Contribution to the methodology of determining the optimum mud density-a case study from the o ff shore gas condensate fi eld D in the Persian Gulf

Drilling the wells using water based mud through shale formations, causes their exposure to serious time-dependent wellbore instability due to shale swelling. Operating companies, before drilling operations through demanding shale formations, usually conduct drilling fl uid optimization studies in order to defi ne the proper mud type, mud density, salt type and concentration for inhibition. Through the analysis of off set wells, they are interpreting data about mud fi ltrate breakouts into the rock formations and chemical potential mechanisms to understand their infl uence on the time-dependent wellbore instability. The main objective of this paper is to give an insight in time-dependent and mechanical wellbore instability problems faced while drilling the wells through diff erent shale formations in the gas condensate fi eld D in the Persian Gulf. The importance of drilling fl uid design optimization and solutions applied to overcome hole instability problems were analysed and highlighted. Besides the development of a model for mud density calculations, a concept of eff ective hoop stress and its infl uence on time dependent failure mechanisms is discussed. As a contribution to the method improvement, mud density calculation is verifi ed by taking into the consideration the relationship between pore pressure and eff ective hoop stress and it is based on measured data from Well A in gas condensate fi eld D from the Persian Gulf.


Introduction
Wellbore drilling operations in a phase foreseen for installation of one of the intermediate casings, generally is considered as the most demanding in the entire wellbore drilling process, as it is, due to inherent complexity, related to the uncertainty in the lithological composition and the petrophysical properties of the rocks (Zadravec, 2012).The causes of such uncertainties are the overpressurized zones in the shales, problems of lost circulation or disturbed wellbore stability due to changes in the mud properties associated with insuf cient hole cleaning or mud ltrate penetration into the rock formations.In order to reduce the technical risks such as cavings in a hole, unplanned hole reaming, a stuck pipe or lost pipes in a hole and a consequently longer duration of drilling operations, it is necessary to apply proper drilling parameters for the selected bottom hole assembly, and to determine the optimal density and rheological properties of the mud.This paper will present a review and the consideration of the time-dependent and mechanical wellbore instability dif culties faced while drilling development wells through Gudair, Wara, Mauddud, Burgan, Zubair (shale formations) and argillaceous limestone before reaching the pay zone in gas condensate eld D in the Persian Gulf.The case study and method for drilling uid design optimization applied to overcome wellbore instability problems in shale formations in eld D will be presented and analysed.In addition, as contribution to determining optimal drilling mud density, a concept of effective hoop stress, time dependent failure mechanisms and an optimized mud density calculation that took into consideration the relationship between pore pressure and effective hoop stress with original data from Well A in gas condensate offshore eld D will be presented.The nal result of the drilling uid optimization study includes precisely determined mud density, salt concentration and salt type recommendation for inhibition of each shale formation and optimised drilling practice to improve entire wellbore stability.

