Growth Of Multiple Fractures Research Articles

Thermo-mechanical modelling of spalling around the deposition boreholes in an underground nuclear waste repository during its thermal phase

This paper presents a three-dimensional numerical analysis of multiple fracture growth leading to the development of excavation disturbed zones and spalling around deposition boreholes in a geological disposal facility. The development of fracture patterns is simulated with the Imperial College Geomechanics Toolkit, a finite-element based simulator that can model the simultaneous nucleation, growth, and coalescence of multiple fractures in quasi-brittle rock. In these simulations, fractures develop due to the stress concentrations around the borehole wall, caused by the local in situ stresses, and due to the thermal stresses caused by the radioactive decay of the waste. Fracture patterns, and the extent of the spalled zone, are computed after the borehole drilling, heating, and cooling stages, at the Forsmark repository site in Sweden. The effect of temperature on the nucleation and growth of spalling fractures, as well as on the reactivation of pre-existing fractures, is assessed qualitatively, by comparing fracture patterns, and quantitatively, in terms of the maximum spalling depth, width, and increase in the total fractured surface area. Overall, the simulations presented herein indicate that thermal spalling will increase the depths (away from the borehole) and angular widths of the spalled zone, but is not likely to lead to major increases in fracture aperture, and concomitant increases in hydraulic transmissivity and permeability of the spalled zone, above that which has already been caused by mechanical spalling.

Numerical Modelling of the Influence of Tidal Stresses on Fracture Patterns on the Surface of Europa

AbstractJupiter’s satellite Europa is covered by an ice shell exhibiting many surface features, including linear structures called lineae, which in this work are treated as fractures. A three-dimensional finite-element simulator is used to numerically model fracture nucleation, growth, and interaction, assuming the ice is an isotropic, linear elastic medium. Tidal stresses are exerted upon the ice through the Jovian orbital relationship. These stresses are calculated using a closed-form model derived from first principles. The fractures grow in response to stress concentration around their tips, and a damage criterion models the weakening of the ice matrix. Three-dimensional non-planar multiple fracture growth is modelled as a function of geometric multi-modal stress intensity factors computed at the fracture tips. Fracturing is evaluated over multi-scale periods, from days to millions of years, thus capturing multiple tidal effects. Fracture behaviour is modelled across the Europan surface in one domain. The patterns are dense clusters of lineae about the stress maxima with diffuse fracturing in outlying regions. Fractures are also modelled in the vicinity of subsurface meltwater lenses, where fractures form parallel to the surface in contrast to the usual perpendicular orientation. The resultant fracture patterns are qualitatively compared against images from NASA’s Galileo mission. This work contributes to the understanding of Europan lineae by illustrating how they behave in a fracture mechanics framework, and suggests interesting results regarding lineae interaction with meltwater lenses. This work is also a proof of concept for this modelling approach, and will serve as the framework for future work.

Surrogate modeling and global sensitivity analysis for the simultaneous growth of multiple hydraulic fractures

Hydraulic fracturing has been widely used in enhancing the conductivity of the rock formations and increasing the rate of extraction of unconventional resources. During hydraulic fracturing treatments, there are considerable uncertainties in the completion operations and measurement of the geomechanical parameters such as the perforation geometry and elastic modulus of the rock matrix, which may result in a large error in fracture pattern prediction and parameter optimization when deterministic models are implemented. Therefore, a good understanding of the impact of the input uncertainties on the output predictions, also referred to as uncertainty quantification, has become a major issue. In this paper, a non-intrusive stochastic model is developed by combining a fully coupled hydraulic fracturing model based on the dual boundary element method with a surrogate model using polynomial chaos expansion. The perforation geometry, mechanical parameters of the rock formation, orientation and magnitude of the in-situ stress are treated as random variables. The surrogate model is constructed using data from the hydraulic fracturing model and is capable of providing fast approximations of the objectives, thereby making Monte Carlo simulations and sensitivity studies feasible. The stochastic model is validated against the random responses predicted by semi-analytical solutions for the single fracture case and shows excellent agreements with a relative error less than 0.1% for the injection pressure and 1% for the maximum aperture. The impact of the geomechanical and geometric parameter randomness on the growth of multiple fractures is investigated. The results show that the randomness in the fracture toughness and Young’s modulus plays an important role in fracture growth among geomechanical parameters, and the uncertainty of the fracture pattern is mostly attributed to the randomness in the initial length and aperture of the inner fracture among geometric uncertainties.

