Coupled hydro-mechanical simulation in the carbonate reservoir of a giant oil field in southwest Iran

Abstract

The Asmari reservoir in southwest Iran has been producing oil continuously for over 50 years. However, due to an essential pressure decline, the reservoir is now a potential candidate for injection projects. The geomechanical analysis is essential for a successful injection operation to enhance reservoir production and address possible challenges. An accurate estimation of the injection pressure is necessary to maintain optimal conditions during the injection process and reduce possible risks. In this work, a coupled reservoir-geomechanical model, as well as rock mechanical tests, is performed to evaluate not only pressure variation and the associated in situ stress changes but also their potential influences on fault reactivation, reservoir–caprock stability, and surface displacement. For geomechanical evaluation, empirical correlations are derived between static and dynamic rock properties based on core data and existing petrophysical logs for the studied reservoir–caprock system. Based on the hydro-mechanical results, the maximum displacement is limited to the vicinity of the injection wells, where the highest pressure changes occur. The geomechanical analysis of the reservoir–caprock system shows that this system is stable until the injection pressure reaches 4.3× the initial reservoir pressure. Also, the injection pressure is not high enough to compromise the integrity of faults, indicating that the loading on the fault planes is too low to reactivate the pre-existing faults. The approach followed in this study can be applied to future field development strategies and feasibility considerations for CO₂ sequestration and underground gas storage projects.

Introduction

Reservoir geomechanical study has been of prime importance in recent decades in the oil industry, especially during drilling, development, and exploitation of hydrocarbon fields (Radwan 2022a). Geomechanics plays a critical role in all stages of oil and gas exploration and production. In particular, geomechanics has a great influence on exploration evaluation, field development, and even enhanced oil recovery scenarios (e.g., injection techniques). Enhanced oil recovery (EOR) operations are known for their efficiency in increasing oil production (Wu et al. 2016, 2018; Syed et al. 2021). One of the most effective techniques in EOR widely used in the industry is gas injection operation (Chen et al. 2016). Besides the improvement in oil recovery, the gas injection may disturb the balance of underground structures, leading to geomechanical problems in reservoirs. During the gas injection, the changes in the reservoir pore pressure may lead to stress re-distribution and re-orientation in the field (Geertsma 1973; Deflandre et al. 2013; Selvadurai and Kim 2016; Golian et al. 2020; Radwan et al. 2021a, b; Baouche et al. 2022). These changes can impose the risks of surface displacement (subsidence and uplift), loss of reservoir–caprock system integrity, fault reactivation, hydraulic fracture propagation, and well integrity problems, all of which are of prime considerations during the gas injection EOR (Anis et al. 2019; Ahmed and Al-Jawad 2020; Tadayoni et al. 2022). Therefore, conducting geomechanical studies during gas injection into the reservoirs seems essential to ensure the integrity of the impermeable boundaries (e.g., caprock, fault, etc.) and surface deformation (Han et al. 2012; Eslamian et al. 2018).

From a geomechanical perspective, two significant steps related to the troubles and risks associated with the injection activities are determining the magnitude of stress changes and evaluating the geological disturbances on the caprock–reservoir stratum, faults, fractures, etc., caused by the induced stress (Archer and Rasouli 2012). As the reservoir pressure is changed and the stress is induced, the failure of the reservoir–caprock system is likely to occur due to variations in the rock properties, such as permeability and porosity (Segall 1985; Chan and Zoback 2002; Zivar et al. 2019). If the increase in reservoir pore pressure is too high, the response may extend to the top of the reservoir and possibly to the ground surface or sea floor. Shear failure may occur at the interface between the reservoir and the caprock, as the caprock is not permeable. If this shear failure spreads in the caprock, its integrity may be compromised (Song et al. 2023). The caprock may contain a fault, or the failure caused by the fault may propagate into the caprock, in which case the stability of the caprock is not secure. When the caprock stability is not safe, the leakage of the injection fluid due to flotation is possible, which should be avoided considering its potential environmental hazards.

In other words, the increase in reservoir pore pressure during gas injection operations can damage the integrity of the faults near the injection wells and reactivate the pre-existing faults (Rutqvist et al. 2014). The reactivated faults may act as pathways for the injected fluids and cause micro-seismicity or even earthquakes may feel by the general public. Reactivation of the fault has the potential to increase the caprock permeability, resulting in fluid leakage from the reservoir to shallow aquifers or the atmosphere (Song and Zhang 2013; Michael et al. 2018; Ostad-Ali-Askari et al. 2019).

Surface displacement is another geomechanical concern that requires investigation during injection and production activities. When reservoir pressure decreases during production, the effective vertical stress increases, which may lead to subsidence in the reservoir and caprock (Ahmed and Al-Jawad 2020). On the other hand, the release of the effective vertical stress associated with the fluid injection into the reservoir can increase the potential uplift of the reservoir section (Bond et al. 2013). Several factors, including diameter, depth, time, injection rate, pore pressure, and height, can significantly impact subsidence and heave, according to the report by Wang et al. (2010). Furthermore, as caprock permeability increases, the rate of heave and subsidence will also accelerate (Rutqvist 2011). Although uplifting can have positive effects, such as reducing surface subsidence in low-lying coastal regions, surface deformation can damage the stability and integrity of human-made structures and infrastructures and the hydraulic efficiency of natural watercourses and drainage networks (Cooper 2008). For instance, subsidence or heave of the formation can cause severe damage to the wellbore and facility since the wellhead equipment is fixed on the surface.

In order to effectively analyze and investigate the geomechanical risks associated with injection scenarios and address the complexities and coupled interactions that arise from these operations and stress changes, a numerical method is necessary and of prime importance. This method should involve the coupling of geomechanics with fluid flow in porous media. Numerical modeling, specifically mechanical earth modeling (MEM), has been shown to be a practical and effective method for combining diverse data sets and accurately simulating the hydro-mechanical response of reservoir formations under various operational conditions throughout their lifetime (Tenthorey et al. 2013; Fischer and Henk 2013; Guerra et al. 2019).

Many numerical geomechanical modeling studies have been conducted in the past decade to investigate the injection and production processes. Heffer et al. (1994) were among the pioneers who coupled a geomechanical model with reservoir fluid flow to simulate water flooding sweep efficiency. This study is widely recognized as the forerunner of coupled geomechanical simulation. Then, a great body of research was devoted to defining the theory and governing equations to apply them in stress-sensitive reservoirs (Gutierrez 1994; Khan and Teufel 1996; Chen et al. 1995; Osorio et al. 1997; Koutsabeloulis and Hope 1998; Gutierrex and Lewis 1998).