Concepts of the e ective stress and time-dependent wellbore instability in shales
Drilling wells of complex geometry, under high pressure and high temperature conditions, particularly in a demanding deep-sea offshore environment or highly de- The Mining-Geology-Petroleum Engineering Bulletin and the authors ©, 2018, pp.95-104, DOI: 10.1177/rgn.2018.4.9 viated or horizontal extended reach wells, is characterized by the requirement of maintaining equivalent circulating density (ECD) of the mud, sometimes within the narrow limits between pore pressure and fracturing pressure gradients.ECD is the effective density exerted by a circulating uid against the formation that takes into account the hydrostatic head and the pressure drop in the entire annulus above the point being considered.Furthermore, determining the exact relationship between pore pressure gradient and fracture pressure gradient of the rocks is one of the priorities in understanding the interaction between pay zone rocks and cap rocks.The main purpose of understanding this relationship is a prerequisite for the well design and the optimization of drilling parameters between patterns of the trends in the development of the pore pressure and fracture pressure gradients.The origin of the determination of a safe drilling area, between the mentioned pressure gradients at a certain depth of the well, is prediction of the pore pressure gradient (Zadravec, 2012).Therefore, "the accuracy of its determination is of fundamental importance for casing design, casing setting depth determination, and the prevention of the kicks and blowouts while drilling operations" (Mouchet and Mitchel, 1989).For well design, especially of the exploratory wells in new unknown exploration areas, different methods or models for the prediction of the pore pressure gradient have been developed.Some methods, introduced by Bowers (Bowers, 1994), Eaton (Eaton, 1976), and the "d" exponent method (Jorden and Shirley, 1966), use the data collected during drilling operations and their interpretation indirectly predicts the trend of the change in the pore pressure gradient.The d-exponent method is widely accepted as a method suitable for determining the pore pressure gradient while drilling in shale formations.According to Solano et al. ( 2007) "the limitation of this method stems from the fact that the trend of normal rock compaction should be interpreted from data collected by geological monitoring and collecting drilling cuttings and thus depends on the skill and experience of eld geologists or interpreters".Thus, the data collected is subjected to inaccuracies and prediction errors in the trend of normal rock compaction determination.To reduce the geological uncertainties, calculation methods are developed based on the relationship between effective stress and the "d" exponent for each individual well with the purpose of de ning the trend of normal rock compaction for a particular eld.This approach implies the knowledge about the petrophysical and geomechanical properties of rocks, and in particular the understanding of stress genesis in rocks through the stress strain relationship, which is also one of the pressure generator (Zadravec, 2012).According to Moss, "the mathematical relationship between in situ rock stress and associated pore pressure is de ned by the concept of effective stress" (Moos, 2006).The implicit, "effective stress is a part of the total loads that the rock itself carries" (Moos, 2006).
While drilling with water-based mud in an overbalance condition through shale formations without an effective ow barrier present at the wellbore wall, mud ltrate will penetrate progressively into the rock formation (Tan et al., 1996a).Due to the low permeability of the shale formation that is typically in the range between 10 -21 and 10 -18 m 2 (10 -9 to 10 -6 Darcy) lter cake or effective barrier will not be formed on the wellbore walls.The low ltration rate will result in negligible deposition of drilling uid solids on the wellbore wall and any solid deposition will be eroded by the hydrodynamic action of the drilling uid.Due to the water saturation and low permeability of shales, penetration of a small volume of mud ltrate into the formation results in a considerable increase in pore pressure near the wellbore wall.The increase in pore pressure reduces the effective mud support i.e., reduces the acting of mud as a hydrostatic column over pore pressure of the rocks formation at a selected depth, which leads to a less stable wellbore condition.The very ne pores and negative clay charges on pore surfaces lead to shales exhibiting membrane behaviour.Due to the chemical potential mechanism, induced formation water owing out the shale rocks or mud ltrate owing into the shale rocks is almost similar to the water owing through a semi permeable membrane (Tan et al., 2002).The driving force for water transportation in no overbalance conditions due to low mud density and the chemical potential gradient across the membrane, that is generally related to the difference in solute, in this case the salt concentration in the mud.In the case that water activity of the drilling uid becomes less than the shale activity, an osmotic out ow of pore uid from the formation will occur through a semipermeable membrane which is permeable for water and not permeable to soluble ions or molecules.Shale rocks exhibit a non-ideal semipermeable membrane behaviour to water-based solutions because it has a range of pore sizes, including wide pore throats, which result in signi cant permeability to solutes.The wide throats reduce the solute interaction with the pore surfaces, which increases the permeability of the membrane to solutes.The solutes transferred across the membrane system will reduce the chemical potential (water activity) of the pore uid, which will gradually reduce the chemical potential difference between the drilling uid and the shale, and consequently will reduce the effective mud support (Qadmani et al., 2009).
