How To Draw A Polar Plot For Mud Weight

Abstract

The challenges behind this research were encountered while drilling into the Ilam, Mauddud, Gurpi, and Mishrif Formations, where astringent drilling instability-related issues were observed across the weaker formations in a higher place the reservoir intervals. In this paper, geomechanical parameters were carried out to determine optimum mud weight windows and safe drilling deviation trajectories using the geomechanical parameters. We advise a workflow to determine the equivalent mud window (EMW) that resulted in 11.eighteen–12.61 ppg which is suitable for Gurpi formation and 9.36–13.13 ppg for Ilam and Mishrif Formations, respectively. To estimate condom drilling trajectories, the Poisson's ratio, Young's modulus, and unconfined compressive forcefulness (UCS) parameters were determined. These parameters illustrate an optimum drilling trajectory bending of 45° (Azimuth 277°) for the Ilam to Mauddud Formations and less than 35° for the Gurpi Formation. Our analysis reveals that maximum horizontal stress and Poisson'southward ratio have the about impact on determining the optimum drilling mud weight windows and safe drilling divergence trajectories. On the opposite, vertical stress and Young's modulus have minimum touch on on drilling mud weight windows and condom drilling departure trajectories. This study can be used every bit a reference for the optimal mud weight window to overcome drilling instability issues in futurity wellbore planning in the study.

Introduction

A question that may come into the readers' mind is: why does the determination of the geomechanical parameters have the most affect on decreasing risks during wellbore operation, and why this written report is focused on the Ilam, Mauddud, Gurpi, and Mishrif formations. The respond is that generally, the breakout happens effectually the wellbore at the same orientation as the minimum principal stress, with a high-stress concentration. Therefore, the borehole enlargement happens when drilling fluid density is less than the strength of the rocks. Thus, shear failure happens at a low drilling fluid density, while the tangential stress is high. On the other hand, the Ilam, Mauddud, Gurpi, and Mishrif formations consist of argillaceous limestone and marl with scattered asphalt, with the salt aquifer. Therefore, the estimation of the geomechanical parameters is necessary to be adamant and implemented to reduce the drilling risks during operation. Another question that may come into the readers' minds is: what is the novelty of this inquiry? The reply is that the novelty of this research refers to the determination of the mud weight window, optimum drilling trajectory, and wellbore stability, including new observations which lead to new results in the study area.

The geomechanical parameter estimation is frequently used to forestall lost apportionment and the determination of optimum drilling trajectory. To make up one's mind the safe mud weight window and the best drilling trajectory, information technology is required to determine the intervals of tensile rock failure and shear rock failure. The pressure of the drilling mud will cause a tensile failure in the wellbore, and drilling mud will be lost into the germination if the mud weight is applied college than the safety mud window. Shear failure or breakout will occur while this weight is applied lower than the safe mud window (Le and Rasouli 2012; Zhang 2013; Zoback et al. 2003). Tensile stone failure occurs in the upper meters near the surface, while shear rock failure takes place at greater depth, below which, rock failure does not occur. Parameters such as wellbore deviation and principal stress directions play a remarkable role in calculating the mud weight window. Principal stresses directions are important to be quantified for petroleum field development (Radwan 2021a). Geomechanical modeling, wellbore stability analysis, and associated parameters have been examined in many research in recent years. Radwan et al. investigated pore force per unit area and fracture gradients using a variety of data and methods (Radwan et al. 2019, 2020, 2021). They also carried out reservoir geomechanical modeling in lodge to analyze in situ stress and its human relationship with reservoir backdrop such equally depletion, product, and wellbore stability (Radwan and Sen 2021a, 2021b; Radwan et al. 2021). To improve nether-balanced drilling, Abdelghany et al. practical the depth-of-damage method in geomechanical modeling (Abdelghany et al. 2021). Kassem et al. (2021) calculated the geomechanical parameters to investigate the effect of depletion and fluid injection in a sandstone reservoir (Kassem et al. 2021). Shahbazi et al. (2020) investigated the impact of reduced production rates on wellbore stresses by amalgam a second geomechanical model using log data and drilling data in two Iranian oil fields.

Optimization of mud weight window is the most critical factor to forbid wellbore instability during directional drilling. An optimum mud weight window entails wellbore stability (Li and Zhang 2011) and prevents lost apportionment.

Before drilling, the stress on the ground is less than the force of the rocks and thus the balance of the ground is retained. Just both during and afterwards the drilling, function of the rock column is drilled and moved out of the well, and the drilling mud replaces that and puts pressure on the wellbore wall, thus spreading stress around the wellbore, and the balance of stress in the basis is disrupted and the stress generated past the drilling is created. To maintain wellbore stability and regulate these stresses, the well must be drilled with the advisable mud weight (Darvishpour et al. 2019). Failure to pay attention to this issue causes wellbore instability and problems such as collapse, kick, wash-out, or tighten, increasing drilling costs, stopping production, and eventually might indeed cause well loss (Das and Chatterjee 2017).

To determine wellbore stresses, the rock strength must be known, an appropriate model must exist selected, and an advisable stone failure benchmark should exist called. Rock strength is an essential parameter in wellbore stability considering it shows the behavior of the stone when information technology is under in situ stress conditions (Radwan 2021a, b, c). The rock strength properties can exist obtained from well logs data and empirical equations (Peng et al., 2001; Rahimi 2014).

Heller and Zoback (2014) provided 28 relationships by different researchers for estimating the unconfined compressive force (sandstones or carbonate rocks and shale). In virtually of these relationships, the chief variables are transit time of sonic waves, ultrasonic wave velocity, Young's modulus, and porosity.

