A coupled thermo- hydro-mechanical simulation of reservoir CO 2 enhanced oil recovery

Abstract

Carbon dioxide sequestration is an effective mechanism for enhanced oil recovery. In a carbon dioxide enhanced oil recovery project, the temperature of the injected carbon dioxide is usually considerably lower than the formation temperature. The heat transfer between the injected fluid, reservoir fluids, and rock has to be investigated in order to test the viability of the target formation to act as an effective enhanced oil recovery unit and to optimize the process. Simulation of carbon dioxide injection based on a suitable modeling is very important for explaining the fluid flow behavior of carbon dioxide in a reservoir. Geomechanical aspects between fluids and carbonate rocks can change porosity and permeability during carbon dioxide flooding which may significantly impact well injectivity, reservoir integrity, and oil recovery. This article presents development of a simulator using implementation of a program (FORTRAN 90 interface code) for coupled thermo-hydro-mechanical processes in multiphase reservoir modeling. The simulator is denoted ECLIPSE-ABAQUS, because it utilizes two established computer codes, ECLIPSE and ABAQUS, which are linked and jointly executed for analysis of coupled thermo-hydro-mechanical processes. The capabilities of the ECLIPSE-ABAQUS simulator are demonstrated on a complex coupled problems related to injection of carbon dioxide in an oil reservoir. The coupled thermo-hydro-mechanical analysis of the reservoir showed that the reservoir production rate/total and production time in the coupled thermo-hydro-mechanical simulation is more than the uncoupled one. Also permeability and porosity changes in the coupled thermo-hydro-mechanical simulation are different from the coupled hydro-mechanical simulation. Furthermore, the Finite Element Method analysis showed no sign of plastic strain under production and carbon dioxide injection scenarios in any part of the reservoir.

Keywords

Reservoir geomechanics coupled porosity permeability THM

Introduction

CO₂ enhanced oil recovery (EOR) is one of a series of engineering strategies designed to increase the rate and ultimate amount of oil produced. As reservoir and mobility of oil decrease, ending the period of primary production, operators of many oil reservoirs increase production by moving into a higher level of engineered assistance, known as secondary recovery. Water or recycled natural gas is injected (flooded) into the reservoir through a pattern of injection wells to maintain pressure and guide oil toward production wells. When recovery again declines, tertiary recovery methods can be employed; among the methods commonly used is the injection of substances not native to the reservoir, defined as EOR.¹ Introduction of allochthonous additives at higher cost can once again increase the rate of oil extraction and extend the economic and productive life of the field, increasing the percentage of original oil in place (OOIP) extracted.

EOR techniques include addition of products such as N₂, flue gas, CO₂, acid gases, hydrocarbon products, engineered solvents, polymers, foams, in situ combustion, and steam.¹ Cases in which CO₂ is the primary injected fluid are known as CO₂-EOR floods. In most CO₂-EOR, the injected fluid is nearly pure (>99%) CO₂ compressed to a dense phase (liquid or supercritical fluid).

Increasing pore pressure and temperature reduction during CO₂ injection results in deformation of both the reservoir and surrounding rocks. A portion of injected CO₂ can escape the storage domain if the integrity of the seal rock is violated by geomechanical mechanisms such as propagation of induced fractures or rock shear failure.

Petroleum geomechanics has become more-and-more part of oil industry analysis approaches to explain and evaluate phenomena such as wellbore stability in shale, reservoir compaction and surface subsidence during depletion, injection, hydraulic fracture stimulation, and so on.^2–9 In order to study the mechanical deformations during CO₂ sequestration, numerical modeling of fluid flow through porous medium coupled with a geomechanical analysis of the medium at different pore pressure distributions^10–13 is required.

Once CO₂ is injected, the pressure and temperature of the formation is affected by the mass and heat transfer between the injected and in place fluid. These changes have geomechanical consequences on stresses, displacements, fracture pressure, and its propagation. Since geomechanical effects induced by injection could lead to formation or reactivation of fracture network, rock shear failure and fault movements which could potentially provide pathways for CO₂ leakage, so geomechanical modeling plays a very important role in risk assessment of geological storage of CO₂.¹⁰

In the last years, the inclusion of thermal effects into the theory of hydro-mechanical (HM) coupling has become more and more of relevance.¹⁴ Important issues are for instance the modeling of the thermo-mechanical (TM) processes in nuclear waste disposals.

