Proppant Transport Model Research Articles

Modeling proppant transport and settlement in 3D fracture networks in geothermal reservoirs

In this paper, we develop an efficient proppant transport model using the Eulerian-Eulerian approach for simulating proppant transport in fractures and 3D fracture networks in geothermal reservoirs. The proposed model accounts for proppant settling, pack/bed formation, bridging/screenout, proppant concentration effect, fracture wall effect, and the transition from Poiseuille flow (fracture channel) to Darcy flow (proppant pack). Notably, the heat transfer process and its impact on proppant transport are also considered—a facet often overlooked in previous proppant transport models. A three-dimensional displacement discontinuity method (3D DDM) that incorporates the stress shadow effect is employed to generate the fracture geometry. The governing equations for slurry flow, proppant transport, and heat transfer are discretized and solved using the finite volume method (FVM). The model is verified against analytical solutions and published experimental data, demonstrating good agreement with these references. To demonstrate the proposed model, we applied it to both low-temperature (depleted hydrocarbon wells) and high-temperature (dry hot rocks) enhanced geothermal systems (EGS). The simulation results highlight the significant influence of reservoir temperature on proppant transport and settlement in a reservoir environment. Heating of the slurry by higher temperature reservoir rocks reduces fluid viscosity and accelerates proppant settling, thereby shortening the transport distance and reducing the coverage area of the proppant. Both ultra-light and micro-proppant are effective in mitigating proppant settlement in enhanced geothermal systems. However, proppant is susceptible to bridging at fracture intersections, where the fracture widths are narrower due to more pronounced stress shadow effects in these areas. Consequently, the use of micro-proppant could offer substantial benefits over ultra-light proppant in enhancing proppant coverage area in enhanced geothermal systems.

Numerical simulation study on the ultimate injection concentration and injection strategy of a proppant in hydraulic fracturing

The injection volume and the distribution of a proppant inside a fracture have a direct impact on the stimulation effect of fracturing. In this study, a new proppant transport model was established based on the Euler method. In this model, the proppant plugging element allows fluid to pass through. Furthermore, the proppant plugging process was successfully simulated based on this model. The proppant transport and ultimate injection concentration under different injection modes were discussed. The numerical simulation results indicate that compared with the strategy of constant concentration, the strategy of a stepwise increasing concentration can make the proppant distribution in the fracture more uniform. The strategy of injection with a stepwise increasing concentration and a periodic injection with a stepwise increasing concentration can increase the injection volume of the proppant by 25%. In the fracture network, a 67% increase in the number of branch fractures resulted in a 17% increase in the maximum proppant injection volume. If the branch fracture width is reduced by 50%, the maximum proppant injection volume is reduced by 17%.

A resolved CFD-DEM coupling method to simulate proppant transport in narrow rough fractures

A proppant transport model was proposed to simulate the fluid-granular interactions in rough narrow fractures. The Computational Fluid Dynamic (CFD) was used to describe the fluid flow, while the Discrete Element Method (DEM) was adopted to describe the particle motion. Considering the roughness characteristics of narrow fractures, the resolved CFD-DEM coupling method was employed to simulate the fluid-granular interactions. Firstly, the resolved CFD-DEM coupling method was validated by previous simulation/experimental results. Then, simulations of proppant transport in synthetic rough fractures with different fractal dimensions and random number seeds were conducted. The results showed that roughness characteristics increased the possibility of proppant settling at a location with a large roughness height. A fracture with a higher fractal dimension had a higher proppant coverage ratio, leading to a better fracture propping effect. The proppant coverage ratio in rough fractures increased with increasing proppant size and decreasing injection rate.