Yang et al. (2018) presented a coupled geomechanical/reservoir simulation workflow to investigate the impacts of stress alternations on the long-term production performance of a high-pressure/high-temperature naturally fractured reservoir. Meanwhile, Younessi et al. (2018) conducted a coupled geomechanical simulation in two adjacent deep-water fields in South East Asia to study reservoir compaction during production. The results showed that reservoir compaction and pore collapse were negligible for the expected level of depletion. Anis et al. (2019) performed a geomechanical simulation in a fractured carbonate reservoir in the Ujung Pangkah field to reduce nonproductive time (NPT) related to wellbore instability and reservoir management. They investigated reservoir compaction and surface subsidence, where they found a controllable deformation. In addition, Abdideh and Hamid (2019) evaluated rock integrity and fault reactivation in a carbonate fracture reservoir using empirical equations to obtain the rock's mechanical properties. The threshold of the fault reactivation and the critical pressure for fracture induction was evaluated using a coupled simulation. Ahmed and Al-Jawad (2020) coupled a 3-D geomechanical model with a dual porosity/permeability simulation model to investigate effective stress variations upon decreasing reservoir pressure during gas production of a carbonate fractured reservoir. They found that the Klinkenberg effect had a negligible impact on gas production and high fracture permeability. Also, according to the reported results, as the pressure decreases, the matrix permeability is reduced by about 20%, and the effective permeability of natural fractures decreases insignificantly. However, the cumulative production curves showed an insignificant decline and remained almost intact.

Similarly, Al-Zubai and Al-Neeamy (2020) constructed a 3-D mechanical earth model for the Zubair oil field in southern Iraq based on a 1-D model to identify the spatial distribution of appeared problems in wellbore stability analysis. The results showed an abnormally pressured-zone in the Tanuma shale formation and a narrow mud-weight window in front of this formation. Taghipour et al. (2021) carried out a 2-D coupled pore fluid diffusion/stress model based on the average value obtained from 1-D MEM to investigate the potential of fault slippage and propagation of shear stress and plastic strain in one of the carbonate reservoirs. They reported the injection pressure of 30 MPa as the safe lower limit of gas injection during the numerical simulations. Tadayoni et al. (2022) investigated the potential of fault and fracture reactivation using geomechanical coupled modeling in a depleted carbonate oil field in southwest Iran. They studied stress and strain variations associated with depletion as simulated by the reservoir flow model in different time steps. The results showed that all faults were stable over time and during oil production operations. Finally, Konstantinovskaya et al. (2023) conducted a 3-D reservoir simulation of CO₂ injection in a deep saline aquifer of the Potsdam sandstone in Quebec. Their study aimed to evaluate the safe range of CO₂ injection rates during reservoir pressure alternation and estimate the risk of seal failure and the reactivation of pre-existing faults. The modeling results indicated that the risk of fault shear-slip reactivation was low, and fault plastic shear strain remained zero after the CO₂ injection.

For the reservoir studied here in, the pressure has been significantly reduced over several decades of production, and it now sits below the hydrostatic pressure. Therefore, maintaining the reservoir pressure is essential to increase the ultimate recovery. However, injection operations may have negative geomechanical impacts, highlighting the need to understand the geomechanical aspects of the field. This understanding will help ensure efficient production during injection design and lead to a longer and more productive life for the reservoir by predicting variations in the reservoir conditions over time.

An integrated workflow to set up and populate a 4-D coupled reservoir/geomechanical simulation for a gas injection operation is presented in this study. The 4-D hydro-mechanical model allows for the analysis of reservoir behavior during the injection phase, including the changes in stress, strain, and deformation of the rock formations. This work provides simulation analysis and experimental data on an oil field in southwest Iran. Integrating experimental data with the simulation model leads to an optimized model, improving the prediction accuracy of the reservoir behavior. The work starts with collecting data from various sources (e.g., log data, rock mechanical tests, drilling data, etc.) to achieve the required study parameters, data auditing, and creating 1-D MEM. Then, an initial 3-D geomechanical model is developed by integrating the static model and geomechanical data. In the next step, the one-way coupling between the geomechanical model and reservoir fluid flow simulation is performed to obtain several specific outputs of interest. The use of one-way coupling between the geomechanical and fluid flow simulations enables the simulator to capture the feedback mechanisms between fluid injection and geomechanical responses. The results of geomechanical modeling provide valuable information on stress changes within and around the reservoir sector in selected time steps. The stress and strain outputs from the simulation present much information on the magnitude of deformation and failure behavior of both intact and jointed (e.g., faults) rocks. Overall, the integrated workflow provides a comprehensive approach to understanding and optimizing the gas injection operations in the studied field.

The main highlight of this work is the workflow for the best application of the consistent field-collected data to develop a calibrated 1-D MEM and a 4-D hydro-mechanical couple to diagnose and predict future problems and risks that should be considered in any field development plan. Due to the lack of core samples, most researchers in the field used empirical correlations for geomechanical evaluation. Also, the average values of mechanical properties may be used in numerical modeling for a specific geological formation (e.g., reservoir and caprock).

However, in this work, continuous values of mechanical properties are derived from core samples and log data. Then, geostatistical methods are employed to assign these values to all cells of the structural model. The geomechanical models already developed often include 1-D and 2-D ones. It is worth noting that few 4-D models are present, emphasizing particular consequences of production and injection. Nevertheless, this work evaluates a wide range of geomechanical effects, including surface displacement, reservoir–caprock system integrity, and fault reactivation under the gas injection scenario. This approach can aid in screening production and injection forecast scenarios, making better decisions for well placement, and be applicable in CO₂ sequestration, underground gas storage, and geothermal projects worldwide. Overall, the paper offers valuable insights into the importance of geomechanical considerations in field development planning and highlights the benefits of an integrated approach using field data and simulation models.

The main highlight of this work is the workflow for the best application of the consistent field-collected data to develop a calibrated 1-D MEM and a 4-D hydro-mechanical couple to diagnose and predict future problems and risks that should be considered in any field development plan. Due to the lack of core samples, most researchers in the field used empirical correlations for geomechanical evaluation. Also, the average values of mechanical properties may be used in numerical modeling for a specific geological formation (e.g., reservoir and caprock).

Geological setting

The studied field is located in the Zagros fold and thrust belt and is one of the largest Iranian oilfields in the Dezful Embayment. Combining the rich source rocks, permeable and porous reservoirs, and a suitable caprock creates ideal conditions for forming a rich petroleum province in Zagros, particularly in Dezful Embayment (Bordenave and Hegre 2005). This field is renowned for being one of the most significant oilfields in the Oligocene–Miocene and middle Cretaceous carbonate (Cenomanian–Turonian) horizons (Shaban et al. 2011). From the Cretaceous to Early Miocene, the petroleum system in this field comprises two formations, Asmari and Sarvak–Illam, which are covered by the Gachsaran and Gurpi formations as caprock (Darvishzadeh 2009). Around 75% of Iran’s total hydrocarbon reserves are in the Asmari formation (Rezaie and Nogole-Sadat 2004). The Asmari formation in this field generally has a low lithological diversity and includes limestone, dolomite, dolomitic limestone, and marly limestone (Darvishzadeh 2009). The Miocene Gachsaran formation comprises seven members named by numbers 1 to 7, with the lowermost member (member 1) containing mainly lithologies of anhydrite, bituminous shale, gray marl, and limestone, considered the caprock of the Asmari reservoir formation (James and Wynd 1965; Nairn and Alsharhan 1997). Figure 1 exhibits the location and simple geological column of the oil field studied in this work.

Fig. 1

a The location of the studied oil field in Iran (violet star), b The stratigraphic column of the field (Geological Society of Iran, GSI 2018)

Methodology

The present study was done on one of the oil fields in the southwest Dezful Embayment region, focusing specifically on the Asmari (reservoir) and Gachsaran (caprock) formation. The depth of these formations varies across the field, with the average thickness of the caprock and reservoir being 60 m and 300 m, respectively. To develop a coupled reservoir-geomechanical model for the studied area, laboratory tests, a 3-D static geological model, a dynamic flow simulation model, and adequate knowledge of the local in situ stress tensor are required.