Multicluster Fractures Propagation during Temporary Plugging Fracturing in Naturally Fractured Reservoirs Integrated with Dynamic Perforation Erosion

Summary Temporary plugging technology has been widely applied in multicluster fracturing for the uniform growth of multiple fractures. To investigate the propagation behavior of multiple fractures and explore a better fracturing scheme during temporary plugging fracturing, a 2D finite element method (FEM)-discrete fracture network (DFN) model is established. An improved traction-separation law is used to describe the constitutive behavior of fractures under different types of stress. The model is further integrated with the perforation pressure drop model, considering the dynamic perforation erosion effect to simulate the fracture geometry more accurately. Based on the model, the impact of the perforation erosion effect on the propagation of multicluster fractures in the naturally fractured reservoir is quantitatively evaluated first. The result showed that the effect can intensify the nonuniformity among multicluster fractures, especially under the condition of small cluster spacing. Then, the simulation for temporary plugging fracturing is carried out under different cluster spacings. Finally, the plugging time optimization in temporary plugging fracturing is explored. The model and results presented in this paper can provide new insight into the impact of the perforation erosion effect and exploration for plugging time optimization in temporary plugging fracturing.

Phase Field Modeling of Multiple Fracture Growth in Natural Fractured Reservoirs

In recent years, hydraulic fracturing techniques have been widely used in extracting unconventional reservoir resources. During multicluster fracturing process, the stress shadowing effect can lead to a nonuniform distribution of fracturing fluid. In this paper, a two-dimensional multiple fracture propagation model is developed based on phase field method considering the distribution of fracturing fluid within each fracture during fracturing process. The distribution of fracturing fluid injected into each fracture is calculated through solving governing equations of perforation friction as well as wellbore friction. Numerical results demonstrate that the natural fractures in the reservoir have a significant influence on the distribution of injected fluid and the morphology of fracture network. In addition, higher injection rates and higher fluid viscosity stimulations are in favor of inducing uniform distribution of injected fluid into each cluster. The presented numerical model provides an effective tool to extend our understandings in generating fracture networks.

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.

Parametric effects on fracture geometries from multi-fracture propagation emanating from neighbouring wellbores in quasi-brittle rocks

An integrated approach is presented using field data input from measured geological information into numerical simulation for understanding effects of induced stress on geometries of multiple fracture propagation. We establish a benchmark study based on comparison of field result with numerical computations. The comparison then acts as reference measures for studying effects of changing in-situ stress, fracturing fluid viscosity and fracture spacing on propagation and geometries of multiple fractures between neighbouring wellbores in an undisclosed gas field. This leverages understanding of more complexities associated with inter-well multiple fracture growth that are idealized as straight from certain perspectives. Although some studies focus on stress interference from pre-existing fractures, actual fracture propagation geometries may be far from the idealized scenarios. Therefore, the stress shadow effects between growing multiple hydraulic fractures, if not taken into account, can lead to unrealistic estimation of hydraulic fracture trajectories. Consequently, more attention should be paid to the actual propagation of hydraulic fractures. Actual field geologic information is provided through well-logging and field mapping data. Very short fractures were propagated in these wells before the operation was terminated due to technical problems. The reservoir depth in the area is about 2170 m. At such depth, quasi-brittleness of shale should be accounted for by using relevant methods that capture rock ductility such as traction separation law. Abaqus commercial software is used to conduct the numerical computation using extended finite element method based on cohesive zone modeling. Application of this technique is further validated using Kristianovich-Geertsma-de Klerk analytical solution. This study is important in field implementation of infill drilling with well-informed mechanism of fracture interference in the inter-well region.