The general concept of THM coupled modeling is shown in Figure 1.

Figure 1.

Thermo-hydro-mechanical coupling approach and the respective constitutive laws.¹⁵

THM-induced stress–strain also has an impact on processes related to the usage of geothermal energy. For computing such processes numerically on the respective relevant scales, stress–strain relationships resulting from fluid pressure and temperature have to be computed and coupled to the regional flow and transport regime dynamically.

In case of THM coupling application examples are for instance the productivity of reservoir doublet systems with several production and injection wells, which can be influenced due to mechanical changes and a related change of the hydraulic conductivity.¹⁶

A general review with respect to THM coupled processes is given in Wang et al.,¹⁷ Watanabe et al.,¹⁸ and Kolditz et al.¹⁹

Thermo-mechanical coupling is mainly working only in one direction as thermal expansion induces volume changes of the rock (similar to pore pressure changes in case of hydro-mechanical coupling); vice versa the mechanics do not alter the temperature directly but only due to changes of the (convective) flow field.

In this article, the THM effect of CO₂ injection on oil recovery and the possibility of failure in the reservoir and burdens are studied. This study utilized an explicit sequential coupling implementation, the Coupled Geomechanical Reservoir Simulator (THM) that uses Schlumberger ECLIPSE 300²⁰ for the fluid flow simulation and ABAQUS²¹ for the geomechanical analysis. Both ECLIPSE and ABAQUS represent two of the most advanced and most widely used (both in academia and the hydrocarbon industry) software packages of their respective genre. First, a description of the problem and of the general methodology has been given by providing an overview of the workflow that has been developed. Next, the application of this approach to a realistic test case has been illustrated. Finally, we conclude with a discussion on the obtained results.

Geological and geomechanical properties of the studied area

A coupled flow, thermal, and geomechanical model has been developed in order to study the THM response of the injection on the reservoir and surrounding layer to increasing of pressure and reduction of temperature after CO₂ injection. The studied oil region is located in south west of Iran. The region has little folding, with numerous reservoirs. Sequence stratigraphy of the region, respectively, from top to the target depth includes Aghajari, Gachsaran, Asemari, Pabdeh, Gurpi, Ilam, Lafan, Sarvak, Kazhdumi, Darlyan, Gadvan, Fahliyan, and Garau.²²

In this study, Sarvak formation was the target reservoir. This reservoir is an anticline structure directed to north-south with no exposure and it was detected by geophysical (seismic) survey. No major faults and fractures have been reported in this reservoir.

The Sarvak formation (Cretaceous, thick 650–1100 m) is a thick carbonated unit that was deposited in Neotethys southern margin of Zagros area. It is one of the most important hydrocarbon horizons in Iran. Laboratory and field observation lead to recognition of four facies environments: open marine, shale, and lagoon in coastal area of Fars, Khuzestan, and Lurestan. The lower lithostratigraphic limit of Sarvak formation, which is conformable and gradational, overlies the Kazhdumi formation. Upper lithostratigraphic limit of that is secant with Ilam-Lafan formation (Figure 2). Also thickness and layers slope of Sarvak formation is approximately constant.

Figure 2.

Sequence stratigraphy of the studied region.²²

The reservoir depth is about 2700 m and has a thickness of approximately 110 m. Limestone is the dominant rock type in this reservoir and also upper structure. The reservoir geometry has been indicated by five wells drilled in the structure and the information related to the distance between the wells and connection depth of them to Sarvak formation.

The reservoir upper surface was sketched by introducing the intersection points from wells and the formation in Surfer software (Figure 3). Finally, the reservoir geometry was determined by its upper surface and the thickness of layers.

Figure 3.

The reservoir upper surface.

The mechanical properties and initial stress profile is required to be added to the geomechanical model and coupled with the flow model in order to be able to study the mutual effect of pressure and stresses and the resulting effect on integrity and injectivity. The reservoir rock mechanical parameters including, uniaxial compressive strength, young modulus, Poisson ratio, and tensile strength was obtained from Dipole sonic imager (DSI) logs and imperical relationships. The reservoir young modulus, Poisson ratio, cohesion, friction angle, and uniaxial compressive strength are 25 GPa, 0.20, 3.5 MPa, 32, and 60 MPa respectively. Also the reservoir Initial pressure is around 4100 psi. Other characteristics of the reservoir layers are given in Table 1.