The first step of the study was data auditing and constructing 1-D mechanical earth models (1-D MEMs). The 1-D MEM of the wellbore was used to generate a 3-D geomechanical model that provides insight into the response of the rock properties to pressure changes during an injection operation. A well-mechanical earth model (MEM) was constructed by examining the mechanical characteristics of the rock using wireline data from the borehole, then calibrated with the results of laboratory (mechanical) tests. Mechanical tests were conducted on 11 vertical plug samples collected from the reservoir and caprock formations of well X3 in the depth interval of 4590 to 5500 ft. Later, a series of uniaxial tests were conducted on the nominated core plugs to determine the mechanical properties of the reservoir–caprock system. Dynamic rock mechanical properties and in situ stresses were estimated using the wireline data from four boreholes, including dipole shear sonic (DSI) and density (RHOB) logs, and compared with those of the core measurements in well X3. The overburden weight (RHOB log) was used to calculate the magnitude of the vertical stress. Horizontal stresses were evaluated using the elastic modulus, and then, the accuracy of the calculations was calibrated by an extended leak-off test (XLOT) performed in the field. The directions of principal horizontal stresses were ascertained by detecting the orientation of the breakouts in image logs.

The finite element method (FEM) was used in the second phase to determine the distribution of the mechanical properties of the rock, principal stresses, and associated strains at the initial conditions of the reservoir. The 3-D MEM, comprising the reservoir, overburden, underburden, and sideburdens, was developed using a 3-D static geological model. Geostatistical methods were used to upscale the continuous mechanical properties from the well locations (1-D MEM) to the whole model domain (3-D MEM). The 3-D MEM was calibrated by comparing calculation results with observational data (e.g., in situ stress estimation). In the case of the studied reservoir–caprock system, the stress field was calibrated using the obtained in situ stress profiles from Phase 1, i.e., 1-D MEM, by adjusting the applied boundary conditions.

In the final phase of the work, an evaluation of the stress and strain changes associated with the injection-production scenario was done as simulated by the reservoir simulation model. The goal was to investigate how the reservoir pressure variations may affect the bounding faults in terms of stability, surface deformation and displacement, and the integrity of the reservoir–caprock system. For this purpose, a one-way coupled technique was employed to combine the 3-D MEM of the studied area with a flow simulation model.

As illustrated in Fig. 2, the modeling scheme utilized the Schlumberger software suite, including Techlog for 1-D MEM, Petrel for the 3-D static geological model, Petrel RG (reservoir geomechanics) for 3-D MEM, and Eclipse 100 for fluid flow simulation.

Fig. 2

Flowchart of the work steps followed in this work

1-D geomechanical model

A mechanical earth model (MEM) is a numerical representation of the mechanical properties of a formation rock that is used to determine the rocks' geomechanical properties and in situ stresses near a wellbore (Ezati et al. 2020). In this work, the MEM was developed using the mechanical properties of the rock obtained from petrophysical logs and laboratory test results. The rock mechanical properties, pore pressure, and the orientation and magnitude of horizontal and vertical stresses are defined in a 1-D MEM for a specific stratigraphic or lithology span (Darvish et al. 2015; Aghajanpour et al. 2017; Ezati et al. 2020). Therefore, the availability of the well logs data and laboratory tests on core samples is vital to ensure the representativeness of a 1-D MEM model. This study utilized a comprehensive data set, including geological properties, petrophysical logs, drilling records, and the rocks' static and dynamic mechanical properties, to develop a 1-D MEM of the Asmari reservoir and its caprock formation. The type of data employed for the 1-D MEM model development in this work is categorized in Table 1.

Table 1 The commonly used data for the development of the 1-D MEM in the studied area

The rock mechanical tests

Based on the cored segments, the results of uniaxial tests for measuring the geomechanical properties, including static Young’s modulus (${\text{E}}_{\mathrm{s}}$) and uniaxial compression strength (UCS), of the reservoir and caprock formations were available for 11 plug samples, as listed in Table 2. For the mechanical testing of the rock, the vertical plug samples were taken from the cores collected in well X3. The diameters and lengths of the plugs were 0.125 ft and 0.25 ft, respectively (diameter to length ratio of 1:2). In other words, their length was considered twice the diameter (length to diameter ratio of 2:1). Uniaxial tests were carried out following the ASTM D3148-93 standard by placing the plugs in a loading frame and monitoring the axial and lateral deformations caused by each of the load. The axial load applied to the sample was continuously increased during the test, and the deformations were recorded simultaneously.

Table 2 The results of uniaxial tests on the studied core plugs

Mechanical Properties

To estimate the dynamic values of Poisson’s ratio $\left( {\nu_{{\text{d}}} } \right)$ and Young’s modulus (${\text{E}}_{\mathrm{d}}$), compressional and shear wave velocities (V_p and V_s) along with the rock density (ρ) are used as follows (Fjaer et al. 2008):

$$E_{{\text{d}}} = \rho V_{{\text{s}}}^{2} \frac{{3V_{p}^{2} - 4V_{{\text{s}}}^{2} }}{{V_{p}^{2} - V_{{\text{s}}}^{2} }}$$

(1)

$$\nu_{{\text{d}}} = \frac{{V_{p}^{2} - 2V_{{\text{s}}}^{2} }}{{2\left( {V_{p}^{2} - V_{{\text{s}}}^{2} } \right)}}$$

(2)

Dynamic and static elastic parameters have different values due to measurement conditions. The elastic properties derived from the acoustic log are considered dynamic parameters, whereas those obtained from laboratory tests are assumed static. Static parameters have more realistic results than dynamic properties (Xie et al. 2022; Zhao et al. 2022). As, typically, elastic parameters obtained under dynamic conditions have a higher value than static conditions, dynamic parameters should be converted into static ones using rock mechanical tests (Zoback 2007). Hence, it is necessary to provide empirical correlations between the dynamic and static parameters for reliable and continuous prediction of the mechanical properties of rocks along the borehole. Various empirical correlations have been established between the dynamic and static elastic parameters using local information for a specific lithology and region (Lacy 1997; Ameen et al. 2009; Asef and Farrokhrouz 2010). In this regard, the following expressions were developed to correlate the static Young’s modulus (${E}_{\mathrm{s}}$) and uniaxial compression strength (UCS) as a function of the dynamic Young’s modulus (${E}_{\mathrm{d}}$):

$$E_{{{\text{s}}1}} = 0.057677E_{{\text{d}}}^{1.5751}$$

(3)

$${\text{UCS}}1 = 0.0925E_{{\text{d}}}^{1.6802}$$

(4)

To validate the derived static Young’s modulus values from Eq. (3), the proposed equation by Seyed Sajadi and Aghighi (2015) for one of the nearby fields was used:

$${E}_{s2}\text{=}0.731{E}_{d}+2.337$$

(5)

In addition, since the Asmari reservoir is a carbonate formation, Asef’s equation (Asef and Farrokhrouz 2010), derived for uniaxial compression strength in the carbonate rocks, was used to verify the accuracy of Eq. (4).

$${\text{UCS}}2{ = }2.65\left( {\frac{{E_{{\text{s}}}^{0.8 } }}{{{\text{PHIE}}^{0.2 } }}} \right)$$

(6)

In this study, cohesion (c) and friction angle (φ) were estimated based on empirical correlations as follows (Plumb 1994; Jaeger et al. 2009):

$$c = \frac{{{\text{UCS}}}}{{2\tan \left( {45 + \frac{\varphi }{2} } \right)}}$$

(7)

$$\varphi = 26.5 - 37.4\left( {1 - {\text{NPHI}} - V_{{{\text{sh}}}} } \right) + 62.1\left( {1 - {\text{NPHI}} - V_{{{\text{sh}}}} } \right)^{2}$$

(8)

where c is cohesion, UCS is uniaxial compressive strength, φ is friction angle (degree), NPHI is neutron porosity, and ${V}_{\mathrm{sh}}$ is shale volume obtained from the GR log.

