محمد فاتحی مرجی

Around 70% of the world's hydrocarbon fields are situated in reservoirs containing low-strength rocks, such as sandstone. During the production of hydrocarbons from sandstone reservoirs, sand-sized particles may become dislodged from the formation and enter the hydrocarbon fluid flow. Sand production is a significant issue in the oil industry due to its potential to cause erosion of pipes and valves. Separating grains from oil is a costly process. Oil and gas companies are motivated to reduce sand production during petroleum extraction. Hydraulic fracturing is one of the parameters that can influence sand production. However, understanding the complex interactions between hydraulic fracturing mechanisms and sand production around wellbores is critical for optimizing reservoir recovery and ensuring the integrity of production wells. This article explores the integrated simulation approach to model hydraulic fracturing processes and assess their effects on sand production. Two-dimensional models were created using the discrete element method in PFC2D software for this research. The fractures' length in the models varies based on the well's radius. The angle between two fractures at 90 and 180 degrees to each other was also modeled. In the first case, the length of the fracture is less than the radius of the well, in the second case, the values are equal and finally, the fracture length is assumed to exceed the well radius. The calibrated and validated results demonstrate the change in sand production rate in comparison to the unbroken state.

The mechanical behavior of rock-rock bolt interface considering the effects of indents’ shape and their number was numerically simulated based on discrete element method using the two-dimensional particle flow code. The conventional and standard uniaxial compressive and Brazilian tensile strengths tests were used to calibrate the modelled samples with 100 cm 100 cm in dimension. The numerical models were prepared such that different indent shape and number were inserted in the cable bolts arrangements during the rock reinforcement process. The effects of confining pressure 3.7 MPa and different shear failure loads were modeled for the punch shear test of the concrete specimens. The results of this study showed that the dominant failure mode of the rock-cable bolt interface was of tensile mode and the shape and number of cable indents significantly affected the strength and mechanical behavior of the modelled samples. It has also been showed that the indent dimensions and number affected the shear strength of the interfaces.

Complexity of geomaterial’s behavior is beyond the capabilities of conventional numerical methods alone for realistically model rock structures. Coupling of numerical methods can make the numerical modeling more realistic. Discontinuous Deformation Analysis (DDA) and Displacement Discontinuous Method (DDM) are hybridized for modeling block displacement and crack propagation mechanism in a blocky rock mass. DDA is used to compute the displacements of the blocks, and DDM is used to predict the crack propagation paths due to the specified boundary conditions. The displacements obtained from DDA are converted into stress and considering Kelvin's solution of the problem the crack propagation mechanism within each block is investigated. Boundary stresses are updated due to crack propagation and new stress boundary conditions in DDA. This cycle continued until crack propagation stopped or a new block formed. Numerical solutions of the experimental rock samples including two random cracks with crack 1 fixed and crack 2 created with different angles and one crack with a slope angle of 30 degrees are compared with the existing experimental and numerical results. This comparison validates the accuracy and effectiveness of the proposed procedure because crack propagation paths predicted are in good agreement with the corresponding experimental results of rock samples.

Crack propagation in the low permeable reservoir rock as an explosive fracturing technique can be used to increase the permeability and productivity of unconventional reservoirs. This technique is the same as hydraulic fracturing but uses blast-induced shock waves and gas pressure to generate and propagate radial cracks around the wellbore in a particular reservoir. In this study, we want to simulate the explosion-induced crack initiation and propagation around a wellbore as a stimulation method of unconventional reservoirs using an analytical-numerical technique. Therefore, the dynamic crack initiation and propagation process of deep rock caused by the explosion is considered both analytically and numerically. The mechanical process of rock cracking under the action of an explosion stress wave is theoretically analyzed and simulated with a finite difference method. Then the coupling effect of explosion load in the form of shock wave and gas pressure is established numerically based on the two-dimensional explicit finite difference and displacement discontinuity methods, respectively. The analytical method involved the solution of the Lame-Navier equation in elasto-dynamics based on the Green’s function solution. The simulation procedure consists of coupling the explicit finite difference method with the displacement discontinuity method in the form of higher-order displacement discontinuities along the boundaries of the problem. All of the mentioned processes have been done in an oil field with a density of 2.5 gr/cm3, Poisson’s ratio of 0.2, and elastic modulus of 20 GPa. The numerical results of this research show that shock waves are responsible for the initiation and propagation of radial cracks around the wellbore which in turn is filled with pressurized gas due to explosion. Then, these shock wave-induced radial cracks are propagating in the reservoir rock because of the explosive gas pressure inside them. This rock fracturing mechanism can help to improve the permeability and productivity of the highly low-permeable reservoirs in horizontal wells.