In situ stresses, which are carried out in various methods, have been published by Radwan et al. (2021a, b, and c). The International Social club of Rock Mechanics suggests "hydraulic fracturing" as the about reliable arroyo to determine in situ stress. This technology can increase the product of a well, and the proper use of this method can improve reservoir permeability and consequently improve the product of the wells (Gao et al. 2019a, b, c; Kassem et al. 2021; Radwan et al. 2021d).

In this research, we carried out an optimum mud weight estimation using geomechanical parameters in two steps. Consequently, we propose a drilling deviation survey based on the geomechanical models.

Geological setting

The written report area is located in the Persian Gulf. The Persian Gulf Basin is considered the richest region in the globe in terms of hydrocarbon resources (Ghazban 2007). The studied reservoir in this oil field is referred to as Sarvak Formation.

The Mesozoic stratigraphy of the Persian Gulf basin is characterized past episodic development of intra-shelf basins over the northeastern margin of the Arabian plate (Sharland et al. 2001; Van Buchem et al. 2011). During Aptian and Cenomanian, these basins resulted in deposition of organic-rich sediments which adjoined porous rim carbonates on their margins (Vahrenkamp et al. 2015). The Cenomanian intra-shelf basin was adult following the deposition of the lower parts of the Sarvak Germination, which are regionally continuous and dominated by carbonates (Razin et al. 2010). These carbonates are overlain in the west and e by shallow-marine carbonates of the Mishrif platform rimming an NE-SW trending intra-shelf basin in the key parts of the study area (Vahrenkamp et al. 2015). Recent seismic studies in the Iranian sectors of the prolific Persian Gulf region (OEOC 2014) have resulted in numerous oil and gas discoveries within the Cretaceous Serial. The Middle Sarvak Formation (Cenomanian) is considered to be an of import source rock inside the Cretaceous petroleum system of the eastern Persian Gulf basin (Alipour 2017; Hosseiny et al. 2016). This source stone is suggested to accuse the overlying Mishrif and Ilam carbonates in some oilfields of the report surface area (Alipour et al. 2017; Alizadeh et al. 2017; Hosseiny et al. 2017).

Sarvak formation is function of the Bangestan Grouping, containing a neritic carbonate consisting of limestone and dolomite, and this formation has shallow and deep facies. The lower office of the Sarvak Formation consists of limestone and pelagic stone. The upper role includes massive limestone containing algae, echinoderms, and rudists (James and Wynd 1965; Ghazban 2007). The Sarvak Formation is derived from Tange Savrak in the mount Bnatsegnan (northwest of Behbahan Urban center) in Khuzestan Province (James and Wynd 1965; Rahimi and Riahi 2020). The Sarvak Formation in stratigraphical terms is equivalent to Khatiyah, Mauddud, Ahmadi, and Mishrif Formations in this area (Ghazban 2007). The Upper Sarvak Germination is equivalent to the Mishrif Formation deposited in the south part of the Persian Gulf. This formation is regarded equally a significant hydrocarbon reservoir of this area (Van Buchem et al. 1996; Rahimi and Riahi 2020). The lower part of Mishrif is Khatiyah Formation that consists of organic matter-rich mudstone and wackestone. The Mauddud Germination with Albian–Cenomanian historic period consists of a shallow-water carbonate with widespread distribution in the Persian Gulf. The Mauddud Formation is a carbonate-dominated succession that emerged from transgression afterward the Nahr Umr Formation-related clastic-dominated sediments in the Western farsi Gulf (James and Wynd 1965) Fig. one.

Petrophysical backdrop

Petrophysical parameters such as effective and full porosity, water saturation, shale volume, and volume of minerals in this reservoir were calculated using probabilistic assay. Just get-go, the mineralogy composition was determined. Iii lithology cross-plots for the Ilam, Mauddud, Mishrif, and Khatiyah formations, based on neutron vs. density and sonic vs. Vp/Vs logs, were performed. The average shale book calculated for the studied formations is near 2.6%, which indicates that these formations are composed by and large of limestone and calcite. Since the velocity of sonic waves varies according to the textile and lithology of the formation, shale, limestone, and dolomite are easily distinguishable. According to the bachelor sonic log, the lithology of the studied formations is made of calcite and limestone with a few corporeality of shale.

In the next pace, neutron density logs are used every bit a basis for depth matching of other logs, similar compensated gamma ray (CGR), thermal neutron (CNL/TNPHI) porosity, compressional slowness (DTCO), photoelectric factor (PeF), and resistivity from the wellbores (HE-E1 and HE-E2). These logs were employed to perform the petrophysical model. The petrophysical evaluation results (Fig. two) propose a carbonate reservoir with limited shale volume (2.6%) and a porosity average of 10%. Figure ii shows the volume of water saturation in the 2d track and the volume of minerals in the 3rd track, both from the right side.

In tracks 1 and ii, the corporeality of water saturation and porosity is observed from the right, respectively. At the depth of 3750 m, low porosity is evident in the shaly interval and an increment in water saturation is observed. In tracks 6 and seven from the right, according to the PEF log, the presence of limestone tin be seen throughout the depths interval of the wellbore. The PeF log shows a value of well-nigh 5, representing the presence of limestone but decreases at a depth of 3750 g. The decrement of the PeF value proves the existence of the inter-shaly layer. On the other hand, the electrical resistivity log value increases at a depth of 3750 m. The density and neutron logs (tracks 6 and 7) decrease at a depth of 3750 1000, representing the shaly interval. The conventional well logs that were employed in the petrophysical model were displayed in the other column of Fig. two. It is worth mentioning that the shale volume was calculated using a corrected gamma-ray log (SGR).