Pore pressure calculation

Calculating in situ stress magnitudes, wellbore stability, and discontinuity reactivation analysis during depletion and injection stages requires knowledge about the initial pore pressure, which can be obtained using direct measurements such as RFT (repeat formation tester), MDT (modular formation dynamics tester), and DST (drill stem test). Since these tools provide discontinuous data throughout the wellbore, pore pressure can be continuously estimated using petrophysical data. For the calculation of pore pressure, various techniques such as Eaton, Holbrook, and Bowers are used in the oil industry, among which a predominant equation is Eaton's method (Eaton 1975):

$${\text{PP}} = S_{{\text{v}}} - (S_{{\text{v}}} - {\text{PP}}_{{{\text{Hyd}}}} )\left( { \frac{{{\text{DT}}_{n} }}{{\text{DT}}}} \right)^{3}$$

(9)

where PP, ${{\text{P}}{\text{P}}}_{\text{Hyd}}$, and ${\text{S}}_{\text{v}}$ denote the pore pressure, hydrostatic pore pressure gradient, and vertical stress gradient, respectively. DT denotes sonic transit time and ${{\text{DT}}}_{n}$ represents the sonic transit time of shales with normal pore pressure. Eaton’s equation for estimating pore pressure, modified by Zhang (2011), is presented by Eq. (10) (Zhang 2011):

$${\text{PP}} = S_{{\text{v}}} - (S_{{\text{v}}} - {\text{PP}}_{{{\text{Hyd}}}} ) \left( {\frac{{{\text{DT}}_{m} + \left( {{\text{DT}}_{ml} - {\text{DT}}_{m} } \right)e^{ - cZ} }}{{\text{DT}}}} \right)^{3}$$

(10)

where c represents an experimental constant, ${{\text{DT}}}_{m}$ and ${\text{DT}}_{ml}$ are P-wave slowness in shale lithology with zero porosity and mud line, respectively, and Z denotes depth. Although Eaton’s method is applicable to some hydrocarbon fields, its application in geologically complex regions, such as formations with uplifts, is constrained as it does not consider the effects of unloading. Therefore, Zhang (2011) modified Eq. (9) by substituting an exponential depth function for the term ${\text{DT}}_{n}$, which makes it easier to handle conventional compaction trend lines. The study conducted by Azadpour et al. (2015) on several carbonate reservoirs showed that the modified Eaton’s method is an appropriate approach for predicting pore pressure in these types of reservoirs. Accordingly, in this work, Eaton’s method was employed to predict continuous pore pressure along the well of the studied reservoir (Asmari carbonate formation). As shown in Fig. 3, there is a good match between MDT points (black points in track 10) and the pore pressure curve predicted by modified Eaton’s method.

Fig. 3

Summary of the calculated mechanical properties of Well X4. Track 3 to Track 6 are the petrophysical raw data (GR, bit size (BS) and caliper (CALI), bulk density (RHOB) and neutron porosity (NPHI), compressional and shear transited time (DT_p & DT_s)). Tracks 7 to 9 are the calculated rock mechanical properties (static Young’s modulus (E_s) and dynamic Young’s modulus (E_d), unconfined compressive strength (UCS), and dynamic Poisson ratio (ν_d)). Track 10 is the in situ stress calculation (S_v, S_hmin, and S_Hmax), leak-off test (LOT), Eaton’s pore pressure (PP), modular formation dynamics tester (MDT) point, and hydrostatic pressure gradient (PP_HYD)

Magnitude of principal stresses

From the earliest stages of oil and gas field development to well abandonment, having an adequate knowledge about the magnitudes and directions of principal stresses is essential. Also, current stress fields are needed to understand petroleum geomechanics, tectonics, and structural analyses. For making decisive decisions in petroleum geomechanics, like directional trajectory drilling, wellbore stability, and drilling design, distributions of horizontal and vertical in situ stresses should be evaluated (Radwan et al. 2021c; Bashmagh et al. 2022).

The vertical stress magnitude (S_v) is determined using the density log (RHOB) and integrating the rock density from the surface to the desired depth (Zoback et al. 2003):

$$S_{{\text{v}}} = \mathop \int \limits_{0}^{z} \rho (z)g{\text{d}}z$$

(11)

where $\rho (z)$ represents the average density of overburden formation as a function of depth, z denotes depth, and ${\text{g}}$ is Earth's gravitational acceleration.

To determine the magnitude of the horizontal in situ stresses, a variety of laboratory and field techniques, including extended leak-off test (XLOT), leak-off test (LOT), strain recovery, core disking, jacking, and focal mechanism, are recommended (Zoback et al. 2003). Additionally, poroelastic equations can be used to calculate the magnitudes of the horizontal stresses (S_hmin and S_Hmax) as follows (Fjaer et al. 2008):

$$S_{{{\text{h}}\min }} = \frac{\nu }{{\left( {1 - \nu } \right)}}\left( {S_{{\text{v}}} - \alpha {\text{PP}}} \right) + \alpha {\text{PP}} + \frac{{E_{{\text{s}}} }}{{\left( {1 - \nu^{2} } \right)}} \varepsilon_{x} + \frac{{\nu \times E_{{\text{s}}} }}{{\left( {1 - \nu^{2} } \right)}} \varepsilon_{y}$$

(12)

$$S_{{{\text{H}}\max }} = \frac{\nu }{{\left( {1 - \nu } \right)}}\left( {S_{{\text{v}}} - \alpha {\text{PP}}} \right) + \alpha {\text{PP}} + \frac{{E_{{\text{s}}} }}{{\left( {1 - \nu^{2} } \right)}} \varepsilon_{y} + \frac{{\nu \times E_{{\text{s}}} }}{{\left( {1 - \nu^{2} } \right)}} \varepsilon_{x}$$

(13)

where $\nu$ denotes Poisson's ratio, S_v is overburden stress, $\alpha$ is Biot’s constant, PP is pore pressure, E_s is static Young’s modulus, and ${\varepsilon }_{x}$ and ${\varepsilon }_{y}$ are tectonic strains.

