Scaling-up dynamic elastic logs to pseudo-static elastic moduli of rocks using a wellbore stability analysis approach in the Marun oilfield, SW Iran

Abstract

Wellbore stability analysis is a critical component of petroleum engineering, evaluating the risks of sanding, reservoir compaction, and casing failures. Laboratory rock mechanical measurements must be scaled up to reservoir scales to achieve accurate results. One challenge lies in upscaling dynamic measurements from petrophysical logs to pseudo-static elastic properties, which has significant implications for oil and gas operations. We present a novel approach that combines laboratory rock mechanical measurements with well-log data to develop a mechanical earth model (MEM) for an Iranian oilfield with over 350 wells. We conducted static elastic property measurements on 40 core samples from various layers and depths of carbonate and sandstone rocks, demonstrating the practical application of our approach. By integrating these measurements with dynamic log data and static-dynamic correlations, we established a framework for evaluating the mechanical properties of different layers. Our findings indicate that the safe mud weight window ranges from 41.5 to 118.59 pcf, while the stable mud weight window ranges from 41.5 to 156 pcf. We demonstrate the importance of conducting parallel rock mechanical studies on cores and logs to reduce uncertainties, costs, and risks during oil and gas operations. We also propose a novel methodology combining lithological characteristics, abnormally high pressure, and borehole instability mechanisms to evaluate the stability of borehole walls. This framework provides a fresh perspective on wellbore stability analysis and offers practical solutions for the industry. Essential novel techniques include developing a geomechanical model that integrates laboratory rock mechanical measurements with well-log data to evaluate mechanical properties and calculate safe and stable mud-weight windows. Our study advances wellbore stability analysis by providing a new method for addressing this long-standing challenge. It offers valuable insights for petroleum engineers working in the oil and gas industry.

Introduction

Borehole instability during drilling is a significant problem worldwide. A “tight hole” or “stuck pipe” incident occurs when a well becomes unstable. The primary cause of such incidents is the mechanical collapse of the borehole^1,2,3,4,5. Instabilities are most common in shale or mudstone, often in the overburden but sometimes within the reservoir. Wellbore instabilities account for 5–10% of drilling costs^6,7,8,9,10.

New challenges have emerged, making stability more critical to address. The industry demands more complex well trajectories, such as deviated, multilateral, and horizontal wells. However, stable drilling is typically more challenging in deviated wells than vertical boreholes. Instabilities can also arise in infill drilling, tectonically active areas, and deep, geologically complex surroundings^{11,12,13,14,15,16,17}.

When designing a well, factors like mud weight and composition, casing setting depths, and well trajectory are carefully considered to ensure safe and stable drilling. If an unexpected instability occurs, adjusting the mud composition may be the only feasible solution^{18,19,20,21,22}.

Identifying the underlying cause of an instability is essential before selecting a solution. For example, if the cause is hole collapse, increasing the mud weight may be necessary. If differential sticking is the cause, decreasing the mud weight may be required. However, an incorrect diagnosis can lead to destabilizing the borehole.

Dynamic elastic logs, such as sonic and seismic logs, provide information on the elastic properties of rocks under dynamic conditions. These logs are sensitive to lithology and fluid content and are commonly used to estimate rocks’ shear and bulk moduli. However, dynamic elastic moduli are not directly applicable to wellbore stability analysis, which requires static loading conditions^{23,24,25,26,27}.

Pseudo-static elastic moduli are derived from dynamic elastic moduli by scaling them to pseudo-static conditions. It is crucial for wellbore stability analysis, as it represents the elastic behavior of rocks under static loading conditions^24,28,29,30. Wellbore stability analysis involves assessing the mechanical stability of wellbores to prevent failures such as hole collapse, breakouts, and sand production. Accurate estimation of pseudo-static elastic moduli is essential for wellbore stability analysis to ensure the safety and integrity of wellbores^{5,9,31,32,33,34}.

Previous studies have demonstrated the importance of scaling dynamic elastic moduli to pseudo-static conditions for accurate wellbore stability analysis. Our study aims to contribute to this field by examining the scaling-up of dynamic elastic log data to pseudo-static elastic moduli in the Marun oilfield in SW Iran. Several recent studies have investigated the Mohr–Coulomb and Hoek–Brown failure criteria for specific rock types. Colmenares and Zoback³⁵ found that these criteria worked for specific rock types but noted limitations. Other studies have proposed alternative criteria, such as the Drucker–Prager failure criterion and the Mogi–Coulomb failure criterion^36,37.

Zhang et al.³⁸ developed a dual-porosity fully coupled finite element solution to model inclined wellbores drilled in naturally deformable fractured media. Al-Ajmi and Zimmerman³⁹ introduced the fully polyaxial Mogi-Coulomb failure criterion. They proposed a new 3D analytical model to estimate the mud weight required to avoid failure for vertical wells based on the Mogi-Coulomb failure mechanism coupled with elastic theory. Zhang et al.⁴⁰ developed a dual-porosity fully coupled finite element solution to model inclined wellbores drilled in naturally deformable fractured media.

Researchers have also investigated the effects of chemical and thermal influences on local stress distribution and rock mechanical properties in shale formations. Gallant et al.⁴¹ attempted to use a plane-of-weakness model to account for the effects of weak bedding planes and other discontinuities in high-angle wells drilled into finely laminated rocks. Mody et al.⁴² studied the sustainable development of geomechanics technology to reduce well construction costs.

Dutta and Farouk⁴³ presented a geomechanical risk analysis for a planned horizontal dual-lateral well based on stress regime and well failure with the significance of choosing proper mud weight and drilling parameters using a proper mechanical earth model from a nearby offset well. Siratovich et al.⁴⁴ found that pre-existing fracture occurrence dramatically influences the strength, porosity, elastic moduli, and permeability of an andesite rock in a geothermal reservoir in New Zealand. Eshiet and Sheng²⁰ performed a stochastic design in wellbore drilling operations. Sharifi et al.⁴⁵ evaluated an innovative application of extended elastic impedance (EEI) for the geomechanical interpretation of hydrocarbon reservoirs.

More recently, Heap et al.⁴⁶ presented a method to upscale laboratory measurements to the rock mass scale with more realistic values of elastic moduli for volcano modeling. Sharifi et al.⁴⁷ developed a relationship between static Young’s modulus and seismic parameters. Qiu et al.²⁸ proposed a pseudo-3D coupled hydraulic-mechanical model for inclined wellbores in transversely isotropic formations. Pirhadi et al.⁵ presented a finite element analysis of coupled thermo-poro-elastic units for wellbore stability in the Mansouri depleted reservoir in SW Iran. Finally, Khah et al.²⁴ estimated the elastic properties of sediments by generating pseudo-wells using a simulated annealing optimization method^25,48,49.

The main objectives of this study are:

• To understand petroleum-related rock mechanics and its applications in petroleum engineering.

• To comprehend mechanical earth models, including the procedures and data required to construct them.

• To make regional correlations between different mechanical properties of reservoir rocks.

• To investigate the mechanisms and procedures for complete log-based wellbore stability and determine safe and stable mud windows.