Materials and methods

Wireline logs consisting of compressional density, gamma ray, resistivity, FMI log (rose diagram), petrophysical evaluation results, and pore pressure points from MDT tools are the available data in this analysis. Based on the log data coverage in the entire well likewise equally the availability of direct downhole measurements, we have advisedly chosen one well, namely HE-E2 for the geomechanical analysis presented here. Drilling and well reports were studied and used in this work. Applied methods are discussed below.

Wellbore stresses and pore pressure (pp)

Unremarkably, in situ stress is divided into three parts: vertical stress, minimum horizontal stress, and maximum horizontal stress. The germination rocks are in forepart of the field stresses before drilling, but after drilling these rocks are pushed out in the cutting form and the wellbore must withstand the stresses of the field. These stresses relate to the wellbore trajectory besides as the impact of the field dominant stress on the well-drilling location (Nelson et al. 2006).

Maximum and minimum horizontal stresses

The minimum and maximum horizontal stresses are two of the three major stresses required for each geomechanical study (wellbore stability analysis, sand production, and hydraulic fracture) (Sh_min and Sh_max). Estimation of horizontal stresses is one of the chief steps in geomechanical modeling and contributes to an cess of the accuracy of the measured geomechanical model (Gholilou et al. 2017). The stresses applied to the rocks underground are nigh identical in various directions nether isotropic conditions and before well drilling (S5 = Shmin = Shmax). Still, these values change after drilling and these changes are more noticeable on a significant regional scale in active tectonic areas such equally anticlines, fault-side by side areas, salt domes, and other active tectonic areas. Mechanical failures in the wellbore are induced by adjusting the horizontal stress values. These mechanical failures can exist in the maximum horizontal stress direction in the course of tensile failures or breakdown, and shear failures or breakouts are in the minimum horizontal stress direction which both are produced roughly parallel to the wellbore centric. Using acoustic and density logs, as well as reservoir properties similar Poisson's ratio, vertical stress, and pore force per unit area, the stress contour in the reservoir is determined (Almalikee and Al-Najim 2018). At that place are many methods to assess the direction and location of these stresses. Image logs are i of the near detailed methods to classify the features of these stresses. Figure 3 shows the location and direction of breakouts created by shear stress observed on the rose diagram.

The minimum horizontal stress (Shmin) tin exist determined direct from the minifrac test, hydraulic fracture, or LOT/XLOT examination; nevertheless, the maximum horizontal stress (Shmax) cannot exist computed directly. Even though both of them can exist calculated using indirect methods with acceptable accuracy. The poroelastic stress equation is used in conventional means to estimate the minimum horizontal stress slope every bit a function of vertical depth. The theory of poroelasticity, which explains how a lithified, porous medium-like rock deforms when the pore space is filled with fluid and pressurized, describes the fluctuation of Sh every bit a role of. Pp (Kumpel 1991). I of the most oftentimes used approaches in the industry for determining horizontal stresses under isotropic weather is the poroelastic method. Changes in elastic stiffness characteristics acquired by structural anisotropy are used to predict the minimum and maximum horizontal stresses in this method (Abdelghany et al. 2021; Maleki et al. 2014). Equally a effect, one of the conventional methods for indirectly determining the minimum and maximum horizontal stresses is to employ the poroelastic method (Blanton and Olson 1997) (Eqs. ane, 2):

$$ Sh_{{MIN}} ~ = \frac{\upsilon }{{i~{-}\upsilon }}SV - \frac{\upsilon }{{1~ - \upsilon }}\alpha P_{P} + \alpha P_{P} + 10^{3} \frac{E}{{1 - ~\upsilon ^{2} }}\varepsilon _{10} + 10^{3} \frac{{\upsilon Due east}}{{1 - ~\upsilon ^{two} }}\varepsilon _{y} $$

(one)

$$ Sh_{{MAX}} ~ = \frac{\upsilon }{{1~{-}\upsilon }}SV - \frac{\upsilon }{{ane~ - \upsilon }}\alpha P_{P} + \alpha P_{P} + x^{three} \frac{{\upsilon E}}{{ane - ~\upsilon ^{2} }}\varepsilon _{x} + x^{three} \frac{Due east}{{1 - ~\upsilon ^{2} }}\varepsilon _{y} $$

(ii)

where $\upupsilon $ is the Poisson'south ratio, α is Biot coefficient, P _P is the pore pressure, Eastward is the static Young'southward modulus, and $\varepsilon $ is the tectonic strain in the x and y directions (Aghajanpour et al. 2017).

Model prediction and calibration with wellbore data (observed breakouts on FMI or caliper logs) were used to place these tectonic strains. Biot coefficient or constructive stress coefficient (α) tin can be calculated using diverse parameters such as bulk modulus (Biot 1941), porosity (Krief et al. 1990), and permeability (Klimentos 2003). Theoretically, it is in the range of 0–1 (0 ≤α ≤ 1). This parameter is unremarkably derived from Eq. iii:

$$ \alpha = ~1 - \frac{{K_{b} }}{{K_{g} }} $$

(three)

where K _b is the volumetric parameter of the rock total book and K _thousand is the volumetric parameter of the stone grains. The British indian ocean territory coefficient was considered 1 in this analysis. If LOT/XLOT is available, the horizontal stresses are adjusted to decide the actual tectonic strain values (Gholami et al. 2015; Zoback 2010).

Fracture analysis using germination micro-imager (FMI)

Analysis of natural fractures such as determining the management of extension and slope, morphology (open or closed), density, and opening charge per unit of fractures, peculiarly in Iranian carbonate reservoirs, can be the basis of further studies. Fractures are of swell importance in the exploration, evolution of hydrocarbon fields, and hydraulic failure.