Numerical Simulation of Fracture Propagation of Multi-Cluster Perforation and Fracturing in Horizontal Wells: A Case Study of Mahu Oilfield

Mahu oilfield is a typical tight gravel oil reservoir. At present, long-stage multi-cluster fracturing is widely used for reservoir stimulation, and multiple-clusters treatment is realized through cluster perforation. Field monitoring indicates that not all perforation clusters produce hydraulic fractures in the fracturing process, and each cluster of hydraulic fractures in the section will expand unevenly. The unbalanced expansion of multiple clusters of fractures in the section seriously affects the effect of reservoir reconstruction of horizontal wells. Aiming at the long-stage multi-cluster fracturing of horizontal wells, a multi-fracture propagation calculation model considering wellbore flow, performance friction, different fracture criteria at the tip, and the interaction stress among multiple fractures is established in this paper. In order to improve the calculation efficiency, an explicit Runge Kutta Legendre algorithm is proposed to solve the structural mesh, and the solution program is compiled, which provides a basis for the theoretical analysis and rapid solution of the mechanism of multiple fracture growth. Finally, taking Mahu oil field as an example, we calculate the multi fracture propagation and flow distribution under different geological conditions, perforation conditions, and construction parameters. The research results will help to improve the fracturing efficiency of long-stage multi-cluster fractures.

Optimization of Non-Uniform Perforation Parameters for Multi-Cluster Fracturing

Stress shadowing affects the simultaneous propagation of fractures from multiple perforation clusters. Employing uniform perforation parameters for all clusters cause the unbalanced growth of fractures, which arouses the demand of optimizing non-uniform perforation parameters. An optimization workflow combining a fracture propagation model and the particle swarm optimization method (PSO) is proposed for multi-cluster fracturing in this study. The fracture model considers the coupling of rock deformation and fluid flow along the wellbore and fractures, and it is solved by using the Newton iteration method. The optimization is performed by taking the variance of multiple fracture lengths as fitness value function in the frame of the PSO method. Numerical results show that using the same spacings and perforation parameters for all clusters is detrimental to the balanced growth of multiple fractures. The variance of fracture lengths drops greatly through optimization of cluster spacings and perforation number/diameter. Properly increasing the spacing and perforation number/diameter for the middle clusters promotes the balanced growth of multiple fractures. This study provides an efficient optimization workflow for multi-cluster fracturing treatment in horizontal wells.

Numerical study of simultaneous growth of multiple hydraulic fractures from a horizontal wellbore combining dual boundary element method and finite volume method

Horizontal well and multi-stage hydraulic fracturing have been extensively used to extract unconventional oil/gas. The fracture pattern created from the multiple fractures determines the surface area of the reservoir in contact with the wellbore, thus influencing the overall quality of the multi-stage fracturing. Therefore, a good understanding of the HF propagation behavior is of importance for designing the perforation layout. In this paper, a new fully coupled hydraulic fracturing model is developed by combining the dual boundary element method (DBEM) that describes the rock matrix deformation and the finite volume method (FVM) that simulates the fluid flow in the fracture. The DBEM applies displacement boundary integral equation to one crack surface and traction boundary integral equation to the other. The model presented is first validated against the existing semi-analytical and numerical solutions for single and two fractures in the infinite domain. Then the impact of spacing, in-situ stress difference and injection parameters on the competitive growth behavior between multiple HFs is investigated. A parameter formulated in terms of the ratio of fluid volume allocated to different fractures is proposed to be the indicator of simultaneous or preferential propagation. The results show that less isotropic in-situ stress and a larger fluid viscosity or injection rate tend to facilitate simultaneous growth of multiple fractures, in which the influence of the in-situ stress difference is enhanced while that of the injection parameters is weakened when increasing the fracture spacing.

