Fluid Partition Research Articles

Competition among simultaneously stimulated multiple hydraulic fractures: Insights from DEM simulation with the consideration of fluid partitioning

AbstractStimulating long and persistent fractures from multiple perforations in horizontal wells plays a vital role in enhancing the recovery of hydrocarbons from unconventional reservoirs. However, interaction among fractures may lead to dramatic nonuniformity, but the mechanism that drives the competition still eludes explanation. We proposed an improved two‐dimensional discrete element model to simulate fluid competition and stress interaction among perforations in the same fracturing stage. The fluid partitioning is implemented by dynamically dividing the injected fluid into different perforations to maintain pressure consistency and fluid conservation. The model is validated by comparing the induced stress, fracture aperture, and the evolution of the fracture height and the injection pressure with theoretical models. The influences of the perforation friction, fluid viscosity and injection rate are examined systematically. Simulation results reveal that fluid competition tends to stimulate one dominant fracture with other perforations suppressed. The effect of increasing the perforation friction for promoting the fluid partitioning is not remarkable while using more viscous fracturing fluid helps to initiate more fractures at the perforations. With a higher injection rate all fractures can propagate to the borders but the asymmetrical fracture pattern cannot be avoided. Four typical fracture patterns are distinguished by changing operational parameters.

Numerical Simulation Study of the Operating Characteristics of Attached-Wall Bistable Jet Elements.

In this paper, first, the control principle of wall-mounted bistable jet components is analyzed, and the jet components and the main structures of the inner cavity are introduced. Then, the control equations, turbulence models, boundary conditions, and mesh partitioning of multiphase fluids are established sequentially, and the jet element mesh model was obtained. Finally, qualitative and quantitative analyses are conducted on the attachment process, switching process, and attachment point position. Results show that in the steady state of wall attachment, the fluid layer attached to the wall is the fluid flowing from the control channel on the wall side of the jet attachment, rather than the main jet. The geometric parameters of the jet assembly affect the stability of the jet assembly attachment to the wall and the location of the attachment point.

IMPACTS OF USING POROUS CORNER PARTITIONS AND BLADE SHAPED NANOPARTICLES IN BASE FLUID ON THE PERFORMANCE IMPROVEMENT OF THERMOELECTRIC GENERATOR MOUNTED VENTED CAVITIES AND INTERFACE TEMPERATURE ESTIMATION WITH PROPER ORTHOGONAL DECOMPOSITION

Numerous technical applications, such as solar power, refrigeration, waste heat recovery, thermal management, and many more, employ thermoelectric devices because of the numerous advantages they offer. Techniques are required to improve their effectiveness in usage. In this study, a unique technique for improving the performance of a thermoelectric generator (TEG) positioned between vented cavities is proposed. The method combines the effects of blade-shaped nanoparticles in the base fluid and corner porous partitions. A numerical study using the finite element method is conducted for different values of Darcy number of upper and lower cavity (10<sup>-6</sup> ≤ Da<sub>1</sub> ≤ 10<sup>-2</sup>, 10<sup>-6</sup> ≤ Da<sub>2</sub> ≤ 10<sup>-2</sup>), opening ratio (SR between 0.5 and 2.5), and nanoparticle loading amount (SVF between 0 and 0.03). By adjusting the permeability of the partitions and opening ratio of the cavities, significant changes in the flow field can be obtained. TEG power increases with greater opening ratios and lower partition permeabilities. By changing the permeability, the TEG power can increase by up to 27.5 percent, while increasing the opening ratio from SR = 0.5 to SR = 1 can increase the TEG power by up to 140 percent. Using blade-shaped nanoparticles results in additional improvements, with values of 32.7% at SR = 0.5 and 20.26% at SR = 2.5. Using 180 parametric computational fluid dynamics cases, a POD-based low-cost reconstruction model is created for the interface temperatures at the hot and cold sides using five-POD modes. The method may be used for other complicated geometries where 3-D computations are costly and allows for the rapid computation of coupled TEG-vented cavity systems with corner partitions.