The presence of pores and cracks in porous and fractured rocks is mostly accompanied by fluid flow. Poroelasticity can be used for the accurate modeling of many rock structures in the petroleum industry. The approach of the stress to the value of the fracture stress and the effect of pore pressure on the deformation of rock are among the effects of fluid on the mechanical behavior of the medium. Due to the deformation-diffusion property of porous media, governing equations, strain-displacement, and stress-strain relationships can be changed to each other. In this study, constitutive equations and relationships necessary to investigate the behavior and reaction of rock in a porous environment are stated. Independent and time-dependent differential equations for an impulse and point fluid source are used to obtain the fundamental solutions. Influence functions are obtained by using the shape functions in the formulation of the fundamental solutions and integrating them. To check the validity and correctness of provided formulation, several examples are mentioned. In the first two examples, numerical application and analytical solution are used at different times and in undrained and drained conditions. In times 0 (undrained response of medium) and 4500 seconds (drained response of medium), there is good coordination and agreement between the numerical and analytical results. In the third example, using the numerical application, a crack propagation path in the wellbore wall is obtained, which is naturally in the direction of maximum horizontal stress.

In this research work, X-ray diffraction (XRD) tests and petrographic studies are performed to analyze the mineral composition and lamination in the shale rock specimens. Afterward, point load (PL) and uniaxial compressive strength (UCS) tests are carried out on the anisotropic laminated shale rock. Based on the macro-mechanical properties of these tests, the discrete element method implemented in a two-dimensional particle flow code (PFC2D) is adjusted to numerically simulate the shale rock specimens. The aim of this work is to validate the numerical models by failure process, stress-strain curves, and peak failure strengths of the shale samples. Therefore, point load test is used for assessing the pattern failure mechanism, and uniaxial compressive strength test is performed for obtaining the stress-strain curves and peak strength failure points in the laboratory shale rock samples. Validation of peak strengths criteria provides the best results; the determination coefficient values for lab and numerical modeling with (R2 = 0.99). Several numerical models are prepared for estimating the mechanical behavior of shale rocks in PFC2D. The smooth joint model (SJM) is used for preparing the consistent and appropriate constitutive models for simulating the mechanical behavior of laminated shale. It is concluded that SJM provides more reasonable results for laminated shale rock that can be used for several petroleum engineering projects, especially in the central geological zone of Iran.

The tensile strengths of geomaterials such as rocks, ceramics, concretes, gypsum, and mortars are obtained based on the direct and indirect tensile strength tests. In this research work, the Brazilian tensile strength tests are used to study the effects of length and inclination angle of T-shaped non-persistent joints on the mechanical and tensile behaviors of the geomaterial specimens prepared from concrete. These specimens have a thickness of 40 mm and a diameter of 100 mm, and are prepared in the laboratory. Two T-shaped non-persistent joints are made within each Brazilian disc specimen. The Brazilian disc specimens with T-shaped non-persistent joints are tested experimentally in the laboratory under axial compression. Then these tests are simulated in the two-dimensional particle flow code (PFC2D) considering various notch lengths of 6, 4, 3, 2, and 1 cm. However, different notch inclination angles of 0, 30, 60, 90, 120, and 150 degrees are also considered. In this research work, 12 specimens with different configurations are provided for the experimental tests, and 18 PFC2D models are made for the numerical studies of these tests. The loading rate is 0.016 mm/s. The results obtained from these experiments and their simulated models are compared, and it is concluded that the mechanical behavior and failure process of these geomaterial specimens are mainly governed by the inclination angles and lengths of the T-shape non-persistent joints presented in the samples. The fracture mechanism and failure behavior of the specimens are governed by the discontinuities, and the number of induced cracks when the joint inclination angles and joint lengths are increased.  For larger joints when the inclination angle of the T-shaped non-persistent joint is around 60 degrees, the tensile strength is minimum but as it is closed to 90 degrees, the compressive strengths are maximum. However, an increase in the notch length increase the overall tensile strength of the specimens. The strength of samples decreases by increasing the joint length. The strain at the failure point decreases by increasing the joint length. It is also observed that the strength and failure process of the two sets of specimens and the corresponding numerical simulations are consistence.