The innovation and novelty of this research lie in developing a method for scaling up dynamic elastic log data to pseudo-static elastic moduli of rocks, specifically for wellbore stability analysis. This approach addresses the challenge of extrapolating laboratory rock mechanical measurements from core-scale to reservoir-scale.

By utilizing petrophysical log data and incorporating static-dynamic correlations of elastic rock moduli, this study provides a cost-effective and time-efficient solution for estimating the pseudo-static elastic properties of rocks. Accurately predicting these properties at reservoir-scale levels can significantly enhance the efficiency and reliability of wellbore stability analysis and other geomechanical studies.

The incorporation of static-dynamic correlations and developing a mechanical earth model for an oilfield in this study demonstrate this approach’s practical application and effectiveness. The results obtained from this research can serve as a valuable resource for future studies and rock mechanic works in similar geological settings, ultimately reducing uncertainties, costs, and risks associated with wellbore operations.

While the research method in this paper may not revolutionize the field of wellbore stability analysis, it does offer a unique approach to scaling up dynamic elastic log data to pseudo-static elastic moduli of rocks. This methodology, which combines lithological characteristics, abnormally high-pressure mechanisms, and borehole instability mechanisms, provides a novel framework for evaluating the stability of borehole walls. Our research advances wellbore stability analysis by developing a new method for addressing this long-standing challenge.

Moreover, our study’s recommendations for improving laboratory data accuracy and conducting more comprehensive field studies are relevant and innovative. By proposing triaxial compressive strength tests and incorporating stress regimes and directions into geomechanical modeling, our research offers fresh insights and practical solutions for the industry.

Geological setting

Study area

This study gathers information primarily from the Asmari reservoir in Iran’s Marun oilfield, located approximately 50 km southeast of Ahwaz in southwestern Iran^50,51,52,53. The field is elliptical, measuring 65 km long and 8 km wide. It is situated in a belt of northwest-southeast trending fields between the Persian Gulf and the Zagros Mountains^{5,26,54,55,56,57,58}. The nearest field, Aghajari, is less than two kilometers from Marun’s southeastern edge (Fig. 1).

Figure 1

Marun oilfield in Dezful Embayment of Zagros basin^5,54,55.

Structurally, Marun is a symmetrical anticline typical of large Iranian fields. The southwest flank is the steepest, with dips reaching 60°–70°. In contrast, the northeast flank is gentler, with dips rarely exceeding 45°^59,60,61,62.

Stratigraphically, the Asmari reservoir is a 290–350 m thick sequence of Oligocene and Miocene carbonates and sands. Below it lies shaley marls of the Pabdeh Formation. Lithologically, the Asmari reservoir is predominantly a carbonate unit composed of alternating dolomites, limestones, and limey shales^{54,55,63,64,65,66}. In southern Khuzestan, sandstones interface with carbonates. Marun is located where both types are present. Evaporates are present elsewhere in the Asmari reservoir but are evident at Marun^50,67,68.

General stratigraphy

The Asmari Formation is a significant hydrocarbon reservoir in the Marun oilfield in southwest Iran. It consists of carbonate rocks deposited during the Oligocene–Miocene epochs, comprising limestone, dolomite, marl, sandstone, and shale^{49,54,55,60,63}. The rocks indicate a shallow marine environment with high-energy bioclastic facies and intense wave action. Fossil remains are abundant, further supporting a shallow marine depositional environment^59,61. The reservoir rocks exhibit high porosity and permeability due to diagenetic alterations such as cementation and fracturing (Fig. 2).

Figure 2

General stratigraphy of the Marun oilfield in the Dezful Embayment of Zagros basin^54,61,63.

The structural geology and stratigraphy of the Marun oilfield have significantly impacted the productivity and potential of the Asmari reserve^25,68,69. The heterogeneous formation poses challenges to fluid flow and oil recovery. Faults and folds within the field create traps for hydrocarbons, making it essential to understand the geology to optimize oil extraction. Ongoing research and exploration efforts improve our understanding of the field and enhance oil recovery techniques. The Asmari reserve in the Marun oilfield represents a significant hydrocarbon-bearing reservoir with favorable properties crucial for regional oil and gas production^{50,54,55,63,70}.

Methodology

The flowchart for this study is presented in Fig. 3. It illustrates the general steps involved in scaling up dynamic elastic logs to pseudo-static elastic moduli using a wellbore stability analysis approach in the Marun Oilfield, southwest Iran. The flowchart allows for iterative process refinement, enabling more accurate predictions of rock mechanical behavior and reduced uncertainty.

Figure 3

General study flow chart including pseudo-static elastic moduli using a wellbore stability analysis approach in the Marun Oilfield.

Laboratory tests for rock mechanic property determination

The stress level at which a rock fails is generally referred to as its strength. Rock strength is meaningful only when the stress geometry, including test type and laboratory setting, is specified. If the test involves zero confining stress, it is a uniaxial test. Otherwise, a triaxial test is performed^{12,71,72,73,74,75}. This study focuses on uniaxial stress tests based on unconfined compression tests.

Anisotropy is a crucial concept in rock mechanics that affects how rocks behave in different layers. In wellbore stability, anisotropy refers to the variation in rock properties with direction. Rock properties change depending on the measurement direction, impacting accuracy. Ignoring anisotropy can lead to inaccurate wellbore stability predictions, incorrect minimum horizontal stress estimation, and incorrect mud weight calculations. The study highlights the importance of anisotropy and suggests using advanced data integration techniques like machine learning and AI to mitigate its effects. The study addresses anisotropy by relating lab data to log data using regional correlations. The authors recognize that rocks are not homogeneous and isotropic, so they use non-destructive measurements to solve stability problems.

Drained and undrained test conditions

In drained tests, the pistons’ outlets are open, allowing pore fluid pressure to be maintained at a specified value. Typically, the outlets are open to the atmosphere, resulting in a pore fluid pressure of zero. In this case, the sample’s effective stresses equal its total stresses. However, conducting tests under actual reservoir conditions is sometimes necessary, where pore pressure is maintained at the reservoir pressure level.

In undrained tests, the outlets are closed, preventing pore fluids from escaping. If pore fluid pressure is to be measured, hydraulic contact must be established through one outlet, but fluid flow must not occur^16,17,76. Undrained conditions are commonly used for testing highly low-permeability rocks, such as shale.

Unconfined (uniaxial) compression tests (UCS)

In an unconfined compression test, a sample is inserted into a load frame and subjected to increasing axial load under zero confining pressure. Our experiments tested the specimens at room temperature and in dry conditions. The specimens from the reservoir were not washed to preserve their natural conditions. All specimens were tested at a stress rate of 0.75 to 1.0 MPa/s. The typical sample diameter for petroleum applications is 38 mm. The axial stress and axial and radial deformations were monitored during the test. Under drained conditions, measuring the axial stress and deformations is possible^5,15,77,78.

The unconfined compressive strength (C₀) is the peak stress reached during the test.

Young’s modulus (E_t), the tangential modulus, is the slope of the axial stress versus the axial strain curve.

Poisson’s ratio (ν) is calculated as the radial strain to axial strain ratio.

