Finite Element Method Simulation of Wellbore Stability under Different Operating and Geomechanical Conditions

The variation of the principal stress of formations with the working and geo-mechanical conditions can trigger wellbore instabilities and adversely affect the well completion.A finite element model,based on the theory of poro-elasticity and the Mohr-Coulomb rock damage criterion,is used here to analyze such a risk.The changes in wellbore stability before and after reservoir acidification are simulated for different pressure differences.The results indicate that the risk of wellbore instability grows with an increase in the production-pressure difference regardless of whether acidification is completed or not;the same is true for the instability area.After acidizing,the changes in the main geomechanical parameters(i.e.,elastic modulus,Poisson’s ratio,and rock strength)cause the maximum wellbore instability coefficient to increase.

Borehole stability in naturally fractured rocks with drilling mud intrusion and associated fracture strength weakening:A coupled DFN-DEM approach

Borehole instability in naturally fractured rocks poses significant challenges to drilling.Drilling mud invades the surrounding formations through natural fractures under the difference between the wellbore pressure(P w)and pore pressure(P p)during drilling,which may cause wellbore instability.However,the weakening of fracture strength due to mud intrusion is not considered in most existing borehole stability analyses,which may yield significant errors and misleading predictions.In addition,only limited factors were analyzed,and the fracture distribution was oversimplified.In this paper,the impacts of mud intrusion and associated fracture strength weakening on borehole stability in fractured rocks under both isotropic and anisotropic stress states are investigated using a coupled DEM(distinct element method)and DFN(discrete fracture network)method.It provides estimates of the effect of fracture strength weakening,wellbore pressure,in situ stresses,and sealing efficiency on borehole stability.The results show that mud intrusion and weakening of fracture strength can damage the borehole.This is demonstrated by the large displacement around the borehole,shear displacement on natural fractures,and the generation of fracture at shear limit.Mud intrusion reduces the shear strength of the fracture surface and leads to shear failure,which explains that the increase in mud weight may worsen borehole stability during overbalanced drilling in fractured formations.A higher in situ stress anisotropy exerts a significant influence on the mechanism of shear failure distribution around the wellbore.Moreover,the effect of sealing natural fractures on maintaining borehole stability is verified in this study,and the increase in sealing efficiency reduces the radial invasion distance of drilling mud.This study provides a directly quantitative prediction method of borehole instability in naturally fractured formations,which can consider the discrete fracture network,mud intrusion,and associated weakening of fracture strength.The information provided by the numerical approach(e.g.displacement around the borehole,shear displacement on fracture,and fracture at shear limit)is helpful for managing wellbore stability and designing wellbore-strengthening operations.

An analytical solution to wellbore stability using Mogi-Coulomb failure criterion

Deep wellbores/boreholes are generally drilled into rocks for oil and gas exploration,monitoring of tectonic stresses purposes.Wellbore and tunnel in depth are generally in true triaxial stress state,even if the ground is under axisymmetric loading condition.Stability of such wellbores is very critical and collapse of wellbore must be avoided.Mogi-Coulomb failure criterion is a better representation of rock strength under true triaxial condition.In this paper,an analytical solution is proposed using Mogi-Coulomb failure criterion.The solution is obtained for rock mass exhibiting elastic-perfectly plastic or elastic-brittle-plastic behaviour considering in-plane isotropic stresses.The proposed solution is then compared with exact analytical solution for incompressible material and experimental results of thickwall cylinder.It is shown that the results obtained by the proposed analytical solution are in good agreement with the experimental results and exact analytical solution.A reduction of about 13%e20%in plastic zone from the proposed closed-form solution is observed,as compared to the results from the finite element method(FEM)based Mohr-Coulomb criterion.Next,the influences of various parameters such as Poisson’s ratio,internal pressure(mud weight),dilation angle,and out-of-plane stress are studied in terms of stress and deformation responses of wellbore.The results of the parametric study reveal that variation in the out-of-plane stress has an inverse relation with the radius of plastic zone.Poisson’s ratio does not have an appreciable influence on the tangential stress,radial stress and radial deformation.Dilation angle has a direct relation with the deformation.Internal pressure is found to have an inverse relation with the radial deformation and the radius of plastic zone.