In this study, the poroelastic equations were used for the continuous estimation of the magnitude of the horizontal stresses (S_Hmax and S_hmin) along the well profile, as shown in Fig. 3. The calculated minimum horizontal stress from the poroelastic horizontal strain model was validated by the direct measurements of the LOT data (two green points in track 10 of Fig. 3). Also, the magnitude of overburden stress ${\text{(}{\text{S}}}_{\text{v}})$ was calculated based on the bulk density information. As observed in Fig. 3, ${\text{S}}_{\text{v}}$ is the maximum principal stress (σ₁), S_Hmax is the intermediate one (σ₂), and S_hmin is the minimum principal stress (σ₃). According to Anderson’s faulting theory (Anderson 1951), the tectonic stress regime in the reservoir zone is a normal faulting regime (${\text{S}}_{\text{v}}>{{S}}_{\text{Hmax}}>{{S}}_{\text{hmin}})$.

Orientations of principal stresses

Determining the orientation of the in situ stress is crucial for analyzing borehole stability in various circumstances. Stress-induced breakouts and drilling-induced tensile fractures (DIFs), known as compressive and tensile failures, occur as soon as drilling begins (Zoback 2007). Image logs are the best direct indicator of stress orientations. Therefore, the analysis of borehole well logs has been applied successfully to estimate the in situ stress magnitudes. Enlargements on the orthogonal calipers of the formation micro-imager (FMI) and long dark regions on the FMI log indicate breakouts occurring in the direction of S_Hmax, which is the maximum horizontal stress direction (Zoback et al. 2003; Kingdon et al. 2016). The oil-base micro-imager (OBMI) log, ultrasonic borehole imager (UBI) log, and Caliper log (four-arm) have all been extensively used to approximate the direction of horizontal stress from breakout orientations (Zoback 2007). In this work, the orientation of breakouts was determined based on compressively stressed zones observed in the UBI, OBMI, and FMI logs, along with the Caliper and bit size logs of the studied wells. Based on the orientation of the breakouts, the azimuths of S_hmin and S_Hmax were determined as N55.5° W and N34.5° E, respectively, as shown in Fig. 4a.

Fig. 4

a A pair of observed breakouts on the FMI static image in well X3. The breakout is identified as a pair of poorly resolved conductive zones observed on the opposite sides of the borehole (purple boxes in Track 4) and shows caliper enlargement (caliper 2 greater than caliper 1) in the same direction (Track 3), b The azimuth of maximum and minimum horizontal stresses based on the breakouts orientation in the studied wells. The breakouts herein were oriented approximately NW–SE; therefore, present-day S_Hmax orientation is approximately NE–SW, and c orientation of regional stresses in the Arabian Peninsula and Iran based on borehole breakouts and drilling-induced fracture data (Akbar and Sapru 1994)

Figure 4b also illustrates the maximum and minimum horizontal stress orientations in Iran. The trend of the maximum horizontal stress in the studied area corresponds to the NE-SW direction, consistent with the World Stress Map. The principal horizontal stress directions in most parts of the Arabian Peninsula (Akbar and Sapru 1994) and Iran are NE–SW and NW–SE for the maximum and minimum horizontal stresses, respectively, which aligns with the principal horizontal stress direction in Zagros.

Geological (static) model

The three-dimensional geological model is a complex and powerful tool for hydrocarbon reservoir modeling that is crucial for reservoir assessment and simulation to achieve successful development and better exploitation. In recent years, significant progress has been made in 3-D visualization of geological and geophysical data to simulate and predict subsurface systems. The 3-D geological property models for the reservoir can integrate data from various sources. The cell-specific characteristics of the geological model play a critical role in quantitative reservoir models, allowing attributes to be assigned to each cell. Compared to conventional models, these models are much more challenging for geologists since they require a detailed description of every location in the 3-D volume of a reservoir (Radwan 2022b).

To construct the reservoir and geomechanical models for the Asmari reservoir, a three-dimensional model of the studied sector was developed using seismic and well data at a regional scale via the use of Petrel software. In the studied segment, the area of the Asmari model was 16 km × 11.3 km × 4.2 km in X, Y, and Z directions, respectively. The model was parameterized using available geological and geophysical data, well logs, core data, and lithology. Four main faults were identified based on the previous studies and the seismic maps, as illustrated in Fig. 5. In the static geo-model of the Asmari reservoir, the average value of the permeability and porosity was 0.138 mD and 4.5%, respectively. Also, all reservoir boundaries were assumed as no-flow boundaries.

Fig. 5

Detected faults in the studied sector

Dynamic flow simulation

In this phase, the static model constructed earlier was utilized to develop a dynamic flow model for the Asmari reservoir. The dynamic flow simulation model used in this case study was a compositional model with a 3-D Cartesian grid system comprising a total of 83,204 grid blocks (Nx × Ny × Nz = 62 × 61 × 22). The Asmari reservoir model consists of 12 layers with specific petrophysical properties. The initial pressure and the temperature of the Asmari reservoir at the datum depth of 5085 ft (subsea) were reported as 3527 psi and 186 °F, respectively. The initial GOC (gas–oil contact) and WOC (water–oil contact) were at 676 ft and 8000 ft, respectively. This work considered the simulation case scenario from 2020 to 2040. The average reservoir pressure during the studied case scenario is depicted in Fig. 6, where the reservoir pressure increases from 2350 to 2710 psi in this scenario.

Fig. 6

The profile of the average reservoir pressure during the simulation period of 2020 to 2040

3-D mechanical earth model and coupled hydro-mechanical model

The 3-D mechanical earth model (MEM) is an effective tool used to analyze the effects of stress and strain on rock compaction, surface deformation and displacement, rock integrity, and fault stability related to any changes in pore pressure during the lifetime of the reservoir. The 3-D MEM consists of the reservoir structural model, the rock mechanical properties, the magnitude and direction of the principal in situ stresses, and the pore pressure distributions. The Petrel RG (reservoir geomechanics) tool is used to construct 3-D models of rock stresses, strains, and reservoir failure. The workflow consists of geomechanical grid construction, material modeling, properties populations, simulation launch, and execution management, followed by the verification and visualization of outputs. A one-way coupling simulation is then performed between the 3-D geomechanical model constructed by Petrel RG (VISAGE) and the dynamic flow model developed by the ECLIPSE simulator to determine the numerical stress and displacement for intact and faulted rocks. The workflow steps to develop a 3-D MEM and run a hydro-mechanical simulation, followed in this study, are illustrated in Fig. 7.

Fig. 7

Workflow stages of developing a coupled hydro-mechanical model

The equations and numerical approaches applied to fluid flow inside reservoir grids differ from those used in geomechanical modeling, meaning that changes and modifications must be made to the reservoir grids before starting the geomechanical investigation and modeling procedures. Therefore, the first step in constructing a 3-D MEM is to expand and embed the reservoir model by adding additional grids to approximate the actual conditions.

To simulate the exact values and the continuous distributions of the in situ stresses in each block of the reservoir grids, the overburden, sides (sideburden), and underneath (underburden) were added to the 3-D reservoir model. This step of the workflow, in which an embedded model is created, was a crucial procedure to ensure that any changes in the far-field in situ stresses do not affect the reservoir stress state. The overburden grids in the geomechanical network represent the weight of the rock layers above the reservoir, extending from the ground surface to the top of the reservoir formation. The vertical stress due to overburden can be calculated by utilizing the overburden grids. The Petrel Geomechanics section provides the option to use pre-existing surfaces of the reservoir grids as overburden. Gachsaran (caprock), Aghajari, and Mishan formations were chosen in the study area for this purpose. Similarly, for the underburden component, Petrel Geomechanics section offers two choices: using pre-existing geological surfaces or extending the geomechanical grid to the desired depth.