In order to optimize proper drilling parameters and mud density, understanding of the concept of effective stress is of high importance.Numerous laboratory tests, theoretical analyses, case studies and considerations have shown that rock properties, such as speci c resistance, the rate of sound speed through the rock, the density, the conductivity, the porosity and the mechanical strength, are consequences or functionally depend on the intensity of the effective stress (Moos, 2006).Accordingly, by measuring the aforementioned physical proper- The Mining-Geology-Petroleum Engineering Bulletin and the authors ©, 2018, pp.95-104, DOI: 10.1177/rgn.2018.4.9 ties of shale rocks and by analysing the measured values, in particular the rate of sound speed through the rock and the resistance, it is possible to determine the effective stress.According to Moss et al. (1998) such analyses are the basis for creating algorithms for predicting pore pressure in the rocks.In addition, "the effective stress determines the strength of the faults surfaces, the permeability of the fractures and affects the stability and geometry of the cross section of the well bore" (Schutjens et al., 2004).For example, in areas exposed to large variations in horizontal stresses, (stress which acts perpendicular to the axis of a vertical well), the circular borehole shape takes the shape of an ellipse (see Figure 1), while the cross section of the borehole section increases in the direction of minimal horizontal stress.Under such conditions, cracks in the rock are formed at the edges of the elliptical cross section of the wellbore, enabling mud ltrate breakouts into the rock and enlarging the hole diameter (washouts).By measuring the orientation of the fractures or the increase of the borehole diameter, the direction of the minimal horizontal stress in the observed area and thus the in-situ stress conditions can be determined.An increase in borehole diameter can be determined by using electric wireline measurements (CBIL, FMI or EMI) (Image logs) or by orientated x/y caliper measurement of the borehole diameter.In addition, through the interpretation of electric wireline measurements, it is possible to detect drilling induced fractures, which occur in the direction of the maximal horizontal stress.Fractures induced by the drilling process occur in the rock due to the dynamic conditions while mud circulates through the open hole as the functional requirement of wellbore stability based on the relationship between pore pressure in the rock and hydrostatic pressure of the mud column.Drilling induced fractures and breakouts are occurrences as the result of completely different conditions and stress relations in the wellbore.In the case of drilling induced fractures, the force due to the hydrostatic pressure of the mud is greater than the force due to horizontal stress in the rocks.Growth or elliptical wellbore deformation occurs when the tangential (hoop) stress in the wellbore becomes larger than the shear strength of the rock.By measuring the width of the mentioned breakouts on a rock sample, the maximal horizontal stress can be determined in the nearby wellbore (grooving) zone.In the vertical wellbores, the breakouts are concentrated in the direction of the minimal horizontal stress, because this is an area of action of the maximal tangential (hoop) stress.
Figure 1 shows the characteristic stresses in the nearby zone of the vertical wellbore where the breakouts and the enlargement of the wellbore diameter are oriented in the direction of the minimal horizontal stress ( h ) and in the direction of the maximal tangential (effective hoop) stress ( ' H ) respectively, where:   Broken rock fragments in the areas of breakouts due to the maximal tangential stress after the initial sagging in the form of splinters, took the shape of tubes (see Figure 3) or polyhedral angular (see Figure 4).They have a visible conjugated shear surface which is the result of the rock fracturing due to shear stress.The above-mentioned peeling can be detected during sampling of the drilling cuttings and by electrical wireline logging of the diameter of the wellbore (caliper logs) and previously mentioned image logs.
Furthermore, rock fragments due to peeling can have an irregular polyhedral form with one or more clearly expressed tabulars.The mentioned cracking occurs due to the low strength of the contact surfaces between the layers or the cleavage of the existing fractures.Finally, it can be concluded from the aforementioned points that wellbore stability is a function of the drilling mud density, the effective wellbore cleaning and cavings resulting from peeling in the areas of the greatest tangential stress.