To calculate these properties, we first determine the axial Young’s modulus (E) by calculating the slope of the more or less straight line portion of the stress–strain curve. The tangent modulus (E_t) is reported as the value of E at 50% of the maximum strength, as described in Eq. (1).

$$\begin{gathered} E = \frac{\Delta \sigma }{{\Delta \varepsilon_{A} }} \hfill \\ \varepsilon_{A} = \Delta L/L \hfill \\ \end{gathered}$$

(1)

where E is the slope of the axial curve, ε_A represents the axial strain, ΔL is the change in measured length (negative for a decrease and positive for an increase). The value of Poisson’s ratio (ν) is calculated from the Eq. (2):

$$\begin{gathered} \nu = - \frac{{\Delta \varepsilon_{L} }}{{\Delta \varepsilon_{A} }} \hfill \\ \varepsilon_{L} = \Delta D/D \hfill \\ \end{gathered}$$

(2)

where Δε_L is the lateral strain, determined using the same methodology as Young’s modulus, and D is the diameter of the original, undeformed specimen^{35,74,79,80,81,82}.

Figure 4A shows a typical result from a uniaxial test. The applied axial stress (denoted σ) is plotted as a function of the axial strain (ε_A) and lateral strain (ε_L) of the sample.

Figure 4

(a) Principle sketch of stress versus deformation in a uniaxial compression test, (b) Mohr–Coulomb strength in effective stress domain. Shear failure plane under triaxial compression, and in the shear plane, (c) Mohr circles and strength criterion^9,74,83.

The most common failure modes in uniaxial and triaxial tests are shear failures caused by excessive shear stress. Another failure mode is tensile failure, resulting from excessive tensile stress. Delving deeper, we find that rock failure is intricately linked to the state of the solid framework. The stresses that trigger failure are the effective stresses the framework experiences. This understanding adds complexity and intrigue to our study of rock mechanics^2,73,77,84.

Mohr–Coulomb criterion

Shear failure occurs when the shear strength of a formation is exceeded. The Mohr–Coulomb failure criterion can be used to determine the failure mechanism for porous media, as described in Eq. (3):

$$\tau = c + \sigma^{\prime}\tan \varphi$$

(3)

where σ′ is the normal effective stress; τ is the shear stress; φ is the angle of internal friction and C is the cohesion (also referred to as the inherent shear strength of the material).

In the principal stress space (σ₁′, σ₂′, and σ₃′), the Mohr–Coulomb failure criterion can be expressed as Eqs. (4–6):

$$\sigma^{\prime}_{1} = UCS + q\sigma^{\prime}_{3}$$

(4)

where σ₁′ and σ₃′ are the maximum and minimum effective principal stresses, respectively

$$q = \frac{1 + \sin \varphi }{{1 - \sin \varphi }}$$

(5)

$$UCS = \frac{2\cos \varphi }{{1 - \sin \varphi }}$$

(6)

Figure 4B,C depict the Mohr circle and Mohr–Coulomb strength envelope. Failure does not occur when σ′ and τ values lie below this envelope. The Mohr–Coulomb criterion has two critical implications: (i) the intermediate principal stress σ₂′ does not affect failure, potentially leading to overestimation; (ii) the plane of shear fracture passes through the direction of the intermediate stress.

Hoek–Brown criterion

Laboratory triaxial test results often show a curved strength envelope^35,85,86,87. Researchers have proposed non-linear criteria based on laboratory tests^47,74,85,88. Hoek and Brown⁸⁵ proposed a criterion for estimating rock mass strength for excavation design. At failure, the relationship between maximum and minimum principal stresses is given by Eq. (7):

$$\sigma_{1} = \sigma_{3} + \sqrt {mc_{0} \sigma_{3} + sC_{0}^{2} }$$

(7)

The material constant of s takes a value 1 for intact rock and less than unity for disturbed rock. The values of m vary from rock to rock, ranging from approximately 1.4–40.7^{11,26,71,89,90}.

Mogi-Coulomb criterion

Mogi³⁶ conducted the first extensive polyaxial compressive tests on rocks. He noted that intermediate principal stress affects rock strength, and brittle fracture occurs along a plane striking in the σ₂ direction. This agrees with later observations from other researchers^{71,81,87,91,92}. Since the fracture plane strikes in the σ₂ direction, Mogi concluded that the mean normal stress opposing fracture is σ_m,2, not the octahedral normal stress (σ_oct). . As a result, Mogi proposed a new failure criterion described by Eq. (8):

$$\tau_{oct} = f(\sigma_{m,2} )$$

(8)

where f here is some monotonically increasing function.

The distortional strain energy is proportional to the octahedral shear stress^{35,93,94,95,96}. This criterion is equivalent to asserting that failure will occur when the distortional strain energy reaches a critical value that increases with σ_m,2. The failure envelope in σ_oct—σ_m,2 space is not explicitly defined by a formula but is typically obtained experimentally.

Tensile failure criteria

Tensile failure occurs when the effective tensile stress across a sample plane exceeds the critical limit of tensile strength, represented by T₀. It represents the same unit as stress, a characteristic rock property. Sedimentary rocks typically have a low tensile strength, usually a few MPa or less. For many applications, the tensile strength is assumed to be zero. Tensile failure occurs when the effective stress becomes tensile and equals or exceeds the formation’s tensile strength (Eq. (9)):

$$\sigma^{\prime}_{3} = - T_{0}$$

(9)

where T₀ is the tensile strength; σ₃′ is the minimum effective principal tensile stresses (note that σ₃′ is negative).

Zhang et al.⁹ suggested that fractures arise from stress concentration at Griffith crack tips, which are assumed to permeate the material. A fracture initiates when the maximum stress near the tip of the most favorably oriented crack reaches a value characteristic of the material. Griffith failure occurs if Eqs. (10–11) are met for a dry material:

$$\begin{gathered} {\text{If }}\;\sigma_{1} + 3\sigma_{3} > 0 \hfill \\ (\sigma_{1} - \sigma_{3} )^{2} = 8T_{0} (\sigma_{1} + \sigma_{3} ) \hfill \\ \end{gathered}$$

(10)

$$\begin{gathered} {\text{If }}\sigma_{1} + 3\sigma_{3} < 0 \hfill \\ \sigma_{3} = - T_{0} \hfill \\ \end{gathered}$$

(11)

when σ₃ = 0 i.e. uniaxial compression, so the uniaxial compressive strength (UCS) predicted by Eq. (10) (UCS = σ₁) could be written as Eq. (12):

$$UCS = 8T_{0}$$

(12)

It is worth noting that Eq. (11) underestimates the uniaxial compressive strength of some rocks. According to the modified Griffith theory, there is a relationship between the uniaxial compressive strength and tensile strength, which can be described by Eq. (13):

$$UCS = \frac{4(1 + \sin \varphi )}{{1 - \sin \varphi }}T_{0}$$

(13)

where φ is the internal friction angle of the material. Another extension of the Griffith criterion gives that the uniaxial compressive strength is 12 times of the tensile strength as Eq. (14) ^87,96:

$$UCS = 12T_{0}$$

(14)

Selecting a reasonable strength criterion, a process of significant complexity is crucial in determining the critical collapse pressure of a wellbore. However, the current study must clearly explain how to select a reasonable strength criterion scientifically. There are several intricate factors to consider when selecting a strength criterion.

