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.

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.

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.

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.

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.

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.

Geomechanical analysis of an oil field:Numerical study of wellbore stability and reservoir subsidence

Geomechanics as the knowledge of rock deformation and stability is an indispensable part of all field development plans.Conducting geomechanical analyses leads to a safer and more efficient operation otherwise different kinds of instability and distortion might occur.In this study,the geomechanical behavior of Ilam and Sarvak formations of an oil field in southwest of Iran was investigated.The research objectives can be summarized as wellbore stability evaluation and predicting the value of reservoir subsidence due to pressure drop as a result of reservoir fluid production.To fulfill these,a set of petrophysical logs run in the exploration well of this green field were collected.Next,using empirical correlations and statistical methods,required data for evaluating wellbore stability during drilling,specifying safe mud window to discover reservoir breakdown pressure,predicting the possibility of wellbore collapse in field lifetime,and assessing reservoir subsidence were determined.The results revealed that the average subsidence value as the consequence of production within 21 years is 0.275 ft Which is not significant.In terms of wellbore stability,it was concluded that all horizontal and vertical wells remain stable during this time period.Briefly to conclude,field development is not associated with alarming incidents from geomechanical aspect.

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.

The influence of water-based drilling fluid on mechanical property of shale and the wellbore stability

Because of high cost and pollution of oil-based drilling fluid,the water-based drilling fluid is increasingly used now.However,bedding planes and micro-cracks are rich in shale formation.When water-based drilling fluid contacts formation rock,it causes the propagation of crack and invasion of drilling fluid,which decrease shale strength and cause wellbore instability.In this paper,we analyzed influence of water-based drilling fluid on shale strength and failure mode by mechanics experiment.Based on those experimental results,considering the effect of bedding plane and drilling time,we established modeling of wellbore stability for shale formation.The result from this model indicates that in certain azimuth of horizontal well,collapsing pressure increases dramatically due to shale failure along with bedding plane.In drilling operation,those azimuths are supposed to be avoided.This model is applicable for predication of collapsing pressure in shale formation and offers reference for choosing suitable mud weight.

Wellbore stability analysis of layered shale based on the modified Mogi-Coulomb criterion

Borehole instability was frequently encountered during shale gas drilling.Most conventional models are not applicable to layered formation's wellbore stability analysis on account of anisotropic strength characteristic.In this study,an empirical equation for predicting anisotropic strength was implemented in the Mogi–Coulomb criterion to describe variations of cohesive strength and friction angle of shale formations.A collapse pressure model and its appropriate solution method for layered shale formations were proposed.The impact of different strength criteria and rock anisotropy type on rock strength and collapse pressure was investigated.The analysis indicated that the predicted strength of our modified criterion was usually higher than the weak plane failure criteria.The collapse pressure calculated by the modified Mogi–Coulomb criterion was lower than the weakplane failure criteria.Furthermore,it was more consistent with real mud weight.Additionally,the anisotropy type of rock notably influences wellbore stability.More significant anisotropy coefficients correspond to higher strengths,which results in smaller collapse pressure values.Improper anisotropy coefficients can over-or underpredict the collapse pressure.Reasonable estimates of collapse pressure of anisotropic rocks can be made through the modified Mogi–Coulomb criterion using limited experimental data and the anisotropy rock type.

A review of the shale wellbore stability mechanism based on mechanicalechemical coupling theories

Wellbore instability in hard brittle shale is a critical topic related to the effective exploitation of shale gas resources.This review first introduces the physicalechemical coupling theories applied in shale wellbore stability research,including total water absorption method,equivalent pore pressure method,elasticity incremental method of total water potential and non-equilibrium thermodynamic method.Second,the influences of water activity,membrane efficiency,clay content and drilling fluid on shale wellbore instability are summarized.Results demonstrate that shale and drilling fluid interactions can be the critical factors affecting shale wellbore stability.The effects of thermodynamics and electrochemistry may also be considered in the future,especially the microscopic reaction of shale and drilling fluid interactions.An example of this reaction is the chemical reaction between shale components and drilling fluid.