Table 1.

Mechanical properties of the reservoir layers.

Layer	Thickness (m)	Water saturation (%)	Porosity	Permeability (md)	Density (kg/m³)
1	5	90	0.01	2	2600
2	20	15	0.1	40	2600
3	30	20	0.14	40	2600
4	60	45	0.1	40	2600
5	5	90	0.01	2	2600

As mentioned before, since the temperature of injected CO₂ is smaller than the formation temperature, thermal effects of injection on fluid flow and geomechanics must be included in the model. This coupling is achieved by solving the energy balance equation within the fluid flow model, and including the thermoplasticity term in the geomechanical model (included in the constitutive model of the rock).

Densities of water, oil, and gas are 1190, 850, and 0.90 kg/m³, respectively. Also average thermal properties for the rock, as well as injected and in-place fluids used for this study are listed in Table 2.

Table 2.

Thermal properties of fluids and rock.

	Rock	Water	Oil	Gas	CO₂
Volumetric thermal expansion coefficient (1/K)	5.4E-6	2.1E-4	1.0E-3	1.5E-3	3.003E-3
Heat capacity (kJ/kg K)	0.9	4.2	1.88	3.20	0.84
Thermal conductivity (W/m K)	2.34	0.65	0.15	0.037	0.084

Flow, thermal, and geomechanical coupling modules

A reservoir-geomechanical link takes multiphase pressures and temperature from the reservoir simulator and provides updated temperature, and pore pressure to geomechanics simulator (Figure 4).

Figure 4.

Schematic of linking ECLIPSE and ABAQUS for a coupled THM simulation.

In order to calculate the new compressibility and porosities as a function of pressure and volumetric strain, the change in pore pressure and the elemental volumetric strain values are averaged over the grid block. A simple and empirical relationship is proposed by Touhidi-Baghini²³ for predicting the evolution of the absolute permeability changes induced by stress changes. This simple relationship linking permeability changes to volumetric strain reads

\frac{\ln k_{1}}{k_{0}} = \frac{c}{φ_{0}} ɛ_{v}

(1)

This equation allows the computation of absolute permeability k₁ from its initial value k₀, the volumetric strain $ɛ_{v}$ , and the initial porosity value ( $φ_{0}$ ). An appropriate value for the constant c has to be picked. According to Touhidi-Baghini, the values c = 5 and c = 2 appear to be appropriate to match with vertical and horizontal permeability evolutions, respectively.

The porosity ( $φ$ ), is related to the volumetric strain as²⁴

φ = φ_{0} + α (ɛ_{v} - ɛ_{v 0}) + \frac{1}{ϕ} (P - P_{0})

(2)

where

ɛ_{v 0}

is volumetric strain at the beginning of each time step. Also

α

and

ϕ

are constant parameters.²⁵

We report here the development of an explicit coupled multiphase flow and geomechanical approach to analyze THM coupled processes relate to CO₂ injection into oil reservoir. The explicit coupled study utilizes a reservoir model for simulation of fluid flow through porous media using the commercial reservoir simulator ECLIPSE 300²⁰ and the optimized finite element discretization using the commercial finite element solver ABAQUS²¹ for the geomechanical analysis of rock deformation that is caused by the pore pressure difference associated to EOR using carbon dioxide (CO₂-EOR).

Because an ECLIPSE (finite difference code) mesh uses one gridpoint within each element, and ABAQUS (finite element method) nodes are located in element corners, data have to be interpolated from midelement (ECLIPSE) to corner locations (ABAQUS) as shown in Figure 5.

Figure 5.

Coexisting ECLIPSE and ABAQUS mesh for a coupled THM simulation.

The external part (side-burden, over-burden, and under-burden) of the grid, needed to correctly simulate the geomechanical behavior of the system, is automatically built by the interface code, provided that the final model size is given. The element type attributed to the reservoir regions is eight-node brick stress/displacement/pore pressure (C3D8P), while eight-node brick stress/displacement (C3D8) is assigned to the external regions.

The user subroutine option in ABAQUS makes the program to a very versatile tool. It is even possible to define your own finite element in ABAQUS. However, developing and maintaining such computer code is not a part of our strategy.