Borehole stability in naturally fractured reservoirs luring production tests

Based on the plane of weakness theory, a model for predicting borehole stability in fractured reservoirs under different stress states was estiblisted and the equations for solving borehole stability were developed. The minimum downhole pressures required to maintain borehole stability under different natural fracture occurrences were calculated by using the data from a well in the Tazhong （central Tarim） area, Tarim Basin, west China. Several conclusions were drawn for naturally fractured reservoirs with a dip angle from less than 10° to greater than 30°. Application in three wells in the Tazhong area indicates that this model is practically useful.

Safety analysis of stability of surface gas drainage boreholes above goaf areas

As longwall caving mining method prevails rapidly in China coal mines, amount of gas emission from longwall faces and goaf area increased significantly. Using traditional gas drainage methods, such as drilling upward holes to roof strata in tailgate or drilling inseam and cross-measure boreholes, could not meet methane drainage requirements in a gassy mine. The alternative is to drill boreholes from surface down to the Iongwall goaf area to drain the gas out. As soon as a coal seam is extracted out, the upper rock strata above the goaf start to collapse or become fractured depending upon the rock characteristics and the height above the coal seam. During overlying rock strata being fractured, boreholes in the area may be damaged due to ground movement after the passage of the Iongwall face. The sudden damage of a borehole may cause a Iongwall production halt or even a serious mine accident. A theoretical calculation of the stability of surface boreholes in mining affected area is introduced along with an example of determination of borehole and casing diameters is given for demonstration. By using this method for the drilling design, the damage of surface boreholes caused by excessive mining induced displacement can be effectively reduced if not totally avoided. Borehole and casing diameters as well as characteristics of filling materials can be determined using the proposed method by calculating the horizontal movement and vertical stain at different borehole depths.

Fluid-solid coupling model for studying wellbore instability in drilling of gas hydrate bearing sediments

As the oil or gas exploration and development activities in deep and ultra- deep waters become more and more, encountering gas hydrate bearing sediments （HBS） is almost inevitable. The variation in temperature and pressure can destabilize gas hydrate in nearby formation around the borehole, which may reduce the strength of the formation and result in wellbore instability. A non-isothermal, transient, two-phase, and fluid-solid coupling mathematical model is proposed to simulate the complex stability performance of a wellbore drilled in HBS. In the model, the phase transition of hydrate dissociation, the heat exchange between drilling fluid and formation, the change of mechanical and petrophysical properties, the gas-water two-phase seepage, and its interaction with rock deformation are considered. A finite element simulator is developed, and the impact of drilling mud on wellbore instability in HBS is simulated. Results indicate that the re- duction in pressure and the increase in temperature of the drilling fluid can accelerate hydrate decomposition and lead to mechanical properties getting worse tremendously. The cohesion decreases by 25% when the hydrate totally dissociates in HBS. This easily causes the wellbore instability accordingly. In the first two hours after the formation is drilled, the regions of hydrate dissociation and wellbore instability extend quickly. Then, with the soaking time of drilling fluid increasing, the regions enlarge little. Choosing the low temperature drilling fluid and increasing the drilling mud pressure appropriately can benefit the wellbore stability of HBS. The established model turns out to be an efficient tool in numerical studies of the hydrate dissociation behavior and wellbore stability of HBS.