Drilling uid optimization research for gas condensate o shore eld D
Very often, in worldwide drilling operations, dif culties are faced while drilling especially highly deviated or horizontal wells through shale formations before reaching pay zones.According to Qadmani et al. ( 2009), similar problems were described, and dif culties were highlighted after drilling development wells in offshore Khafji and Dorra elds in the ex-neutral zone between Kuwait and Saudi Arabia in the Persian Gulf.These wells intersect various shale formations and "severe time-dependent wellbore instability problems due to shale sloughing were experienced" (Qadmani et al., 2009).While drilling a 0.311 m (12 1/4") section of hole, on several wells, tools were held up due to the presence of ledges, different shale formations failed due to insuf cient mud density, severe tight spots, overpulls and pack-offs occurred while tripping due to excessive cavings into the wellbore which required hard back reaming and led to inadequate hole cleaning, high torque and dynamic pressure increments.These problems have led to several stuck pipes and drilling sidetracks from the original wells.Qadmani et al. stated that "wellbore instability was attributed to insuf cient salinity in the drilling uid which resulted in pore pressure increase due to the mud ltrate penetration mechanism being not adequately counteracted by the chemical potential mechanism" (Qadmani et al., 2009).As a direct consequence, the pore pressure increased in the nearby wellbore wall area, which reduced the effective mud support, increased ineffective hoop stress and led to unstable wellbore conditions.The same phenomenon is not new, and it was detected while drilling through shale formations with water-based mud in numerous oil and gas elds in the Persian Gulf and worldwide (Last et al., 1995).
To overcome problems with wellbore instability in gas condensate offshore eld D, research and a drilling uid optimization study was performed based on highly deviated and horizontal well data collected while drilling in the eld (area of interest) prior to commencement of the drilling operations on new in ll wells.The main goal of the study was to evaluate the potential of timedependent wellbore instability mechanism(s) in Gudair, Wara, Mauddud, Burgan and Zubair shales and across argillaceous limestone, to determine the appropriate mud properties for drilling new in ll wells, salt type and concentration, and to develop a solution and strategy to mitigate and/or manage wellbore instability.The optimal drilling mud design, in terms of mud density and type, salt type and concentration, has been developed based on mud logging data, drilling cutting samples collected and cores taken at the critical formations of interest on numerous offset wells drilled in the eld with different levels of success.Wellbore stability analysis was subsequently based on the building of the Mechanical Earth Model (MEM) in order to develop the safe mud weight window and recommend drilling mud weight and inhibition for planned wells intervals.The MEM of the wells was developed (curtain-sectioned) from offset wells data based on the prognosis of formation tops and Figure 3: Rock particles cavings in shape of tubes (Zadravec, 2012) the trajectories of the new planned in ll wells, where offset wells were also used to cross check the developed model.The MEM contains data for uncon ned compressive strength (UCS) of the rocks, tensile failure, wide breakouts and breakdowns based on caliper logs, information about mud losses and upper and lower mud weight margin for new in ll wells in the offshore oil eld.The theoretical background for developing the MEM was a re ection on the fact that, according to Tan and group of authors, the "occurrence of time-dependent wellbore instability is largely attributed to the increasing of pore pressure in the rock formation with time, due to mud pressure penetration mechanism" (Tan et al., 1996b).Initially for building the MEM, it is important to understand the local geology, type, genesis and petrophysical properties of the rocks in the eld.Based on this knowledge, a detailed laboratory analysis and in situ measurement led to developing pro les of elastic and rock-strength parameters including uncon ned compressive strength (UCS).These parameters are important to predict pore pressure gradients, minimal ( h ) and maximal horizontal stresses ( H ) which can be identi ed and measured in the drilling phase and vertical stress, ( V ).Finally, determining intensity and horizontal stress direction is important for proper drilling parameters and drilling mud densi ty optimization (Ali et al., 2003), which will be described in more detail further on in this paper.