The raw data of the FMI logs are processed, analyzed, and interpreted to identify the types of fractures and also to determine the current stress direction in Santoniane carbonates (Ilam Formation) in southwestern Iran. The tectonic tendency of the fractures was determined in the wells, and the results are presented as a rose diagram of slope and the extension of discontinuities:

Figure 3 shows the results obtained from the FMI log, the extension and slope of induced fractures due to drilling operation, and maximum horizontal stress at an angle of 61.2 and 318.2 degrees (right figure). The extension and gradient of the breakouts and minimum horizontal stress are in the management of 134.v and 44.4 degrees (left figure).

Vertical stress

The pressure level exerted by combining the vertical column pressure level of various rock layers and the fluids inside themselves at a certain depth is overburden stress, commonly called vertical stress (Almalikee and Al-Najim 2018). Overburden pressure level at each point in the subsurface is due to the weight of upper layers and the office of different factors, such every bit rock blazon, porosity type, stone density, and the density of fluid filling the pores, diagenetic impact, tectonic factors, etc. This pressure includes lithostatic and hydrostatic pressures. Lithostatic pressure is the weight of the rock column, and hydrostatic pressure is the weight of the fluid column filling the pore spaces. These pressures are a function of the specific gravity of the rocks and fluids within the pores and increase in proportion to the depth. The sum of these ii pressures refers to overburden stress. In a homogeneous property, vertical stress can be easily adamant from Eq. 4:

$$ S_{V} = {\text{ }}x^{{ - 3}} _{{~\rho gz}} $$

(four)

Just in most situations, to measure the vertical stress, the initial intervals of the drilled well practise not have the density information. Consequently, a density can be calculated using a linear equation at the initial intervals from the footing to the target depth (Rana and Chandrashekhar 2015):

$$ \rho EX = \rho _{{ML}} + a_{0} (tvd - ag)^{a} $$

(v)

where ρ _EX is the estimated density, ag is the distance drilling floor to ground level, tvd is the true vertical depth, ρ _ML is the surface density which is almost 2 (thousand/cm3), and a and a ₀ are the scale parameters in this equation (Eq. 5). The hydrostatic pressure is also determined using Eq. vi, which is the pressure level at the depth of the fluid column (Bjørlykke et al. 2015):

$$ ~P_{{h~}} = \mathop \int \limits_{0}^{z} g \times \_f~ \times ~dz $$

(6)

where ρ _f is the fluid density (gm/cm3). As a consequence, with increasing depth, the pressure slope increases. For the analyzed interval, the amount of overburden stress was measured and the vertical stress gradients at the tiptop and bottom of the formations are presented in Table ane.

Tabular array i Geomechanical units adding in Gurpi up to Mauddud zones

Full size tabular array

Ane of the vertical stress parameter applications is to utilise information technology to estimate the pore force per unit area. In that location are ii ways to measure pore pressure. The beginning technique is direct pore force per unit area measurement using special logging tools such as MDT and RFT. Pore fluid trapped in the formation porosities greatly affects the in situ stress magnitudes. Abnormal formation force per unit area yields increased complication in drilling and nonproductive times. Direct downhole measurements provide the best PP estimates; even so, these data are usually recorded only in the reservoir intervals (Sen et al., 2019, 2020; Agbasi et al. 2021; Radwan 2021b).

The second approach utilizes the indirect measurement of pore pressure from well log information such as density, resistivity, and acoustic. But experimental equations that use well logs can be used in non-reservoir periods, such as Eaton's equation (Eaton 1975). Modular Formation Dynamic Tester (MDT) tools data has been fabricated available in this analysis at reservoir intervals. The pore pressure slope was obtained from MDT pore pressure points in this reservoir.

Sonic log (DT) is sensitive to force per unit area changes because there is a relationship between porosity, compression, pore force per unit area, and sonic parameters. An increase in the depth interval of the wellbore increases compaction and in turn decreases porosity. Therefore, the bulk modulus and shear modulus increase and the compressibility decreases. By variation of these parameters, the contact surface of the grains will increment, and every bit a result, the velocity of the sonic wave volition increment. But in the high-pressure zone, the compaction rate volition decrease (Fig. 4).

Many of the failure criteria have been proposed: Mohr–Coulomb (Coulomb 1973), Mogi–Coulomb (Mogi1971), Hoek–Brown (Chocolate-brown and Hoek 1980), and unmarried-parameter parabolic failure criteria (Li et al. 2005). It should be noted that the most common cases in the normal breakout and breakdown stress regime are Sθ >Southwardz >Sr and Sr >Sz >Sθ (Al-Ajmi 2012; Gholami et al. 2014). Several researchers take identified some issues related to the estimated values of rock forcefulness or lack of adequate cognition of stress levels in the estimated stress values for failure criteria (Vocal and Haimson 1997; Vernik and Zoback 1992). The Mohr–Coulomb failure criterion is 1 of the failure criteria that is commonly used in the oil industry due to better efficiency in terms of time and its linear consistency (Gholami et al. 2017, 2014, 2015). Of form, past ignoring the impact of intermediate stress and using the minimum and maximum stress values, this failure benchmark is used only to measure out the maximum mud pressure level for wellbore stability. This criterion'southward mathematical relationship focused on the principal stresses is as follows (Mohr 1900) (Eqs. 7, 8):

$$ S_{ane} - P_{P} = {\text{ }}UCS{\text{ }} + q\left( {S_{3} - P_{P} } \right) $$

(7)

$$ q = \frac{{\left( {1~ + ~\sin \varphi ~} \right)}}{{\left( {1 - ~\sin ~\varphi } \correct)}} $$

(viii)

The Mohr–Coulomb failure criterion's linearity is presented every bit follows (Tan et al. 2019):

$$ S_{one} = S_{C} + {\text{ }}\tan ^{2} (\frac{\pi }{four} + \frac{\varphi }{2})S_{three} $$

(nine)

where S _ane and Due south _three are the primary maximum and minimum stresses and South _C is the unconfined compressive strength (Eq. 9). Equation 10 describes the relationship between normal and shear stress when two adhesion coefficients and internal friction angle factors are used in this benchmark:

$$ ~\tau = ~Sn~ \times ~\tan \left( \varphi \right)~ + ~C $$

(10)

where τ is the shear stress, $\mathrm{\varphi }$ is the internal friction angle, S _n is the normal stress, and C is the adhesion coefficient. Table 2 presents the calculation of mechanical failure stresses (breakout and breakdown) using the Mohr–Coulomb failure criterion in various modes of induced stresses.