STABILITY OF BOREHOLES IN A GEOLOGIC MEDIUM INCLUDING THE EFFECTS OF ANISOTROPY

An analytical formulation is developed to investigate the stability of a deep, inclined borehole drilled in a geologic medium and subjected to an internal pressure and a non_hydrostatic stress field. The formulation consists of a three_dimensional (3_D) analysis of stresses around a borehole, combined with internal pressurization of the borehole to obtain an approximate solution of the overall stress distribution. The orientation of the borehole, the in_situ stresses and bedding plane can all be arbitrarily related to each other to represent the actual field situations. Both tensile failure and shear failure potentials of a borehole are investigated. The failure criteria applied assume that when the least principal stress exceeds the strength of the formation in tension, a tensile failure occurs. Shear failure is represented using the modified Drucker_Prager failure criterion for anisotropic materials. A parametric study is carried out to assess the effect of material anisotropy, bedding plane inclination and in_situ stress conditions on borehole stability. Results of the parametric study indicate that wellbore stability is significantly influenced by a high borehole inclination, high degree of material anisotropy, in_situ stress conditions and high formation bedding plane inclination. The stability of a borehole in an elasto_plastic medium is also investigated. In order to evaluate the extent of the plastic zone around a borehole and the effect of anisotropy of the material on this plastic zone, a mathematical formulation is developed using theories of elasticity and plasticity. The borehole is assumed to be vertical, subjected to hydrostatic stresses, and drilled in a transversely isotropic geologic medium. A parametric study is carried out to investigate the effect of material anisotropy on the plastic behavior of the geologic medium. Results indicate that the stress distribution around a borehole, the extent of the plastic zone, and the failure pressure are influenced by the degree of material anisotropy and value of in_situ overburden stresses. It was observed that the borehole becomes less stable as the degree of anisotropy of the geologic medium increases.

Effects of creep characteristics of natural gas hydrate-bearing sediments on wellbore stability

Natural gas hydrate(NGH)reservoirs consist of the types of sediments with weak cementation,low strength,high plasticity,and high creep.Based on the kinetics and thermodynamic characteristics of NGH decomposition,herein a heat-fluid-solid coupling model was established for studying the wellbore stability in an NGH-bearing formation to analyze the effects of the creep characteristics of NGH-bearing sediments during long-term drilling.The results demonstrated that the creep characteristics of sediments resulted in larger plastic yield range,thus aggravating the plastic strain accumulation around the wellbore.Furthermore,the creep characteristics of NGH-bearing sediments could enhance the effects induced by the difference in horizontal in situ stress,as a result,the plastic strain in the formation around the wellbore increased nonlinearly with increasing difference in in situ stress.The lower the pore pressure,the greater the stress concentration effects and the higher the plastic strain at the wellbore.Moreover,the lower the initial NGH saturation,the greater the initial plastic strain and yield range and the higher the equivalent creep stress.The plastic strain at the wellbore increased nonlinearly with decreasing initial saturation.

Sensitivity analysis of geomechanical parameters affecting a wellbore stability

Wellbore stability analysis is a growing concern in oil industries. There are many parameters affecting the stability of a wellbore including geomechanical properties (e.g., elastic modulus, uni-axial compressive strength (UCS) and cohesion) and acting forces (e.g., field stresses and mud pressure). Accurate determination of these parameters is time-consuming, expensive and sometimes even impossible. This work offers a systematic sensitivity analysis to quantify the amount of each parameter’s effect on the stability of a wellbore. Maximum wellbore wall displacement is used as a stability factor to study the stability of a wellbore. A 3D finite difference method with Mohr model is used for the numerical modeling. The numerical model is verified against an analytical solution. A dimensionless sensitivity factor is developed in order to compare the results of various parameters in the sensitivity analysis. The results show a different order of importance of parameters based on rock strength. The most sensitive properties for a weak rock are the maximum horizontal stress, internal friction angle and formation pressure, respectively, while for a strong rock, the most sensitive parameters are the maximum horizontal stress, mud pressure and pore pressure, respectively. The amount of error in wellbore stability analysis inflicted by the error in estimation of each parameter was also derived.

Wellbore stability analysis to determine the safe mud weight window for sandstone layers

The wellbore stability of a vertical well through the sandstone reservoir layers of the Asmari oil-bearing formation in south-west Iran is investigated.The safe drilling-fluid density range for maintaining wellbore stability is determined and simulated using FLAC3 D software and a finite volume model established with drilled strata geomechanical features.The initiation of plastic condition is used to determine the safe mud weight window(SMWW)in specific sandstone layers.The effects of rock strength parameters,major stresses around the wellbore and pore pressure on the SMWW are investigated for this wellbore.Sensitivity analysis reveals that a reduction in cohesion and internal friction angle values leads to a significant narrowing of the SMWW.On the other hand,the reduction of pore pressure and the ratio between maximum and minimum horizontal stresses causes the SMWW to widen significantly.The ability to readily quantify changes in SMWW indicates that the developed model is suitable as a well planning and monitoring tool.

