of the proppant bank under HRNCs (mean deviation = 3.8%).

Experimental and Numerical Investigations of the Role of Proppant Embedment on Fracture Conductivity in Narrow Fractures (includes associated Errata)

Summary With the advancement of drilling and completion technologies in unconventional reservoirs, more extended reach wells are developed, and narrow-fracture environments are created in these reservoirs. Proppant embedment in monolayer/thin-layer-propped fractures can be significantly different from multilayer-propped fractures. In this study, a comprehensive investigation combining laboratory experiments with numerical simulations was conducted to explore the factors affecting proppant embedment and induced fracture conductivity loss in narrow fractures. The fracture-conductivity experiments were performed using monolayers of sand and ceramic proppant particles sandwiched between Berea Sandstone and Eagle Ford Shale plates under different closure pressures. The experiment study demonstrated that the long-term rock/fluid interaction leads to significant proppant embedment, and the fracture having a rough rock surface has higher fracture conductivity in monolayer-propped fractures. To further quantify the influence of proppant layer number, size, distribution variations, and particle crushing on proppant embedment, a numerical modeling approach that coupled continuum mechanics, discrete element method (DEM), and the lattice Boltzmann (LB) method was developed. In the simulation, the fracture/proppant system was constructed by filling proppant, modeled by DEM, between two fracture surfaces that were modeled by FLAC3D (Itasca Consulting Group 2012); LB simulation was then performed on the changing proppant pack to compute its time-dependent permeability. The numerical model was validated by comparing numerical results with measured fracture conductivities in the laboratory experiment. The simulation results demonstrated a strong correlation between proppant embedment and rock mechanical properties. When the Young’s modulus of the rock plate is less than 5 GPa, large magnitudes of proppant embedment can be expected in fractures supported by monolayers of ceramic proppant particles. Moreover, large-size proppant particles are more sensitive to the variations of Young’s modulus of the rock plate. When the rock formation in a narrow fracture environment has a relatively high Young’s modulus, the proppant diameter distribution has a lesser effect on the fracture conductivity. The outcome of this study will provide insights into the role of reservoir rock characteristics, proppant properties, and closure pressure on proppant embedment in narrow fractures.

Surface Modification of Proppant Using Hydrophobic Coating To Enhance Long-Term Production

Summary Proppant bed can play a critical role in enhancing oil and gas production in stimulated wells. In the last 2 decades, there have been consistent efforts to improve shape characteristics and mechanical strength properties to guarantee high permeability in the resultant propped fracture. However, engineering the surface properties of proppants, such as tuning their wettability, has not received considerable attention. Considering that water-wet proppants can not only limit production because of reduced hydrocarbon relative permeability but also facilitate fines migration through the proppant bed, a methodology is presented here to alter the wettability of proppants using graphite nanoplatelets (GNPs). The idea benefits from the intrinsic hydrophobicity of graphitic surfaces, their relatively low cost, and their planar geometry for coating proppants. Conductivity tests are conducted according to ISO 13503-5:2006 (2006) and API RP 19D (2008) to examine how the coating process changes the relative permeability to water and oil. According to the simulation results, the newly developed graphite-coated proppants speed up the water cleanup and increase long-term oil production in an oil-wet reservoir.

Study of Degradable Fibers with and without Guar Gum as a Proppant Transport Agent Using Large-Scale Slot Equipment

Summary Hydraulic fracturing with slickwater is a common practice in developing unconventional resources in North America. The proppant placement in the fractures largely determines the productivity of the well because it affects the conductivity of fractures. Despite the wide use of slickwater fracturing and the importance of proppant placement, the proppant transport is still not fully understood, and the efficiency of the proppant placement is mostly bound to the changes to proppant properties, friction reducers, and guar technology. Although the degradable fiber is currently used in some cases, it has not been well investigated. In this experimental study, we conducted a proppant transport experiment using different fluid compositions of fiber and guar gum in three types of proppant transport slot equipment. After the experiments, simulation was conducted with the commercial fracture software StimPlan™ (NSI Technologies 2020) to simulate and compare the fracture fluid performance with and without the fibers. The results indicate that using degradable fibers with or without the guar gum as a viscosifier can produce a fracture slurry applicable in both conventional and unconventional fracturing operations, helping proppant placement in the reservoir.

Theoretical and Experimental Determination of Proppant Crushing Rate and Fracture Conductivity

Abstract Proppant is an important material for hydraulic fracturing that impacts the production and production cost of oil and gas wells. The key properties of proppant are crushing rate and fracture conductivity. The most common way to evaluate the key properties of proppant is physical testing, but this method is time-consuming and costly, and it may result in different results under the same experimental conditions. This paper presents a method for calculating proppant crushing rate and fracture conductivity, which are obtained by combining a series of simple and economical laboratory experiments with a significant amount of numerical calculations under various experimental conditions. First, the arrangement of proppant particles was simulated, and the location of particles was determined with the Monte Carlo method, the optimization model, and search algorithm in this process. Second, by mechanical analysis of proppant particles, a mathematical model of force was established, and the singular-value decomposition (SVD) method was used to calculate the force of each particle. Third, the crushing rate of proppant particles was calculated under irregular conditions using mathematical statistics. The Kozeny–Carman equation was improved on to establish a fracture conductivity model. Finally, the average fracture conductivity was calculated on the basis of the simulation results. The calculated fracture conductivity is consistent with the experimental results, which verifies the accuracy of the model.