The type of rock being studied is essential. Different rock types have distinct mechanical properties, affecting the strength criterion selection. For example, sandstone and shale have different failure mechanisms and require different strength criteria. Stress conditions should also be considered when selecting a strength criterion. Rocks under compressive stress may require a different strength criterion than those under tensile stress. Additionally, factors such as overburden pressure, pore pressure, and tectonic stress can affect the selection of the strength criterion.

Drilling parameters like mud weight, mud composition, and well trajectory can also influence the selection of a strength criterion. Experimental data from triaxial tests or other experiments can provide valuable information on the rock’s mechanical properties and help select a reasonable strength criterion. The scale at which the rock is being studied should also be considered. For instance, laboratory tests may require a strength criterion different from field measurements. Finally, uncertainty associated with measuring rock properties and selecting a strength criterion should be considered.

By considering these factors and providing a clear explanation of the selection process, researchers can provide a more comprehensive discussion on selecting a reasonable strength criterion for predicting borehole stability. This study recommends using the Mohr–Coulomb failure criterion to determine shear failure conditions but also suggests considering alternative methods, such as numerical models or experimental testing, to provide more accurate results.

Static and dynamic elastic moduli of rock

Elastic moduli can be derived from various methods, yielding static or dynamic constants. Static elastic properties are measured through static deformation in an open system, whereas dynamic properties are derived from wave propagation measurements.

Although reservoir rocks deform relatively statically in situ, obtaining static elastic moduli is often impractical. Even when core samples are available, measuring elastic properties for the entire well column is not feasible. In contrast, full-waveform sonic logs with density logs provide continuous data to derive dynamic moduli. Corrections are necessary to convert dynamic properties into their static equivalents^45,46,74.

There is no universal relationship or method for deriving static values from dynamic measurements. Empirical relationships have been applied conventionally, but care must be taken when using them, as they were obtained for specific rock types and conditions. Static elastic properties of rocks are typically measured using standard stress–strain tests, where strain gages are attached to core samples in one or multiple directions (Table 1). Confining pressures or uniaxial loading are then increased incrementally while the gages measure deformation^47,97,98,99.

Table 1 Elastic properties of rocks^{11,72,97,101,102,103}.

Static tests involve high strain amplitudes (typically > 10^–2), causing flat pores, cracks, and grain boundaries to undergo anelastic deformation, making the rock appear more compressible^42,72,97,100.

Wave propagation measurements determine the dynamic elastic moduli in laboratory cores or through sonic logging in wells. In the laboratory, resonance and seismic pulse methods can be employed to measure the elastic moduli. The resonance method involves measuring the resonant frequency of a vibrating bar at 500 kHz to determine the dynamic Young’s modulus. The seismic pulse method uses piezoelectric transducers to emit pulses of compressional and shear waves and measures the travel times. The relationships between elastic moduli and V_s and V_p are as expressed by Eqs. (15–18):

$$E = \rho V_{S}^{2} \frac{{3V_{P}^{2} - 4V_{S}^{2} }}{{V_{P}^{2} - V_{S}^{2} }}$$

(15)

$$\nu = \frac{{V_{P}^{2} - 2V_{S}^{2} }}{{2(V_{P}^{2} - V_{S}^{2} )}}$$

(16)

$$K = \rho \left( {V_{P}^{2} - \frac{4}{3}V_{S}^{2} } \right)$$

(17)

$$G = \rho (V_{s}^{2} )$$

(18)

where K, G, E, and ν refer to the bulk modulus, shear modulus, Young’s modulus, and Poisson’s ratio, respectively.

In dynamic measurements, strains are typically less than 10^–6. Under these low strain amplitudes, the deformation of flat pores, cracks, and grain boundaries is elastic, making the rock appear less compressible or deformable^5,24,45,104.

Static – dynamic correlations

Static and dynamic values exhibit distinct differences, with static values typically being lower than their dynamic counterparts. The disparity between these values is attributed to various factors, including measurement technique and rock features. Factors such as strain amplitudes, frequencies, system type, and measurement uncertainties are among those related to the measurement technique.

The geometry and density of pores, cracks, fractures, and grain boundaries significantly impact the differences between static and dynamic elastic properties. However, it is now widely accepted that strain amplitude has the most significant effect on these differences.

As previously mentioned, the nature of rocks prevents the development of a general relationship between static and dynamic properties. Therefore, empirical correlations must be developed. Wang and Nur⁹⁷ have summarized many empirical correlations for Young’s modulus, which primarily apply to reservoir rocks such as unconsolidated sands, sandstones, and carbonates. These correlations typically follow a general form, as shown in Eq. (19)^{45,47,104,105}.

$$E_{s} = a \times E_{d} + b$$

(19)

The static Young’s modulus, E_s, relates to the dynamic Young’s modulus, E_d. Coefficients ‘a’ and ‘b’ range from 0.41 to 1.15 and − 15.2 to 10.81, respectively. Moduli and coefficient ‘b’ are measured in GPa. These correlations are shown in Fig. 5, with the numbers following the lines indicating the source.

Figure 5

Compilation of static-dynamic correlations^7,72,97.

.

Recent triaxial measurements were conducted on thirteen consolidated cores, including clean sandstones, shaley sandstones, limey sandstone, and dolomite. Confining pressures ranged from 0 to 5,000 psig (pounds per square inch gauge), and differential stresses reached 5,000 psig. Researchers found that the relationship between static and dynamic Young’s modulus for stress-cycled sandstone cores can be described by Eq. (20).

$$\left( {\frac{{E_{s} }}{{E_{d} }}} \right) = 0.81 + (2 \times 10^{ - 4} \times P)$$

(20)

In this regard, the differential stress, P, is measured in pounds per square inch (psi). It is evident that when pressures exceed 950 psi, the static Young’s modulus becomes more significant than the dynamic Young’s modulus.

Studies investigated the relationships between the static Young’s modulus (E_s), dynamic Young’s modulus (E_d), and bulk density (ρ) for 76 samples sourced from three locations. By creating a correlation matrix, the researchers selected a relation that best fits the data, yielding Eq. (21) with a high correlation coefficient (r = 0.96).

$$\log (E_{s} ) = 0.02 + 0.77 \times \log (\rho E_{d} )$$

(21)

where E_s and E_d are in GPa and ρ is in g/cm^{3 47,74,87}.

Limitations and advantages

Limitations

• The primary limitation of scaling up dynamic elastic log data to pseudo-static elastic moduli of rocks is that the relationship between dynamic and static elastic properties may not remain constant across different rock types and formations, leading to potential inaccuracies in the analysis.

• The accuracy of correlations and data used in the upscaling process is also a limitation, as improper validation and calibration can result in erroneous predictions of wellbore stability and other geomechanical issues^105,106.