In this study, a discrete element method based on linear parallel bond model (LPBM) has been used to investigate the growth path of cracks and the amount of force required to create it. The formation of cracks in this method is due to the breaking of the bond between the particles, which forms macro cracks by joining the microcracks. It was found that the average normal forces for breaking the bond in wing crack are about 11 and 30% in oblique and coplanar cracks by investigate the load on the coal sample containing pre-existing cracks, therefore, the growth of wing tensile cracks in the sample is due to the low value of normal forces. The value of shear force required to overcome the parallel bond of particles in oblique and coplanar cracks is about 7.5 and 3.5 times in wing crack, respectively, in order for crack propagation, it is necessary to break the shear bond between the particles in the oblique and coplanar crack path. The average shear force required to break a bond in the coplanar crack path is about 47% in the oblique crack path, which makes the coplanar crack faster than the oblique crack. The wing crack has the highest value in terms of length compared to other secondary (induced) cracks before the peak point (in stress-strain curve), and this causes the pre-existing cracks in the coal seams to be joined using wing cracks.

The study of factors affecting wellbore stability has become very important in the oil and gas industry because they will save time and costs. In studying the stability of oil and gas wells, different factors such as mechanical properties, in-situ stresses, and pore pressure can be used. Consequently, knowing and calculating these parameters will be helpful in analyzing the wellbore stability. This study evaluated the effects of changing stresses on the wellbore stability and drilling mud weight window using a ratio of different stresses for the first time in one of the wells of the Zireh gas field, located in the southwest of Iran. Due to the lack of laboratory data, each of the parameters of the geomechanical model were determined by empirical correlation. Using Mohr-Coulomb and Mogi-Coulomb criteria, the drilling mud weight window was determined to be 76.99-128.17 (pcf) and 67.56-128.17 (pcf), respectively; however, Mogi-Coulomb provided better results. The wellbore stability is also investigated by using 3D numerical modeling using ABAQUS software and the Mohr-Coulomb criterion. According to the results of the numerical and analytical methods, the well is completely stable. Ultimately, five different in-situ stress ratios were examined to determine how in-situ stress distribution affected wellbore stability. According to the results, the mud weight window range decreases as the stress changes from an isotropic to an anisotropic state, indicating wellbore instability.

In this work, an effective methodology is introduced for simulation of the crack propagation in linear poroelastic media. The presence of pores and saturated cracks that can be accompanied by fluid flow makes the use of poroelastic media inevitable. In this work, involvement of the time parameter in crack propagation is of particular importance. The order of doing the work is such that first, derives the fundamental solutions of a poroelastic higher order displacement discontinuity method (PHODDM). Then will be provided a numerical formulation and implementation for PHODDM in a code named linear element poroelastic DDM (LEP-DDM). Analytical solutions use different times to check the correctness and validity of the proposed solution and the newly developed code. The numerical results show a good agreement and coordination with the analytical results in time zero and 5000 seconds . The code is able to pursue crack-propagation in time and space. This topic is introduced and shown in an example.

In this work, the mechanical behavior of strata deformation due to drilling and surface loading is investigated using a 3D physical model. For this purpose, a scaled-down physical model is first designed. Then the tunnel drilling and support system are built. The subsidence experiments performed due to tunnel excavation and loading in a very dense and loose soil are performed. Soil is clayey sand (SC), and the percentages of its components are as sand (S = 1. 41%), gravel (G = 25%), and clay (C = 9.33%). Unstable tunnel support experiments are also carried out using physical simulation. Finally, deformations of soil surface and subsidence of strata are observed and recorded. In the tunnel with segmental support, 18.75% more load is applied than in the unsupported tunnel, and the total subsidence of the strata is reduced by 36.2%. The area of the deformed inner layers is decreased by 74.2%, and the length of the affected area in the largest layer is decreased by 48%. The depth of the cavity created at the surface is 46.66% less.

In this work, the machine learning prediction models are used in order to evaluate the influence of rock macro-parameters (uniaxial compressive strength, tensile strength, and deformation modulus) on the rock fracture toughness related to the micro-parameters of rock. Four different types of machine learning methods, i.e. Multivariate Linear Regression (MLR), Multivariate Non-Linear Regression (MNLR), copula method, and Support Vector Regression (SVR) are used in this work. The fracture toughness of mode I and mode II (KIC and KIIC) is selected as the dependent variable, whereas the tensile strength, compressive strength, and elastic modulus are considered as the independent variables, respectively. The data is collected from the literature. The results obtained show that the SVR model predicts the values of KIC and KIIC with the determination coefficients (R2) of 0.73 and 0.77. The corresponding determination coefficient values of the MLR model and the MNLR model for KI and KII are R2 = 0.63, R2 = 0.72, and R2 = 0.62,0.75, respectively. The copula model predicts that the value of R2 for KI is 0.52, and for KII R2=0.69. K-fold cross-validation testing method performs for all these machine learning models. The cross-validation technique shows that SVR is the best-designed model for predicting the fracture toughness mode-I and mode-II.