The pore pressure increase will lead to a decrease in the effective mud support on the wellbore wall and possibly swelling/generation of hydration stress with time in the formation (Tan et al., 1997) which will both result in less stable wellbore walls.Hence, to avoid time-dependent wellbore instability, the water activity of the drilling uid needs to be suf ciently low (i.e.drilling uid should contain a suf ciently high salt concentration) to induce the required osmotic ow from the formation to the borehole (chemical potential mechanism) to counteract the pore pressure increase due to mud ltrate penetration (Tan et al., 1996a).During the preparation of drilling uid design, optimization was done for different shale formations for several new in ll wells and both mud pressure penetration and chemical potential mechanisms have been taken into consideration.The information required and used in the analysis included the shale (rock) genesis and mineral composition, petrophysical properties, drilling uid properties, overbalance pressure, formation temperature, mud density which will induce breakouts and mud weight used while drilling offset wells in the eld (Mohiuddin et al., 2010).The analysis and optimizations were based on properties for proposed water based mud.The estimated mud ltrate adhesion (Amf) was 0.0386 N/m (38.6 dyne/ cm) and membrane ef ciency was 26.8 -39.5 %.A temperature gradient used in the analysis was 3.88 o C/100m.The depths for different shale formations for a new in ll well were mapped and correlated with the corresponding depths from offset wells.The recommended mud weight for a 0.311 m (12 ¼") hole section for mechanical wellbore stability was used together with the formation pressure gradient to determine the overbalance pressures and gradients for the planned well.The main target of the optimization study was to manage generated overbalance pressure that will result in a pore pressure increase due to the mud pressure penetration mechanism which, ideally, should be counteracted by the chemical potential mechanism.Mud weights for drilling through the mentioned different shale formations of new in ll wells were optimized based on the validated design criteria for net mud weight reduction as a percentage up to 10% of breakout mud weight versus hole enlargement (due to formation breakouts).Input data were collected by running a caliper and FMI logs on offset wells in the eld and by mapping and analysing the multiple drilling events such as tight hole, overpulls, torque increase, pack off, back reaming, reaming down, etc.Additionally, pore pressure changes due to mud pressure penetration and chemical potential mechanisms were laboratory measured on the cores, and after 7 days of exposure, based on the measured rock properties for the selected shale formations, drilling mud properties and overbalance pressure were determined (Mohiuddin et al., 2010).The nal result of the drilling mud optimization study was precisely determined mud density, salt concentration and salt type recommendation for inhibition of each shale formation (see Table 1), with the corresponding measured depth based on the well trajectory plan for the selected new in ll well.The key components optimised for the proposed mud were: shale hydration suppressant, dispersion inhibitor i.e., encapsulator, sealing additive, anti -accrete and ROP enhancer.It is important to remember that the proposed data is only valid for the selected well as the mud salinity is dependent on the recommended mud weight and formation pressure gradient which may be different for the other planned wells.
In addition to the recommended mud density and salinity for the proposed mud, the following set of recommendations for proper drilling practice were attributed to minimize the potential drilling hazards (Mohiuddin et al., 2010): • Great attention should be paid on proper hole cleaning while drilling (application of optimum ow rate, rotary speed, mud rheology and drill string reciprocation) to avoid tight hole, packing off and bottom hole assembly or casing string differential sticking.• Use stable geometry bottom-hole assembly to minimize dynamic impact on the wellbore wall.• Using mud with good sealing capacity, e.g. containing asphaltene with a wide range of particle size distribution and strengthening materials, since micro-fractures are likely to be generated due to rock failure.• Monitor ECD for swab effect while reciprocating pipe off bottom, and while tripping.• Closely monitor any increase in drag that could be an indication of wellbore walls condition deterioration or mechanical caving based on improper drilling parameters or practice.• Monitor ECD trend for signs of annular loading, pump pressure and hook load/drag that could indicate wellbore walls condition deterioration.• Use annular pressure-while-drilling measurements to monitor and to verify the ECD while drilling.• Conduct a wiper trip every 24 hrs or after drilling every 5 or 6 stands to clean the hole, whichever comes rst.