User subroutines in ABAQUS can control the coupling and execution of ECLIPSE and ABAQUS for the linked reservoir geomechanics simulation. In this case, it was done within the ABAQUS input file using FORTRAN 90 interface codes. The calculation is stepped forward in time with the transient TH analysis in ECLIPSE, and at each time step a quasi-static mechanical analysis is conducted with ABAQUS to calculate stress-induced changes in porosity and intrinsic permeability. The resulting THM analysis is explicit sequential, meaning that the porosity and permeability is evaluated only at the beginning of each time step. In the explicit sequential procedure (Figure 6), the ECLIPSE code is executed for a TH analysis between time t^k to t^k+1 until mass conservation is assured by solving the ECLIPSE flow and heat equation.

Figure 6.

Numerical procedure of a linked ECLIPSE and ABAQUS simulation with explicit sequential solutions.

Prescribed conditions

The initial effective stresses are generated in the ABAQUS subroutine, SIGINI. The in-situ stress regime for the case study is NF stress regime with stress ratio (horizontal/vertical stress of 0.41). The depth and the unit weight of overlying material determine the vertical stress distribution throughout the model. The horizontal stresses are calculated by multiplying the vertical stress by the stress ratio (k) ratio.

The initial geostatic stress field must be in equilibrium with the applied loads and boundary conditions. Ideally, the loads and initial stresses should exactly equilibrate and produce zero deformations. This state is obtained performing an initial ABAQUS analysis fixing all displacements degree of freedoms. Calculated reaction forces written to the ABAQUS output file are then used to create nodal point forces, which are applied in the first step of the actual ABAQUS analysis.

The pore pressure depletion and injection history within the reservoir is transferred from the ECLIPSE reservoir model to ABAQUS utilizing the user subroutine DISP. A file containing the pore pressure in each ECLIPSE block is read for each time step analyzed by ABAQUS.

The initial porosity distribution is transferred from the ECLIPSE reservoir model to ABAQUS utilizing the user subroutine VOIDRI for reading initial porosity in ABAQUS. The initial void ratio e₀, defined as the ratio between the pore volume and the solid volume, is related to the porosity $φ$ through: $e_{0} = φ / (1 - φ)$ .

The boundary condition for the fluid flow model is that there is no flow across the boundary of the reservoir. The constraints for the geomechanical model are as follows. The right, left, front, and back sides of the model are fixed in the x-direction and y-direction so there would be no displacement in the x and y directions. The bottom side of the model is fixed in all directions and the top of the model is free to move in all directions.

Results and discussion

The reservoir dynamic model is built with the ECLIPSE reservoir simulator, which is a fully implicit, three phases and 3D finite difference code. The dynamic model takes as input all the information of the static model and by introducing a series of additional parameters regarding the characteristics of the fluids, the rock, and the well system, provides the information required for the field management such as the dynamic reserve evaluation and the production and injection profiles as a function of the development scenarios. The dynamic model provides as output sets of data that are used in the geomechanical finite element simulation such as the grid discretization of the reservoir and of the surrounding areas, the initial values of porosity and permeability, the evolution of the fluid pressure and temperature as a function of space and time. As explained in detail in the above section, all these information are converted with an interface code and used to build the ABAQUS FE model.

As an example, in Figure 7 the finite difference discretization of a dynamic model for the reservoir is shown. The initial reservoir temperature is 200°F and the reservoir was targeted by five wells. Production conditions and restrictions are as follow:

Oil production rate of each well is 3500 stb/day (standard barrels per day) and the minimum bottom hole pressure is 1450 psi.

Oil production of each well will be terminated if the well production rate is less than 500 stb/day or GOR (reservoir gas and CO₂ oil ratio) is greater than 20 mscf/stb (thousand standard cubic feet per stock tank barrel).

Figure 7.

Flow model: grid discretization, well system, and pressure distribution on 1 January 2010.

Also production and injection strategies are as follow:

Oil production of all wells was started at January first 1997. If any of the wells production was terminated (because of mentioned restrictions) the well will be used as a CO₂ injection well. Injection strategy involves the injection of 200 mmscf/day (million standard cubic feet per day) with an injection temperature of 80°F and a maximum bottom hole pressure of 5000 psi.