The in-situ coal is converted to the synthetic gas in the process of underground coal gasification (UCG).  In order to increase the rate of in-situ coal combustion in the UCG process, the contact surfaces between the steam, heat, and coal fractures should be raised. Therefore, the number of secondary cracks should be increased by raising the heat and existing steam pressure during the process. This paper emphasises on the secondary crack growth mechanism of the pre-existing cracks in the coal samples under different loading conditions. Different geometric specifications such as the length of the pre-existing cracks (coal cleats) and their inclinations are considered. The numerical modeling results elucidate that the first crack growths are the wing cracks (also called the primary or tensile cracks) formed due to unbonding the tensile bonds between the particles in the assembly. Ultimately, these cracks may lead to the cleat coalescences. On the other hand, the secondary or shear cracks in the form of co-planar and oblique cracks may also be produced during the process of crack growth in the assembly. These cracks are formed due to the shear forces induced between the particles as the initial cleat length is increased and exceed the dimension of coal blocks. The cavity growth rate increases as the secondary cracks grow faster in the coal blocks. In order to achieve the optimum conditions, it is also observed that the best inclination angle of the initial coal cleat changes between 30 to 45 degrees with respect to the horizon for the coal samples with the elasto-brittle behavior.

Nowadays, hydraulic fracturing is used in various fields such as stimulation of oil reservoirs, measurement of in-situ stresses, extraction of geothermal energy and extraction of conventional and unconventional hydrocarbon resources.Meanwhile in-situ stresses and porosity are the most important factors that affecting the propagation, opening and extension of the crack. In this research, the above parameters have been investigated using analytical and numerical methods. For numerical modeling in this research, the numerical method of displacement discontinuity, has been used, which is one of the methods with high ability in modeling discontinuity and failure. The program used is a quadratic element based on solid mechanics and fracture mechanics. In this research, by addition of the fluid flow module, the fluid mechanics is included in the analysis. In the fluid mechanics module, the effect of fluid flow on crack opening displacement is investigated. This part of the program is created by finite difference method in mode of forward time central space. Finally, after validation of the program, the effects of in situ stress and porosity on crack propagation were investigated. In order to generalize the results, the studied parameters have been presented in dimensionless forms. It is concluded that the best direction for creating a hydraulic fracture is in the direction of maximum principal stress. As the in-situ stress difference increases, less injection pressure is required to propagate the crack. In the crack with a 45 degrees angle relative to the maximum stress, a lower injection pressure is required to propagate the crack; then this crack after several step of growth deviates to the maximum stress direction. Increasing the porosity of the formation reduces the amount of Young's modulus and Poisson's ratio, which leads to increases the crack opening at higher porosity values.

In this work, an effective methodology is introduced for modeling the fatigue crack propagation in linear elastic brittle media. The displacement discontinuity method is used to accomplish the analysis, and the boundaries are discretized with quadratic elements in order to predict the stress intensity factors near the crack tips. This procedure is implemented through 2D linear elastic fracture mechanics. The normal and shear displacement discontinuity around the crack tip is applied to compute the mixed-mode stress intensity factors. The crack growth is incremental, and for each increment of extension, there is no need to use a re-meshing procedure. This method has benefits over the finite element method due to its simplicity in meshing. The crack growth direction is assessed using the maximum principal stress theory. In these analyses, a repetition method is used in order to estimate the correct path of crack propagation. Therefore, the different lengths of incremental growth do not affect the crack growth path analysis. The results are exhibited for several examples with different geometries to demonstrate the efficiency of the approach for analyzing the fatigue crack growth. The accuracy represents that this formulation is ideal for describing the fatigue crack growth problems under the mixed-mode conditions.