Integrated simulation of three-dimensional hydraulic fracture propagation and Lagrangian proppant transport in multilayered reservoirs

The numerical simulation of hydraulic fractures is a critical yet challenging computational problem due to its multi-physics nature. This paper develops an integrated hydraulic fracturing simulator by coupling a planar three-dimensional (PL3D) fracture propagation model with an efficient Eulerian–Lagrangian (E–L) proppant transport model. The fracture propagation model uses the finite volume method (FVM) and displacement discontinuity method (DDM) to solve the fluid flow and rock deformation, respectively. For proppant transport, we develop a pseudo-3D multiphase particle-in-cell (P3D MP-PIC) model, in which the fluid flow is addressed by FVM as a continuum, but the particles are tracked in a Lagrangian fashion as discrete phases. In contrast to Eulerian–Eulerian (E–E) proppant transport models, the P3D MP-PIC can efficiently deal with multi-modal particle simulations (i.e., particles of different sizes or materials) and avoid the problem of numerical diffusion. The fracture propagation and proppant transport models are validated by analytical solutions and laboratory experiments. We adopt a one-way coupling strategy to consider the effect of complex fracture propagation and fluid leak-off on slurry transport, in which the dynamic fracture geometry and fluid leak-off is first computed via the fracture propagation model, followed by the fully coupled fluid–particle simulation using the P3D MP-PIC. The integrated model can simulate the fracturing treatments in multilayered reservoirs with varying confining stresses at an industrial field scale. The simulation results can improve the prediction of effective/propped fracture geometries and better the fracturing designs.

The influence of heterogeneous proppant pack on fracture closure and productivity

Even though hydraulic fracturing is a common and well adopted well stimulation method in petroleum industry, there are still open scientific questions in the area, mainly due to complexity of the phenomena involved in the process. In this paper, we particularly address the problem of fracture closure and productivity in situations, when proppant distribution inside the fracture is strongly heterogeneous. This can happen, for instance, during pulsed injection, in which a pulse of clean fluid is alternated with a pulse of slurry with proppant. Such a combination leads to Saffman–Taylor instability and, consequently, to spatially heterogeneous distribution of proppant. To address the problem, a coupled hydraulic fracturing and proppant transport model is utilized to simulate proppant placement in a fracture. After that, a three-dimensional finite element model is used to compute fracture closure and fluid inflow or productivity. Several numerical examples with various pumping schedules are presented to better understand the influence of proppant heterogeneity on fracture closure and the resulting production. In addition, to get insights about the observed behavior, an analytical model for fracture closure between two proppant pillars is presented. The model provides a single dimensionless parameter that quantifies the degree of fracture closure between the pillars of proppant. Numerical results are analyzed and discussed in relation to this dimensionless number.

Numerical Study on Proppant Transport in Hydraulic Fractures Using a Pseudo-3D Model for Multilayered Reservoirs

Summary In this paper, we incorporated a kinematic proppant transport model for spherical suspensions in hydraulic fractures developed by Dontsov and Peirce (2014) in a pseudo-3D hydraulic-fracture simulator for multilayered rocks to capture a different proppant transport speed than fluid flow and abridged fracture channel by highly concentrated suspensions. For pressure-driven proppant transport, the bridges made of compact proppant particles can lead to both proppant distribution discontinuity and increased fracture aperture and height because of the higher pressure. The model is applied to growth of a fracture from a vertical well, which can contain thin-bedded intervals and more than one opened hydraulic-fracture interval, because the fracture plane extends in height through layers with contrasts in stress and material properties. Three numerical examples demonstrate that a loss of vertical connectivity can occur among multiple fracture sections, and proppant particles are transported along the more compliant layers. The proppant migration within a narrow fracture in a thin soft rock layer can result in bridging and formation of a proppant plug that strongly limits fluid speed. This generates an increase of injection pressure associated with fracture screenout, and these screenout events can emerge at different places along the fracture. Next, because of the lack of pretreatment geomechanical data, the values of layer stress and leakoff coefficient are adjusted for a field case so that the varying bottomhole pressure and fracture length are in line with the field measurements. This paper provides a useful illustration for hydraulic-fracturing treatments with proppant transport affected by and interacting with reservoir lithological complexities.