Crushing and embedment of proppant packs under cyclic loading: An insight to enhanced unconventional oil/gas recovery

Crushing and embedment are two critical downhole proppant degradation mechanisms that lead to a significant drop in production outputs in unconventional oil/gas stimulation projects. These persistent production drops due to the non-linear responses of proppants under reservoir conditions put the future utilization of such advanced stimulation techniques in unconventional energy extraction in doubt. The aim of this study is to address these issues by conducting a comprehensive experimental approach. According to the results, whatever the type of proppant, all proppant packs tend to undergo significant plastic deformation under the first loading cycle. Moreover, the utilization of ceramic proppants (which retain proppant pack porosity up to 75%), larger proppant sizes (which retain proppant pack porosity up to 15.2%) and higher proppant concentrations (which retain proppant pack porosity up to 29.5%) in the fracturing stimulations with higher in-situ stresses are recommended to de-escalate the critical consequences of crushing associated issues. Similarly, the selection of resin-coated proppants over ceramic and sand proppants may benefit in terms of obtaining reduced proppant embedment. In addition, selection of smaller proppant sizes and higher proppant concentrations are suggested for stimulation projects at depth with sedimentary formations and lower in-situ stresses where proppant embedment predominates. Furthermore, correlation between proppant embedment with repetitive loading cycles was studied. Importantly, microstructural analysis of the proppant-embedded siltstone rock samples revealed that the initiation of secondary induced fractures. Finally, the findings of this study can greatly contribute to accurately select optimum proppant properties (proppant type, size and concentration) depending on the oil/gas reservoir characteristics to minimize proppant crushing and embedment effects.

Preparation and characterization of high silicon ceramic proppants using low grade bauxite and fly ash

For the sake of weakening the influence of crystal transformation of SiO2 in the cooling process on the properties of proppants, a new research method was explored by preparing the high silicon proppant from low grade bauxite and solid waste fly ash. The effects of chemical compositions, sintering temperature and holding time on the properties of proppants were studied in this paper. The results showed the bulk density of proppants was 1.352 g cm−3, the performances were 4.2% of acid solubility and 5.3% of breakage ratio under 35 MPa when the sintering temperature was 1240 °C for 20 min. And the breakage ratio satisfied the requirement of 5K grade in the standard of SY/T5108-2014 and ISO13503-2.

Simulation of proppant distribution in hydraulically fractured shale network during shut-in periods

Proppant distribution is an important topic, because it is closely related to the success or failure of hydraulic fracturing treatment. Although, many proppant transport models have been published, there is still relatively limited research on proppant distribution between the created fracture network in shale especially during the post-treatment shut-in periods.In this paper, based on the intercoupling of particle hydrodynamics, fluid hydrodynamics, and poro-elastic rock mechanics, a mathematical model regarding the transport of liquid-solid phases has been established to simulate the behavior of the proppant transport and the carrying fluid migration in the fractured shale network during the well shut-in. The coupled model takes main hydraulic fractures, secondary induced fractures and matrix into account, namely a three-dimensional triple-porosity medium. All the important processes in fractured shale network can be explained by the liquid-solid transport simulation with the coupled model, including (1) liquid transport driven by viscous and gravity forces, (2)proppant particle transport driven by the horizontal forces of drag, inertia and collision, and the vertical gravity and buoyancy, and (3) hydraulic-fracture closure, which is considered as a poro-elastic rock deformation during the shut-in periods. Based on the conservation of mass and momentum, the liquid-solid transport coupled with rock deformation, are described by a set of partial differential equations, which are solved by the semi-implicit finite-difference method.The evolution of the proppant concentration and fluid pressure profiles is calculated. The fluxes of the proppant and proppant-carrying fluids between the main fracture and secondary fracture during the post-stimulation well shut-in are also calculated. The influences of proppant properties (concentration, density and size) and proppant-carrying fluid properties (viscosity and density) on the proppant distribution are investigated.The results of this study are expected to provide a better understanding of the proppant and proppant-carrying fluid distribution for different physical properties of proppant and carrying fluids, and explain which is the predominant factor influencing the proppant distribution during the shut-in periods.

Development of a New Mathematical Model To Quantitatively Evaluate Equilibrium Height of Proppant Bed in Hydraulic Fractures for Slickwater Treatment

Summary The proppant bed develops and its height grows until it reaches the critical velocity and equilibrium height. This paper proposes a comprehensive mathematical model to evaluate the equilibrium height for slickwater treatment. We use well-accepted published experimental data and models from other groups to validate our model. After that, we investigate the effects of proppant properties and fluid properties on the equilibrium height. This work can provide critical insights to optimize the design of proppant parameters in a hydraulic fracture. Meanwhile, this model can be incorporated into fracture-propagation simulators for simulating proppant transport.