Calculation method for optimal drilling mud density determination
Mud density should not be determined or optimized solely to satisfy the condition of the hydrostatic pressure overbalance at a certain depth, but also due to maintaining the well bore stability.Apart from the overburden pressure (geostatic pressure), fracturing pressure and maximal and minimal horizontal stresses, which may vary to the equivalent circulating density of the mud (ECD) value of 1 600 to 3 900 kg/m 3 (Moos, 2006), the calculations take into consideration the uncon ned compressive strength of the rock (UCS), which is denoted as F in Equation 1. Uncon ned compressive strength of the rock depends on the mineral composition, i.e. the type of rock and the burial depth, and has the value for different rocks in a range from 6.9 MPa to 172 MPa (Moos, 2006).Determining the required mud density for wellbore drilling is of the utmost importance for primary well control, preservation of wellbore stability and it can be calculated from hydrostatic pressure of a mud column from Mohr-Coulomb's elasticity Equation 1 (Last et al., 1995): (1) Where: P W -Hydrostatic pressure of mud column (MPa), H -Maximal horizontal stress (MPa), h -Minimal horizontal stress (MPa), F -Uncon ned compressive strength of the rock (MPa), N -constant determined by the internal friction angle as a function of the rock type; P p -pore pressure (MPa).Mud density also affects the rate of penetration and it is therefore very important that it is not too high but it must be exactly de ned in accordance with the functional requirements of the wellbore stability.In case of excessive mud density, induced fractures occur in the direction of the action of the maximal horizontal stress, and in contrast to, in the case that the mud density is too low for drilling, induced breakouts and cavings of the rock fragments into the wellbore will occur, in the direction of the minimal horizontal stress.From the above, it is apparent that the hydrostatic pressure of the mud column needs to achieve a precise pressure (mud window) within the wellbore to avoid induced breakouts and a pressure at which no induced fracture in the rock will occur.
The calculations that describe the determination of the required mud density in accordance to the measured eld data from the well in gas condensate eld D in the Persian Gulf in order to satisfy the mentioned wellbore stability condition uses the actual input data (Zadravec, 2012) as follows: • Vertical depth (TVD): 3050 m;  Therefore, in order to avoid drilling induced breakouts due to insuf cient mud density, it is mandatory to maintain hydrostatic pressure of the mud column inside the wellbore of 37.92 MPa, which at depth of 3050 m corresponds with equivalent mud density of 1267 kg/ m 3 .
To avoid formation fracturing the difference between the minimal tangential (effective hoop) stress and the difference between hydrostatic pressure of the mud and the pore pressure in the well must be greater than 0; 16.97 -(P w -34.47) > 0, P w 51.44 MPa.
Hydrostatic pressure of a mud column that is higher than 51.44 MPa will result in formation fracturing and mud losses, which at a depth of 3050 m corresponds to the equivalent mud density of 1719 kg/m 3 .
For a horizontal well, in order to avoid drilling induced breakouts, it is necessary to meet the same initial condition as required for vertical well: Maximal vertical stress ( ' V ): ' V = G -P P (7) where: G -overburden pressure (MPa), P P -pore pressure (MPa).Maximal vertical stress ( ' V ) at the depth of 3050 m with overburden pressure gradient of 0.0226 MPa/m is: 68.93 -34.47 = 34.46At hydrostatic pressure of a mud column of 46.60 MPa at a depth of 3050 m, the equivalent mud density is 1537 kg/m 3 , which is the minimal mud density to be achieved in order to avoid drilling induced breakouts and peeling of the rock fragments into the wellbore.
Furthermore, in order to avoid the generation of drilling induced fractures in the horizontal well it is necessary to satisfy the condition that minimal tangential (effective hoop) stress must be greater than zero: ' h > 0.
The Mining-Geology-Petroleum Engineering Bulletin and the authors ©, 2018, pp.95-104, DOI: 10.1177/rgn.2018.4.9 Minimal tangential (effective hoop) stress ( ' h ) for horizontal well is: At hydrostatic pressure of a mud column which is greater than 62.22 MPa, formation fracturing and mud losses will occur, which at a depth of 3050 m corresponds to a mud density of 2074 kg/m 3 .