Investigation on influence of drilling unloading on wellbore stability in clay shale formation

Wellbore collapse frequently happens in the clay shale formation.To maintain wellbore stability,appropriate mud pressure is a vital factor.When clay formation is opened,drilling unloading occurs,modifying rock structure and strength at the wall of borehole,which affects the selection of mud pressure.Currently,mechanism of drilling unloading is still poorly understood which in return will bring a concern to wellbore stability.Therefore,in this study,a combination of triaxial compressive test and ultrasonic wave test has been used to simulate drilling unloading and analyze its mechanism.Results indicate that more void space is created inside the clay shale sample due to unloading.This structure change leads to a decline of strength and acoustic amplitude.Additionally,unloading influence is depended on varying drilling unloading parameters.Small unloading range and fast unloading rate are able to enhance stability.With various degrees of unloading impact,collapse pressure equivalent density has a clear modification,proving that unloading is a non-negligible influencing factor of wellbore stability.Besides,the unloading effect is much stronger in large confining pressure,implying that more attention should be given to unloading when drilling is in extreme deep or high geostress formation.Findings in this paper can offer theoretical guidance for drilling in the clay shale formation.

Research regarding coal-bed wellbore stability based on a discrete element model

Wellbore instability is a key problem restricting efficient production of coal-bed methane. In order to perform thorough and systematic research regarding coal-bed wellbore stability problems, a new discrete element model which fully considers the features of cleat coal-beds is established based on the Kirsch equation. With this model, the safe pipe tripping speed, drilling fluid density window and coal- bed collapse/fracture pressure are determined; in addition, the relationships between pipe tripping speed and pipe size, cleat size, etc. and wellbore stability are analyzed in the coal-bed drilling and pipe tripping processes. The case studies show the following results： the wellbore collapses （collapse pressure： 4.33 MPa） or fractures （fracture pressure： 12.7 MPa） in certain directions as a result of swab or surge pressure when the pipe tripping speed is higher than a certain value; the cleat face size has a great influence on wellbore stability, and if the drilling fluid pressure is too low, the wellbore is prone to collapse when the ratio of the face cleat size to butt cleat size is reduced; however, if the drilling fluid pressure is high enough, the butt cleat size has no influence on the wellbore fracture; the factors influencing coal-bed stability include the movement length, pipe size, borehole size.

Critical condition study of borehole stability during air drilling

The purpose of this paper is to establish the existence of the critical condition of borehole stability during air drilling. Rock Failure Process Analysis Code 20 was used to set up a damage model of the borehole excavated in strain-softening rock. Damage evolution around the borehole was studied by tracking acoustic emission. The study indicates that excavation damaged zone （EDZ） is formed around borehole because of stress concentration after the borehole is excavated. There is a critical condition for borehole stability; the borehole will collapse when the critical damage condition is reached. The critical condition of underground excavation exists not only in elastic and ideal plastic material but in strainsoftening material as well. The research is helpful to developing an evaluation method of borehole stability during air drilling.

Time-dependent borehole stability in hard-brittle shale

Rock damage appears in brittle shale even prior to peak stress(i.e.,before failure)due to the occurrence of microcracks in these rocks.In this work,a coupled hydromechanical model was built by incorporating the mechanical and fluid seepage induced stresses around a wellbore during drilling.The borehole instability mechanism of hard-brittle shale was studied.The results show that even if a well is simply drilled into a hard-brittle shale formation,the formation around the borehole can be subjected to rock damage.The maximum failure ratio of the formation around the borehole increases with drilling time.A lower drilling fluid density corresponds to a faster increase in the failure ratio of the borehole with time and a shorter period of borehole collapse.When the initial drilling fluid density is too low,serious rock damage occurs in the formation around the borehole.Even though a high-density drilling fluid is used after drilling,long-term borehole stability is difficult to maintain.While drilling in hard-brittle shale,drilling fluid with a proper density should be used rather than increasing the density of the drilling fluid only after borehole collapse occurs,which is more favorable for maintaining long-term borehole stability.