Table 2 Determining breakout and breakdown pressures in a vertical wellbore by Mohr–Coulomb failure criterion (Al-Ajmi and Zimmerman 2006)

Full size tabular array

Two internal friction angles and adhesion coefficient are significant parameters defined past the Mohr–Coulomb failure benchmark. It is used to determine these 2 parameters in the laboratory through iii-axis testing on drilling core samples. But there are too empirical relationships in which it is possible to quantify these parameters. The following equations are provided to quantify these two parameters:

$$ ~\varphi = {\text{ }}26.5{\text{ }} - {\text{ }}37.4\left( {one{\text{ }} - {\text{ }}NPHI{\text{ }} - V_{{shale}} } \right){\text{ }} + {\text{ }}62.one\left( {1{\text{ }} - {\text{ }}NPHI{\text{ }} - V_{{shale}} } \right)^{ii} $$

(11)

$$ C = UCS \times {\text{ }}(one - \sin \varphi /~2{\text{ }}\cos \varphi )~ $$

(12)

where $\mathrm{\varphi }$ is the internal friction angle, NPHI is the neutron porosity, V _shale is the shale volume (commonly calculated from the gamma-ray log), UCS is the uniaxial stress, and C represents the adhesion coefficient (Eqs. eleven,12).

In the shale segment, the internal friction angle and Young'due south coefficient are decreasing; on the contrary, these related subjects increase in thick limestone segments such as Ilam and Mishrif. Too, the Poisson'due south ratio in all formations decreases relatively with an increase in shale book (Table3).

Tabular array 3 Geomechanical parameters calculated in the Gurpi and Mauddud zones

Full size table

Effigy v shows the results of dynamic parameters, which include the following from left to right, respectively:

The first track includes logs of drill bit size (BS), well bore (CAL), and amount of radioactivity (SGR) which are considered in understanding with dynamic parameters. The second rail represents Young'southward modulus, which is lower in the shaly interval than in the limestone interval. The 3rd and 4th tracks show the Poisson'south ratio and rigidity, which increases as a bulk modulus in track five in limestone and decreases in shaly formations. The sixth and seventh tracks, which include the compressional shear moving ridge velocity and the Poisson ratio, respectively, show a good agreement with lithology too equally other dynamic parameters.

The obtained results of UCS, the Poisson'southward ratios, the Immature coefficient, and the prophylactic drilling deviation bending are shown in Tabular array 4. These results in the reservoir segment all comprise Ilam and Mauddud formations with more than 150 MPa unconfined compressive strength (UCS). The Poisson's ratio is less than 0.25 psi, and the Young's coefficient is between 80 and 64 GPa. Considering the calculated results, the optimum wellbore difference angle for the reservoir segment is more than 45° (277° azimuth). These calculations for shale and flysch Gurpi segments are variable, so the amount of UCS has a range of changes from 30 to 150 MPa, Poisson's ratio from 0.25 psi to 0.iii psi, and Young's coefficient included some changes from 32 to 64GPa.

Tabular array 4 Geomechanical units adding in Gurpi up to Mauddud zones

Full size table

The calculated issues in different Gurpi formation segments and safe drilling trajectories indicated 30° to 45° deviation.

In Table 5, formations depth and their intervals are provided with lithology blazon.

Table 5 Formations depth and their intervals

Total size tabular array

The effect of wellbore's azimuth and diversion on mud weight window and rubber mud weight window estimation

To calculate the geomechanical parameters, raw information and information of drilling wells in the Ilam, Mauddud, Mishrif and Khatiyah formations are collected. Petrophysical and geomechanical evaluation of the mentioned formations is investigated and performed (Fig. half-dozen). Figure 6 illustrates the acoustic, density, shear, Immature's modulus, and Poisson's ratio logs.

In Fig. six, the first track from the left represents the density log, which shows the lithological changes with respect to depth. In the second and third tracks, the sonic logs testify the changes in sonic slowness at different depths, which increase with decreasing density and vice versa. The fourth rail is Immature's modulus, which increases in magnitude and velocity with increasing density which shows a smaller value in clay content, and its low value indicates a decrease in the amount of bulk and shear modulus. The fifth track shows the Poisson'due south ratio increasing in carbonate formations compared to shaly formations, which bespeak more stability in the carbonate formations.

To calculate the dynamic and static geomechanical parameters, information technology is necessary to calculate the uniaxial compressive strength (UCS) and the equivalent mud weight (EMW) which is the mud weight needed to remainder formation fluid pressure level. In Figs. 7 and viii, Young'southward modulus and Poisson'southward ratio window are used to summate the UCS and EMW. In this section, shale volume log is also used to validate these calculations.