Influence of the bedding plane on the propagation of multiple hydraulic fractures

The presence of bedding planes (BPs) in unconventional shale reservoirs is common and widespread. BPs always affect fracture propagation. The objective of this study was to investigate the impacts of BPs on multiple hydraulic fracturing. The BPs were assumed to be perpendicular to the direction of the fractures. Based on the block distinct element method, we established a numerical model to simulate multiple fracture propagation in reservoirs with BPs. The model considered the fluid partitioning of multiple fractures and the fracture interaction by stress shadow. The numerical simulations clearly showed that the BPs reduced the non-uniform growth of multiple fractures. The results indicated that when hydraulic fractures met BPs, the BPs likely prevented the hydraulic fractures from passing through the formation with a smaller stress contrast. When hydraulic fracturing in a formation containing BPs, the key problem is how to reduce the obstructive effects of the BPs to increase the length of the main fractures.

Fluid partitioning between veins/fractures and the host rocks in Carlin-type Au deposits: a significant control on fluid-rock interaction and Au endowment

Fluid partitioning between veins/fractures and the host rocks in Carlin-type Au deposits: a significant control on fluid-rock interaction and Au endowment

Contribution of deep-earth fluids to the geothermal system: A case study in the Arxan volcanic region, northeastern China

Investigations of the hot spring water and gas in the volcanic region are involved in assessing geothermal resources and understanding groundwater circulation, volcano, and earthquake activities. The origins of water and gas of the hot springs, lakes, rivers, and rain in the Arxan volcanic region (AVR), northeastern (NE) China, were investigated by conducting a field survey and geochemical analysis. The low electrical conductivity (40–835 μS/cm) and low total dissolved solids (TDS, 23.83–540.00 mg/L) of the water samples indicate that they are fresh water. δ18O and δD values of the water samples range from −4.1% to −16.0% and from −61.3% to −119.9%, respectively. Enrichment of heavy isotopes in the rainwater and the crater lake waters was caused by evaporation. The component H2O of the water samples predominantly originated from the meteoric water, with less than 1 vol% contributed by deep-earth fluids. Ions in the rain sample were predominantly derived from sea salt and continental aerosol. Ions in the surface water samples had multiple origins (mineral dissolution, atmospheric, and anthropogenic sources). While the ions in the hot spring water were predominantly derived from both the dissolution of rocks and deep-earth fluids, the latter contributed 73%–87% of Cl− and 86%–99% of Na+ to the hot spring waters. Gases from the hot springs were composed of more than 95% N2 and less than 5% O2 and Ar, with 3He/4He ratios of 0.14–1.17 RA (RA=1.4×10−6). Excess N2, Ar, He, and CO2 of the hot springs were mainly derived from both the crust and upper mantle. About 3%–23% of the total He in the bubbling gases from the crater lake waters and hot springs is derived from the mantle, implying a supplement of heat energy from the mantle to the geothermal systems. Significantly, about 12% of the He dissolved in the Budonghe water is derived from the mantle, indicating that plenty of mantle-derived heat transported by deep-earth fluids keeps the river water from freezing. Our results indicate that Cl and Na ions and 3He/4He ratio are the feasible geochemical indicators for source partitioning of geothermal fluids.

Assessment of Epithelial Lining Fluid Partitioning of Systemically Administered Monoclonal Antibodies in Rats

For systemically administered monoclonal antibodies (mAbs) with pharmacological targets in the epithelial lining fluid (ELF), information on the partitioning of mAb between plasma and ELF is instrumental for dose predictions. Bronchoalveolar lavage (BAL) combined with measurements of urea as indicator of sample dilution is often used to estimate ELF concentrations of a drug. However, unbalanced extraction of mAb and urea could potentially lead to a systematic bias in the back-calculated ELF concentration. In the present study 0.5, 1, or 4 mL phosphate-buffered saline was instilled to lungs of rats to obtain lavage samples after systemic dosing of mAb and tool small molecule (n≥4/group). Furthermore, extraction of urea, mAb and the small molecule was assessed by repeatedly lavaging the lung (n = 4). There was no statistically significant difference in the calculated partitioning into ELF between the evaluated instillation volumes. Repeated BAL demonstrated that urea and the small molecule were extracted from other sources than the ELF. In contrast, there was limited to none in-flow of mAb into the lavage fluid. The unbalanced extraction of urea and mAb could theoretically result in underestimated ELF concentrations and the calculated partitioning of 0.17±0.062 might therefore constitute a lower boundary for the true partitioning.