Fracturing With Height Control Extends the Life of Mature Reservoirs in the Pannonian Basin

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 200588, “Fracturing With Height Control Extends the Life of Mature Reservoirs: Case Studies From the Pannonian Basin,” by Ruslan Malon, SPE, Independent, and Jonathan Abbott, SPE, and Ludmila Belyakova, SPE, Schlumberger, et al., prepared for the 2020 SPE Europec featured at the 82nd EAGE Conference and Exhibition, originally scheduled to be held in Amsterdam, 1-3 December. The paper has not been peer reviewed. Hydraulic proppant fracturing is an effective tool in mature, low-permeability reservoirs found in the Pannonian Basin. However, for wells already producing with high water cut, even a small fracture extension into a water-bearing zone offsets the gains in hydrocarbon production. Fracture-geometry-control (FGC) techniques limit increases in water cut. The complete paper describes the first implementation of a solution to control fracture height for conventional wells in the Pannonian Basin. An integrated engineering approach was applied, including a new proppant-transport model to predict fracture geometry improvement using the FGC solution. Decreased Recovery in A and B Fields Oilfield A began producing in 1984. In addition to an interruption by the war in Yugoslavia in the 1990s, production has been in decline, and most wells are at risk of being shut in because of low production rates. During the last 10 years, propped fracturing was integrated into the production strategy for this mature field. Field A comprises Lower Pontian (Miocene) sandstones. Another sandstone formation exists between 5 and 15 m below the production target reservoir, with high water saturation as confirmed by log analysis and well testing. The proximity of the oil target to the water-bearing interval still presents a risk to production considering that hydraulic fracturing is required to extend field life. An impermeable shale streak that may act as a geomechanical barrier exists below the target formation. With a lower risk of fracture propagation into the water zone, Field A was one of the first candidate fields for propped fracturing and was later considered for advanced fracture-height-control techniques to prevent the increase of water cut after stimulation. Hydraulic fracturing would not be trialed in Field B—the characteristics of which are provided in the complete paper—until the advanced height-control techniques had been proved on the basis of experience with Field A. Oilfield A: Early Fracturing Results Early campaigns proved the economic feasibility of propped fracturing, resulting in a 2.1-fold average increase in oil production during the first 6 months of production. Unfortunately, production after this early period declined rapidly. Increases in water cut, seen in several fracturing campaigns, clearly were related to hydraulic fracture growth. Although the resulting uplift in oil production warranted continued fracturing, avoiding water was a key issue to address before expansion of propped fracturing further in this field and to other fields with an even higher risk of water.

Numerical simulation of proppant transport in liquid nitrogen fracturing

Liquid nitrogen (LN) fracturing has the potential to reduce the breakdown pressure, avoid formation damage, and eliminate the water usage. However, the proppant-carrying capability of LN fracturing is still unknown since the properties of nitrogen vary significantly with the reservoir temperature and pressure. In this paper, we simulated the proppant transport during LN fracturing in a straight fracture. First, we built the proppant transport model based on a hybrid Eulerian Lagrangian Method. Then, we validated this model against published experimental data. Subsequently, we applied the model to elucidate the factors that affect the transport efficiency. Finally, suggestions for improving the proppant placement are given. The results show that the proppant-carrying capacity of nitrogen increases with the increasing migration distance during LN fracturing. Furthermore, the most effective way to improve the sand placement is reducing proppant density. The key findings can help to understand the proppant migration capacity during LN fracturing.