Determine Stability Wellbore Utilizing by Artificial Intelligence Systems and Estimation of Elastic Coefficients of Reservoir Rock

Rock elastic properties such as Young’s modulus, Poisson?s ratio, plays an important role in various stages upstream of such as borehole stability, hydraulic fracturing in laboratory scale for observing mechanical properties of the reservoir rock usually using conventional cores sample that obtained from underground in reservoir condition. This method is the most common and most reliable way to get the reservoir rock properties, but it has some weaknesses. Currently, neural network techniques have replaced usual laboratory methods because they can do a similar operation faster and more accurately. To obtain the elastic coefficient, we should have compressional wave velocity (VP), shear wave (Vs) and density bulk due to high cost of (Vs) measurement and low real ability of estimation through the (Vp) and porosity. Therefore in this study, neural networks were used as a suitable method for estimating shear wave, and then elastic coefficients of reservoir rock using different relationships were predicted. Neural network used in this study was not like a black box because we used the results of multiple regression that could easily modify prediction of (Vs) through appropriate combination of data. The same information that were intended for multiple regression were used as input in neural networks, and shear wave velocity was obtained using (Vp) and well logging data in carbonate rocks. The results showed that methods applied in this carbonate reservoir was successful, so that shear wave velocity was predicted with about 92% and 95% correlation coefficient in multiple regression and neural network method, respectively.

A cost-effective chemo-thermo-poroelastic wellbore stability model for mud weight design during drilling through shale formations

Drilling through chemically-active shale formations is of special importance due to time-dependent drilling fluideshale interactions.The physical models presented so far include sophisticated input parameters,requiring advanced experimental facilities,which are costly and in most cases unavailable.In this paper,sufficiently-accurate,yet highly practical,models are presented containing parameters easilyderived from well-known data sources.For ion diffusivity coefficient,the chemical potential was formulated based on the functionality of water activity to solute concentration for common solute species in field.The reflection coefficient and solute diffusion coefficient within shale membrane were predicted and compared with experimental measurements.For thermally-induced fluid flow,a model was utilized to predict thermo-osmosis coefficient based on the energy of hydrogen-bond that attained a reasonably-accurate estimation from petrophysical data,e.g.porosity,specific surface area(SSA),and cation exchange capacity(CEC).The coupled chemo-thermo-poroelastic governing equations were developed and solved using an implicit finite difference scheme.Mogi-Coulomb failure criterion was adopted for mud weight required to avoid compressive shear failure and a tensile cut-off failure index for mud weight required to prevent tensile fracturing.Results showed a close agreement between the suggested model and experimental data from pressure transmission tests.Results from a numerical example for a vertical wellbore indicated that failure in shale formations was time-dependent and a failure at wellbore wall after 85 min of mudeshale interactions was predicted.It was concluded that instability might not firstly occur at wellbore wall as most of the conventional elastic models predict;perhaps it occurs at other points inside the formation.The effect of the temperature gradient between wellbore and formation on limits of mud window confirmed that the upper limit was more sensitive to the temperature gradient than the lower limit.

Wellbore stability model in shale formation under the synergistic effect of stress unloading-hydration

According to the transversely isotropic theory and weak plane criterion, and considering the mechanical damages due to stress unloading and hydration during drilling, a shale wellbore stability model with the influence of stress unloading and hydration was established using triaxial test and shear test. Then, factors influencing the wellbore stability in shale were analyzed. The results indicate that stress unloading occurs during drilling in shale. The larger the confining pressure and axial stress, the more remarkable weakening of shale strength caused by stress unloading. The stress unloading range is positively correlated with the weakening degree of shale strength. Shale with a higher development degree of bedding is more prone to damage along bedding. In this case, during stress unloading, the synergistic effect of weak structural plane and stress unloading happens, leading to a higher weakening degree of shale strength and poorer mechanical stability, which brings a higher risk of wellbore instability. Fluid tends to invade shale through bedding, promoting the shale hydration. Hydration also can weaken shale mechanical stability, causing the decline of wellbore stability. Influence of stress unloading on collapse pressure of shale mainly occurs at the early stage of drilling, while the influence of hydration on wellbore stability mainly happens at the late stage of drilling. Bedding, stress unloading and hydration jointly affect the wellbore stability in shale. The presented shale wellbore stability model with the influence of stress unloading and hydration considers the influences of the three factors. Field application demonstrates that the prediction results of the model agree with the actual drilling results, verifying the reliability of the model.

