Wellbore Stability Prediction Research Articles

An insight into modeling wellbore stability using the extended Mogi-Coulomb criterion and poly-axial test data

The cost of drilling oil and gas wells is likely to be charged by billions of dollars each year due to wellbore stability problems. In engineering practice, a linear poroelasticity stress model in combination with a rock strength criterion is commonly used to determine a minimum mud weight for stable well drilling. In this paper, new models for predicting the stability of vertical wellbores using the nonlinear form of Mogi criterion and poly-axial test results were perfumed. Afterward, by applying analytical models to the real field data, the applicability of the models has been verified. From comparing the results of this nonlinear and the liner Mogi-Coulomb criterions, the impact of the nonlinearity on the wellbore stability prediction has been identified. Thus, the results of nonlinear form of Mogi failure criterion were very close to the field mud weight used to successfully drill the borehole.

A New Model for Real-Time Prediction of Wellbore Stability Considering Elastic and Strength Anisotropy of Bedding Formation

Severe wellbore stability issues were reported while drilling in laminated formation with weak planes such as beddings. To accurately determine the safe mud weight according to the changing environment is of primary importance for safety control of drilling. Considering both the elastic and strength anisotropy of bedding formation, a novel theoretical model is established and the stress and failure around wellbores are analyzed. The accuracy and applicability of the theoretical model is verified by in situ field data. For the purpose of fulfilling real-time prediction, the method flowchart of programming is also provided. The results show that the model built can be conveniently used to predict the stress distribution, failure area, and collapse and fracture pressure while drilling, and rather good predictions can be made compared to real field data. In addition, the inhomogeneity of in situ stress and elastic parameters affect the upper limit of the safe mud weight window (SMWW) greater than the lower limit. Negative SMWW may appear with the direction change of the wellbore or weak plane, especially when the azimuths of them change. As to the magnitude of SMWW, the anisotropic effects of Young’s modulus are greater than the Poisson’s ratio. The method established in this paper can greatly help with the precise prediction of wellbore stability as drilling proceeds in bedding formation.

A porothermoelastic wellbore stability model for riserless drilling through gas hydrate-bearing sediments in the Shenhu area of the South China Sea

Wellbore instability during the gas hydrate drilling process frequently occurs due to the metastable character of sediment-hosted hydrates and weakly consolidated sediments. An accurate prediction of wellbore stability in gas hydrate drilling is very important. In this paper, a transient heat transfer model between the wellbore and sediment in a gas hydrate reservoir is proposed to simulate temperature profiles inside the drilling string and annulus. Using these temperature profiles, a porothermoelastic model is proposed to compute the temperature and pore pressure field in the entire formation during riserless drilling. Then, the thermodynamic stability of the gas hydrate and wellbore stability are analysed. The findings indicate that it is not necessary to use low-temperature drilling mud during riserless drilling. The risk of in situ hydrate dissociation is very low with a drilling mud density of 1.1 g/cm3. Then, a safe mud density window is obtained for future riserless drilling in the gas hydrate reservoirs in the Shenhu area.

Elastic properties of rock salt in the Santos Basin: Relations and spatial predictions

Most subsurface rock models consider salt bodies as homogenous masses and set to evaporite minerals constant values of elastic properties such as density, compressional and shear velocities, Young's modulus and Poisson's ratio. Lithological analyzes of outcrops and wells indicate that evaporites present large vertical and lateral heterogeneities. Recent studies have demonstrated that the knowledge of the elastic properties of rock salt can substantially benefit velocity modeling, seismic imaging, reservoir geomechanical analysis, prediction of wellbore stability and calculation of optimum fluid weight. However, few papers document the spatial estimation of elastic properties for salt formations. We propose an approach to characterize the internal structures of the salt bodies in the Santos Basin, offshore Brazil, using well and 3D seismic data. It starts with a rock-physics analysis at well-log scale, which reveals that the elastic properties of rock salt are highly correlated. Once the relationships of the elastic properties are established, we explore the functionality of the empirical equations as property predictors. We demonstrate that the elastic properties can be empirically estimated from compressional velocity. The comparison between the estimated and the measured well logs validates the estimation. Then, we perform the seismic inversion to generate the spatial distribution of the acoustic impedance. We derive compressional and shear velocities, density, Young's modulus and Poisson's ratio volumes by applying the empirical equations to the acoustic impedance volume. The blind well points out that, through this workflow, the seismic data can successfully predict the elastic properties of the salt formation in undrilled portions.