According to the previous reports, to prevent buckling, the aspect ratio of the geomechanical model must be 1.3, which was achieved by adding underburden grids to the reservoir model (Donoso 2016; Schlumberger 2017). The sideburden, consisting of grids around the reservoir, is added to the model with a larger size than the reservoir grid to reduce run time. In this study, five grids were added to each side of the reservoir model, and the rock type of the sideburden was considered the same as that of the reservoir. Additionally, to ensure uniformity in the sideburden, a stiff plate was added as extra cells around the sideburden, representing a rigid and incompetent rock mass that would not bend or warp under compression or tension. The finalized 3-D geomechanical grid of the studied area comprised 74 × 73 × 51 cells in the X, Y, and Z directions, as shown in Fig. 8b.

Fig. 8

a 3-D reservoir grid of the model, b applied geomechanical grid, and c top view of the reservoir model embedded in the 3-D geomechanical model

The next step in developing a 3-D MEM involves selecting the rock type and assigning the material model and geomechanical functions to the defined lithologies. Material refers to a set of geomechanical parameters of rocks, including Poisson’s ratio, bulk density, Young’s modulus, Biot constant, and porosity, as well as parameters associated with faults and fractures such as stiffness, strength, and spacing. These parameters were assigned to the desired sections of the geomechanical grid, including the overburden, reservoir, underburden, and sideburden. There are two types of material, as described below:

• Intact rock materials, according to the variety of elasticity models and yield criteria

• Discontinuity materials for fractures and faults modeling

The materials used in geomechanical modeling can be described as either linear or nonlinear, with examples of nonlinear models, including plastic models. These materials include linear elastic parameters and failure criteria such as Mohr–Coulomb, Drucker-Prager, and Tresca. In the studied field, the intact rock was modeled as linear isotropic material, and the failure criterion was based on the Mohr–Coulomb failure criterion.

The geomechanical grid and its portions were constructed in the preceding stages, but the defined properties were not allocated to each grid cell. Petrel software enables the selection of materials and assigning them to the geomechanical grid portions either by a constant value from the library or by the log-derived parameters obtained from 1-D MEM. In the studied field, the continuous mechanical properties of the rock, such as static Young’s modulus, UCS, tensile strength, cohesion, and Poisson’s ratio, were obtained from 1-D MEM and upscaled from the well locations to the whole domain of the reservoir model using geostatistical methods like the kriging method. The grid blocks of the reservoir and caprock formations were filled with continuous properties obtained from the logs (1-D MEM). Since the rock type of the sideburdens was considered similar to the reservoir rock, the constant average values calculated from reservoir properties were assigned to the sideburden grids. Figure 9 provides an example of the typical distribution of properties, such as static Young's modulus, in the developed 3-D model.

Fig. 9

Distribution of the static Young’s modulus in the reservoir model

The next step in developing the 3-D MEM is optional and involves modeling the discontinuities of existing faults and DFNs in the simulation model. In the studied area, seismic data confirmed the presence of four faults in the geological model. A fault mapping object was used to associate the present model with a set of faults, each object containing a list of intersected cells with faults and a set of fault properties. To evaluate their activation, it is necessary to estimate the geomechanical properties of the faults. However, no data on the properties of the faults, such as their cohesion strength (c) and the coefficient of static friction (µ_s), was available in the current study. According to Byerlee (1978), the coefficient of static friction is approximately 0.85 and 0.6 when the confining pressure is smaller than 200 MPa and greater than 200 MPa, respectively. In literature reports where fault data was unavailable, the coefficient of static friction was assumed to be 0.6 (Rutqvist et al. 2007; Zoback 2007). The values of the fault parameters used in the studied hydro-mechanical model are listed in Table 3.

Table 3 Fault parameters used in the hydro-mechanical simulation model

The PTS stage is a crucial step in the workflow, which determines the pressure, temperature, and saturation conditions for a particular simulation case at the required time steps. The VISAGE simulator uses this information to run the initialization, one-way, and two-way coupled methods. The initialization method is particularly important as it allows for the simulation of initial stress conditions before any reservoir depletion occurs. To achieve this, the magnitude and orientation of principal stresses in 1-D MEM are modeled and distributed to each grid cell of 3-D MEM to represent local field stresses. The accuracy of the geomechanical model can be verified by calibrating the calculated stresses from the 3-D MEM against the evaluated in situ stress profiles of the 1-D MEM by adjusting the applied boundary conditions. The VISAGE simulator offers two methods for imposing boundary conditions:

• Using gravity loading (constants or gradients) and strains or stresses applied to the lateral edges of the model

• Using pre-existing stress properties and the ratios of the horizontal stresses to the vertical stress applied to each cell of the model

In this study, the initial in situ stresses were initialized as the ratios of the horizontal to vertical stresses. Then, the log-derived stress curves (${\text{S}}_{\text{v}}{\text{, }{\text{S}}}_{\text{Hmax}} \, {\text{and}} \, \, {\text{S}}_{\text{hmin}}$) of the four studied boreholes were compared with the observed stress state from the entire 3-D geomechanical model domain. The accuracy of the model was evaluated by examining how well these initial stresses match the available data. Based on the satisfactory fit between these, the constructed 3-D model was deemed valid in mechanical terms and used to couple with the fluid flow (Fig. 10).

Fig. 10

Correlation between calculated stresses from the 3-D MEM and evaluated stresses from the 1-D MEM. The first and second tracks of each section show horizontal stresses (S_hmin and S_Hmax), and the third one presents vertical stress (S_v)

The as-developed model utilized a partially coupled modeling approach, specifically a one-way coupled method that employs 20 pressure steps (from 2020 to 2040) from the reservoir simulation as input data to the geomechanical equilibrium equation. In this approach, the geomechanical behavior of the reservoir was evaluated only at specific time steps, and the stresses and strains were calculated based on the defined pressure data. Once a solution was found, VISAGE progressed to the next pressure step, updating the stresses and strains until all the selected pressure steps were simulated. The temperature has a minimal impact on the calculated stresses and was not used in this geomechanical model. All relevant information from the previous stages, such as geomechanical properties, fault mapping data, pressure data from the dynamic flow model, and boundary conditions, was ultimately imported into the dynamic geomechanical simulation model to perform the reservoir geomechanics simulation case.

Results and discussion

Choosing an appropriate coupling method is a crucial aspect of reservoir geomechanics simulation. Different approaches, such as one-way, two-way, interactive, fully coupled, and other coupling patterns, can be used to solve the geomechanical problem combined with fluid flow. A fully coupled approach involves running dynamic flow and geomechanical simulations simultaneously at specific time steps, providing an accurate solution but with high computational complexity and long run times (Tran et al. 2005; Wang et al. 2015). In contrast, the one-way coupling approach is less complex, allowing daily use by drilling, well planning, and reservoir teams. Moreover, the one-way hydro-mechanical coupling is performed to precisely simulate the geomechanical effects on the changes in rock properties. This coupling model facilitates not only identifying how the injection process alters the stress state, rock matrix, and faults behavior over time but also quantifying its impact on reservoir performance and field development. Therefore, in this section, the effects of gas injection on reservoir displacement as well as the integrity of the reservoir–caprock system and faults are discussed.