The coupling of an enhanced pseudo-3D model for hydraulic fracturing with a proppant transport model

This paper presents the coupled model of a hydraulic fracturing and proppant transport. The former is described in terms of enhanced pseudo-3D model that considers height growth across two symmetric stress barriers, while the latter is given by two-dimensional transport model, stemming from the solution of an elliptical equation for fluid pressure and advection equation for the proppant transport. These two sub-modules are solved numerically using implicit time integration in the hydraulic part and explicit time stepping in the transport part. In addition, interpolation is used to couple the two models with different grids. Results of several numerical simulations are presented for different configurations to demonstrate the interplay between these two modules. In particular, the developed coupled scheme allows us to study phenomena associated with complex fluid flow within the fracture, such as for the case of Saffman-Taylor instability.

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.

A Novel Hydraulic Fracturing Method Based on the Coupled CFD-DEM Numerical Simulation Study

For the development of tight oil reservoirs, hydraulic fracturing employing variable fluid viscosity and proppant density is essential for addressing the problems of uneven placement of proppants in fractures and low propping efficiency. However, the influence mechanisms of fracturing fluid viscosity and proppant density on proppant transport in fractures remain unclear. Based on computational fluid dynamics (CFD) and the discrete element method (DEM), a proppant transport model with fluid–particle two-phase coupling is established in this study. In addition, a novel large-scale visual fracture simulation device was developed to realize the online visual monitoring of proppant transport, and a proppant transport experiment under the condition of variable viscosity fracturing fluid and proppant density was conducted. By comparing the experimental results and the numerical simulation results, the accuracy of the proppant transport numerical model was verified. Subsequently, through a proppant transport numerical simulation, the effects of fracturing fluid viscosity and proppant density on proppant transport were analyzed. The results show that as the viscosity of the fracturing fluid increases, the length of the “no proppant zone” at the front end of the fracture increases, and proppant particles can be transported further. When alternately injecting fracturing fluids of different viscosities, the viscosity ratio of the fracturing fluids should be adjusted between 2 and 5 to form optimal proppant placement. During the process of variable proppant density fracturing, when high-density proppant was pumped after low-density proppant, proppants of different densities laid fractures evenly and vertically. Conversely, when low-density proppant was pumped after high-density proppant, the low-density proppant could be transported farther into the fracture to form a longer sandbank. Based on the abovementioned observations, a novel hydraulic fracturing method is proposed to optimize the placement of proppants in fractures by adjusting the fracturing fluid viscosity and proppant density. This method has been successfully applied to more than 10 oil wells of the Bohai Bay Basin in Eastern China, and the average daily oil production per well increased by 7.4 t, significantly improving the functioning of fracturing. The proppant settlement and transport laws of proppant in fractures during variable viscosity and density fracturing can be efficiently revealed through a visualized proppant transport experiment and numerical simulation study. The novel fracturing method proposed in this study can significantly improve the hydraulic fracturing effect in tight oil reservoirs.

Rigorous Estimation of the Initial Conditions of Flowback Using a Coupled Hydraulic-Fracture/Dynamic-Drainage-Area Leakoff Model Constrained by Laboratory Geomechanical Data