Investigating the Relation Between Sorption Tendency and Hydraulic Properties of Shale Formations

Routine measurement of hydraulic diffusivity of ultralow permeability rocks, such as shale, is a prolonged process. This study explores the effects of a sorptive characteristic of the porous medium on hydraulic diffusivities of shale rocks. The examined rock types include Mancos Shale, Catoosa Shale, Eagle Ford Shale, and core samples from the Gulf of Mexico. First, the adsorption isotherms of the selected shale rocks were obtained. Then, the hydraulic properties of the selected shale rocks were determined using Shale/Fluid Interaction Testing Cell, which employs pore pressure transmission technique. The experimental results show that the moisture content of shale is correlated with water activity using a multilayer adsorption theory. It is found that the adsorption isotherms of various shale formations can be scaled using their respective cation exchange capacity (CEC) into a single adsorption curve. Analyzing the transient pore pressure response in the downstream side of shale sample allows calculating the transport coefficients of shale samples. Hydraulic properties of shales are obtained by matching the pore pressure history with one-dimensional coupled fluid flow model. The experimental results indicate that sorptive properties can be inversely related to the hydraulic diffusivity of shale rocks. It is found that with an increase in the magnitude of sorption potential of shale, the hydraulic diffusivity decreases. This study is useful for shale characterization and provides a correlation, which can have various applications including, but not limited to, wellbore stability prediction during well planning.

Prediction of Wellbore Stability in Conglomerate Formation Using Discrete Element Method

Wellbore collapse and drilling fluid leakage are prone to occur when drilling a conglomerate formation. The conventional method for predicting wellbore stability cannot achieve sufficient accuracy when used in conglomerate formations. In this study, the particle size distribution in the conglomerate formation is characterized by the statistics of particle size analysis. Based on microstructure analysis and laboratory tri-axial tests, physical and mechanical properties of conglomerate can be obtained. Discrete element method, by particle flow code software $$\hbox {PFC}^{2\mathrm{D}}$$ , is applied to simulate the failure process of the conglomerate formation near the borehole region and investigate the influence of gravel size distribution, drilling mud density and fluid infiltration on the severity of wellbore instability. The simulation results show that the process of wellbore instability within the conglomerate formation correlates with the particle size of the gravels and their spatial distribution: in the fine-grained conglomerate formation, the cracks dominantly extend toward the direction of maximum horizontal stress; in the coarse-grained conglomerate formation, the cracks initially generate around large gravels and preferentially extend toward the gravel-concentrated zone. In addition, the variation of drilling mud density substantially affects the number of cracks in terms of mechanical analysis. The favorable mud density for specific conglomerate formation is found to minimize crack numbers. Further, while considering fluid infiltration into formation, more cracks should be accounted and worse instability state is reached in comparison with counterpart without infiltration. In this sense, practical operations are recommended to allow for the pressure equilibrium and sealing capability of drilling fluid.

The geology of offshore drilling through basalt sequences: Understanding operational complications to improve efficiency

Offshore drilling in basins with a significant basaltic component poses a number of complications to drilling operations. These include slow and variable rates of penetration (ROP), drilling fluid losses, drill bit or string sticking, overpressured formations, wellbore spalling and collapse. In this contribution we investigate features of large igneous province (LIP) volcanic facies that may directly contribute to drilling complications. Combining borehole and field based examples we identify highly vesicular brecciated lava flow tops and hydro-volcanic facies as a major potential cause of catastrophic drilling fluid losses. The risk for drilling losses is generally higher in the upper parts of thick volcanic successions where hydrothermal secondary mineralization and alteration may be less pervasive. We demonstrate how these facies may be identified early by integrating real time mud logging data with characteristic drill cuttings and LWD (logging while drilling) wireline data as it becomes available. We highlight the potential of basaltic formations to maintain porosity and permeability to greater depths than is typical for sediments due to the high compressive strength of crystalline basalt frameworks. The heterogeneous sub surface distribution of key volcanic facies commonly includes intimate mixing and layering of hard and dense with soft and weak volcanic rock which may promote complex in-situ stresses to develop during burial compaction. Where this occurs, wellbore stability predictions such as the fracture and wellbore collapse gradients for volcanic sequences may deviate from those expected in basin equivalent sedimentary sequences. Examples of swelling volcanic clay horizons, unstable volcaniclastic sequences, and intrusion related ledge effects are used to characterize the main causes of drill bit and string sticking. A greater understanding of drilling complications encountered within prospective areas containing volcanic sequences is needed if better pre-drilling risk assessment, cost prediction, real-time identification and mitigation is to be achieved.

