Proppant Distribution Research Articles

Simulation and analysis of proppant transportation and distribution rules under multi-cluster perforation in horizontal wellbore

Unconventional reservoirs require segmented multi-cluster fracturing technology for commercial development. Due to the settling and inertial effects of proppant particle flow, even if the fracturing fluid is evenly distributed among each perforation, the proppant may still be unevenly distributed. However, the uniform distribution of proppant in multi-fracture is a favorable condition for high-yield gas wells. Based on the proppant dynamics model in the wellbore, coupled with the non-uniform fracture propagation model, a mathematical model of proppant wellbore transportation flow under multi-fracture is established. Through numerical calculations, the proppant transport and distribution mechanism are studied. The study shows that due to gravity, distribution in the upstream is more uniform, and the proppant in the downstream gradually settles and most particles flow toward the bottom. Proppant distributed in each cluster is affected by the flow rate of slurry to a certain extent, and is also controlled by its own properties. The turning efficiency determines the inflow of proppant in perforations. Increasing the pump rate can alleviate gravity but reduce turning efficiency. The perforation azimuth primarily regulates the flow of proppant into downstream perforations. The research results can provide theoretical guidance for the design of proppant transport and cluster perforation in hydraulic fracturing.

The influence of fracturing fluid temperature and viscosity on the migration and distribution of proppants within a fracture

The influence of fracturing fluid temperature and viscosity on the migration and distribution of proppants within a fracture

Experimental and Simulation Investigations of Proppant Transport and Distribution Between Perforation Clusters in a Horizontal Well

Summary Multistage hydraulic fracturing is widely used to stimulate tight reservoirs by means of plug and perforation technology. The proppant distribution between perforation clusters significantly impacts fracture conductivity and well productivity. Uneven slurry distribution is often the norm rather than the exception. Proppant transport behaviors and distribution characteristics are still poorly understood in a horizontal wellbore with clusters, especially at field scales. The objective is to propose an innovative and feasible method to quantitatively evaluate the distribution uniformity of proppant between clusters. In this work, we systematically investigate proppant migration and placement by means of laboratory tests and numerical simulation. Computational fluid dynamics (CFD) and the discrete element method (DEM) are coupled to analyze proppant-fluid flow. The experimental observation and results validate the numerical model and calibrate critical parameters. The transport efficiency (E) and normalized standard deviation (NSD) are used to evaluate proppant distribution. The effects of nine parameters on the E and NSD are investigated at field ranges. The calibrated CFD-DEM model is accurate in studying proppant distribution between multiple clusters. The toe bias is the primary distribution between clusters because of the large inertia originating from high injection rates. Fluid distribution and perforation configuration are critical factors that significantly change the toe bias at the cluster level. Fluid redistribution changes proppant distribution toward the heel. The inline up pattern has the best uniformity, followed by the 180° up-down pattern. The secondary characteristic is bottom-biased within a cluster. Increasing fluid viscosity, using small and light proppants, and pumping high-concentration slurry can improve proppant distribution. The slurry diversion into perforations is hardly changed unless external conditions change. The combination of high-concentration slurry and a large bed quickly induces premature screenout at the toe-side cluster, especially when injecting large and high-density particles. Slurry redistributes toward the heel if the toe-side cluster is blocked. The investigation provides a rational and feasible method for operators to understand proppant transport between clusters and optimize pumping parameters under field situations.

Numerical investigation of proppant transportation characteristics in hydraulically fractured wedge fractures

Hydraulic fracturing creates multiple induced fractures and micro-fractures, forming a complex fracture network in the reservoir. The study of the transport and distribution of the proppant within the fracture network is critical to the design and evaluation. However, existing simulation studies of proppant transport tend to be overly idealized and neglect the inhomogeneity of fracture widths that occur after fracturing. To address these issues, this study employs computational fluid dynamics (CFD) to study the transportation of fracturing fluid and proppant within a fracture network. The flow dynamics of solid-liquid two-phase flow in fractures are simulated using the Euler-Euler multiphase flow model. Considering the actual variables in field construction and the inherent inhomogeneity in realistic fracture structures, a three-dimensional model was established to capture the gradual variation in fracture width. The accuracy of this model was verified through a comparative analysis with physical experiments. On this basis, an investigation was conducted to explore the impact of particle size, particle density, particle volume concentration, and injection velocity on proppant transportation. The results demonstrate that, in contrast to conventional rectangular fractures, sandbanks formed from wedge fractures exhibit a lower height, which facilitates improved transportation into deeper fractures. Furthermore, particle concentration primarily influences distal fractures, with proppant particle size being second. The injection velocity has a significant impact on the height of the sandbank located in proximity to the fracture inlet. The research findings provide a deeper understanding of the transport and distribution of proppants within wedge fractures, thereby establishing a theoretical basis for the analysis and engineering guidance in on-site hydraulic fracturing construction.