Summary The application of rate-transient-analysis (RTA) concepts to flowback data gathered from multifractured horizontal wells (MFHWs) completed in tight/shale reservoirs has recently been proposed as an independent method for quantitatively evaluating hydraulic-fracture volume/conductivity. However, the initial fluid pressures and saturation in the fracture network and adjacent reservoir matrix are generally unknown at the start of flowback, creating significant uncertainty in the quantitative analysis of flowback data. In this study, we present a semianalytical flow model, coupled with a hydraulic-fracture (fracture) model and constrained with laboratory-based geomechanical data, for evaluating the initial conditions of flowback. In previous work, a semianalytical model based on the dynamic-drainage-area (DDA) concept was used to simulate water-based fluid leakoff from an MFHW into a tight oil reservoir (Montney Formation, western Canada), with minimal mobile water, during and after fracturing operations. The model assumed that each fracturing stage can be represented by a primary hydraulic fracture (PHF) containing the majority of the proppant, and an adjacent nonstimulated reservoir (NSR) or enhanced fracture region (EFR), which is an area of elevated permeability in the reservoir caused by the stimulation treatment. Each region was represented by a single-porosity system. The DDA propagation speed within the PHF during the stimulation treatment was constrained through using a simple analytical fracture model. Although this approach was considered novel, several improvements and additional laboratory constraints were considered necessary to yield more accurate predictions of initial flowback conditions. In the current work, the modeling approach described previously was improved by representing the EFR with a dual-porosity system; fully coupling the fracture model (used for PHF creation and propagation) with the DDA model for fluid-leakoff simulation into the EFR and adding a proppant-transport model; and modeling the shut-in period. Finally, to ensure that model geomechanics were properly constrained, a comprehensive suite of previously gathered laboratory data was used. Laboratory-derived propped (PHF) and unpropped (EFR) fracture-permeability/conductivity data as a function of pore pressure, as well as fracture-compressibility data, were used as constraints for the model. It should be noted that our model assumes that fracture closure has no effect on the pressure/saturation of the PHF/EFR/matrix. The improved model was reapplied to the tight oil field case and yielded more realistic estimates of initial flowback conditions, enabling more confident history matching of flowback data. The results of this study will be important to those petroleum engineers interested in quantitative analysis of flowback data to accurately obtain fracture properties by ensuring proper model creation.

Optimization of Plug-and-Perforate Completions for Balanced Treatment Distribution and Improved Reservoir Contact

Summary Heel-dominated treatment distribution among multiple perforation clusters is frequently observed in plug-and-perforate (plug-and-perf) stages, causing small propped surface areas, suboptimal production, and unexpected fracture hits. A multifracture simulator with a novel wellbore-fluid and proppant-transport model is applied to quantify treatment distribution among multiple perforation clusters in a plug-and-perf operation. A simulation base case is set up on the basis of a field treatment design with four clusters. Simulation results show that the two toe-side clusters screened out early in the treatment and the two heel-side clusters were dominant. The simulated proppant placement is consistent with distributed-acoustic-sensing observations. The impact of different perforating strategies and pumping schedules on final treatment distribution is investigated. Two criteria are defined that quantify the proppant distribution and fracture area: the weighted average (WA) and standard deviation (SD) of the final fluid and proppant distribution, as well as the hydraulic surface area (HSA) and propped surface area (PSA) of the created fractures. An optimal plug-and-perf design is defined as one that minimizes the SD of the treatment distribution among perforation clusters, and maximizes the PSA. Both perforating strategy and pumping schedule are found to affect the final treatment distribution significantly, and uniform treatment distribution is shown to create more PSA. Having fewer perforations per cluster was found to promote uniform fluid and proppant placement. Other helpful strategies include reducing the number of perforations near the heel and using small, lightweight proppant. The stress shadow effect is accounted for using the displacement discontinuity method (DDM) and was found to play a smaller role than perforation friction and proppant inertia in most cases. An automated process is developed to optimize plug-and-perf completion design with multiple decision variables using a genetic algorithm (GA). Thirteen parameters are optimized simultaneously. The optimal design solution creates an almost even treatment distribution and more than doubles the PSA compared with the base case. The multifracture model presented in this paper provides a way to quantify fluid and proppant distribution for any perforating strategy and pumping schedule, and provides more insight into the physics relevant to plug-and-perf treatment distribution. The perforation and pumping schedule recommendations presented in this paper provide directional guidance for the design of fracturing jobs with balanced treatment distribution and large PSA.

A new CFD approach for proppant transport in unconventional hydraulic fractures

For hydraulic fracturing design in unconventional reservoirs, the existing proppant transport models ignore the fluid leak-off effect from the fracture side wall and the effect of fracture roughness. In this paper, a model is proposed using three-dimensional computational fluid dynamics approach with fluid leak-off rate defined along the fracture length and considering the effect of fracture roughness on proppant distribution. Based on the simulation results, it is recommended that neglecting the fracture roughness in the proppant transport model can result in over predicting the proppant bed length and underpredicting the proppant suspension layer by 10–15%. Furthermore, neglecting the fluid leak-off effect can result in under predicting the proppant bed height by 10–50% and over predicting the proppant suspension layer by 10–50%. This study has enhanced the understanding of the proppant-fracturing fluid interaction phenomenon by accounting detailed physics to optimise the hydraulic fracturing design.