Figure 8 presents the calculated reservoir production rate and reservoir production total with and without consideration of the stress-dependent rock mass petrophysical properties (permeability and porosity) and temperature-dependent fluids properties (THM coupling). The reservoir production rate, total, and production time in the coupled THM reservoir simulation is more than the uncoupled one, because in the coupled THM simulation the lower injection temperature than the reservoir temperature will decrease CO₂ mobility. So some production wells will reach the restriction of GOR >20 mscf/stb late. Note that the changes in permeability and porosity are low because of a rather insensitive stress–permeability relationship for the porous reservoir rock (Figure 12).

Figure 8.

Reservoir oil production rate (left) and oil production total (right) with and without consideration THM coupling.

Figure 9.

Reservoir pressure rate.

Figure 10.

Well No. 1 CO₂ injection rate.

Figure 12.

Permeability (left) and porosity (right) changes around the injection well (zone No. 2677) with HM and THM coupling.

As shown in Figure 8, at the beginning, each well production rate is 3500 stb/day. Because of reservoir pressure reduction, the oil production rate will be decreased gradually. After about 3410 days from the start of production the production rate of well No. 1 falls under 500 stb/day, so its production will be halted and it will be prepared for CO₂ injection rate of 200 mmscf/day. After CO₂ injection, the reservoir pressure gradually increased and so the rate of production in four other production wells will increase.

Over the time of the reservoir injection and production, oil production from the wells will be halted at different times because of low production rate or GOR >20 mscf/stb. The wells production termination time and reasons for this event with and without coupled THM consideration are listed in Table 3.

Table 3.

The wells production termination time and termination.

Method	Well No. 1		Well No. 2		Well No. 5		Well No. 4		Well No. 3
Method	Day	Reason	Day	Reason	Day	Reason	Day	Reason	Day	Reason
Uncoupled	3420	OPR < limit	6020	OPR < limit	6727	OPR < limit	15,058	OPR < limit	18,554	OPR < limit
Coupled THM	3410	OPR < limit	6052	OPR < limit	6762	OPR < limit	15,592	OPR < limit	19,312	OPR < limit

OPR < limit: the well oil production rate is less than 500 stb.

Due to the difference between the reservoir pressure and pressure at the bottom of injection well, CO₂ flow path is from bottom of the injection well to around it. In spite of production from the four wells (No. 2, 3, 4, and 5) by increasing the time of gas injection from the well No. 1, the reservoir pressure gradually increases and by reduction of difference between the reservoir pressure and injection pressure the gas injection rate decreases. Therefore, the slope of the reservoir pressure changes rate will be reduced (Figure 9). Also the reservoir CO₂ injection rate is shown in Figure 10.

The in-situ stress regime for the case study is NF stress regime with stress ratio (k) of 0.41 and Mohr–Coulomb elasto-plastic criterion was used for geomechanical simulation of the reservoir during CO₂-EOR. Also for studding the surrounding rocks the elastic model was used.

As mentioned above, due to the lower injection temperature than the reservoir temperature, with increasing injection time, temperature around the injection well (No. 1) drops gradually and thermal strain will occur around it (Figure 11).

Figure 11.

Reservoir temperature distribution (left) and related maximum thermal strain (right).

The change in porosity and permeability due to the change in pore pressure, temperature, and the state of stress is reflected in the analysis by updating of corresponding parameters. The coupling module treats permeability as a nonlinear function of stresses and is capable of detecting plastic deformation.

In the case of hydro-mechanical (HM) modeling, with the increase in pore pressure the reservoir permeability and porosity values has increased and also both decrease by pore pressure reduction. But this is not true in THM modeling, because as stated above, the reservoir temperature changes around the injection well (well No. 1) induce thermal strains (apart from induced strain by pore pressure variations) and therefore change the permeability and porosity (Figure 12). Note that the changes in permeability and porosity are low because of a rather insensitive stress–permeability relationship for the porous reservoir rock.

The FEM analysis of the reservoir showed no sign of plastic strain under production and gas injection phases in any part of the reservoir (Figure 13). During depletion and before the injection scenario of well No. 1, the reservoir has shown subsidence. However by injection of well No. 1 and production from other four wells, at the same time, the reservoir displacement reversed (Figure 14). Though, such displacements are ignorable because of less potential for instability of the reservoir.

Figure 13.

Maximum plastic strain in the reservoir.

Figure 14.

Vertical displacement changes around the well No. 1 (layer 3) during production and injection scenarios.

Evolution of stress perturbations within the reservoir can be conveniently analyzed by plotting the stress path diagrams using the Mohr–Coulomb criterion for the characteristic locations in the model (Figure 15).