Advantages

• The primary advantage of scaling up dynamic elastic log data to pseudo-static elastic moduli is the high cost and time savings compared to traditional laboratory tests on core samples. Well log data, collected during drilling operations, allows for rapid estimation of rock mechanical properties.

• This approach enables a more comprehensive and detailed analysis of wellbore stability and geomechanical issues applicable to many wells and formations. This leads to a more robust understanding of subsurface conditions and better-informed decision-making during well planning and drilling operations.

• Combining laboratory measurements with well log data improves the accuracy and reliability of results, leading to more confident interpretations of rock geomechanical properties. This ultimately helps optimize well designs, reduce risks, and increase efficiency and productivity in oil and gas operations^{5,24,54,56,107,108}.

In summary, the limitation of scaling up dynamic elastic log data requires standard stress–strain tests. However, this approach offers the advantage of integrating laboratory rock mechanical measurements with petrophysical log data to ensure more accurate wellbore stability analysis. This method reduces uncertainties, costs, and risks in designing and operating oil wells by correlating an Iranian south oilfield’s static and dynamic elastic properties.

Results

Wellbore stability evaluation in the Marun field

The focus of this study is the Asmari reservoir in the Marun oilfield. To establish correlations, we required core data from various layers. The Marun oilfield has over 350 drilled oil wells, of which 42 have undergone coring operations, with 20 of these operations occurring in the Asmari reservoir. The remaining wells are part of the lower Bangestan group Formations. To ensure a comprehensive range of data, we utilized cores from 9 wells.

The Marun anticline is divided into eight sectors, stretching from East to West. The following wells were selected for core sampling: W507N (No. 351) and W465N (No. 263) in Sector 1, W358N (No. 63) in Sector 2, W293N (No. 292) in Sector 3, W13N (No. 20) and W149N (No. 359) in Sector 5, and W130N (No. 68) and W5N (No. 16) in Sector 7. Figure 6 illustrates the location of the wells considered in this study on the Marun Underground Contour Map (UGC).

Figure 6

Marun oilfield and the location of considered wells to use in correlation (M351, M263, M63, M292, M20, M359, M68, and M16) and wellbore stability analysis (M350)^50,51,52,53, (Created by AUTODESK Map 6, and edit by Photoshop CS.8).

Laboratory results of UCS tests

This study tested all specimens at dry and room temperatures to maintain their natural state. This test measured samples in dry and vacuumed conditions and the fluid was added to the sample. Specimens from reservoirs were unwashed to preserve their natural conditions. We present a description of the UCS tool’s schematic. The triaxial apparatus consists of:

Cylindrical chambe: A cylindrical chamber, 38 mm in diameter and 76 mm long, where the sample is placed.

Lateral arms Three orthogonal arms (x, y, and z axes) apply confining pressure to the sample, connected to a load cell that measures the applied force.

Axial load cell This load cell measures the axial force on the sample.

Control panel The panel sets test parameters, including confining pressure, stress rate, etc.

Data acquisition system The system records axial and lateral deformation of the sample during the test.

The triaxial apparatus tests UCS samples by applying a constant stress rate of 0.75–1.0 MPa/s while monitoring axial and lateral deformation. The typical diameters of the samples ranged between 36 and 38 mm. Figure 7 shows a characteristic curve for the stress–strain test of sample number 20F. Table 2 summarizes the results of the uniaxial compressive strength tests, including the unconfined modulus of elasticity and Poisson’s ratio. Of the 40 samples, 25 came from carbonate and 15 from sandstone layers..

Figure 7

Typical stress–strain curve for uniaxial test (sample number 20F carbonate rock).

Table 2 Results of uniaxial compressive strength tests plus unconfined modulus of elasticity and Poisson’s ratio in the Marun oilfield Asmari reservoir.

While the provided information does not offer a direct explanation for why some carbonate samples in Table 2 have a Poisson’s ratio greater than 0.3, it is worth noting that this parameter can be influenced by various factors, such as the material’s microstructure, porosity, and the presence of defects. Carbonate rocks, including limestone and dolomite, exhibit a wide range of Poisson’s ratios due to their complex mineralogical and textural composition. The presence of significant porosity or vuggy space in these rocks can impact their mechanical behavior, leading to a higher Poisson’s ratio. Further investigation would be necessary to determine the specific reasons behind the elevated Poisson’s ratios observed in certain carbonate samples. Nevertheless, it is possible that high porosity or defects within the samples may contribute to their higher values.

To obtain Dynamic elastic Young’s Modulus, Eq. (22) and the density and Acoustic logs in each well have been employed.

$$E_{d} \left[ {psi} \right] = \frac{{\rho \left[ {gr/cc} \right]}}{{\Delta t_{s}^{2} }} \times \frac{{9\Delta t_{s}^{2} - 6\Delta t_{p}^{2} }}{{3\Delta t_{s}^{2} - \Delta t_{p}^{2} }}$$

(22)

The triaxial test measures the mechanical properties of rock samples by applying three types of stresses: axial compression, lateral confinement, and shear stress. The test design refers to the experimental setup used in the triaxial test. The sample is subjected to a constant axial load during the test, while lateral deformation is monitored over time. A pressure–time curve is obtained by plotting the measured pressure against elapsed time. The curve shows the sample’s deformation and stress response, providing valuable information on its mechanical properties, such as Young’s modulus, Poisson’s ratio, and uniaxial compressive strength. The curve helps determine the sample’s elastic behavior and identify potential failure mechanisms. In wellbore stability analysis, triaxial test data can be correlated with field data to develop a model that accounts for mechanical effects in different rock layers, enabling prediction and prevention of wellbore instability.

In none of the Marun field wells, dipole sonic logs were rarely used; therefore, Eqs. (23–24) were employed to convert compressional to shear wave velocities.

$$\Delta t_{s} = 2.53169 \times \left( {\Delta t_{c} } \right)^{0.9317}$$

(23)

$$\Delta t_{s} = 1.7891 \times \Delta t_{c} + 7.622$$

(24)

Figures 8a,b and 9a,b depict the relations between static and dynamic Young’s modulus, static and dynamic Poisson’s ratio, and also dynamic Young’s modulus and uniaxial compressive strength in sandstone and carbonate formations respectively. The correlation of Eqs. (25–28) obtained for different rock types:

$$E_{s} = 7 \times 10^{ - 8} \times \left( {E_{d} } \right)^{7.959} Sandstone \, Formation$$

(25)

$$E_{s} = 0.432 \times \left( {E_{d} } \right)^{0.741} Carbonate \, Formation$$

(26)

$$UCS = 0.292 \times \left( {E_{d} } \right)^{2.15} Sandstone \, Formation$$

(27)

$$UCS = 11.36 \times \left( {E_{d} } \right)^{0.327} Carbonate \, Formation$$

(28)

Figure 8

Static-Dynamic correlation for Young’s Modulus in (a) sandstone formation, (b) carbonate formation.

Figure 9

Correlation between UCS and dynamic Young’s Modulus in (a) sandstone formation, (b) carbonate formation.