Geomechanical-Evaluation Enabled Successful Stimulation of a High-Pressure/High-Temperature Tight Gas Reservoir in Western China

SummaryThe Keshen reservoir in China is a deep, tight-gas-sandstone reservoir under high tectonic stress with reservoir pressure at more than 16,000 psi (110 MPa) and temperatures up to 165°C. Development wells for this field are in excess of 6500 m in true vertical depth (TVD). Stimulation is required to provide sufficiently high production rates that compensate for the high cost of drilling and completing wells. Hydraulic-fracture design and execution must be optimal to ensure economic production.To effectively stimulate a more-than-200-m-thick sandstone reservoir with consistently high performance, it is necessary to understand the mechanical behavior of the reservoir, especially mechanical properties and in-situ stresses because the two control the creation and propagation of each hydraulic fracture. The mechanical behavior is complicated by high tectonic stresses, significant compaction, and high overpressure.To gain an in-depth understanding of the mechanical properties and in-situ stresses of the Keshen reservoir, an integrated geomechanical evaluation was conducted. The evaluation used the core from two wells, KS205 and KS207, and log data obtained from 15 wells including the wells with core evaluation in the field. A laboratory-testing program to investigate the mechanical behavior of the reservoir sandstone under realistic in-situ stresses, pore pressures, and temperature was performed. The description of mechanical behavior obtained from the laboratory testing was used to calibrate and augment mechanical Earth models (MEMs) constructed from well-log data. The reliability of the completed MEMs was validated through comparison between wellbore-stability predictions with observation of borehole failure from the borehole-microresistivity image.The geomechanics information was delivered to the stimulation-engineering team. Hydraulic-fracture design and execution was conducted on the basis of this information. The outcome of hydraulic fracturing was very encouraging.This study demonstrated that successful stimulation of a tight reservoir in high pressure/high temperature (HP/HT) relies on integrated geomechanical analysis.

Wellbore stability analysis based on a new strength criterion

Wellbore stability is critical to the overall safety of drilling. The adoption of a better strength criterion greatly improves the accuracy of wellbore stability prediction. Although the Mohr–Coulomb strength criterion is widely used for wellbore stability analysis, it is difficult to use its linear form to accurately describe the nonlinear characteristics of the rock strength under different confining pressures. In the present study, we developed a new criterion, which we refer to as the single-parameter parabolic criterion, for wellbore stability analysis based on the Mohr strength criterion with a parabolic failure envelope. The fitting precisions of the Mohr–Coulomb criterion, the Hoek–Brown criterion, and the developed single-parameter parabolic criterion were statistically analyzed. It was found that the single-parameter parabolic criterion accurately describes the relation between the rock strength and confining pressure. Based on the single-parameter parabolic strength criterion, a collapse pressure calculation model for vertical and inclined wells was developed and applied to a field case, and the new criterion was further demonstrated to be superior to the Mohr–Coulomb criterion.

Continuous deep microseismic monitoring of the Karachaganak Field, Kazakhstan: integrating reservoir geoscience, drilling and engineering

The Karachaganak Field is an oil and gas condensate supergiant field located in the western Kazakhstan Pricaspian Basin. As part of the challenge to improve reservoir knowledge, KPO has been continuously monitoring the reservoir using a microseismic array deployed downhole since February 2009. Continuous deep recording of microseismic activity is an innovative technique for reservoir monitoring; progressive refinements were made to fine-tune the acquisition and processing techniques. By December 2010, 8074 events had been detected and, from this group, 2556 events have been located. Events within the reservoir were recorded up to 8 km from the array to a depth of 5 km with moment magnitudes (Mw) ranging from −2.4 to +1. Microseismic events are continuously located and their spatial and temporal distribution analysed. This basic analysis is the input to an integrated study that considers the static model for the reservoir, in addition to dynamic and operational aspects such as production and injection rates, pressure baffles, drilling behaviour and casing perforations. The results to date indicate valuable reservoir information concerning the location of lateral and vertical reservoir pressure baffles and delineation of zones of instability at the reservoir–seal interface, important for well integrity issues. This new information is helping to improve dynamic and geomechanical reservoir models and also wellbore stability predictions. This article presents the details of the Karachaganak microseismic array and how microseismic events were located. Discussion follows on the interpretation and the possible impact on reservoir monitoring and drilling. The Karachaganak array is one of the deepest installations of a passive microseismic monitoring system and also represents one of the longer periods of continuous monitoring, with two years of data available.