In Figs. vii and 8, the first track from the left, a gamma-ray log is displayed, which shows the shale volume. In the 2d rail, the UCS log shows that the uniaxial compressive strength has drastic changes in the studied formations and that the highest compressive strength is observed in limestone and calcite thick layers. In this rails, both static and dynamic values are depicted side by side, which validates the results obtained from the dynamic log. In the third and fourth tracks, Immature's modulus and the equivalent mud weight (EMW) logs are shown. These logs indicate that the drilling mud weight increases in areas of shale where Young's modulus decreases. Also, the calculated drilling mud weight indicates that in the intervals where the amount of uniaxial compressive strength decreases, the corporeality of mud weight increases to increase wellbore stability (Fig. vii).

Estimation of mud weight window

Optimum mud weight estimation comprises an allowable range of drilling mud weight. Mechanical earth modeling (MEM) analyzes wellbore stability based on failure criteria. Failure criterion is a mathematical equation that models the behavior of a rock at the moment of failure. Coulomb (1776) introduced the simplest yet most of import failure criterion. Co-ordinate to this criterion, rock failure will occur when shear stress in a plane overcomes the strength of friction and rock cohesion in that plane. According to Mohr'south theory, friction in a airplane is opposite to the direction of motion, and its value is straight proportional to the tension that compresses the two planes. Therefore, this criterion can be written as follows (Colmenares and Zoback 2002):

$$ \tau = C + \mu \sigma _{north} $$

(13)

${\sigma }_{north}$ influences perpendicular to the fracture aeroplane and plays a positive role in stone stability. In the above equation, $\tau $ is the coefficient of internal friction and C is the cohesion (Eq. 13). The master disadvantage of the MC criterion is to ignore the effect of intermediate stress. In this failure criterion, the intermediate stress does not affect the normal and shear stresses. Moreover, information technology is assumed that intermediate stress does not affect the occurrence of stone failure. MC failure benchmark can be expressed past maximum ($\sigma $ ₁) and minimum ($\sigma $ ₃) principal stresses. The maximum and minimum principal stresses can be easily calculated from Mohr'south circumvolve (Gholami et al. 2014):

$$ \sigma _{n} = \frac{{(\sigma _{1} + \sigma _{3} ) + (\sigma _{1} - \sigma _{3} )\cos \left( {2\theta } \right)~}}{two} $$

(14)

$$ \tau = \frac{{\sigma _{1} - \sigma _{3} ~}}{ii}\sin \left( {2\theta } \right) $$

(15)

In the above equations, $\uptheta $ is the angle between normal to the plane and maximum chief stress direction (Eq. 14, xv).

$$ ~\theta ~ = \frac{\pi }{4} + \frac{\varphi }{2} $$

(sixteen)

In the higher up equation, $\varphi $ (angle of internal friction) is the refraction angle that tin theoretically alter from 0 $^\circ $ to ninety $^\circ $. However, the practical range of changes in this angle is smaller and ranges from 0 $^\circ $ to 30 $^\circ $, so, co-ordinate to the above equation, it is obvious that Ten can vary betwixt 45 $^\circ $ and 90 $^\circ $ (Eq. sixteen).

Figure 9 specifies the low level of drilling mud weight in blackness colour. If the weight of drilling fluid reaches lower than the black line, borehole collapse pressure would occur and might bring up wellbore plummet in shale formations and brand the bore bigger or smaller. In the lower level of the least mud weight, the shear failure tin occur, called collapse pressure.

Tensile failure occurs in the upper meters near the surface, while shear failure takes place at greater depth, beneath which, failure does not occur. The tensile failure region shown in carmine color is related to the failure pressure of the formation or high drilling mud weight level. It implies that if the weight of drilling fluid inside the wellbore is more than the ruby-red line, it might bring up a tensile failure. It increases the probability of archway of drilling fluid to the formations, namely lost circulation.

A higher amount leads to the tensile failure range called fracture pressure level (Gao et al. 2019a, b, c). Shearing strength is often defined past the Mohr–Coulomb failure criterion and ii parameters: failure envelope cohesion and internal friction angle.

Regarding the results, whatever observed in Gurpi germination shows a distinct value in the weight of drilling fluid and other geophysical parameters such every bit maximum horizontal stress, formation pore pressure (Gao et al., 2019a; Radwan 2021; Baouche et al. 2021), the safe mud window range between minimum horizontal stress and minimum mud weight for wellbore collapse, shear failure, and tensile failure. Consequently, these changes indicate the shale segment in the depth of 3800 1000. Therefore, to preserve wellbore stability, it is vital to increment the weight of drilling fluid. In the Ilam and Khatiyah formations, the weight of the drilling fluid window is increased, whereas some changes occurred in other parameters, which are presented beneath: Albeit the weight of drilling fluid in the reservoir area in the Ilam is decreased, the maximum horizontal stress is increased. In this surface area, the formation pressure indicates changes in the shear failure region from the least level of mud weight to the least level of formation fluid pressure.

In Khatiyah formation, the maximum horizontal stress is decreased. By dissimilarity, the loftier level of mud weight increases, reducing the tensile failure boundary (Fig. 9).

Figures 10, 11, and 12 depict safe zones in terms of mud weight and drilling management, indicating certain stable and unstable depths along the investigated well. The bluish colour in Stereonets denotes the safe locations for drilling orientation without whatsoever breakout or breakup (stable orientation), whereas the red color denotes the unstable orientation. The mud weight employed at that depth is shown past the bespeak marked on these figs. The optimal difference, azimuth, and mud weight are provided to forbid shear and tensile failures. Figures 10, eleven, and 12 are the typical polar plots in STABview. The geomechanical analysis indicates that the direction of minimum horizontal stress (σ_h) and maximum horizontal stress) σ_H (in Gurpi is NW–SE and NE–SW. Drilling more than 50° deviations in Gurpi formation might bring up diverse problems such as wellbore breakup. Therefore, the safe mud weight window in Gurpi formation is from xi.18 to 12.61 ppg, with 35° drilling inclination and 277° azimuth (Fig. ten). It should exist noted that 1 pound per gallon (ppg) is equivalent to seven.48 pounds per cubic foot (pcf).