Uniaxial compressive strength (UCS) measurements are expected to be highly sensitive to sample heterogeneity and cracking caused by coring and core treatment procedures. This is particularly true for weak rocks, where significant experimental uncertainties are anticipated. As UCS is a crucial parameter in many petroleum-related rock mechanics applications, it is essential to consider alternative methods to obtain or estimate it. One potential approach is to perform triaxial tests, which can provide more accurate results. It is important to note that static elastic parameters used in these correlations are derived from laboratory tests on intact rock samples. In contrast, dynamic elastic parameters are obtained from log data and rock mass characteristics.

In Fig. 8a,b, the correlation coefficient of 0.6 is relatively low; our findings reiterate the importance of further research into the correlation between static and dynamic Poisson’s ratio, particularly in the context of wellbore stability applications. While our study did not find a significant correlation, this is an area of immediate relevance and worthy of further investigation, given the crucial role of Poisson’s ratio in wellbore stability applications.

Most of the correlations available in the literature are for Young’s modulus, making it challenging to find correlations reported for Poisson’s ratio. None of the previous studies reviewed in the literature found a correlation between static and dynamic Poisson’s ratio. However, even in this case, no correlation between the static and dynamic Poisson’s ratio was observed. Our study also needed help finding suitable matches between static and dynamic values of Poisson's ratio. Figure 10a,b show the results of dynamic versus static Poisson’s ratio for sandstone and carbonate formations, respectively.

Figure 10

Dynamic versus Static Poisson’s ratio for (a) Sandstone formation and (b) Carbonate formation, no correlation between the static and dynamic Poisson’s ratio was observed.

Our findings underscore the need for further research into the correlation between different values of Poisson’s ratio. While the specific value of Poisson’s ratio may not significantly affect our calculations, it is a crucial parameter in wellbore stability applications, typically chosen within the range of 0.2–0.6. In our study, we used a value of 0.3. This lack of correlation could potentially impact the accuracy of such applications, highlighting the importance of our proposed further research.

Discussion

Constructing mechanical earth model (MEM)

At least four fundamental properties, including in-situ stresses, pore pressure, uniaxial compressive strength, and elastic modulus, must be known as input parameters for a geomechanical model to ensure a safe mud window. A log-based model is presented here for weighted block simulation (WBS) analysis. In our study, we chose well number 350 due to its newness and availability of mud log data, which allowed us to retrieve the required data to create a preferred model. The procedure for modeling to obtain the necessary parameters is presented in a sequential manner below:

Overburden Stress (S_v), E and UCS profile

Mathematically, the magnitude of S_v can be calculated by integrating rock densities from the surface to the depth of interest, z (Eq. (29)):

$$S_{V} = \int\limits_{0}^{z} {\rho (z) \times } g \times dz \approx \overline{\rho }_{avg} gz$$

(29)

where ρ(z)is the density as a function of depth, g is the gravitational acceleration constant and $\overline{\rho }$ is mean overburden density, and "g" is the gravitational acceleration (9.81 m/sec2) . The density log is used to find the overburden stress; at first, the bulk density data is extrapolated to the surface by an exponential trend and satisfying the density of 1.8 g/cc at 26 m; the Eq. (30) was designed.

$$\rho_{b} (D) = 1.8 \times \left( e \right)^{A \times (D - 26)}$$

(30)

where A is a parameter to be determined, we used MATLAB 2021a [https://www.mathworks.com/academic] to determine the value of A, a common practice in geophysics and engineering.

The Eq. (30) is an empirical model, not derived from first principles. It is only valid for the specific dataset used to determine the value of A. The model assumes a single lithology with a uniform density-depth relationship, which may not accurately represent real-world overburden compositions. This equation also does not account for other factors that affect overburden stress, such as pore pressure, rock strength, and anisotropy. We obtained Eq. (31) through this analysis.

$$\rho_{b} (D) = 1.8 \times \left( e \right)^{{7.969 \times 10^{ - 5} \times (D - 26)}}$$

(31)

To find the overburden stress at D = 3300 m, an integration of Eqs. (29–31) is needed as Eq. (32):

$$S_{V} (D = 3300) = \int\limits_{0}^{3300} {1.8 \times } e^{{7.969 \times 10^{ - 5} \times (D - 26)}} dD = 74,045.88\;{\text{KPa}}$$

(32)

For the next sections, the trapezoidal integration role was used to find the overburden stress as Eq. (33):

$$S_{V2} = S_{V1} + (D_{2} - D_{1} ) \times \frac{{\rho_{b2} + \rho_{b1} }}{2} \times g$$

(33)

The results of calculating overburden stress is shown in Fig. 11. As it evident, the overburden stress gradient is about 13.3 kPa/m. To apply obtained correlations it is needed to know the formations along the borehole. Here mud log data from well number 350 was used to specify the rock type in each depth. Figure 12 illustrate a section of mud log data which shows the lithology across the drilled well. Figure 12 presents the graphical mud log data for Well Number 350 in the Asmari Formation of the Marun oilfield. The data represents the lithology, depth, and penetration rate (ROP) along the wellbore. The graph shows:

• Rate of Penetration (ROP): The y-axis displays the penetration rate, measuring how fast the drilling bit moves through rock. ROP is higher in limestone and sandstone, indicating that these formations are more easily drilled than shale.

• Depth: The x-axis represents the wellbore depth, with increasing values indicating deeper depths.

• Lithology: The graph shows the types of rocks, including limestone, shale, and sandstone. Limestone is the dominant lithology, with smaller amounts of shale and sandstone.

• Main Lithology: The graph shows that the main lithology present in the wellbore is limestone, with a smaller amount of shale and sandstone.

Figure 11

Overburden stress corresponding to extrapolated (upscaled) density log.

Figure 12

Graphical mud log data shows the lithology along well number 350 in the Asmari Formation of Marun oilfield.

The graphical mud log data in Fig. 12 visually represents lithology and ROP along the wellbore, which helps understand geomechanical properties and predict wellbore stability.

To calculate in situ horizontal stresses (σ_h and σ_H) it is necessary to know the amount of Young’s modulus. To find these values across the well first we used sonic and density log data and calculate dynamic Young’s modulus by implementing Eq. (22). Graphical well log was then used to specify type of lithology in each depth. Finally by utilizing obtained correlations for each lithology we estimate static Young’s modulus by Eqs. (25) and (26). Figure 13a illustrate the results of these calculations in well number 350. Equations (27) and (28) were also used to estimate UCS profile accrues the wellbore for each lithology. Figure 13b shows UCS profile in reservoir section in well 350.

Figure 13

(a) Dynamic and Static Young’s modulus, (b) Uniaxial Compressive Strength for Asmari reservoir section across borehole.

Pore pressure

Pore pressure was estimated using the Drilling Office X 2.8.572 [https://www.bundlecg.com/product/schlumberger-drilling-office-x-2-8-572/] software and the PPW (pore pressure window) toolbox. The PPW toolbox predicts pore pressure profiles using the Eaton method based on resistivity, gamma ray, and sonic logs. Other methods, such as Bowers, sequential Gaussian simulation (SGS), machine learning, and artificial intelligence (AI) techniques, can be employed to analyze large datasets and estimate pore pressure. These methods are suggested for future work in this oilfield.