A Study of Proppant Transport With Fluid Flow in a Hydraulic Fracture

SummaryThe effective placement of proppant in a fracture has a dominant effect on well productivity. Existing hydraulic-fracture models simplify proppant-transport calculations to varying degrees. A common assumption applied is that the average proppant velocity caused by flow is equal to the average carrier-fluid velocity, while the settling-velocity calculation uses Stokes’ law. To more accurately determine the placement of proppant in a fracture, it is necessary to account for many effects not included in previous assumptions.In this study, the motion of particles flowing with a fluid between fracture walls is simulated with a coupled computational-fluid-dynamics/discrete-element method (CFD/DEM) code that uses both particle dynamics and CFD calculations to account for both particles and fluid. These simulations (presented in metric units) determine individual particle trajectories as particle-to-particle and particle-to-wall collisions occur, and include the effect of fluid flow. The results show that the ratio of proppant diameter to fracture width governs the relative average velocity of proppant and fluid.A proppant-transport model developed from the results of the direct numerical simulations and existing correlations for particle-settling velocity has been incorporated into a fully 3D hydraulic-fracturing simulator. This simulator couples fracture geomechanics with fluid-flow and proppant-transport considerations to enable the fracture geometry and proppant distribution in the main hydraulic fracture to be determined. For two typical shale-reservoir cases, the proppant placement and width distribution have been determined, allowing comparison at the hydraulic-fracture scale, including effects observed at the particle scale. This allows for optimization of the treatment to a specific application, and the results are presented in oilfield units, considered more familiar to our readers.

A new model for simulating particle transport in a low‐viscosity fluid for fluid‐driven fracturing

Fluid‐driven fracture (i.e., Hydraulic fracturing) is an important way to stimulate the well productivity in the development of unconventional reservoirs. A low‐viscosity fluid called slickwater is widely used in the unconventional fracturing. It is a big challenge to simulate the particle (or proppant) transport in the low‐viscosity fluid in a field‐scale fracture. A new model to simulate particle transport in the low‐viscosity fluid in a field‐scale fracture is developed. First, a new parameter is defined, called the rate of proppant bed wash‐out, by which we incorporated the mechanism of proppant bed wash‐out into Eulerian‐Eulerian proppant transport model. Second, we proposed a novel way to consider the effect of proppant settling on the proppant concentration in the upper layer (or suspending layer) to accurately simulate the proppant transport. Additionally, a dimension reduction strategy was used to make the model quickly solved. Our simulation results were compared with published experimental data and they were consistent. After validation, the effect of fluid viscosity, injection rate, fracture height, and proppant concentration on the proppant distribution in a fracture is investigated. This study provides a new model to simulate particle transport. Meanwhile, it gives critical insights into understanding particle transport in the field‐scale fracture. © 2018 American Institute of Chemical EngineersAIChE J, 64: 3542–3552, 2018