Conclusion
A case study presented in this paper showed implications of wellbore instability while drilling through shale formations with water based mud on the duration of drilling operations, created lost time and possible effective solutions to ful l requirements for well bore stability.According to the presented theoretical analysis, determination and quanti cation of the mechanism of wellbore instability requires knowledge and understanding of several complex facts, such as: identi cation of magnitude and direction of minimal and maximal horizontal stresses, pore pressure, fracturing pressure and overburden pressure gradients (in-situ stress), induced effective hoop stress around the wellbore, rock properties as UCS and internal friction angle, mineral composition of the rocks and determination of failure criteria.An important (advantage) is that all of the mentioned features and properties could be identi ed and measured while drilling operations (pore pressure gradient determination by ''d'' exponent or other applicable methods, derived fracturing gradient determination by FIT or LOT, minimal and maximal horizontal stresses quantication by FIT and veri cation by caliper logs, core analysis for the determination of UCS and the internal friction angle), and in addition, numerous eld based drilling mud properties analyses and optimizations are available, which can be veri ed later on, con rmed or optimized by laboratory measurements and analysis.Related to the speci c case study of wellbore instability in different shale formations in offshore eld D in the Persian Gulf, problems while drilling arose due to the insufcient salinity of drilling mud, which resulted in pore pressure increment since the mud pressure penetration mechanism was not counteracted by the proper chemical potential mechanism.
As a contribution to determining the drilling mud density, this paper explicitly shows the sequence of the calculation method for optimum mud density taking into consideration the acting of the effective stress on the well bore stability and the method of their determination.The improved calculating method took into consideration only tangential (effective hoop) stress.A pro-posed solution for vertical wells calculated hydrostatic pressure of the mud column inside the wellbore which will not induce breakouts due to insuf cient mud density.In addition, for vertical wells, calculations showed that to avoid formation fracturing, the difference between the minimal tangential (effective hoop) stress and the difference between hydrostatic pressure of the mud and the pore pressure in the well must be greater than 0. For horizontal wells, to avoid the generation of drilling induced fractures, it is necessary to satisfy the condition that the minimal effective hoop stress must be greater than zero: ' h > 0 In addition, it was shown that the drilling mud density (mud weight) should not be optimized (determined) solely to satisfy the condition that the hydrostatic pressure of the mud column must be greater than or equal to the value of the formation pore pressure at a certain depth, but also complying with maintaining the well bore stability.
Finally, the following conclusions can be drawn from the post drilling well analysis which were related to the drilling uid optimization study and drilling practice applied in the new in ll well A in the Persian Gulf.
In terms of moderately low water activity of the shale formations and relatively low overbalance pressure, an optimum drilling uid design for selected mud, whereby the mud ltrate penetration was fully counteracted by the chemical potential mechanism, was very successfully developed for different shale formations in the newly drilled in ll well A and together with the application of the presented recommended optimal drilling parameters for certain lithology and strengthening materials kept them stable through drilling operations.There was no non-productive time associated to the wellbore instability in shale formations, no stuck pipe incidents, no loss circulations occurred, electrical wire line logging was completed and multi days MDT logging and the uid sampling program were successfully conducted with intermittent wiper trips in between.A 0.244 m (9 5/8") casing was run and cemented successfully with signi cant time saving and appreciation from the Operating Company Management.
H -Maximal horizontal stress, h -Minimal horizontal stress ' H -Maximal tangential (effective hoop) stress; ' h -Minimal tangential (effective hoop) stress.If the rock inside area of the breakouts does not have suf cient compressive strength, due to the tangential stress in the nearby zone of the wellbore, it will lead to caving of the tiny rock fragment into the well.Initially, it will be expressed in the form of "splinters" and most often occurs due to mud density that is too low (see Figure2).

Figure 1 :
Figure 1: Characteristic stresses in nearby zone of the vertical wellbore

Table 1 :
(Mohiuddin et al., 2010)and salinity for proposed mud(Mohiuddin et al., 2010) The Mining-Geology-Petroleum Engineering Bulletin and the authors ©, 2018, pp.95-104, DOI: 10.1177/rgn.2018.4.9 The main task is to de ne mud column hydrostatic pressure i.e. equivalent mud density, which needs to be precisely optimized to avoid breakouts and tensile failure in vertical well and especially in horizontal well, which is parallel to minimal horizontal stress. MPa.