A three-dimensional Generalized Finite Element Method for simultaneous propagation of multiple hydraulic fractures from a wellbore

In this article, a 3-D methodology for the simulation of hydraulic fracture propagation using the Generalized Finite Element Method (GFEM) is extended for the simultaneous propagation and interaction of multiple hydraulic fractures. A 3-D isotropic elastic material for the rock and Reynolds lubrication theory for the fluid flow in the fractures are assumed. The elastic solid governing equation is discretized in space with a quadratic GFEM and the equation for the flow in the fractures is discretized in space with a quadratic FEM. With the GFEM, the solid mesh does not need to fit the fracture and accuracy is improved around the fracture front with the use of singular enrichment functions. Discretization error is further controlled by employing mesh adaptivity around the fracture front. The injected fluid partitioning among fractures is computed by modeling the wellbore, where the flow is assumed to be governed by the Hagen–Poiseuille relation. The pressure losses between wellbore and hydraulic fractures are modeled with the sharp-edged orifice equation and with the use of 1-D connecting elements. A linear FEM is adopted for the spatial discretization of the equation governing the flow in the wellbore and the connection between wellbore and hydraulic fracture. A propagation criterion based on a regularization of Irwin’s criterion is adopted and a methodology to automatically estimate the time step that leads to the propagation of fractures based on linear interpolation/extrapolation is presented. Three verification problems are solved and compared with results from the literature. A problem with initial fractures not aligned with the in situ stresses is analyzed. Complex final fracture geometries are observed due to this misalignment.

Finite discrete-element modeling of multifracture propagation in fractured reservoirs

Abstract The topology of induced fractures by hydraulic fracturing is important for well performance in unconventional low-permeability reservoirs. Natural fractures are a common feature in geological formations and are preferred failure paths during hydraulic fracturing. Therefore, the interaction of hydraulic fractures and natural fractures is fundamental to the fracture growth in fractured reservoirs. Field observations of induced fracture systems show modeling fracture complexity to be needed for improving completion design and interpreting stimulated reservoir volume. In this study, a finite discrete-element model is presented to investigate multifracture propagation in fractured reservoirs. The numerical model captures the fracture complexity including branched, stranded, and kinked fractures, as well as offset crossing of natural fractures. The results show biased fracture growth in the fractured reservoir, which demonstrates the impacts of rock heterogeneity on multifracture propagation. This work also emphasizes the control of fluid partition at the wellbore and among the intersecting fractures. Fluid partition at the wellbore is found to be a major challenge to the completion design of tight cluster spacing, which has been shown to improve production in recent years.

A Rapid Numerical Method to Constrain 2D Focused Fluid Flow Rates Along Convergent Margins Using Dense BSR‐Based Temperature Field Data

AbstractEstimates of the sub‐seabed fluid flow rates are important for understanding hydrological budgets, biogeochemical cycles, and physical properties of the sediments. Fluid flow rates and directions, however, are difficult to measure, particularly beneath the seafloor. We developed a rapid method to estimate regional fluid migration rates using an extensive database of seismic reflection profiles taken offshore SW Taiwan. We observe bottom‐simulating reflector (BSR) that deflects toward the seafloor near thrust faults that indicate localized heat flow variations. At these sites, advecting warm pore fluids transport heat to shallower depths and force the BSR shallower. Our 2D steady‐state numerical method quantifies the fluid flow rates required to cause such thermal anomalies. We found that fluid flow rates near the trench of the accretionary wedge range between 0.1 and 16 m3 yr−1 m−1, with slower and faster rates generally associated with slope basin discontinuities and faults, respectively. To evaluate the fluid pattern evolution from subduction to collision, we studied three transects: one along the Manila subduction zone in the south and two in Taiwan's initial collision zone in the north. We quantified the fluid budget and partitioning of fluid flow between focused discharge through faults and diffusive flow through the wedge. Faults in Taiwan's accretionary wedge capture on average 25% of the total dewatering flux in the younger subduction zone and 38.5% in the tectonically mature collision zone. Our method provides estimates of fluid migration rates along convergent plate boundaries, and contributes to our understanding of focused fluid flow processes in many other regions.