Numerical simulation of proppant transport in hydraulic fractures

A central issue in hydraulic fracturing treatment in petroleum wells is the transport of proppant particles by the injection fluid. In this paper, we present an innovative proppant transport model in a fixed rectangular- and elliptic-shaped slots. The proposed model is an improvement to the current modeling of proppant transport by applying a non-oscillatory numerical scheme which has high accuracy everywhere in solution domain, even close to the steep gradients. In addition, inertia, fracture wall, and concentration effects on proppant settling along with slurry evolution as a function of proppant concentration has been considered.This paper introduces the mathematical equations that govern the proppant transport phenomenon and discusses special front capturing numerical techniques, boundary conditions, coupling between proppant and slurry mass conservation equations and time stepping restrictions required for the solution stability. We incorporated published correlations obtained from proppant transport laboratory experiments in our numerical model to better capture the physics of the problem. 5th- order WENO scheme was used to avoid oscillation and diffusion at the proppant front since traditional finite difference discretization was found to be insufficient in solving the hyperbolic transport partial differential equations. Results show that the technique used in this study can capture the proppant distribution with minimum oscillation and diffusion.A series of sensitivity analysis was conducted to explore the legitimacy of these assumptions and to provide guidelines that allow more accurate predictions of the proppant and fluid transfer. Numerical results are presented to show how proppant distribution is impacted by the injection fluid viscosity, density difference between proppant particles and injection fluid, proppant size, and fluid flow injection rate. Results of the sensitivity analysis illustrate the significance of choosing appropriate viscosity of the injection fluid as small changes in the viscosity may cause noticeable effects on the concentration distribution. In addition, we found that variation of proppant size and density within a reasonable range have a modest effect on proppant concentration distribution.Furthermore, we also investigated the amount of gravity driven vertical motion of proppant which is driven by density differences (convection) and compare it to a second gravity driven motion which is proppant settlement. Both of these two well recognized mechanisms can occur inside a fracture during proppant placement, however, the importance of each mechanism as a function of proppant injection design parameters is not fully understood.

Model development of proppant transport through hydraulic fracture network and parametric study

A model capable of simulating proppant transport through hydraulic fracture network is developed and summarized in this paper. The proppant transport model (PTM) is able to capture multiple proppant transport patterns, including suspension, saltation and creeping. These patterns are first identified, and then quantified to establish proppant transport equations. The governing equations are programed into a three-dimensional, finite-difference model to simulate the proppant transport process. The PTM is coupled to a previously developed hydraulic fracture network propagation model, which updates essential input parameters such as fracture geometry, velocity distribution and pressure profile for each step. In every step, the proppant transport model extracts values for these parameters and solves the mass transport equations for all three patterns. Finally, the PTM generates proppant concentration, fracture conductivity and distribution throughout the created fracture network and predicts, at the end of the designed treatment the propped stimulated reservoir volume (PSRV) – a critical indicator of long-term stimulation effectiveness for hydraulically fractured oil/gas reservoirs. Parametric Studies of several important treatment, operational, reservoir, and geomechanical parameters are done in this paper to illustrate the impact of each factor on the PSRV.

A Lagrangian Approach to Modelling Proppant Transport with Tip Screen-Out in KGD Hydraulic Fractures

This study introduces a continuum approach to model proppant transport in hydraulic fractures in a Lagrangian frame of reference. The model for the proppant transport is based on the recently obtained slurry flow solution inside a channel, where the latter utilizes a phenomenological constitutive relationship for a slurry. This approach allows us to describe the transition from Poiseuille flow with an effective viscosity to Darcy flow as the particle concentration increases towards the maximum value. The algorithm is presented for the one-dimensional case, for which propagation of a symmetric Kristinovich–Zheltov–Geertsma–De Klerk fracture is considered. To examine the effectiveness of the Lagrangian approach for proppant transport modelling, a set of parameters, for which proppant particles reach the fracture tip and cause the development of a proppant plug is selected. In this situation, the coupling between the hydraulic fracture propagation and proppant transport is the most significant. To estimate the accuracy of the Lagrangian proppant transport model, the results are compared to the predictions of an Eulerian proppant transport model, which utilizes the same algorithm for hydraulic fracture propagation. It is shown that, although both approaches have the same convergence rate, the error of the Lagrangian approach is three to five times smaller, which depends on the number of proppant elements used in the Lagrangian approach. This permits us to use a coarser mesh for hydraulic fracture propagation, and to obtain results with similar accuracy up to a hundred times faster.