Propagation of interfered hydraulic fractures by alternated radial-circumferential extensions and its impact on proppant distribution

The fracture extension mechanisms and proppant transport characteristics play key roles for optimizing hydraulic fracturing in unconventional reservoirs. In this work, the visual physical simulation method was used to analyze the 3D dynamic extension processes of multi-stage hydraulic fractures and the subsequent impact on proppant distribution. The interfered fracture in multi-stage hydraulic fracturing exhibit alternated radial-circumferential extension behavior. More specifically, these behavior changes from unilaterally radial initiation, circumferential extension to radial extension. Unilaterally radial initiation results in the formation of both mirror and conchoidal features, while circumferential extension leads to stepped feature, and radial extension gives rise to feather feature. The four features of hydraulic fractures result in four types of non-uniform proppant distribution: uniform, scattered, cluster, and regional distribution. The proppant transport shifted from linear to radial mode, promoting further fracture extension. The effects of segment spacing and proppant injection sequence were studied. The results showed that the influence on the interfered fracture decreases as the segment spacing increases. In addition, the propped fracture area is larger when the small-size proppant is injected first, followed by large-size one. The research can improve understanding and optimization of multi-stage hydraulic fracturing in unconventional oil and gas reservoirs.

Permeability of large‐scale fractures with ununiform proppant distributions in coalbed methane development

AbstractThe coalbed methane (CBM) productivity is directly determined by the fracture permeability during hydraulic fracturing, which is regulated by the distribution of proppants. The proppant may be unevenly distributed in the fracture because of variables like the architecture of the fracture and the characteristics of the sand‐carrying fluid. This study used two types of random functions to produce different ununiform distributions of proppant clusters in large‐scale fractures, with the aim of investigating the effect of these distributions on the overall permeability of the fracture. A model of fluid‐structure coupling is proposed. The closure of large‐scale fractures under in‐situ stress is analyzed using solid mechanics and the penalty function; the CBM flowing in proppant clusters and the high‐speed channel between them is simulated using Darcy's law and the Navier–Stokes equation, respectively; and the overall permeability of fractures is computed using the fluid pressure drop throughout the fracture and the fluid flowing velocity in the fracture's outlet. Since most CBM flows along high‐speed channels between the proppant clusters, the simulated findings show that the overall permeability of fractures with an uneven distribution of proppant clusters is significantly higher than that of the proppant cluster itself. As CBM becomes more discretely distributed, the proportion of CBM flowing within the proppant cluster continuously drops. As the permeability of the proppant cluster increases, the volume ratio of proppant clusters decreases, and the distribution of proppant clusters becomes more discrete, the overall permeability of the fracture continuously increases.

Detailed effects of reservoir permeability distribution differences on enhanced geothermal systems performance

In enhanced geothermal systems, fractured reservoir permeability significantly affects geothermal exploitation efficiency. However, the detailed effects are not fully understood while most previous literature ignored the spatial differences of reservoir permeability because of the complexity and heterogeneity of fracture distribution. This study aims to reveal the quantitative relationship between the geothermal system’s heat extraction performance and the distributed permeability, through investigating heat extraction ratio and flow impedance by building a 3D thermal-hydraulic coupled model with discrete fracture network. The current study also compared the effects of twenty-nine kinds of fracture network distributions at various depths. It is found that higher fracture permeability around production well (800×10−12 m2) more significantly improves heat extraction rate by 30% rather than higher permeability in other areas in the first year. It is also found that fracture permeability changes on both sides of predominant flow regions cause a lower heat extraction rate. Lower fracture permeability at bottom and top layers (25×10−12 m2) increases the heat extraction rate by 1.17 MW in the 30th year. The proppant distribution affects the pressure distribution in fractured reservoirs. Permeability distribution variation has small effects on the heat extraction ratio. These results provided theoretical basis for fractured reservoir construction, optimal proppant pumping scheme and reservoir thermal output prediction.