Numerical modeling of multiple fractures competition propagation in the heterogeneous layered formation

Separate-layer fracturing technology is one of the key stimulation technologies in the multi-layer reservoirs However, multiple fractures cannot evenly propagate due to the strong heterogeneity of the layers. In this paper, a three-dimensional model considering heterogeneity and fluid partitioning is developed to simulate the competitive propagation of multiple fractures in heterogeneous layered formation. The fracture pressure, fracture morphology, fluid volume and fracture length were systematically analyzed under different heterogeneous physical parameters. The following conclusions were obtained: (1) Formations with high rock strength, low permeability or high horizontal minimum principal stress will increase the fracture pressure and reduce the fluid volume within the fracture and fracture length. (2) Hydraulic fractures are easy to propagate into the interlayers if the pay zones have high rock strength and low permeability. (3) In heterogeneous layered formations, hydraulic fractures are more likely to gain competitive advantage in the high Young’s modulus and high permeability formations, while have the disadvantage in the high rock strength and high minimum principal stress formations. Poisson’s ratio has a little effect on the fracture propagation. This paper provides some helpful design guidance for the separate-layer fracturing in the heterogeneous layered formation.

Dynamic fluid states in organic-inorganic nanocomposite: Implications for shale gas recovery and CO2 sequestration

Despite wide research on organic-inorganic composites in various fields, the molecular-scale partitioning of fluids in nanoporous organic-inorganic composites remains poorly understood. The microscopic characteristics of fluid states in nanopores of shale composites during gas production are key to the enhancement of shale gas recovery, which remain unexplored. Here we conduct a microscopic modeling for shale nanocomposite, which realizes separate force field parameterization and controllable pore network optimization. A shale clay-kerogen nanocomposite with heterogeneous pore structure is thereafter built to investigate the dynamic characteristics of fluid states during pressure depletion and CO2 sequestration using molecular simulations for the first time. In this study, the different gas recovery mechanisms for pressure depletion and CO2 sequestration are revealed: pressure depletion mainly produces CH4 free state, while CO2 injection predominately extracts CH4 dissolved state. We propose CH4 adsorbed state as the potential target for enhanced shale gas recovery in the late production stage due to its minimal recovery. Three distribution forms of water molecules and two developing trends of water clusters are distinguished in the nanocomposite. Increasing water content can reduce the CH4 recovery during pressure depletion, but improve the CH4 recovery during CO2 injection. We suggest low water content may optimize the shale gas recovery efficiency. The deformation of the kerogen structure is observed to enhance the gas solubility in the kerogen matrix. In the CO2 injection stage, multi-components can promote the recovery of the CH4 adsorbed state. In a broader perspective, the microscopic modeling is widely applicable to other natural and synthetic organic-inorganic nanocomposites interacting with fluids.

A numerical method for simulating planar 3D multi-fracture propagation in multi-stage fracturing of horizontal wells

To resolve the issue of design for multi-stage and multi-cluster fracturing in multi-zone reservoirs, a new efficient algorithm for the planar 3D multi-fracture propagation model was proposed. The model considers fluid flow in the wellbore-perforation-fracture system and fluid leak-off into the rock matrix, and uses a 3D boundary integral equation to describe the solid deformation. The solid-fluid coupling equation is solved by an explicit integration algorithm, and the fracture front is determined by the uniform tip asymptotic solutions and shortest path algorithm. The accuracy of the algorithm is verified by the analytical solution of radial fracture, results of the implicit level set algorithm, and results of organic glass fracturing experiment. Compared with the implicit level set algorithm (ILSA), the new algorithm is much higher in computation speed. The numerical case study is conducted based on a horizontal well in shale gas formation of Zhejiang oilfield. The impact of stress heterogeneity among multiple clusters and perforation number distribution on multi-fracture growth and fluid distribution among multiple fractures are analyzed by numerical simulation. The results show that reducing perforation number in each cluster can counteract the effect of stress contrast among perforation clusters. Adjusting perforation number in each cluster can promote uniform flux among clusters, and the perforation number difference should better be 1-2 among clusters. Increasing perforation number in the cluster with high in situ stress is conducive to uniform fluid partitioning. However, uniform fluid partitioning is not equivalent to uniform fracture geometry. The fracture geometry is controlled by the stress interference and horizontal principal stress profile jointly.