Pore-Pressure and Wellbore-Stability Prediction To Increase Drilling Efficiency

Pore-Pressure and Wellbore-Stability Prediction To Increase Drilling Efficiency

Sixty Days Ahead of Schedule: Reducing Drilling Risk at Valhall Using Computational Geomechanics

Summary The Valhall field is an overpressured, undersaturated Upper Cretaceous chalk reservoir located in the Norwegian sector of the North Sea. The reservoirs consist of weak chalk. The weak chalk results in significant reservoir compaction, exceeding 10 m in places, and corresponding seafloor subsidence, exceeding 6 m above the center of the field. Previous papers have documented the increasing drilling challenges in the shale overburden at Valhall because of the subsidence. This paper presents the computational-geomechanics technology developed and implemented to assist drilling into the highly depleted and compacted crest from the new water-injection platform at Valhall. The work focuses on handling the stress changes occurring in the overburden above a compacting reservoir and not the more traditional situation associated with depletion-induced fracture-gradient changes in the reservoir itself. The technology is based on a history-matched full-field finite-element-based geomechanics model to calculate stresses, strains, and displacements. The results are exported from the finite-element model (FEM) to a geological modeling software to perform wellbore-stability calculations using BP best practices for prediction of wellbore stability. In this environment, one can also easily use as supporting data 4D seismic from the permanent life-of-field seismic array at Valhall. By calculating the operational mud-weight window over a high risk interval in the overburden, a good correlation to historical nonproductive time (NPT) was found. The methodology is used in detailed well planning where moving the well 50 m in one direction is the difference between problem-free drilling or huge drilling challenges. The paper presents the first application of this technology on a new water injector delivered 60 days ahead of schedule with reduced costs of approximately USD 20 million and with avoidance of a potential "train wreck" that could have cost USD 60 million.

Technology Focus: Wellbore Integrity, Sand Management, and Frac Pack (September 2009)

Technology Focus Technology development in our industry continues to boost efficiency and profitability in existing fields, while enabling exploration and development in more-remote and -hostile geological environments around the world. Wellbore integrity, sand management, and frac-pack-completion technologies each can have a tremendous effect on oil-/gas-asset performance. When each technical theme is linked to provide a comprehensive model, risk and uncertainty of asset design and operation can be diminished greatly. As an example of linking formation integrity to sand management, one of the papers highlighted this month describes how sand-control campaigns can morph, or change, over time as field performance is monitored, areas of improvement are identified, and solutions are implemented by use of new completion technologies. This sand-control-philosophy change stems from an understanding of the reservoir-failure mechanism, a thorough knowledge of sand-exclusion-device options, and careful consideration of completion-fluid-sensitivity performance. Furthermore, recent implementation of a new sand-control technology for extensive, stacked reservoir intervals provided an option that can significantly reduce rig time associated with the completion. A highlighted paper discusses this completion technique, describing execution for conventional gravel-pack and frac-pack sand-control completions. With regard to borehole-fluid exposure to the formation over time, another highlighted paper introduces a shale-core stability-test procedure that enables field-applicable comparisons of whole water-based muds. The differences in shale-stability preservation are striking. The results are presented in a fashion that blends good science and careful laboratory procedures with practical linkages to the field. Wellbore Integrity, Sand Management, and Frac Pack additional reading available at OnePetro: www.onepetro.org SPE 114273 • "Casing Ultradeep, Ultralong Salt Sections in Deep Water: A Case Study for Failure Diagnosis and Risk Mitigation in Record-Depth Well" by Jincai Zhang, SPE, Shell, et al. (See JPT, May 2009, Page 78.) SPE 120219 • "Prediction of Wellbore Stability Using 3D Finite-Element Model in a Shallow Unconsolidated Heavy-Oil Sand in a Kuwait Field" by K. Ahmed, SPE, Kuwait Oil Company, et al.