Fabrication of a Hydrophobic Hierarchical Surface on Shale Using Modified Nano-SiO_(2)for Strengthening the Wellbore Wall in Drilling Engineering

Wellbore stability is essential for safe and efficient drilling during oil and gas exploration and development.This paper introduces a hydrophobic nano-silica(HNS)for use in strengthening the wellbore wall when using a water-based drilling fluid(WBF).The wellbore-strengthening performance was studied using the linear swelling test,hot-rolling recovery test,and compressive strength test.The mechanism of strengthening the wellbore wall was studied by means of experiments on the zeta potential,particle size,contact angle,and surface tension,and with the use of a scanning electron microscope(SEM).The surface free energy changes of the shale before and after HNS treatment were also calculated using the contact angle method.The experimental results showed that HNS exhibited a good performance in inhibiting shale swelling and dispersion.Compared with the use of water,the use of HNS resulted in a 20%smaller linear swelling height of the bentonite pellets and an 11.53 times higher recovery of water-sensitive shale—a performance that exceeds those of the commonly used shale inhibitors KCl and polyamines.More importantly,the addition of HNS was effective in preventing a decrease in shale strength.According to the mechanism study,the good wellbore-strengthening performance of HNS can be attributed to three aspects.First,the positively charged HNS balances parts of the negative charges of clay by means of electrostatic adsorption,thus inhibiting osmotic hydration.Second,HNS fabricates a lotus-leaf-like surface with a micro-nano hierarchical structure on shale after adsorption,which significantly increases the water contact angle of the shale surface and considerably reduces the surface free energy,thereby inhibiting surface hydration.Third,the decrease in capillary action and the effective plugging of the shale pores reduce the invasion of water and promote wellbore stability.The approach described herein may provide an avenue for inhibiting both the surface hydration and the osmotic hydration of shale.

Development and evaluation of an electropositive wellbore stabilizer with flexible adaptability for drilling strongly hydratable shales

In order to overcome serious instability prob- lems in hydratable shale formations, a novel electropositive wellbore stabilizer （EPWS） was prepared by a new approach. It has good colloidal stability, particle size dis- tribution, compatibility, sealing property, and flexible adaptability. A variety of methods including measurements of particle size, Zeta potential, colloidal stability, contact angle, shale stability index, shale dispersion, shale swelling, and plugging experiments were adopted to characterize the EPWS and evaluate its anti-sloughing capacity and flexible adaptability. Results show that the EPWS has advantages over the conventional wellbore stabilizer （ZX-3） in particle size distribution, colloidal stability, inhibition, compatibil- ity, and flexible adaptability. The EPWS with an average particle size of 507 nm and an average Zeta potential of 54 mV could be stable for 147 days and be compatible with salt tolerant or positive charged additives, and it also exhibited preferable anti-sloughing performance to hydrat- able shales at 77, 100, and 120 ~C, and better compatibility with sodium bentonite than ZX-3 and KC1. The EPWS can plug micro-fractures and pores by forming a tight external mud cake and an internal sealing belt to retard pressure transmission and prevent filtrate invasion, enhancing hydrophobicity of shale surfaces by adsorption to inhibithydration. The EPWS with flexible adaptability to tem- perature for inhibition and sealing capacity is available for long open-hole sections during drilling.

Improving the anti-collapse performance of water-based drilling fluids of Xinjiang Oilfield using hydrophobically modified silica nanoparticles with cationic surfactants

Wellbore instability,especially drilling with water-based drilling fluids(WBDFs)in complex shale for-mations,is a critical challenge for oil and gas development.The purpose of this paper is to study the feasibility of using hydrophobically modified silica nanoparticle(HMN)to enhance the comprehensive performance of WBDFs in the Xinjiang Oilfield,especially the anti-collapse performance.The effect of HMN on the overall performance of WBDFs in the Xinjiang Oilfield,including inhibition,plugging,lu-bricity,rheology,and filtration loss,was studied with a series of experiments.The mechanism of HMN action was studied by analyzing the changes of shale surface structure and chemical groups,wettability,and capillary force.The experimental results showed that HMN could improve the performance of WBDFs in the Xinjiang Oilfeld to inhibit the hydration swelling and dispersion of shale.The plugging and lubrication performance of the WBDFs in the Xinjiang Oilfield were also enhanced with HMN based on the experimental results.HMN had less impact on the rheological and filtration performance of the WBDFs in the Xinjiang Oilfield.In addition,HMN significantly prevented the decrease of shale strength.The potential mechanism of HMN was as follows.The chemical composition and structure of the shale surface were altered due to the adsorption of HMN driven by electrostatic attraction.Changes of the shale surface resulted in significant wettability transition.The capillary force of the shale was converted from a driving force of water into the interior to a resistance.In summary,hydrophobic nanoparticles presented afavorable application potential for WBDFs.