The Eaton method is based on the premise that when acoustic or electrical values of clean shales are read directly from logs and plotted as a function of depth on semi-log paper, a normal trend line exists through the normally pressured section. A deviation of the log-derived values from this normal trend line indicates abnormal pore pressure. The calculation is based on the generic Terzaghi effective stress principle equation for shale, as expressed in Eq. (34):

$$G_{pp} = G_{ob} - (G_{ob} - G_{N} ) \times \left[ {\frac{{R_{o} }}{{R_{N} }}} \right]^{a}$$

(34)

where: G_pp = pore pressure gradient of a given depth (psi/ft), G_ob = overburden pressure gradient at the given depth (psi/ft), G_N = normal pore pressure gradient (0.465 psi/ft), R_o = shale resistivity at the given depth, refers to a measured log value (ohm-meters), R_N = normal compaction line shale resistivity, refers to what that log values would read in the absence of over-pressure, (ohm-meters), a = exponent coefficient, it is normally 1.2, but can have a range from 0.9 to 2.00.

While the Eaton method is widely used for predicting pore pressure in various geological settings, it may only partially be suitable for predicting pore pressure in a formation that includes multiple lithological types, such as shale, sandstone, carbonate rock, and others. The Eaton method assumes that the normal trend line for clean shales can be used to estimate pore pressure, but this assumption may only hold for some lithological types.

In this study, the Asmari reservoir is a complex sequence of carbonates and sands of the Oligocene and Miocene ages, with carbonates and sandstones present. A single method, such as the Eaton method, may not accurately capture the varying pore pressure responses in different lithological types.

Future studies could consider employing more advanced methods, such as Bowers, sequential Gaussian simulation (SGS), machine learning, and artificial intelligence (AI) techniques, which can account for the complexities of multiple lithological types and provide more accurate estimates of pore pressure. These methods can also analyze large datasets and incorporate multiple data types, including logs, well tests, and seismic data.

In the context of this study, using the Eaton method to predict pore pressure in the Asmari reservoir may be reasonable due to the dominant presence of carbonate rocks. However, it is essential to acknowledge the limitations of this approach and consider alternative methods for future studies that aim better to understand the pore pressure distribution in this complex reservoir. This response acknowledges the potential limitations of the Eaton method and suggests future directions for improving pore pressure prediction in complex geological settings. It also highlights the importance of considering multiple methods and approaches to ensure accurate predictions. We use the DST or MDT formation test results and formation pressure in the reservoir to correct the obtained profile. The pore pressure profile is shown in Fig. 14a.

Figure 14

(a) Pore pressure (PP) profile vs. depth (m) in reservoir section, (b) Minimum and maximum horizontal in-situ stresses (S_h and S_H) profile along the borehole depth (m).

Horizontal in-situ stresses

Horizontal stresses are more challenging to determine. The most direct approach to gaining the horizontal stresses is to perform a fracture test on the formation. Although fracture testing is crucial to adjust and confirm final results, it is not typically done routinely, and the number of data points will, therefore, mostly be insufficient for determining the horizontal stress with only a few leak-off test (LOT) data. Equations (35) and (36) are employed to evaluate the minimum horizontal stress.

$$\sigma_{h} = \frac{\nu }{1 - \nu }(S_{v} - \alpha P_{w} ) + \alpha P_{w} + \frac{{E\varepsilon_{h} + \nu E\varepsilon_{H} }}{{1 - \nu^{2} }}$$

(35)

$$\sigma_{H} = \frac{\nu }{1 - \nu }(S_{v} - \alpha P_{w} ) + \alpha P_{w} + \frac{{E\varepsilon_{H} + \nu E\varepsilon_{h} }}{{1 - \nu^{2} }}$$

(36)

Since there is no available data for LOT tests to obtain horizontal strains in the Marun field, we used drilling reports in the field and cases where complete loss occurred in the reservoir. The assumption is that when complete loss occurs, the minimum horizontal stress is equal to the hydrostatic pressure of the mud at that depth. It is initially assumed that ε_H = ε_h, and from Eqs. (35) and (36), we can obtain ε_h and σ_H, respectively. By introducing the Mohr–Coulomb failure criterion, constructing a mud window, and using a trial-and-error approach, we continue until a good match is obtained when compared with the caliper log. Using MATLAB 2021a [https://www.mathworks.com/academic] software and four complete loss reports from the field, these values were obtained for the strain parameters: ε_h = 0.0002 and ε_H = 0.0017 (Fig. 14b).

Safe and stable mud weight window

The three types of mud windows that need to be defined are the safe mud window, safe and intact mud window, and stable mud window (see Fig. 15). The safe mud window is the mud weight range between the kick mud weight (pore pressure) and the mud weight that causes mud loss in the borehole wall (equal to the minimum horizontal stress). The safe and intact mud window is the range of mud weights with no mud loss or break out in the borehole wall. The limits of the stable window are between the mud weight that causes mud loss and the break-out mud weight. Finally, the stable mud window is between the break-down and break-out mud weights.

Figure 15

Schematic relationship of mud pressure (mud weight) and wellbore failure behaviors (modified with Photoshop CS.8).

Using the Mohr–Coulomb criterion, the lower and upper limits of the mud weight are determined and plotted. Figures 16 and 17 illustrate the schematic relationship between mud pressure (mud weight) and the well’s window. Figure 18 depicts a stable mud window. The well’s mud weight is 0.97 g/cm³ (61.2 pcf). The calculated safe mud weight window ranges from 0.65 to 1.9 g/cm³ (41.5–118.59 pcf), while the stable mud weight window ranges from 0.7 to 2.5 g/cm³ (43.5–156 pcf). Generally, maintaining the mud weight within certain limits is crucial for safe and efficient drilling operations. In Fig. 18, the lower limit of mud weight is the kick mud weight, below which the well may ingest formation fluids. The upper limit of mud weight, known as the loss mud weight, is above which the drilling mud can fracture the formation, causing uncontrolled mud flow into the formation.

Figure 16

Schematic graph of mud pressure (mud weight) window. To maintain wellbore stability, the mud weight should be within the appropriate range.

Figure 17

Mud pressure window for well number 350, calculated stable mud pressure ranges from 0.7 to 2.5 g/cm³ or 43.5 to 156 pcf.

Figure 18

Mud pressure window for well 350, the calculated safe mud pressure ranges from 0.65 to 1.9 g/cm³ or 41.5 to 118 pcf.

The well is not ovalized in an accurate gauge hole, and the caliper reading is equal to the bit diameter. Caliper logs are valuable tools that can help identify hole ovalization conditions. In a breakout condition, the well is ovalized in one direction while remaining relatively well-calibrated in the perpendicular direction. In a washout condition, the well is ovalized in both directions. In keyseats, which often occur in deviated wells, one-sided ovalization can be generated by the drill pipe. Figure 19a,b,c,d illustrate the different responses of a four-arm caliper in various hole conditions.