Plate tectonic structural geology to detailed field and prospect stress prediction

Arguably the first successful application of the theory of continental drift to petroleum exploration was in 1959 by the pioneers S. W. Carey and L. G. Weeks whose collaboration led to the discovery of the world class Gippsland Basin. Plate tectonics, as the theory is now known, was still nascent and not prominent during peak global oil exploration success in the 1960s. As discovery rates continue to decline, large scale description of separating and colliding continents has become increasingly impotent in the ever more complex hunt for the next barrel. Emphasis is turning from new basins and plays to smaller intra-basin discoveries related to a more detailed understanding of basin forming faults and their local stress effects on traps and trap geometries. Improved oil recovery is not only about finding new fields, but also demands detailed stress information for horizontal wellbore stability to economically and effectively increase reserves and recovery rates by extracting new oil from old fields. As a result, expensive wellbore based measurements have been deployed in the past 15 years. These precision measurements have then been averaged between wells for stress prediction but stress directions are known to vary abruptly by up to 90° over distances of less than 3 km. A solution lies in the seismic recognition of globally synchronous compressional pulses which, like a heartbeat, have added predictability of stress fields hence to stress analysis. This repetition of stress provides a workflow for stress consistent seismic interpretation that can predict horizontal and vertical changes in the direction of the maximum horizontal compressional component of a stress SH (SHD) and also in the magnitude of the stress, SHM. It is now possible to derive pre-drill at any desired point, important exploration and production variables such as stress related fault seal and open fracture orientation. Similarly, important reservoir development parameters such as fracture gradients and wellbore stability prediction will maximise recovery efficiencies and reduce development costs. This technique will also aid in effective carbon dioxide sequestration, a challenging new field of endeavour.

Assuring Stability in Extended-Reach Wells: Analyses, Practices, and Mitigations

This article, written by Technology Editor Dennis Denney, contains highlights of paper SPE 105405, "Assuring Stability in Extended-Reach Wells - Analyses, Practices, and Mitigations," by Stephen M. Willson and Stephen T. Edwards, BP plc; Anthony Crook and Adam Bere, Rockfield Software; Daniel Moos and Pavel Peska, GeoMechanics International; and Nigel Last, BP plc, prepared for the 2007 SPE/IADC Drilling Conference, Amsterdam, 20–22 February. While the departure lengths of proposed extended-reach-drilling (ERD) wells are becoming more challenging, wellbore-stability assurance technologies (both in the preplanning and execution phases) are developing at an equal pace. Several new developments in theoretical understanding and predictive capability of rock failure surrounding wells drilled at a high angle to bedding are described that are required to solve problems encountered in these challenging environments. Rigsite processes for the integration of this new understanding with real-time diagnostic measurement and monitoring provide the means to deliver borehole-stability assurance for ERD wells drilled in the most challenging environments. Introduction Approximately 10 years ago, the ERD program in the Niakuk field, North Slope, Alaska, was suspended because of severe wellbore-instability problems in the 8.5-in. sections of successive ERD wells. Studies to investigate these problems highlighted the importance of integrating results of wellbore-stability prediction, drilling-fluid optimization, hydraulics and cuttings transport, operational practices, and use of a pressure-while-drilling tool. There has been a steady progression in the vertical depth and horizontal-departure length of ERD wells. Wells with horizontal departures in excess of 40,000 ft at vertical depths of less than 10,000 ft are now considered as viable to access satellite reserves from existing facilities or, in the case of environmentally-sensitive arctic environments, to develop offshore fields from onshore locations. New understanding and predictive capability for assessing instability in wells drilled at high angles to bedding are presented. Wellbore Instability in ERD Wells Additional considerations are needed that are subtler compared with conventional high-angle wells, and extra assurance steps are necessary. Significant variations in seabed depth or ground elevation may occur along the ERD well path. Simple assessments of pore pressure, fracture gradient, and in-situ stresses will not apply in these cases. To predict pore pressures and fracture gradients accurately, the varying water depth must be taken into consideration. The lower fracture gradient (relative to that for a shallower-water vertical-well profile) existing over the long tangent section of extended-reach wells drilled from the escarpment to access deeper-water reserves is an important aspect in the well design. The presence of the free surface of the escarpment can reduce the magnitude of the near-surface fracture gradient below that which is expected for intra-basin locations. Failure to recognize this effect in the well-planning stage could lead to circulation losses in the tophole sections of the well. Where such problems are of particular concern, 2D or 3D finite-element predictions of stress states may be warranted.