Effect of proppant injection condition on fracture network structure and conductivity

AbstractThe hydraulic fracturing of shale reservoirs is an important topic, and adjusting the fracturing process can enhance fracturing efficiency. To analyze the effect of injection conditions on the fracture network structure and conductivity, numerical simulations and theoretical calculations are carried out based on the construction data, and the variation patterns of the fracture network parameters are determined. During the theory study, a fracture network conductivity model was obtained by combining the fracture network expansion model and the fracture diversion model. Then a numerical model was set up according to the analysis results of monitoring data. The numerical simulation results showed the fracture network structure and proppant distribution under different conditions. Throughout the simulation process, the structural parameters and conductivity of the fracture network can be determined by controlling the injection amount and adjusting the injection method, speed, and sand ratio. Results indicated that the proppant pulse frequency during the injection process was a major factor affecting the structure and conductivity of the fracture network. At the same time, a comparison of the distribution structure of the proppant revealed that although the intermittent injection of the proppant improved the flow channel, the efficiency of fracture utilization can still be improved.

Research on the transport behavior of microparticle proppants inside natural fractures

As a crucial exploration technique for unconventional reservoirs, hydraulic fracturing enables the formation of complex fracture networks, thereby facilitating the flow of oil and gas. The closure of natural fractures decreases stimulation performance. Microparticle proppants are used to fill natural fractures and effectively increase the stimulation area. The 100-mesh proppant conventionally used in field operations may be insufficiently small to effectively access natural fractures. In order to effectively overcome natural fractures closure, microparticle proppants (i.e., proppants with a diameter of 75 μm (200-mesh) or less) are required. The particle size threshold test of microparticle proppants placement is conducted to determine the size threshold of proppants flowing into natural fractures. The microparticle proppants placement experiment in multi-branch fractures is conducted to investigate the volume difference of proppants in different fractures. Numerical simulations are performed to model proppant transport within fractures of actual dimensions to facilitating the optimization of stimulation parameters. The main conclusions are as follows: (1) Effective inflow of microparticle proppants requires a size threshold of proppants. For the 200-mesh proppants, the size should be less than half of natural fractures width when microparticle proppants effectively flow into natural fractures. (2) Sand concentration affects the size threshold of microparticle proppants. The size threshold should appropriately increase to ensure the inflow of proppant. (3) Difference of multi-branch fracture width has a significant effect on volume of microparticle proppants inside fractures. When the width ratio of multi-branch fractures exceeds 2, this effect becomes obvious. (4) Particle size has an effect on proppant placement. 200-mesh proppants can obtain uniform distribution of proppants among natural fractures. 140-mesh proppants can obtain maximum proppant volume among natural fractures. Sand concentration significantly affects proppant placement performance. The optimal sand concentration is 60kg/m3. The pumping rate for a single cluster fracture should not be excessively low. The pumping rate should be larger than 0.5m3/min and the optimal pumping rate 2m3/min. In this paper, the particle size and concentration of particulate proppant are optimized and the geometric characteristics of fractures are considered. These conclusions provide important practical guidance and scientific basis for the optimization and application of hydraulic fracturing technology.

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%.

Proppant distribution characteristics based on the coring well analysis

It is significant to clarify the proppant distribution pattern under real fracturing conditions to optimize the sand addition process in hydraulic fracturing of the Mahu tight conglomerate reservoir. However, the laboratory experiment is far from the real fracturing condition due to the limitations of scale, pumping scale, and stress conditions. In this paper, the proppant in cuttings and mud was obtained by screening and cleaning samples from the high-deviated coring well of the Mahu conglomerate reservoir in Xinjiang. The sphericity of particles was observed by a continuous variable magnification microscope, and the transparency (TR) of particles and the red-blue difference (RBD) of reflected light were followed by transmitted light. Considering these three factors, the proppant identification method in cuttings was established to obtain the spatial location and distribution of proppant along the whole well section. The effect of proppant transport and placement was evaluated. The results show that: (1) Compared with the formation of mineral particles, the proppant has better sphericity, TR>20%, and RBD > 30. Combined with the surface roughness, luster, and associated minerals, the particle can be evaluated as a proppant. (2) The content of proppant with small particle size (40/70 mesh) is significantly higher than that with large particle size (20/40 mesh), which ranges from 10‰ to 450‰ and 5‰ to 280‰, respectively. (3) Horizontally, 20/40 mesh proppant migrates approximately 10m, and 40/70 mesh proppant migrates approximately 23 m in the hydraulic fracture. (4) In the longitudinal fracture, 20/40 mesh proppant was concentrated at a 12 m vertical distance from the adjacent well, while 40/70 mesh proppant was placed at a larger longitudinal range, approximately 10 m above and 10 m below the adjacent well. The research results have certain reference significance for the improvement measures of the sand-adding process in the Mahu tight conglomerate reservoir.