Figure 19

Four-arm caliper tools measure borehole diameters in two orthogonal directions, C1 and C2. C1 measures the diameter between pad 1 and 3, while C2 measures the diameter between pad 2 and 4. The bit size is also included in log readings as a reference point to track any deviations from the bit size during logging. The first two rows of caliper logs show borehole elongations and responses. Breakouts occur when one caliper reading exceeds the bit size. Common types of enlarged borehole and their caliper log response include (a) In gauge hole, (b) Breakout, (c) washout, (d) Keyseat.

By comparing four-arm caliper data and considering the mud weight window at the same depth, we can assess the accuracy of our stability model. Figure 19a shows an in-gauge hole with a consistent and uniform reading on the caliper log, indicating that the wellbore is drilled to its intended size. Figure 19b presents a breakout characterized by a sudden increase in C1 and C2 readings, suggesting an enlargement or break in the wellbore. Figure 19c displays a washout, featuring a gradual increase in C2 readings and a decrease in C1 readings, indicating erosion or wear on one side of the wellbore. Figure 19d illustrates a keyseat, with symmetrical increases in C1 and C2 readings, revealing a spiral or helical groove (keyseat) formed on one side of the wellbore. These distinct responses can help identify potential issues or anomalies in the wellbore, such as drilling problems, erosion, or damage caused by drilling fluids or rock instability. As evident from the comparisons between the caliper log and mud weight window in Fig. 20a,b, most of the depth points along the borehole exhibit breakouts, and our predicted model can accurately predict these occurrences in some intervals. However, washout occurs between the depths of 3500 and 3525 m, which our model was unable to differentiate from breakouts. Further examination of the gamma-ray log reveals that this interval contains some shaley layers. On the other hand, there are some points where the mud weight window results do not match the caliper data, likely due to the assumptions and uncertainties inherent in our calculations.

Figure 20

Caliper log and bit size data across mud weight window profile.

In conclusion, the results of scaling-up dynamic elastic log data to pseudo static elastic moduli of rocks with a wellbore stability analysis approach have demonstrated the feasibility and benefits of using advanced data integration techniques in geomechanical studies. These findings can have broader implications in the oil and gas industry, leading to more efficient, cost-effective, and reliable geomechanical evaluations for reservoir management and drilling operations.

Uncertainty and limitations

The study demonstrates the feasibility and benefits of using advanced data integration techniques in geomechanical studies. The proposed model integrates various data sources, including log data, drilling reports, and laboratory tests, to comprehensively understand rock behavior in the Asmari Reservoir Marun oilfield.

However, several limitations and uncertainties must be acknowledged. The model’s accuracy depends heavily on the quality and reliability of input data. We relied on logs and drilling reports that may not accurately represent actual conditions. Laboratory tests for static elastic moduli may not reflect in-situ conditions.

Additionally, the model assumes linear elastic rock behavior, which is only partially accurate. Rocks are complex and heterogeneous materials that exhibit non-linear behavior under stress, leading to potential errors in wellbore stability prediction.

Another limitation is the assumption that minimum horizontal stress equals hydrostatic pressure at depth. This assumption is only sometimes valid, as factors like tectonic stress and pore pressure can influence horizontal stress.

In conclusion, while this study shows the potential of advanced data integration techniques in geomechanical studies, it is essential to acknowledge the limitations and uncertainties inherent in these models. Continuous updating of geomechanical models with new data can lead to more accurate predictions and better models.

Assumptions:

• Linear elastic rock behavior.

• Simple relationship between static and dynamic elastic properties.

• Hydrostatic pressure at depth equals minimum horizontal stress.

Limitations:

• Data quality and reliability.

• Laboratory tests may not reflect in-situ conditions.

• Non-linear rock behavior under stress.

• Assumptions about horizontal stress.

• Model simplifications.

Acknowledging these limitations and uncertainties can improve our understanding of wellbore stability and help develop more accurate models for predicting and preventing unstable conditions.

Conclusions and recommendations

Based on the theoretical developments, a comprehensive model is developed to analyze wellbore stability in the Asmari Reservoir Marun oilfield, which includes the mechanical effects of rocks in different layers. Shear and tensile failures are examined to determine the appropriate mud weight stabilizing a vertical borehole. The Mohr–Coulomb failure criterion is used to determine the shear failure conditions. Moreover, regional correlations have been developed to relate static elastic properties of rocks from laboratory data to dynamic elastic properties of formations from log data.

• It was shown that using non-destructive dynamic measurements is important in solving stability problems of engineering projects. Additionally, experimentally obtained static Young’s moduli in the laboratory can be correlated to dynamic measurements from field data. The results have been achieved under simplified assumptions, as the relation for Young’s modulus calculations is valid only for homogeneous and isotropic media, while rocks generally do not fulfill this condition.

• Calculated safe mud weight window range from 41.5 to 118.59 pcf and stable mud weight window range from 41.5 to 156 pcf in this well.

• The described methodology allows for predicting, preventing, and reducing wellbore instability conditions to reduce drilling costs and hazardous conditions.

• The application demonstrated the validity of the linear elastic theory for wellbore instability modeling.

• This application verifies that well logging and formation tests can be used to obtain necessary data for geomechanical formation modeling.

• It was proved that the obtained data from laboratory tests and drilling reports can be used for wellbore stability calibrations.

• Continuous updating of geomechanical models leads to more accurate predictions, resulting in better models.

Furthermore, as recommendations of this study:

• Since the primary source of rock mechanical evaluations is petrophysical data, it is better to measure all rock characteristics, especially shear wave transit time (which can be measured with Dipole Shear Sonic Tool (DSI)), which is versatile for conducting wellbore stability studies.

• Due to our limitations in this study, we only used uniaxial compressive tests to obtain the required laboratory data. It is better to use triaxial compressive strength tests to show the rock behavior in reservoir conditions.

• It would be better to use 1 MHz ultrasonic laboratory tests and make regional correlations based on dynamic and static tests in the laboratory and dynamic values from log data.

• There is a need to conduct a comprehensive study about stress regimes and directions in the field. This can be done by running borehole logs, including caliper logs (four arms) and electrical or acoustic image logs, which are essential tools for this purpose.

• The only fully reliable method for determining horizontal stress magnitudes is conducting fracture tests such as leak-off tests (LOT) or hydraulic fracturing. The lack of these data brings errors in calculations.

• It is recommended that rock mechanical studies on cores and wells be performed as much as possible to reduce uncertainty and risk in designing procedures. The apparatus should be qualified, and accurate data should be obtained. Triaxial and ultrasonic tools are preferred for these studies.

• As anisotropy is crucial in wellbore stability analysis, ignoring it can lead to inaccurate predictions. The study highlights the importance of anisotropy and recommends using advanced techniques to improve geomechanical evaluations.

• To improve the accuracy of overburden stress calculations, use a comprehensive model that incorporates multiple lithologies, their density-depth relationships, and factors like pore pressure and rock strength. Utilize detailed data from well logs and seismic data.

• Eventually, while the Eaton method may be suitable for predicting pore pressure in the Asmari reservoir due to its dominant carbonate rock composition, it is crucial to acknowledge its limitations and consider alternative methods, such as Bowers, SGS, machine learning, and AI techniques, to ensure accurate predictions and account for complexities in multiple lithological types.