Modeling of Simultaneous Propagation of Multiple Blade-Like Hydraulic Fractures from a Horizontal Well

We explore different aspects of the multi-stage fracturing process such as stress interaction between growing hydraulic fractures, perforation friction, as well as the wellbore flow dynamics using a specifically developed numerical solver. In particular, great care is taken to appropriately solve for the fluid partition between the different growing fractures at any given time. We restrict the hydraulic fractures to be fully contained in the reservoir (fractures of constant height) thus reducing the problem to two dimensions. After discussions of the numerical algorithm, a number of verification tests are presented. We then define via scaling arguments the key dimensionless parameters controlling the growth of multiple hydraulic fractures during a single pumping stage. We perform a series of numerical simulations spanning the practical range of parameters to quantify which conditions promote uniform versus non-uniform growth. Our results notably show that, although large perforations friction helps to equalize the fluid partitioning between fractures, the pressure drop in the well along the length of the stage has a pronounced adverse effect on fluid partitioning as a result on the uniformity of growth of the different hydraulic fractures.

Scale‐up of extraction processes: Dimensionless modeling and virtualization via lattice Boltzmann method

AbstractWhile modeling and virtualization pose challenges and opportunities to food engineering, lattice Boltzmann method (LBM) is a recent computational technique. By relying on existing dynamic one‐dimensional models, in‐house LBM simulators have been developed toward extraction processes in agitated‐batch or continuous‐flow equipment. In view of supporting process scale‐up, this work aimed at casting the aforesaid extraction models (and related LBM simulators) in dimensionless form. Together with available experimental data for validation, pectin extraction from fruit peels in agitated reactor and essential oil extraction from gorse in fixed bed were taken as case studies. Primitive influencing parameters (e.g., intraparticle diffusivity, solid–fluid partition coefficient, fluid‐phase diffusivity, bed length, and interstitial fluid velocity) were fruitfully lumped into fewer dimensionless parameters (e.g., mass‐transfer Biot, Péclet and Damköhler numbers). In‐house LBM simulators remained operational in their dimensionless versions, with a reduced amount of dimensionless numbers indeed grouping the influence of different process parameters, which may help future sensitivity analyses and scale‐up procedures.Practical ApplicationsInitially used for academic purposes, computational modeling has experienced notable evolution and has become strategic to research, development, and innovation (RD&I) in food processing. Computational modeling can support novel food processes as different parameters and scenarios can be quickly simulated toward scale‐up and cost‐effectiveness. Accordingly, computational modeling may save valuable material, energy, water, and human resources in RD&I activities at industrial scale. The present work casts in‐house computer codes to numerically simulate extraction processes in either agitated‐batch or continuous‐flow equipment into dimensionless form. Related process parameters in primitive form were fruitfully lumped into fewer dimensionless numbers, which may ease scale‐up as well as sensitivity analysis.

Competitive propagation of multi-fractures and their control on multi-clustered fracturing of horizontal wells

For the issue of multi-fracture growth from horizontal multi-fractured wells, a new model of multiple fracture growth model was established based on the approximate solutions of interaction stresses among multi-fractures. The computation amount of the model was reduced because of using an approximate method, and the accuracy of the model was validated by the Implicit Level Set Algorithm, which is a benchmark simulator of multi-fracture propagation simulation. Then simulations about fracture length, fracture width and influx rate under different parameters based on the model show that perforation loss and interaction stress are two dominate factors controlling fluid partitioning into each fracture. Influenced by the compression effect exerted by the exterior fractures, inflow rate, fracture length and fracture width of the middle fractures are less than the exterior fractures, and the effect can be weakened by increasing fracture spacing. Decreasing perforation numbers and diameters, or using non-uniform perforation method can promote homogeneous growth of multiple fractures. The research provides a theoretical basis and reference for optimization of multi-fracture propagation.

A comparison of clustering algorithms applied to fluid characterization using NMR T1-T2 maps of shale

Nuclear magnetic resonance T1-T2 maps are popular for characterizing fluids in shale. The characterization, however, is often done manually, which is difficult for shale due to its complicated nature. This work investigates the clustering approach for fluid characterization on T1-T2 maps by comparing 6 different algorithms: k-means, Gaussian mixture model, spectral clustering, and 3 hierarchical methods. T1-T2 maps are collected on shale samples at as-received and dried conditions. We propose two cluster validity indices to select the optimal cluster number and best algorithm. Our results validate the capability of the two indices. Gaussian mixture model is found to be the best algorithm in most of the cases, as its fluid partitioning shows the highest consistency with theoretical fluid boundaries. In addition, 5 fluid components are identified from Gaussian mixture model, and their values are qualitatively validated by comparing with those in literature. Results also indicate that clustering is sensitive to the fluid distribution. Drying the sample producing better clustering by revealing the footprint of organic matter. This work provides a practical guide for applying cluster analysis in fluid characterization in Nuclear magnetic resonance T1-T2 maps.