Investigating the crack propagation mechanism is of paramount importance in analyzing the failure process of most materials. This process may be exposed during each kind of loading on the materials. In this work, the cracking mechanism in rock-like materials is studied using the numerical methods and compared with the experimental test results. However, the mechanism of crack growth in brittle materials such as rocks is influenced by different parameters. This research work focuses on the effect of the initial crack angles on the crack growth paths of these materials. Some cubic samples containing pre-existing cracks are tested in compression by considering different flaw orientations. The specimens are made of cement, water, and sand. Moreover, the mentioned process is numerically simulated using three different methods the finite difference method for discontinuous bodies or discrete element method, the displacement discontinuity method, and the versatile finite element method. The micro-parameters for simulation are gained by the trial-and-error procedure for the discrete element method. Eventually, the crack growth paths observed in the experiments are compared with the numerically simulated models. The results obtained show that these central cracks propagate in two ways, which are dependent on their initial angle. By increasing the initial crack angle to greater than 30° (α > 30°), the wing crack path moves further away from the initial crack, and by decreasing α to smaller than 30° (α < 30°), only the shear cracks are initiated. Therefore, the validity and accuracy of the results are manifested by comparing all the corresponding results obtained by different methods. Based on these results, it can generally be concluded that the strength of the cubic (rock material) specimens increases with increase in the crack angles with respect to the applied loading direction.

The tensile strength of the anisotropic rock-like material specimens is meastred directly in the laboratory using a new device converting the compressive loading to that of the tensile before the rock breakage. The specially prepared concrete slabs of dimensions 19 cm * 15 cm * 15 cm with a central hole of 7.5 cm in diameter are tested experimentaly. The specimens are located in the compressive-to-tensile load converting device, and tested under a compressive loading rate of 0.02 MPa/s by the universal testing machine. The cubic slab samples are made in three different configurations to have the directions of  0°, 45°, and -45° with respect to the applied loading direction. In order to compare the direct tensile strength of the concrete samples with that of the indirect measuring tests, some Brazilian tests are also carried out on the concrete disc specimens prepared in the laboratory. By comparing the direct and indirect testing results of the concrete tensile strength, it can be concluded that the direct tensile strength values are somewhat lower than those of the indirect ones. The tensile strength values for the three different configurations of the concrete specimens are nearly the same.

Ignoring thermal effects in many applications of geomechanics including hydraulic fracturing of deep oil and gas reservoirs and geothermal energy extraction may result in significant errors in output. Production and stimulation of unconventional oil and gas reservoirs is highly dependent on performance of hydraulic fracturing (HF) jobs. These jobs create a network of fractures which are responsible for elevated hydraulic conductivity of the reservoir formation around the wellbore. The fractures increase inflow of hydrocarbons into the wellbore especially in low permeability reservoirs. A sound understanding of HF’s behavior and its relation to the increased production rate, decreases high costs of HF jobs. Thermal effects on HF propagation and mechanism are studied in this paper using the displacement discontinuity method. Firstly, the thermal effects on a thermoelastic model with a thermal source was studied. Models showed that boundaries of the geometrical model should be place farther from what was expected in elastic analyses to avoid boundary effects. The thermal effects were observed far away from the thermal source in the models.Then, thermal effects on a hydraulic fracture was modeled. It was shown that using a cold fluid for HF can decrease the required HF pressure for propagation. The HF width was also increased compared to an elastic model. This is an important parameter in determining hydraulic conductivity of the formation. The lower required pressure for HF propagation reduces the cost of equipment needed for the job, since they are not required to work at very high pressures.

Determination of the borehole and fracture initiation positions is the main aim of a borehole stability analysis. A wellbore trajectory optimization with the help of the mud pressure may be unreasonable since the mud pressure can only reflect the degree of difficulty for the initial damage to occur at the wellbore rather than the extent of the wellbore damage. In this work, we investigate the failure extension in different arbitrary inclination boreholes under different in-situ stress regimes. Assuming the plane strain condition, the Mohr-Coulomb, Mogi-Coulomb, and Modified Lade rock failure criteria are utilized. We present an analytical equation to determine the optimum drilling trajectory of an Iranian oilfield. In order to predict the degree of wellbore damage, the initial shear failure location, failure width, and failure depth of arbitrary wellbores are determined. Then a new model is derived to calculate the initial failure area of a directional wellbore because it is more efficient in a wellbore stability analysis. The results obtained show that in the target oilfield, the vertical and low-deviated direction is the optimum drilling path. According to the results of this work, optimization of the wellbore trajectory based on the estimated failure zone is a reasonable method if a considerable failure zone takes place around the borehole wall.