Reservoir displacements

One of the fascinating consequences of the geomechanical modeling related to the gas injection process is the induced deformation in the reservoir and surrounding formations. This aspect of the study aims to examine the stress changes that occurred in and around the reservoir, particularly the ground deformation induced in the Asmari reservoir. This deformation results from the rock mass's elastic or non-elastic expansion or contraction during overpressure and under pressure stages. Internal reservoir deformation is critical as it can affect caprock integrity and the reactivation of pre-existing faults. Additionally, deformation resulting from changes in reservoir pore pressure may cause casing collapse, damage surface or seabed facilities, and threaten reservoir production and injection performance (Zoback 2007). From the perspective of surface monitoring and the potential reactivation of faults outside the reservoir section, it is also crucial to determine the deformation at the top of the reservoir and the surface.

Upon variations in reservoir pressure, horizontal movement of the reservoir can be disregarded due to neighboring geological layers; however, it may shift vertically during production and injection stages. The maximum movement of the reservoir occurs around the production and injection sites, while the uplifting and subsidence can extend for several kilometers around the wellbores. In the model used for this study, displacement was estimated in each grid cell of the reservoir at the required time steps. Figure 11 shows the magnitudes of Asmari reservoir displacement during the simulation case scenario at the end of the simulation period. The maximum displacement is approximately 0.0235 ft at the central part of the structure near the injection wells. The displacement value decreases as one moves away from the injection wells until zero at the reservoir edges.

Fig. 11

Vertical displacement of the Asmari reservoir at the end of the simulation period

During the injection period, more movements occur in the surrounding areas of the wells than in other parts of the reservoir formation due to the intense pressure and stress variations in these areas. Furthermore, the uniform pressure variation around the wells causes the uplifting to be circular. The surface displacements predicted in the studied field are smaller than the recorded displacement at some depleted oil and gas fields, which were reported to be at least 0.82 ft (Chan and Zoback 2007; Malman and Zoback 2007). In reality, according to the high depth of the studied field, the estimated value of displacement is less than the various injection and production scenarios from the literature. In the Asmari reservoir, the average pressure of the bottom hole is between 3500 and 4000 psi. Based on the study conducted by Vasco et al. (2010) in the Krechba field, the maximum heave was reported as 0.065 ft at the maximum bottom hole pressure value of 2610 psi (Vasco et al. 2010). The injection pressure value is considered one of the main reasons for the difference between the calculated uplift in the Krechba and the studied field. Due to the heterogeneity of the properties in different sections and the impact of the reservoir structural geometry, the displacement is not necessarily related to pore pressure alterations.

It should be noted that the extent of reservoir displacement depends on various factors, such as fluid pressure during production and injection, changes in fluid volume, the height of the depleted layer, and mechanical properties of the caprock and reservoir formations (Teatini et al. 2011). In this study, the cumulative gas injection from three wells was analyzed to explore the impact of the injected gas on the vertical displacement of the Asmari reservoir surface. The results are presented in Table 4.

Table 4 The gas injection volume and displacement of each well

Figure 12 illustrates the rates of reservoir uplifting in the studied injection wells. The data in Table 4 and Fig. 12 indicates that the injection well with the highest volume of the injected gas, Inj1, experienced the greatest vertical displacement, reaching a maximum of 0.0235 ft. Gas injection is responsible for increasing the pore pressure, which enhances pore volume. The larger volume of the injected fluid leads to more fluid variation in the reservoir, in turn affecting the reservoir pore volume. Therefore, the volume of the injected fluid plays a crucial role in the surface displacement. Moreover, the pressure changes resulting from the gas injection affect the magnitude of the displacement around the three injection wells. These findings are consistent with those reported by Vasco et al. (2008), who demonstrated a direct relationship between the volume of gas injection in wells and the amount of reservoir heave.

Fig. 12

Histogram of vertical displacement for injection wells after 20 years of simulation

Analytical methods could also be used to evaluate the extent of reservoir displacements. Fjaer et al. (2008) presented a simple but applicable analytical approach to estimate the vertical movements of the reservoir as per Eq. (14):

$$\frac{\Delta h}{h}=\alpha \left(\frac{(1+\nu )(1- 2\nu )}{(1-\nu )E}\right)\Delta PP$$

(14)

where h and Δh are the reservoir thickness and vertical displacement, respectively, ν represents the Poisson’s ratio, α is Biot’s constant, E displays Young’s modulus, and ΔPP is the variation in the reservoir pressure. The above-mentioned equation assumes that the reservoir is thin, laterally extended, and encompasses a variety of limitations. For instance, in reality, the displacement does not depend on the well pressure but on the average pressure of the hydrocarbon zone.

In the time step of 20 during the simulation case for the desired grid (23, 53, 12), by substituting the values of parameters in Eq. (14) (ν = 0.28, h = 4,027.88 ft, ΔPP = 826 psi, and E = 37.86 GPa), the displacement is obtained to be 0.14 ft. Due to the assumption that variations in well pressure will spread uniformly and laterally over a wide area, the uplift calculated by Eq. (14) is only a rough estimation. It is a 1-D displacement model, which will probably overestimate the heave but within the correct order of magnitude. The difference between the determined numerical values in this study and those estimated by the analytical method indicated that, although this approach is easy to follow, the results might become unrealistic.

Reservoir and caprock integrity

The stability of the reservoir–caprock system is an important aspect that needs great attention while designing any injection scenarios. The induced stress variations associated with significant changes in reservoir pore pressure may lead to substantial alterations in the reservoir and caprock integrity, which may pose a risk during the injection (Vidal-Gilbert et al. 2009). In this study, the Mohr–Coulomb criterion was employed to evaluate the stability of the reservoir and caprock system. To achieve this, stress variations along the reservoir and caprock formations were characterized, and the rocks' evolution in Mohr–Coulomb space during various time steps was determined. The Mohr–Coulomb method establishes average values of the maximum and minimum principal stresses and fluid pressure for the reservoir–caprock system in specific time steps. The stress profiles for the studied time steps of the reservoir and caprock formations are shown on a Mohr–Coulomb diagram in Fig. 13.

Fig. 13

Mohr circles for matrix failure criteria at the various time steps of the simulation period. a reservoir and b caprock

Changes in pressure resulting from the injection and production can affect the effective and shear stresses of the reservoir, leading to grain matrix rearrangements and pore volume changes. During production, the effective and shear stresses are diminished due to the reduction in pore pressure; therefore, the Mohr–Coulomb circle moves to the right, which shows the possibility of rock failure decreasing over time.

On the other hand, during the injection period, the probability of rock failure increases with the growth of the effective stress and shear stress caused by the increase in the pore pressure. Figure 13a shows the stability of the Asmari reservoir in different time steps. As observed, the Mohr–Coulomb circles are at the compressive side and below the failure line, indicating a low probability of matrix deformation. Although the stress circles are moved toward the intact rock failure over time, the stress variation is not significant enough to disturb the integrity of the reservoir rock. In this case study, the reason for the insignificant changes in the Mohr–Coulomb circles is the simultaneous injection and production in/from the reservoir. The Mohr–Coulomb diagrams of the reservoir confirm a very stiff formation, suggesting that injecting a large volume of fluid into the reservoir is feasible.