Fracture growth leading to mechanical spalling around deposition boreholes of an underground nuclear waste repository

This study presents a three-dimensional numerical analysis of multiple fracture growth leading to spalling around nuclear waste deposition boreholes. Mechanical spalling due to stress amplification after drilling is simulated using a finite element-based fracture growth simulator. Fractures initiate in tension based on a damage criterion and grow by evaluating stress intensity factors at each fracture tip. Tip propagation is multi-modal, resulting in final fracture patterns that are representative of both tensile and shear failure. Their geometries are represented by smooth parametric surfaces, which evolve during growth using lofting. The corresponding surface and volumetric meshes are updated at every growth step to accommodate the evolving fracture geometries. The numerical model is validated by comparing simulated fracture patterns against those observed in the AECL Underground Rock Laboratory Mine-By Experiment. It is subsequently calibrated to simulate fracture initiation and growth around boreholes drilled in the Forsmark granodiorite, subjected to a far-field anisotropic triaxial stress that corresponds to the in situ stress model from the Swedish Forsmark site. The deposition tunnel is implicitly simulated by attaching the deposition borehole to a free domain boundary. Several geomechanical cases are investigated, in which fracture growth is numerically evaluated as a function of in situ stress state, tunnel orientation, borehole geometry, total number of boreholes and borehole spacing. Numerical results show that spalling occurs in all cases, given the underground conditions at Forsmark, with borehole geometry, spacing and stresses affecting the extent of fracture nucleation and growth patterns. The uncertainty in underground stress conditions is evaluated through varying stress magnitudes and orientations relative to the tunnel floor. Whereas tunnel orientation influences the relative locations where fractures initiate with respect to the tunnel floor, fracture growth and its final extent is determined by the relative magnitudes of the in situ stresses. Higher stress differential causes higher spalling depths, but in all cases, failure extent is localised to the borehole vicinity, not exceeding one borehole radius. The cylindrical borehole is modified at the top to provide an access ramp for the spent fuel canisters and fracture growth around several deposition boreholes is simulated for borehole tops having cylindrical, conical, and wedge shapes. The enlargement of the borehole top induces higher stress concentrations at the borehole–tunnel junction, increasing the severity of spalling closer to the tunnel floor. Massive failure occurs when a multiple borehole model is considered and the inter-borehole distance is small enough that adjacent “spalled” areas interact. At Forsmark, through-going fractures are predicted to develop when the borehole spacing is less than 4 m. The effect of spalling on the structural integrity of the deposition boreholes is illustrated for each test case and quantified in terms of maximum spalling depth, spalling width and total fractured surface area.

Evolution mechanism of optical fiber strain induced by multi-fracture growth during fracturing in horizontal wells

A forward model for optical fiber strain was established based on a planar 3D multi-fracture model. Then the forward method calculating distributed fiber strain induced by multi-fracture growth was proposed. Based on this method, fiber strain evolution during fracturing of the horizontal well was numerically simulated. Fiber strain evolution induced by fracture growth can be divided into three stages: strain increasing, shrinkage convergence, and straight-line convergence, whereas the evolution of fiber strain rate has four stages: strain rate increasing, shrinkage convergence, straight-line convergence, and strain rate reversal after pumping stops. Fiber strain does not flip after pumping stop, while the strain rate flips after pumping stop so that strain rate can reflect injection dynamics. The time when the fracture extends to the fiber and inter-well pressure channeling can be identified by the straight-line convergence band of distributed fiber strain or strain rate, and the non-uniform growth of multiple fractures can be evaluated by using the instants of fractures reaching the fiber monitoring well. When the horizontal section of the fiber monitoring well is within the height range of a hydraulic fracture, the instant of the fracture reaching the fiber can be identified; otherwise, the converging band is not apparent. In multi-stage fracturing, under the influence of stress shadow from previous fracturing stages, the tensile region of fiber strain may not appear, but the fiber strain rate can effectively show the fracture growth behavior in each stage. The evolution law of fiber strain rate in single-stage fracturing can be applied to multi-stage fracturing.