In the drilling of oil and gas wells, confining pressure or the pressure at the well bottom is one of the effective factors affecting the rate of drilling and the amount of specific energy (the energy needed to remove a single volume of rock). In this operation, the rock cutting process is a combination of two modes of failures, i.e. brittle and ductile. Each of these failure modes has a different effect on the specific energy and structure of the crushed material, and thus on the rate of drilling. In this paper, the distinct element method is used to understand the relationship between rock fracture and confining pressure and its effect on the specific energy. For this purpose, a particle flow code is used that numerically simulates the mechanical behavior of the granular materials such as rocks. Based on the results obtained in condition of no confining pressure, the force applied to the cutter blade causes failure of the inter-granular connections in a single failure plane. But under confined pressure conditions, a different mechanism is taking place, and the difference in pressure created during the cutting action of PDC drill bits keep the crushed rock on each other and increase the mechanical specific energy of the rock cutters. Also, up to a pressure of about 26 MPa, with increasing tension, the specific energy has a relatively linear increase during the cutting action of the bits. But after this pressure due to the increased confining stresses and near-hydro-static conditions, the incremental increase in the mechanical specific energy decreases as the drilling depth increases.

In this work, we used a grain-based numerical model based on the concept of lattice. The modelling was done to simulate the lab experiments carried out on the mortar samples. Also the analytical solutions corresponding to the viscosity-dominated regime were used to estimate the fracture length and width, and the results obtained were compared with the numerical simulations. As the analytical solutions are proposed for a penny-shaped fracture with no presence of any obstacle such as natural interfaces, in this work, we presented the results of lattice simulations for hydraulic fracturing in the cement sample, similar to the lab, but with no natural fractures, and compared the results obtained with analytical solutions. The results indicated that in the case of a continuous medium, the analytical solutions may present a reasonable estimation of the fracture geometry. Also the viscosity-dominated leak-off model showed a better match between the analytical solutions and the numerical simulation results, confirmed by observing fluid loss into the sample in the lab post-experiment. In the case of assuming leak-off, the results indicated that the fracture width and length would reduce. However, it should be noted that in real cases, rock formations exhibit fractures and inhomogeneity at different scales so that the applications of the analytical solutions are limited.

The explosion process of explosives in a borehole applies a very high pressure on its surrounding rock media. This process can initiate and propagate rock fractures, and finally, may result in the rock fragmentation. Rock fragmentation is mainly caused by the propagation of inherent pre-existing fractures of the rock mass and also from the extension of the newly formed cracks within the intact rock due to the explosion. In this work, the process of extension of blast-induced fractures in rock masses is simulated using the discrete element method. It should be noted that, in this work, fracture propagation from both the rock mass inherent fractures and newly induced cracks are considered. The rock mass inherent fractures are generated using the discrete fracture network technique. In order to provide the possibility of fracture extension in the intact rock blocks, they are divided into secondary blocks using the Voronoi tessellation technique. When the modeling is completed, the fracture extension processes in the radial and longitudinal sections of a borehole are specified. Then a blast hole in an assumed rock slope is modeled and the effect of pre-splitting at the back of the blast hole (controlled blasting) on the fracture extension process in the blast area is investigated as an application of the proposed approach. The modeling results obtained show that the deployed procedure is capable of modeling the explosion process and different fracture propagations and fragmentation processes in the rock masses such as controlled blasting.

In the oil, construction and mining industry, different types of cutting tools using to extract rock materials. Hence, the investigation of the reaction of the cutting tool with the stone can be a suitable method for analyzing the problems associated with the failure occurred at the time of drilling. One of the factors affecting rock failure mechanism At the time of drilling Geometry of the cutting tool (cutter), Which has a significant impact on Mechanical specific energy (energy required to cut through a unit volume of rock). Numerical methods DEM One of the most advanced methods for modeling issues Which is accompanied by a strain and a deformation. The main goal of this research is rock cutting simulation and examining the effect of the bake rake angle on the cutter PDC performance On two samples of sedimentary rock (sand stone, limestone). The instrument used in this study numerical software particle flow code (PFC2D) which simulates the mechanical behavior of material using a distinct elemental method (DEM), Based on the results, limestone needs more Mechanical specific energy than sandstone, This can be due to more limestone resistance to sandstone. But increasing the back rake angle from 10 degrees to 40 degrees increases the Mechanical specific energy consumption. In fact, horizontal force cutting is a major factor affecting the amount of Mechanical specific energy. In addition, the results of the surveys show The mechanism of the flow of crushed material in front of the cutter blades Function of cutter geometry and the friction angle between the cutter and the crushed particles. and is one of the effective factors in the amount of Mechanical special energy.