Simulation and solution of a proppant migration and sedimentation model for hydraulically fractured inhomogeneously wide fractures

The distribution of proppant during hydraulic fracturing may directly contribute to the flow conductivity of the proppant fracture, so research on the migration and sedimentation of proppant in the fracture and the final distribution pattern is of great relevance. The mass conservation equations of proppant solids and fracturing fluid were adopted to describe the distribution of proppant migration and sedimentation in the fracture, improving the additional gravity coefficient by utilizing the density difference between proppant and fracturing fluid and the concentration of proppant, together with the proppant sedimentation velocity at different Reynolds numbers in this study. The flow coefficients were obtained by discretizing the system of equations through the finite volume method combined with the harmonic mean method and the upstream weight method. The concentration additional pressure gradient term was computed by using the Superbee format innovatively to improve the solution convergence of the model. Numerical simulations with identical parameters were compared with indoor test results, which fully verified the correctness of the model and the accuracy of the discrete solution based on the finite volume method. The effects of flow rate of fracturing fluid, ratio of injected sand, viscosity of fracturing fluid, grain size of proppant and density of proppant on proppant migration and sedimentation based on three elliptical fracture morphologies: even-wide, top-wide and bottom-narrow as well as top-narrow and bottom-wide were investigated and analyzed through comparing the rate of proppant front movement, the level of sweeping range and the degree of inhomogeneity in the range under different conditions. Findings of this study suggest that: (1) top-wide and bottom-narrow fractures are more preferable for homogenous sanding in the early stage of proppant injection, and top-narrow and bottom-wide fractures are best for sanding in the later stage; (2) the viscosity of fracturing fluid is the most influential factor on proppant migration and sedimentation, which increases in the range of 100 mPa.s to enhance the sweeping range and homogeneity of proppant sanding and therefore achieve a better fracturing effect.

Numerical Simulation of integrated three-dimensional hydraulic fracture propagation and proppant transport in multi-well pad fracturing

Multi-well pad fracturing is an indispensable technology for the sustainable development of unconventional oil and gas reservoirs, but the integrated simulation of fracture propagation and proppant migration in massive fracturing treatments remains challenging, including complicated numerical implementations and computational bottlenecks due to its multi-physics, fracture front propagation, size differences between proppant particles and hydraulic fractures. In this work, an integrated model of fracture propagation and proppant migration in multi-well pad fracturing was established based on the three-dimensional discontinuous displacement method for fracturing deformation computations and the Eulerian-Eulerian framework for capturing proppant concentration. The proposed simulator not only accounts for key physical processes such as stress shadow, dynamic flow rate distribution in the wellbore, fluid leak-off, perforation erosion, fractures evolution, proppant bridging, and gravitational settling, but also couples the simulation of 3D planar propagating fractures and proppant transport at well-pad scale, and presents excellent computational efficiency and promising applications than conventional fracturing models. To explore the fracture geometries and proppant distribution in typically stacked layers, single-well, multi-lateral wells, and multi-well pad fracturing are simulated from simple to complex. The findings showed that fracture propagation is jointly affected by intra-stage, inter-stage, and inter-well stress interference mechanisms, and fracture geometries are characterized by unevenness, asymmetry, and heel bias. Proppant transport is controlled by the fracture width and geometries, and most of the proppant is concentrated near the wellbore area and bridging at the narrow fractures. Fracture geometries and proppant distribution are sensitive to the landing locations of horizontal wells because hydraulic fractures always grow in the path of least resistance. Although close lateral well-spacing is beneficial to improve the stimulation efficiency, there are some challenges such as overlapped SRV, enhanced inter-well interference, and severe fracturing hits. Compared with the layout of stacked wells, staggered wells are not only beneficial to reduce the vertical inter-well interference, but also improve reservoir stimulation efficiency. Overall, the stimulated area of the high in-situ stress layers is relatively low even with intentionally landed wells.