The direction of minimum horizontal stress (σ_h) and maximum horizontal stress (σ_H) in the Mishrif and Ilam formations is NE–SW and NW–SE, respectively. Drilling more than 60° inclination in the Mishrif and Ilam formations might bring up different problems such equally wellbore breakout. Therefore, the equivalent mud weight window for the Ilam and Mishrif formations is nine.36 to 13.13 ppg, with 45° drilling inclination and 277° azimuth.

Word

The geomechanical modeling approach presented here is used to provide a more than appropriate representation of a stable mud weight window past applying a geomechanical analysis incorporated with UCS, the Poisson's ratios, and Young'due south modulus. Haider Qasim et al. 2017 worked on wellbore instability problems. They conducted that a diversity of factors play a significant role in controlling the instability hassles and in determining an optimum mud weight to avert sticking and borehole plummet pressure, which might bring upwardly wellbore plummet in shale formations and make the bore bigger or smaller.

Haider Qasim et al. (2017) determined the in situ stress and induced stresses using numerous field and laboratory information from the study area. It is carried out by analyzing wellbore failure, core analyses, and field tests such as the triaxial exam and minifrac which are vital to improving geomechanical modeling (Abdelghany et al. 2021). In dissimilarity, in this written report, no core samples nor the core data were available to be used; therefore, using a compressional moving ridge velocity log, reservoir geomechanical parameters are calculated. The sonic log measures shear wave and compressional moving ridge velocities with medium density.

Moreover, with a proper format in Techlog, we yielded dynamic parameter estimations such as the Poisson's ratio, Young'southward modulus, bulk modulus, and other geomechanical parameters of the numerical information process.

Bagheriet al. (2021) used conventional well logs, DSI log, FMI log, petrophysical evaluation results (mineral and porosity), and pore force per unit area points from MDT tools. In this work, we accept compared our data with Bagheri et al. (2021) to figure out how our findings in 1 of the Iranian hydrocarbon reservoirs are far or similar. From our point of review, in Sarvak formation, we have simply divided geomechanical properties based on three different formations (Ilam, Sarvak, Gurpi), and to get the values for each germination, nosotros extracted them to half dozen categories (Gurpi Flysch, Gurpi shale, Ilam, Mishrif, Khatiyah, Mauddud) so divided the issue by six to ascertain the boundaries of the proposed six formations. As far as the reservoir section consists of Ilam and Sarvak formations, we subtracted them to one section to calculate UCS and Phi. The Middle Sarvak Formation (Cenomanian) is believed to exist an important source rock within the Cretaceous petroleum system of the eastern Persian Gulf basin (Alipour 2017; Hosseiny et al. 2016), and every bit far as Baghery et al. (2021) worked on the same reservoir system (Middle Cretaceous (Albian–Thoronian)), we carried out our findings that are similar to them, whereas, by using a simple arroyo, we separated different formations to make information technology more sensible. Equivalent mud weight values in Gurpi formation range from eleven.xviii to 12.61 ppg and in Ilam and Mishrif formations (reservoir section) fluctuated from 9.36 to 13.13 ppg. Similarly, Baghery et al. (2021) concluded that the equivalent mud weight for the reservoir section is from ten to sixteen.8 ppg.

Sensitivity analysis determines how different values of an independent variable affect a particular dependent variable nether a given set of assumptions. In other words, sensitivity analyses study how diverse sources of uncertainty in a mathematical model contribute to the model's overall uncertainty. Tornado charts are usually used for sensitivity analysis, past facilitating the comparison of the effects of one variable (or uncertainty) on the output (value) of an contained variable. Sensitivity assay is performed using tornado plot. Sensitivity analysis reveals the sensitivity of the model to the input parameter variations. The tornado plot is pivotal to agreement some parameters that demand to be more accurately counted every bit practical and useful parameters placed in the plot. Some parameters with maximum variations are placed at the top of the nautical chart. On the contrary, the parameters with minimum variations are placed lower (Fig. 13). The most useful parameter on equivalent mud weight is the maximum horizontal stress slope. On the other hand, the Young'south modulus and Poisson's ratio are the to the lowest degree important (Fig. 13).

Concluding remarks

It was found that the wellbore trajectory and drilling fluid density in operation have a significant impact on the wellbore stability in the study area. Core measurements are very of import to evangelize reliable results, whereas, in our report, no core samples nor the cadre data were available to be used. Still, we have used other datasets utilizing well log data, drilling, and geological data to create a wellbore stability model applicable in the written report area. The unconfined compressive strength (UCS) value in the reservoir zone, including Ilam to Mauddud formations, shows that the condom inclination angle is more than 45° (277° azimuth); alternatively, drilling more than sixty° might bring up different problems such as collapse, boot, increasing drilling costs, and stopping production and somewhen might indeed cause well loss. Consequently, the condom inclination angle for Gurpi germination is 35°, and drilling more l° might bring up diverse problems such as wellbore breakout, wash-out, or tightening.

Geomechanical analysis based on geomechanical parameters illustrates that the direction of minimum horizontal stress and maximum horizontal stress in Gurpi formation is NW–SE and NE–SW, and for Mishrif and Ilam formations is NE-SW and NW–SE, respectively.

Sensitivity analysis shows that the most meaning parameter in the mud weight window is maximum horizontal stress; by contrast, Poisson's ratios and Young's modulus are the least important.