Multiple hydraulic fractures growth from a highly deviated well: A XFEM study

A fully coupled extended finite element (XFEM) model is presented to investigate the effect of different well types (highly deviated and horizontal wells) on simultaneous growth of multiple fractures. The importance of the use of deviated wells is briefly described and the governing equations for multi-cluster hydraulic fracturing in a saturated porous media are stated. The weak forms of both stress equilibrium and fluid mass continuity equations are turned into a system of linear equations through XFEM-type enrichments in space and Newmark scheme in time, which are solved by Newton-Raphson iteration method. In addition, the secant method is employed to impose the pressure continuity and mass conservation conditions at the fracture-well intersections. A numerical example with considering the simultaneous propagation of four hydraulic fractures is first adopted to validate the proposed numerical model. Several examples are then employed to investigate the influence of operational parameter, deviation angle, fracture spacing, placement and number on final fracture patterns. Numerical results show that coefficient of variation in multiple fracture heights for high-angle well is lower than that for horizontal well for all fracture placements. The opposite growth directions for two neighboring fractures, partially arising from the height difference at fracture-well intersection points, can reduce the stress shadow effect, thus promoting uniform growth of multiple fractures. Those results potentially unveil the causes for higher oil and gas production rates measured after multi-cluster hydraulic fracturing along highly deviated wells.

Experimental Study of Hydraulic Fracture Propagation Behavior during Multistage Fracturing in a Directional Well

Due to the limited space of offshore platform, it is unable to implement large-scale multistage hydraulic fracturing for the horizontal well in Lufeng offshore oilfield. Thus, multistage hydraulic fracturing technology in directional well was researched essentially to solve this problem. Modeling of fracture propagation during multistage fracturing in the directional and horizontal wells in artificial cores was carried out based on a true triaxial hydraulic fracturing simulation experiment system. The effects of horizontal stress difference, stage spacing, perforation depth, and well deviation angle on multifracture propagation were investigated in detail. Through the comparative analysis of the characteristics of postfrac rock and pressure curves, the following conclusions were obtained: (1) multistage fracturing in horizontal wells is conducive to create multiple transverse fractures. Under relatively high horizontal stress difference coefficient (1.0) and small stage spacing conditions, fractures tend to deflect and merge due to the strong stress interference among multiple stages. As a consequence, the initiation pressure for the subsequent stages increases by more than 8%, whereas in large stage spacing conditions, the interference is relatively lower, resulting in the relatively straight fractures. (2) Deepening perforation holes can reduce the initiation pressure and reduce the stress interference among stages. (3) When the projection trace of directional wellbore on horizontal plane is consistent with the direction of the minimum horizontal principal stress, fractures intersecting the wellbore obliquely are easily formed by multistage fracturing. With the decrease of well deviation angle, the angle between fracture surface and wellbore axis decreases, which is not conducive to the uniform distribution of multiple fractures. (4) When there is a certain angle between the projection trace of directional wellbore on horizontal plane and the direction of minimum horizontal principal stress, the growth of multiple fractures is extremely ununiform and the fracture paths are obviously tortuous.

A new method for calculating the direction of fracture propagation by stress numerical search based on the displacement discontinuity method

In the traditional, displacement discontinuity method (DDM) simulation of hydraulic fracturing, the stress intensity factor (SIF) method is usually employed to calculate the fracture propagation angle (FPA). However, the SIF method is not suitable for real formation rock stress conditions. Considering the real stress condition of the formation under far-field bidirectional compression, we proposed a stress numerical search method (SNSM) that is based on the maximum circumferential stress criterion at the fracture tip to predict the FPA. Moreover, we compared the results from this model with indoor experiments and numerical simulation results to verify the model. The computation results of the model show that the traditional SIF method simplifies the rock stress, which will cause a large error and that the SNSM method is more consistent with the real situation. The sensitivity parameter analysis shows that the SNSM method can be utilized to predict the fracture propagation trajectory with different rock and construction parameters and to simulate the competitive growth of multiple fractures with the effect of a “stress shadow”. The results of this paper supplement and improve the existing hydraulic fracturing model and can provide guidance for the fracture parameter design of field fracturing construction.