After carefully characterizing the caprock in the studied model, the stress charting tool assessed its integrity, as illustrated in Fig. 13b. It is inferred that the caprock is stable during the studied simulation case. Considering the values of the intercept (cohesion) and the slope (internal friction angle) of the failure envelope as the deciding factors, the Mohr circles cross the failure line in case the value of these parameters becomes too low (Fig. 13b).

To determine the failure pressure of the reservoir rock, the reservoir pressure was increased to 16,000 psi, and the analysis was done, as shown in Fig. 14. If the reservoir formation fails, the failure plane could propagate to the caprock, creating a flow path that could result in unintended fluid leakage to the surface. The pressure failure of the reservoir rock obtains 15,475 psi (Fig. 14a), indicating that the reservoir would reach the failure threshold if the injected fluid pressure approached 4.3 times the initial reservoir pressure. At this pressure value, the reservoir would begin to fail due to its inability to resist the applied stress. However, the caprock would remain stable due to a poor hydraulic connection between the reservoir segment and the caprock formation.

Fig. 14

The integrity of the matrix at the pressure of 15,475 psi. a Reservoir and b caprock

The caprock examined in this study has an average permeability of 0.00098 mD and fractional porosity of 0.0057. It also possesses a higher stiffness value in compression when compared to the reservoir rock, which renders it stable at reservoir failure pressure. The caprock behaves as a sealed pressure due to poor hydraulic connection caused by its low porosity and permeability. As a result, fluctuations in the reservoir pore pressure do not significantly affect the stress state of the caprock formation. Throughout the selected time steps of the study, the caprock remains mechanically intact without experiencing any failures, as depicted in Fig. 14b.

Fault stability

A fault acts as a seal or a conductive channel, which should be considered while designing injection scenarios. From a geomechanical perspective, faults can be reactivated and subsequently cause undesirable leakage pathways and seismicity. These newly formed flow paths may extend beyond the secure geological structure and cause environmental hazards. Therefore, another important characteristic of geomechanical studies is determining the reservoir pressure threshold to prevent fault instability. Before injecting gas into the reservoir formation, natural faults are inactive under the continuous pressure of the reservoir. However, the inevitable increase in pore pressure during gas injection may lead to the instability of the faults.

As the reservoir pressure increases, the effective normal stress applied to the fault plane decreases significantly. Therefore, estimating the threshold pore pressure that could lead to fault slippage is crucial for designing a safe injection scenario. Like formation failure, the Mohr–Coulomb failure criterion can also be applied to fault reactivation analysis. In order to perform a comprehensive failure analysis, additional fault characteristics such as shear strength, friction angle, and permeability of the fault plane are necessary. Therefore, faults require a more thorough Mohr–Coulomb failure analysis compared to intact rocks (Cappa and Rutqvist 2011). The potential risk of fault reactivation can be evaluated using the Coulomb failure stress (CFS) equation developed by King et al. (1994) as follows:

$${\text{CFS}} = \tau {-}(\mu_{{\text{s}}} *\sigma_{{\text{n}}} )$$

(15)

where τ and ${\sigma }_{\mathrm{n}}$ are shear stress and effective normal stress, respectively, and ${\mu }_{\mathrm{s}}$ represents the friction coefficient of the fault, calculated from ${\mu }_{\mathrm{s}}=\mathrm{tan}\varphi$, in which φ is the friction angle of the fault. King et al. (1994) also showed that faults would be activated when CFS ≥ 0. Therefore, fault stability depends on adequate shear stress to prevail over the effective normal stress of the fault plane and surpass the slip resistance of the pre-existing faults during injection and pore pressure increase, i.e., ${\mu }_{\mathrm{s}}\ge \tau/{\sigma}_{\mathrm{n}}$. In this work, the probability of fault activation was determined based on the Coulomb failure stress (CFS) represented by Eq. (15). In this regard, the ratio of the shear stress to effective normal stress for each grid surrounding the available faults was defined to evaluate the possibility of the fault reactivation, as depicted in Fig. 15. As reported in the literature, the value of the friction coefficient varies between 0.6 and 0.85 (Byerlee 1978; Vidal-Gilbert et al. 2009). In the case of the studied field, there is no information about the mechanical characteristics of the faults. Therefore, as an assumption and referring to the literature, the default value of 0.6 was assigned to the static friction coefficient of the fault. The ${\mu }_{\mathrm{s}}\hspace{0.17em}$= 0.6 is a lower bound value and a conservative premise used by numerous researchers who have studied fault stability (Zoback 2007; Rutqvist et al. 2007; Figueiredo et al. 2015; Tadayoni et al. 2022).

Fig. 15

Fault activation analysis at the end of the simulation period (after 20 years of simulation)

Based on the data reported in Fig. 15, the stress-to-strain ratio reaches a maximum value of 0.46 during the studied scenario, which is lower than the assumed value of the fault friction coefficient (0.6). This indicates that the faults are not activated at the maximum reservoir pressure, and the injection scenario is safe from fault reactivation. As observed in Fig. 16, there is no significant change in the elastic shear displacement of the faults during the selected time steps, confirming the capability of the reservoir–caprock system to seal faults in the studied area. However, it should be noted that the accuracy of this result depends on the selected friction coefficient for the faults, which needs to be precisely known. The geomechanical simulation results suggest that the loading on the fault plane is too low to cause the reactivation of pre-existing faults. Therefore, the current simulation case can be conducted safely without any faults slipping in the studied field.

Fig. 16

Fault elastic shear displacement at the end of the simulation period (after 20 years of simulation)

Conclusions

In this work, the geomechanical impacts of gas injection into a giant depleted oil reservoir were investigated. A step-by-step procedure for developing a hydro-mechanical model to simulate a potential gas injection process was described. Although many geomechanical models may exist, there is little information on the development and implementations of these models disclosed publicly. The procedure described in this study is not only relevant to gas injection in the studied field but also can be applied to the development of other potential gas injection/storage sites worldwide, including CO₂ and methane underground storage. The significant results obtained in this study are as follows:

• Most studies used empirical correlations for geomechanical evaluation; however, this study uses experimental correlations between static, dynamic, and rock strength properties derived from core data and available petrophysical logs for the studied reservoir–caprock system.

• The maximum displacement occurs near the injection wells where the most pressure changes are experienced. Also, comparing two analytical and numerical methods to estimate the reservoir displacement showed that the analytical method is easy and fast, but the results can be unrealistic.

• The caprock–reservoir system maintains its integrity during the studied scenario. As the injection pressure increases to 4.3 times the initial reservoir pressure, the integrity of the reservoir formation is lost, but the caprock remains intact at the failure reservoir pressure.

• The geomechanical simulation results indicate that the maximum reservoir pressure cannot trigger fault slippage.

Overall, the results of the geomechanical modeling study indicate that gas injection can be safely and effectively carried out in depleted hydrocarbon reservoirs. These findings are applicable to the studied field and can be implemented in gas injection/storage scenarios in similar depleted hydrocarbon fields.