Characterization of hydraulic fracture geometry in shale rocks through physical modeling

In unconventional shale reservoirs, the presence of natural fractures is common and widespread. Multi-stage hydraulic fracture treatments are used to generate complex fracture geometry and stimulate reservoirs to unlock hydrocarbon in unconventional reservoirs. Natural fractures further complicate the complexity of the fracture geometry. In this paper, the objective is to investigate the impact of natural fractures on multiple hydraulic fracture propagation using an in-house fracture propagation model. We have developed a complex hydraulic fracture model to simulate multiple fracture propagation in naturally fractured reservoirs. The model can calculate partitioning of fluid between multiple fractures, fracture interaction within a stage and between stages, as well as the interaction between hydraulic and natural fractures. For simultaneous multiple fracture propagation, the exterior fractures generally take the majority of fluid and propagate at the expense of the interior fractures. Natural fractures can retard the growth of hydraulic fractures and change the fluid distribution between fractures and propagation trajectories of hydraulic fractures. In a reservoir with a heterogeneous natural fracture distribution, the interruption of natural fractures can complicate fracture geometry. The higher density or smaller spacing of natural fractures can mitigate stress shadow effects and favor more fluid flowing into the inner fractures. Due to the uncertainty of natural fracture distribution, the reliability of the complex fracture geometry provided by numerical models has been challenged. This paper demonstrates the potential of incorporating diagnostic results to constrain numerical results. Through combining diagnostic results with the fracture model, the accuracy of predicted fracture geometry can be improved.

Effect of carrier fluid rheology on shear-induced particle migration in asymmetric T-shaped bifurcation channel

Separation of particles from the carrier fluid of suspension is important in many engineering applications. In this work numerical simulations of particle migration during the flow of concentrated suspension through 3D asymmetric T-shaped bifurcating channels were carried out. The carrier fluids were considered to be non-Newtonian and inelastic. Diffusive flux model of shear-induced migration in conjugation with the power-law and Bird-Carreau constitutive models for the carrier fluid was used in the simulations. The velocity and particle concentration profiles in a non-Newtonian suspending fluid showed marked differences compared to that in the Newtonian carrier. Enhanced migration was observed in the case of shear thinning fluid while low for shear thickening. The symmetric velocity and concentration profiles in the inlet branch become asymmetric in the daughter branches and the degree of asymmetry strongly depends on the carrier fluid rheology. The results showed that the particle partitioning between daughter branches do not follow the fluid partitioning and the degree of separation depends on the relative volumetric flow rate of bulk suspension in the daughter branches. Higher separation efficiency was achieved for suspension in shear thinning fluid and relatively lower in Newtonian and shear thickening fluids.

A semi-analytical model for predicting fluid partitioning among multiple hydraulic fractures from a horizontal well

Multiple fracture growth during multi-cluster fracturing of a horizontal well is closely dependent on fluid partitioning. However, whether injected fluid can uniformly flux into multiple fractures during fracturing remains uncertain.In this study, a semi-analytical model was proposed to simulate fluid rate distribution in multiple fractures. Multi-fracture interaction stresses in the model are solved by a detailed approximation of the elastic solution for a pressurized fracture, which are integrated with rock deformation equations to calculate the multi-fracture width. The semi-analytical model was validated with a well-recognized fully coupled hydraulic fracture simulator. The semi-analytical model can efficiently optimize perforation parameters for multi-cluster fracturing of a horizontal well.Sensitivity analysis was conducted by using the model, and simulation results show that perforation friction and interaction stress are two key factors that determine fluid partitioning among multiple fractures. When interaction stress dominates the flow pressure drop in multiple fractures, fluid partitioning among multiple fractures is uneven due to heterogeneous interaction stresses among multiple fractures; otherwise, fluid partitioning is evenly distributed. Decreasing the total number or diameter of perforation holes can promote uniform multi-fracture growth and fluid partitioning. Homogenous fluid partitioning can be achieved by decreasing the perforation number of exterior fractures, whereas increasing the perforation number of interior fractures minimally affects uniform fluid partitioning among multiple fractures.