A Model for Multiple Hydraulic Fracture Propagation with Thermo-Hydro-Mechanical Coupling Effects

In this study, a coupled thermo-hydro-mechanical model to simulate multiple hydraulic fracture propagation is presented. Fracture propagation with elastic deformation is described by using a displacement discontinuity method. The temperature distribution and induced thermal stress are calculated via a semi-analytical method in an explicit way. An iterative scheme is proposed to solve the coupling between fracture propagation with fluid flow and induced thermal stress. The numerical model is validated against related analytical solutions. Several numerical cases are modeled to investigate the controlling factors for uniform growth of multiple fractures. Results show that using non-uniform fracture spacings and proper increasing the spacing for fractures away from the heel of wellbore promote the uniform growth of multiple fractures by comparison with using uniform fracture spacings. Increasing the perforation diameter for the middle cluster also works. Besides, single-wing fracturing could greatly improve the uniform growth of multiple hydraulic fractures. Finally, it shows that the thermal stress has a significant influence on fracture geometrical size but has limited effect on fracture propagation path. In addition, the thermal effect promotes the uniform growth of multiple fractures.

Growth of three-dimensional fractures, arrays, and networks in brittle rocks under tension and compression

• A fracture mechanics based numerical method for growing multiple three-dimensional fractures in mixed mode conditions is introduced. • Fractures develop complex non-planar surfaces as a result of interaction in arrays and networks. • Cut-plane visualisation of three-dimensional fractures surfaces enables direct comparison to outcrops and experiments. Concurrent growth of multiple fractures in brittle rock is a complex process due to mechanical interaction effects. Fractures can amplify or shield stress on other fracture tips, and stress field perturbations change continuously during fracture growth. A three-dimensional, finite-element based, quasi-static growth algorithm is validated for mixed mode fracture growth in linear elastic media, and is used to investigate concurrent fracture growth in arrays and networks. Growth is governed by fracture tip stress intensity factors, which quantify the energy contributing to fracture extension, and are validated against analytical solutions for fractures under compression and tension, demonstrating that growth is accurate even in coarsely meshed domains. Isolated fracture geometries are compared to wing cracks grown in experiments on brittle media. A novel formulation of a Paris-type extension criterion is introduced to handle concurrent fracture growth. Fracture and volume-based growth rate exponents are shown to modify fracture interaction patterns. A geomechanical discrete fracture network is generated and examined during its growth, whose properties are the direct result of the imposed anisotropic stress field and mutual fracture interaction. Two-dimensional cut-plane views of the network demonstrate how fractures would appear in outcrops, and show the variability in fracture traces arising during interaction and growth.

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.

Progress and development of volume stimulation techniques

Abstract Based on the theoretical study and field application of volume stimulation in horizontal wells over the past 10 years, the core connotation of volume stimulation was further interpreted. The implementation methods, design models and key issues were analyzed, and the future development direction was put forward. The research shows that the multi-cluster limited entry technique can achieve homogenous growth of multiple fractures. The hybrid stimulation of “breaking by rock gel stimulation + carrying proppant by slick water” plus small-particle proppant can reduce the fracture complexity near the well bore and increase stimulated reservoir volume (SRV) in the far-field. The requirement of fracture conductivity in unconventional formations can be met by shear-sustained fractures and proppant-transporting slick water. The optimum well spacing between a child well and a parent well should be determined by the stimulation modes, injection volume and pressure drawdown. Reconstructing seepage field, stress field and stimulation targets is crucial for improving the stimulation results in a horizontal well. Reducing cluster spacing and well spacing is the basis for establishing development modes of fracture-controlled reserves. Fracturing-design decision system based on “spatial-mode stimulation” and geology-engineering integration is an important research direction for volume stimulation techniques.

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.