Influence of the characteristics of fault gouge on the stability of a borehole wall

How to find more effective way to stabilize the borehole wall in the fault gouge section is the key technical challenge to control the stability of the borehole wall in the Wenchuan fault gouge section during the process of core drilling. Here we try to describe the characters of deep fault gouge in fracture zones from the undisturbed fault gouge samples which are obtained during the core drilling. The X- Ray Diffraction （XRD）, X-Ray Fluorescence （XRF） and Scanning Electron Microscope （SEM） provided the detailed information of the fault gouge＇s microscopic characteristics on the density, moisture content, expansibility, dispersity, permeability, tensile strength and other main physical-mechanical properties. Based on these systematic experimental studies above and analysis of the fault gouge instability mechanism, a new technical procedure to stabilize the borehole wall is proposed -- a low water and a low loss low permeability drilling fluid system that consists of 4% day ＋ 0.5% CMC-HV ＋ 2% S-1 ＋ 3%sulfonated asphalt ＋ 1% SMC ＋ 0.5% X-1 ＋ 0-5% T type lubricant ＋ barite for core drilling in fault gouge sections.

Micro/nano structured oleophobic agent improving the wellbore stability of shale gas wells

Through embedding modified nano-silica particles on the surface of polystyrene using the method of Pickering emulsion polymerization,a kind of nano/micro oleophobic agent named OL-1 was developed.The effects of OL-1 on the rock surface properties and its performance in inhibiting the oil phase imbibition into the rock were explored.The performance and mechanisms of OL-1 in improving the wellbore stability of shale gas wells were evaluated and analyzed.OL-1 could absorb on the surface of the shale core to form a membrane with a micro-nano two-stage roughness,making the surface energy of the core decrease to 0.13 mN/m and the contact angle of the white oil on the core surface increase from 16.39°to 153.03°.Compared with the untreated capillary tube,when immersed into 3#white oil,the capillary tube treated by OL-1 had a reversal of capillary pressure from 273.76 Pa to-297.71 Pa,and the oil imbibition height inside the capillary tube decreased from 31 mm above the external liquid level to 33 mm below the external liquid level.The amount of oil invading into the rock core modified by OL-1 decreased by 64.29%compared with the untreated one.The shale core immersed into the oil-based drilling fluids with 1%OL-1 had a porosity reduction rate of only 4.5%.Compared with the core immersed in the drilling fluids without OL-1,the inherent force of the core treated by 1%OL-1 increased by 24.9%,demonstrating that OL-1 could effectively improve the rock mechanical stability by inhibiting oil phase imbibition.

Effects of Sorptive Tendency of Shale on Borehole Stability

Interactions between aqueous drilling fluids and clay minerals have been identified as an important factor in wellbore instability of shale formations. Current wellbore stability models consider the interactions between aqueous drilling fluids and pore fluid but the interactions with shale matrix are neglected. This study provides a realistic method to incorporate the interaction mechanism into wellbore stability analysis through laboratory experiment and mathematical modeling. The adsorption isotherms of two shale rocks, Catoosa Shale and Mancos Shale are obtained. The adsorption isotherms of the selected shales are compared with those of other shale types in the literature. This study shows that the adsorption theory can be used to generalize wellbore stability problem in order to consider the case of non-ideal drilling fluids. Furthermore, the adsorption model can be combined with empirical correlations to update the compressive strength of shale under downhole conditions. Accordingly, a chemo-poro-elastic wellbore stability simulator is developed to explore the stability of transversely isotropic shale formations. The coupled transport equations are solved using an implicit finite difference method. The results of this study indicate that the range of safe mud weight reduces due to the moisture adsorption phenomenon.