A new numerical model for simulation of flow on rough fracture

Hydraulic fracturing is an important means to develop unconventional oil and gas. The fractures produced by hydraulic fracturing have the characteristics of a rough surface, high tortuosity, and strong randomness. The fluid migration law in rough fractures is more complicated, which leads to the change of the law of conductivity in fractures becoming more complex. Meanwhile, it is difficult to get certain regularity for the fracture surface obtained by direct fracturing. As a result, it is an arduous task to explore the influence of fracture roughness on conductivity by experimental means. Therefore, it is a feasible idea to use simulation to study the flow conductivity in rough fractures, which can be calculated by Darcy's seepage equation. In previous studies, quantitative characterization of rough fractures was rarely studied, and the three-dimensional Darcy seepage model of rough fractures was lacking too. In this paper, the rough surface profile and waveform are analyzed by analogy, and the height of the rough fracture surface, as well as the phase and wavelength of the waveform, were taken as the control parameters to generate the rough fracture surface. Then, the fractal dimension was used to characterize the roughness of the fracture surface. Coupled with the rough fracture model and the Darcy flow model, a three-dimensional Darcy flow model of rough fracture was established. Next, a new parameter, equivalent permeability, was defined to quantify and characterize the fracture permeability affected by roughness. Subsequently, the simulation results were verified by the experimental data. Finally, the effects of fracture surface fractal dimension, fracture width, proppant distribution, shear slip, and tortuous angle on the flow field were studied. This study provides a new model for the simulation of a rough fracture flow field, which provides important insight for understanding the properties of rough fracture flow fields.

Prediction of proppant distribution as a function of perforation orientations

In treatments that involve multiple stages and clusters, one of the most important challenges is ensuring that the proppant is evenly distributed across all clusters. It is crucial to distribute the proppant equally to ensure that all perforation clusters are contributing to production. To forecast the proppant distribution between perforation clusters, an experimental correlation was established using data from the literature on horizontal wellbores. A dimensional analysis was performed using the Buckingham Pi-theorem to develop the correlation. Data from different independent variables, such as completion designs and orientations, were incorporated. In this study, an improved novel experimental correlation is proposed to accurately forecast the proppant distribution using various perforation configurations and orientations. The correlation can predict the proppant distribution with a low percentage difference of less than 20%. This correlation may be upscaled to predict the distribution of proppants across multiple clusters in a single-stage hydraulic fracturing stimulation. The developed correlation illustrates that injecting more proppant at a higher rate may help to allocate the proppant more evenly across perforation clusters. However, a nonuniform proppant distribution is obtained by increasing the proppant median diameter.

Effect of proppant distribution in hydraulic fractures on coalbed methane extraction

Fracturing with proppants is often used to improve the permeability of coalbed methane (CBM) reservoir. The fracture is easy to close under the closure stress and the proppant distribution in fractures greatly influences the extraction efficiency of CBM. The past research mainly considered the impact of fracturing damage on the coalbed methane extraction but rarely investigated the influence of the proppant distribution forms on CBM extraction. Therefore, based on the theory of dual-porous media, this paper establishes a theoretical model of CBM extraction with different proppant distribution forms, which considers the proppant compaction, embedment, and fracture aperture change. The model is implemented numerically and is validated against field results of CBM production. The research results show that the extraction efficiency of CBM from high to low is the pulse proppant injection, continuous proppant injection, no proppant injection, no fracturing. The continuous proppant injection should ensure that the proppant placement rate is more than 60 %. The CBM extraction efficiency is the highest when the proppant column length is 0.2 m–0.3 m and the void area length is 0.5 m. The research results provide a theoretical basis for improving the extraction efficiency of coalbed methane using fracturing with sand injection.