Abbreviations

E :: Young's modulus, GPa (Mpsi)
G :: Shear modulus, GPa (Mpsi)
K :: Bulk modulus, GPa (Mpsi)
S _Hmax :: Maximum horizontal stress, MPa (psi)
S _hmin :: Minimum horizontal stress, MPa (psi)
5 _p :: Compressional wave velocity, k/sec (ft/sec)
μ :: Shear modulus
λ :: Lame'due south coefficient
V _s :: Shear wave velocity, grand/sec (ft/sec)
ΔP :: Deviation between wellbore pressure and pore force per unit area, MPa (psi)
ρ :: Bulk density, g/cm^three (kg/m³)
ρ _w :: Water density, thou/cmⁱⁱⁱ (kg/chiliad³)
σ :: Stress, MPa (psi)
σ _ane :: Maximum principle stress, MPa (psi)
σ ₂ :: Intermediate principle stress, MPa (psi)
σ ₃ :: Minimum principle stress, MPa (psi)
σ _r :: Radial stress at the wellbore, MPa (psi)
σ _y :: Stress in y-axis in Cartesian coordinate system, MPa (psi)
σ _z :: Axial stress at the wellbore, MPa (psi)
σ _zz :: Stress in z-centrality in Cartesian coordinate system, MPa (psi)
${\varepsilon }_{\mathrm{zz}}$ ε _zz :: Axial tensile strain ε _xx
${\varepsilon }_{\mathrm{\blastoff \alpha }}$ :: Bulk strain
${\sigma }_{0}$ :: Or ΔP is the hydrostatic stress
$v$ :: Poisson's ratio, dimensionless;
${\sigma }_{\mathrm{c}}$ :: Uniaxial rock strength
${\sigma }_{\mathrm{t}}$ :: Tangential stress, MPa;
${\sigma }_{\mathrm{h}}$ :: Minimum horizontal stress, MPa;
$\alpha $ :: Biot coefficient;
$V$ :: Poisson'south coefficient
${\sigma }_{\mathrm{V}}$ :: Total (volumetric) mean stress
${P}_{\mathrm{f}}$ :: Drilling fluid pressure level
Due east :: Elasticity modulus (Gpa)
${\varepsilon }_{\mathrm{H}}$ :: Tectonic strains in maximum horizontal stresses
${\varepsilon }_{\mathrm{h}}$ :: Tectonic strains in minimum horizontal stresses
${\sigma }_{\mathrm{H}}$ :: Maximum horizontal stress, MPa;
E :: Elasticity modulus
ε _ax :: Strain in axial direction x
σ _x :: Centric strain in axial direction x
υ :: Poisson'southward coefficient
σ _θ ^' :: Hoop stress alteration due to the introduction of osmotic pressure level, MPa (psi)
τ :: Shear stress, MPa (psi)
υ :: Poisson's ratio, unitless
Ф :: Internal friction angle, degrees
φ :: Wellbore azimuth, degrees
Ø :: Germination porosity, fraction
DTC and DTs:: Compressional slowness and shear slowness (sonic log)
FMI:: Germination micro-imager
DSI:: Dipole shear sonic imager
MDT:: Modular formation dynamics tester
ρ and ρb and RHOB:: Density
D and Z and dz:: Depth
g :: Gravity
tvd:: True vertical depth
Ph:: Hydrostatic pressure level
PP:: Pore pressure
Edyn and Esta:: Young'southward dynamic modulus and Immature's static modulus
ν _dyn and ν _sta :: Dynamic Poisson'due south ratio and static Poisson's ratio
UCS:: Uniaxial compressive strength
α and British indian ocean territory:: Biot coefficient
Cane and C2:: Caliper 1 and caliper 2
LOT/XLOT:: Lake off test and extended leak off test
ε :: Tectonic strain
FIT:: Formation integrity exam
Southwardθ and Sz and Sr:: Tangential stress and centric stress and radial stress
C :: Adhesion coefficient
φ :: Internal friction bending
NPHI:: Neutron porosity
Fiveshale:: Shale volume
CMW_KICK:: Kicking pressure
CMW_LOSS:: Mud loss
CMW_MAX_MTS:: Breakdown pressure
CMW_MIN_MC:: Shear failure minimum pressure
MW:: Mud weight
KICK-BREAKOUT:: Difference between shear failure and kicking
LOSS-BREAKDOWN:: Difference between loss and tensile failure
AIc:: Compressional acoustic impedance
AIs:: Shear impedance
RCc:: Compressional reflection coefficient
RCs:: Shear reflection coefficient
Sv and Sn:: Vertical stress and normal stress
PHIE:: Effective porosity

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Acknowledgements

Thanks are given to anonymous domain experts for their input and insight, without which this inquiry would not have been possible. The second author would like to acknowledge the Research Council of the University of Tehran.

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Science and Enquiry Branch, Islamic Azad University, Tehran, Iran

Masoud Hoseinpour
Institute of Geophysics, University of Tehran, Tehran, Iran

Mohammad Ali Riahi

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Correspondence to Mohammad Ali Riahi.

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Hoseinpour, M., Riahi, K.A. Determination of the mud weight window, optimum drilling trajectory, and wellbore stability using geomechanical parameters in one of the Iranian hydrocarbon reservoirs. J Petrol Explor Prod Technol 12, 63–82 (2022). https://doi.org/x.1007/s13202-021-01399-5

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Received: 23 March 2021
Accepted: 25 November 2021
Published: 08 December 2021
Issue Engagement: January 2022
DOI : https://doi.org/x.1007/s13202-021-01399-5

Keywords

Dynamic modulus
Maximum horizontal stress
Mud weight window boundary
Shear rock failure
Tensile rock failure

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