Wellbore-Stability Predictions by Use of a Modified Lade Criterion

Summary The two most commonly used rock failure criteria in wellbore stability analyses are the Mohr–Coulomb criterion and the Drucker–Prager criterion. Neither of these is compatible with three-dimensional rock strength measurements that have explored the influence of the intermediate principal stress. This paper presents a modified Lade criterion which has the following desirable qualities: 1. it correctly describes the influence of the intermediate stress on rock strength, and therefore on wellbore stability, 2. it can be rearranged to give a closed-form solution for critical mud weight, for any wellbore orientation, and 3. only two rock strength parameters are required, such as cohesion and friction angle. The modified Lade criterion predicts critical mud weight values that are less conservative than those predicted by the Mohr–Coulomb criterion yet are not as unconservative as those predicted by the Drucker–Prager criterion. It also reveals that the required increase in mud weight when going from low hole angle to high hole angle is not as great as predicted by either the Mohr–Coulomb or Drucker–Prager criteria.

Wellbore-Stability Predictions Using a Modified Lade Criterion

This article is a synopsis of paper SPE 47251, "Wellbore-Stability Predictions Using a Modified Lade Criterion," by R.T. Ewy, SPE, Chevron Petroleum Technology Co., originally presented at the 1998 SPE/ISRM Eurock, Trondheim, Norway, 8-10 July.

Assessing The Risk Of Wellbore Instability In Horizontal And Inclined Wells

Abstract Wellbore instability can lead to expensive operational problems during the drilling, completion and production of horizontal and inclined wells. This paper reviews the direct and indirect symptoms of wellbore instability, its root causes, and various empirical and deterministic modelling approaches to predicting the risk of hole collapse or convergence. In general, linear elastic models that are only concerned with stability at the wellbore wall often give overly pessimistic predictions. An alternative approach, using the extent of the "yielded" zone around an unstable wellbore and the kinematics of rock detachment, is proposed for practical risk assessments. A case history for an open hole completed horizontal well in a limestone reservoir under high drawdown is described. General guidelines for conducting field-oriented stability assessments conclude the paper. Introduction Wellbore instability during the drilling, evaluation, completion and production phases of a well has become an increasingly important concern for many operators applying horizontal well technology. Traditional conservative completion methods for vertical wells are being challenged as operators attempt to reduce well costs and still derive the improved productivity and access to hydrocarbon reserves offered by horizontal wells. More recent horizontal well innovations include the use of underbalanced drilling techniques(l), slimhole completions, side track or re-entry wells with open hole build sections(2,3), and multiple laterals from a single vertical or horizontal wellbore(4). In applying these new technologies, there are often issues posed during the well planning stage where the risk of hole collapse in the short or long term must be addressed. In many cases, the selection of an optimal strategy to prevent or mitigate the risk of wellbore collapse might compromise one or more of the following other elements of the overall well design: the rate of penetration; the risk of differential sticking; drilled cuttings and mud disposal options; hole cleaning abilities; hole size, and consequently the completion and stimulation options available; formation damage risk; stimulation requirements; the ability to log the hole; and the selection of surface sand handling facilities (where sand production is anticipated). In many cases there may be insufficient experience with a given reservoir and the desired completion, hence the prior performance of vertical wells cannot be used, by itself, to guide the well design. This paper reviews the symptoms of wellbore instability and its fundamental causes. Published approaches to wellbore stability prediction will be described, particularly those which address the most common problems faced in developing normally to slightly under pressured oil and gas fields. Emphasis is placed on techniques and conditions applicable to Western Canada where there has been a rapid pace of horizontal well development, particularly with re-entry wells. Predictive techniques applicable to build, inclined or horizontal sections of a well, during the drilling, completion and subsequent production phases, will then be described. Selected case histories from the literature are cited and an example of a wellbore stability prediction for Shell Canada's first horizontal open hole completion is described. This paper will not review all the wellbore stability models which have been developed for vertical wells.

Advances in shale mechanics — the key to wellbore stability predictions : R.P. Steiger & P.K. Leung, Comprehensive rock engineering. Vol. 5, ed J.A. Hudson, (Pergamon), 1993, pp 629–639

Advances in shale mechanics — the key to wellbore stability predictions : R.P. Steiger & P.K. Leung, Comprehensive rock engineering. Vol. 5, ed J.A. Hudson, (Pergamon), 1993, pp 629–639