Effect of pulse injection on proppant distribution in fracture

The trend of changes in proppant concentration and fracture conductivity is essentially identical. When combined with an analysis of the average conductivity of effectively propped fractures at different locations, it becomes evident that the proppant distribution pattern becomes uneven after pulse injection. However, this pattern displays a discontinuous distribution law on the macro level. Influenced by the proppant distribution pattern, fracture conductivity exhibits significant variation at different locations. During the conventional injection process, the conductivity of fractures near the wellbore gradually decreases from proximity to distance. Conversely, the proppant phase distribution during pulse injection induces fluctuation in fracture conductivity, transitioning from proximity to distance.

Experimental Investigation of the Impact of Particle Size on Its Distribution within a Horizontal Wellbore.

Fracture conductivity is directly affected by an uneven proppant distribution, which affects the productivity of a well. The distributions of 40/70 mesh white sand compared to 100 mesh brown sand in a horizontal wellbore were investigated in this study. The apparatus used to conduct these tests was a 30 ft-long transparent horizontal wellbore with three perforation clusters. The proppant distribution was examined experimentally by injecting slurries at three different injection rates ranging from 20 to 75 gpm. The proppant concentration of both sands increased for each test from 0.5 to 2 ppg. The proppant concentrations and injection rates were used with multiple perforation configurations (orientations) including extreme limited entry perforations. The results confirmed that the injection rates significantly affected the proppant distributions across the different perforation clusters. Even distribution of the 40/70 mesh sand can be obtained using a 1 shot per foot (SPF) top perforation design. The 100 mesh sand was evenly distributed using a 4 SPF perforation configuration. The settling percentage was calculated for each experiment to determine the quantity of 40/70 mesh and 100 mesh sand settled at the bottom of the horizontal wellbore. A carrier fluid can suspend the sand more effectively with a higher injection rate, reducing the average sand settling to 2% in the case of the 100 mesh sand compared with approximately 8% for the 40/70 mesh sand at similar injection rates. This research confirms the need to use a 100 mesh at high injection rates to reduce sand settling during the hydraulic fracturing process.

Fracture propagation, proppant transport and parameter optimization of multi-well pad fracturing treatment

This paper establishes a 3D multi-well pad fracturing numerical model coupled with fracture propagation and proppant migration based on the displacement discontinuity method and Eulerian-Eulerian frameworks, and the fracture propagation and proppant distribution during multi-well fracturing are investigated by taking the actual multi-well pad parameters as an example. Fracture initiation and propagation during multi-well pad fracturing are jointly affected by a variety of stress interference mechanisms such as inter-cluster, inter-stage, and inter-well, and the fracture extension is unbalanced among clusters, asymmetric on both wings, and dipping at heels. Due to the significant influence of fracture morphology and width on the migration capacity of proppant in the fracture, proppant is mainly placed in the area near the wellbore with large fracture width, while a high-concentration sandwash may easily occur in the area with narrow fracture width as a result of quick bridging. On the whole, the proppant placement range is limited. Increasing the well-spacing can reduce the stress interference of adjacent wells and promote the uniform distribution of fractures and proppant on both wings. The maximum stimulated reservoir volume or multi-fracture uniform propagation can be achieved by optimizing the well spacing. Although reducing the perforation-cluster spacing also can improve the stimulated reservoir area, a too low cluster spacing is not conducive to effectively increasing the propped fracture area. Since increasing the stage time lag is beneficial to reduce inter-stage stress interference, zipper fracturing produces more uniform fracture propagation and proppant distribution.

Accurate Prediction of the Proppant Distribution in a Hydraulically Fractured Stage.

One of the greatest challenges in stimulating a single hydraulic fracturing stage with multiple clusters is ensuring that the proppant is equally distributed across all clusters. In this paper, the Buckingham pi theorem was applied to implement a dimensional analysis to establish an empirical correlation. The experimental correlation was developed by acquiring and integrating the data of various independent variables, such as different proppant characteristics (i.e., size, density, and concentration), using a wide range of internal diameters of the horizontal wellbore and multiple perforation configurations, and utilizing many carrier fluids with different viscosities. This work presents a newly enhanced experimental correlation for the distribution of proppants by incorporating the effect of gravity on proppant particles. The correlation proved its reliability in forecasting the proppant distribution with an average percentage error of less than 10%. The developed correlation has the potential to serve as a tool for forecasting proppant distributions among multiple clusters in multistage hydraulic fracturing treatments in the field.