Analysis of a Strong-Inhibition Polyamine Drilling Fluid

Drilling technologies based on oil-based drillingfluids and strong inhibitory saltwaterfluids are affected by draw-backs such as downhole accidents where sticking and wellbore instabilities occur.Existing polyamine drillingfluids also exhibit problems such as easy decomposition and poor inhibition performances.In order to mitigate these issues,additives can be used,such as polyamine inhibitors and the synthesis of nanometerfiltrate reducers.Tests conducted in the frame of this study with a polyamine drillingfluid and such additives show that thisfluid has the same inhibitory,plugging,lubricating,and wellbore-stability performances as oil-based drillingfluids.However,it has long-term anti-wear performances even better than those of oil-based drillingfluids.The out-comes of a series of comparisons with other sample cases(other wells)are reported and the advantages related to the proposedfluid discussed in detail.

Research progress and application prospect of functional adhesive materials in the field of oil and gas drilling and production

By summarizing the composition,classification,and performance characterization of functional adhesive materials,the adhesion mechanisms of functional adhesive materials,such as adsorption/surface reaction,diffusion,mechanical interlocking,and electrostatic adsorption,are expounded.The research status of these materials in oil and gas drilling and production engineering field such as lost circulation prevention/control,wellbore stabilization,hydraulic fracturing,and profile control and water plugging,and their application challenges and prospects in oil and gas drilling and production are introduced comprehensively.According to the applications of functional adhesive materials in the field of oil and gas drilling and production at this stage,the key research directions of functional adhesive materials in the area of oil and gas drilling and production are proposed:(1)blending and modifying thermoplastic resins or designing curable thermoplastic resins to improve the bonding performance and pressure bearing capacity of adhesive lost circulation materials;(2)introducing low-cost adhesive groups and positive charge structures into polymers to reduce the cost of wellbore strengthening agents and improve their adhesion performance on the wellbore;(3)introducing thermally reversible covalent bond into thermosetting resin to prevent backflow of proppant and improve the compressive strength of adhesive proppant;(4)introducing thermally reversible covalent bonds into thermoplastic polymers to improve the temperature resistance,salt-resistance and water shutoff performance of adhesive water shutoff agents.

The assembly of a composite based on nano-sheet graphene oxide and montmorillonite

Graphene oxide （GO） nano-sheets were synthesized using a modified Hummers＇ method from graphite powder. The Raman spectrum of GO displayed a D-band at 1359 cm-1 and a G-band at 1594 cm-l. The ID/IG value of GO was calculated to be 0.97, suggesting the formation of new sp2 clusters upon reduction. A method was designed to investigate the assembly of the GO/montmorillonite （MMT） composite. After the addition of GO, the typical peaks of montmorillonite in FT-IR spectra shifted, indicating the assembly between GO and MMT. The D-band and G-band reduced sharply in the GO/MMT composite. More importantly, the D-band （1344 cm-1） and G-band （1574 cm 1） shifted significantly and the ID/ IG value of the GO/MMT composite was calculated to be 1.13, showing a change in the GO structure. In the addition of 0.04 wt% GO to MMT, the value of interlayer space （d） was up to 13.0 Ameasured by XRD due to the insertion of GO into MMT. The evident increases in contents of carbon atoms （26.59%） and nitrogen atoms （3.44%） indicate that GO was successfully combined with MMT. The nano-pores and clay sheets were not observed in the SEM image of GO/clay, but obvious wrinkles, while flexible sheets were observed in the typical scanning electron microscopy images of GO. This further proves that GO was combining with clay. The TEM image shows that the GO nano-sheets were tiled on the surface of MMT sheets. This observation suggests that a stable assembly structure was formed between GO sheets and MMT sheets. The change in particle size of MMT with the addition of GO shows that interaction occurred between GO sheets and MMT sheets, which was further confirmed by the results of zeta potential. Adsorption and insertion were the main mechanisms to assemble GO and MMT.

Super-amphiphobic, strong self-cleaning and high-efficiency water-based drilling fluids

Based on the amphiphobic theory on underground rock surface, a super-amphiphobic agent is developed and evaluated which can form nano-micro papilla structure on rock, filter cake and metal surface, reduce surface free energy, prevent collapse, protect reservoir, lubricate and increase drilling speed. With this super-amphiphobic agent as the core agent, a super-amphiphobic, strong self-cleaning and high-performance water-based drilling fluid system has been developed by combining with other agents based on drilled formation, and compared with high-performance water-based drilling fluid and typical oil based drilling fluid commonly used in oilfields. The results show that the super-amphiphobic, strong self-cleaning and high-performance water-based drilling fluid has better rheology, and high temperature and high pressure filtration similar with that of oil-based drilling fluid, inhibiting and lubricating properties close to oil based drilling fluid. Besides, the super-amphiphobic system is non-toxic, safe and environmentally friendly. Field tests show this newly developed drilling fluid system can prevent wellbore collapse, reservoir damage and pipe-sticking, increase drilling speed and lower drilling cost, meeting the requirement of safe, high efficient, economic and environmentally friendly drilling. Compared with other drilling fluids, this new drilling fluid system can reduce downhole complexities by 82.9%, enhance the drilling speed by about 18.5%, lower drilling fluid cost by 39.3%, and increase the daily oil output by more than 1.5 times in the same block.

A new environmentally friendly water-based drilling fluids with laponite nanoparticles and polysaccharide/polypeptide derivatives

Considering the increasing environmental pressure,environmentally friendly and high-performance water-based drilling fluids(WBDFs)have been widely studied in recent years to replace the commonly used oil-based drilling fluids(OBDFs).However,few of these drilling fluids are entirely composed of natural materials,which makes it difficult to achieve real environmental protection.Using laponite nanoparticles and various derivatives of natu ral mate rials,including cro sslinked starch,cellulose composite,gelatin ammonium salt,poly-l-arginine,and polyanionic cellulose,a kind of environmentally friendly water-based drilling fluid(EF-WBDF)was built for drilling in environment-sensitive areas.The properties of this EF-WBDF were evaluated by thermal stability tests on rheology,filtration,inhibition,and salt contamination.Besides,biological toxicity,biodegradability,heavy mental content and wheat cultivation tests were conducted to investigate the environmental factor of EF-WBDF.Results showed that EF-WBDF displayed satisfactory thermal resistance up to 150℃,and the rheological properties did not suffer significant fluctuation,showing potential application in high-temperature wells.The optimal rheological model of EF-WBDF was Herschel-Bulkley model.This EF-WBDF performed an eligible filtration of 14.2 mL at 150℃and a differential pressure of 3.5 MPa.This fluid could still maintain colloidal stability after being contaminated by 7.5%NaCl or 0.5%CaC1_(2).Meanwhile,rather low clay swelling degree of 2.44 mm and high shale recovery of more than 95%ensured the inhibitive capability of EF-WBDF.Furthermore,EF-WBDF presented a half maximal effective concentration(EC_(50))of51200 mg/L and a BOD/COD ratio of 47.55%,suggesting that EF-WBDF was non-toxic and easily biodegradable.The wheat cultivated in EF-WBDF could grow healthily,beneficial for reducing the adverse impact on ecological environment.The formed EF-WBDF has a promising future for drilling in environment-sensitive and high-temperature areas.

Investigation of production depletion rate effect on the ne ar-wellbore stresses in the two Iranian southwest oilfields|

Effect of depletion rate on wellbore stability due to production of oil from hydrocarbon-bearing reser-voirs is important and can result in a reduction of the reservoir pore pressure.A reduction in the reservoir pressure,in tum,results in a change in the stresses acting within the reservoir.If these changes are not well analyzed and applied in future calculations,we may be unsuccessful in some cases such as drilling infill wells or extended wells,forecast of sand production and optimum flow rate,preventing of casing collapse,etc.Therefore,knowing the stresses around the well at every stage of production is fundamental to the next calculations.In this paper,we recognized these changes in near-wellbore stresses using data from logging(image log,dipole sonic,full set log,mud log),production data,infor-mation from kick,blow out,loss etc.and determined it using Techlog software and theoretical calcu-lations.Three wells of two huge oilfields of sw Iran were investigated after depletion or production for long years.In each well,state of stresses were calculated in cases of safe drilling mud weight using log data and theoretical equations.At the end effect of depletion rate on wellbore stability was investigated in these three wells.