Figure 15.

Reservoir anticline part stress path for production and injection scenario.

The Mohr–Coulomb criterion is the most common failure criterion encountered in rock engineering. Many geomechanical analysis methods and programs require the use of this strength model. The Mohr–Coulomb criterion describes a linear relationship between normal ( $σ_{n}$ ) and shear (τ) stresses (or maximum and minimum principal stresses) at failure.

The direct shear formulation of the criterion is given by

τ = C + σ_{n} \tan φ

(3)

where C is the cohesive strength and ϕ is the friction angle.

For the reservoir rock, the stress path diagrams show an increase of both the normal effective stress and the shear stress for depletion and large decrease of both stresses for injection. It should be noted that in injection scenario the minimum principal stress reduction in the case of THM coupled is more than HM coupled consideration. Also according to the Mohr–Coulomb criterion envelope, at CO₂ injection pressure of 5000 psi the stress paths do not show a critical behavior, that is, the paths is not converging toward the Mohr–Coulomb failure envelopes plotted for the shear strength parameters. It is noted that in this injection pressure deformation is elastic and the reservoir stress path for injection is fully reversible with reference to the stress path for depletion. Also as shown in Figure 15, the minimum principal stress in the case of THM coupled is less than HM coupled consideration.

Conclusion

Numerical modeling is a proper tool to calculate and analyze fluid flow induced stress changes and to estimate their impact on rock stability and important aspect in reservoir management.

The present work deals with mechanical changes induced in the reservoir and the surrounding rock due to CO₂-EOR method. A geomechanical reservoir modeling tool is established utilizing the ABAQUS scripting interface. The link consists of a set of FORTRAN code that rebuilds the ECLIPSE reservoir geometry and dynamic properties in ABAQUS/CAE and vice versa. It enables us to perform the very large scale hydromechanical simulations. This kind of simulations is necessary to evaluate the hydromechanical assessment for a given production or injection site and to calculate the safety factors for a given scenario. For the given parameters and considered scenario the following results are obtained:

At the start, each well production rate is 3500 stb/day. Due to reservoir pressure reduction, the oil production rate will be decreased gradually. The production rate of well No. 1 falls under 500 stb/day after about 3410 days from the start of production, so its production will be halted and it will be prepared for CO₂ injection.

The reservoir production rate, total, and production time in the coupled THM reservoir simulation is more than the uncoupled one, because in the coupled THM simulation the lower injection temperature than the reservoir temperature will decrease CO₂ mobility. So some production wells will reach the restriction of GOR >20 mscf/stb late.

After CO₂ injection, the reservoir pressure gradually increased and so the rate of production in four other production wells will increase. Over the time of the reservoir injection and production, oil production from the wells will be halted at different times because of low production rate or GOR >20 mscf/stb.

In the HM modeling, with the increase in pore pressure the reservoir permeability and porosity values has increased and also both decrease by pore pressure reduction. But this is not true in THM modeling, because the reservoir temperature changes around the injection well induce thermal and therefore change the permeability and porosity.

Changes in permeability and porosity are low because of a rather insensitive stress–permeability relationship for the porous reservoir rock.

The FEM analysis of the reservoir showed no sign of plastic strain under production and gas injection phases in any part of the reservoir. Also the stress paths are not converging toward the Mohr–Coulomb failure envelopes plotted for the shear strength parameters. Also in injection scenario the minimum principal stress reduction in the case of THM coupled is more than HM coupled consideration.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

Dr. Ayub Elyasi obtained his PhD student in Rock Mechanics from Tarbiat Modares University. Elyasi research interests are petroleum geomechanics including reservoir engineering, EOR, hydrocarbons storage rock caverns, CO2 sequestration and wellbore stability and analysis of ground and underground structures like tunnels, caverns and slopes. Elyasi holds a BSc degree from Sahand University of Technology and an MSc degree from Tarbiat Modares University.

Dr. Kamran Goshtasbi is associate professor of Mining Engineering and rock mechanics in the faculty of engineering, Tarbiat Modares University, Tehran, Iran. He obtained his Ph.D. in mining engineering and rock mechanics from Nottingham University, England. He is currently engaged in teaching and research in rock mechanics and petroleum geomechanics in Tarbiat Modares University.

Dr. Hamid Hashemolhosseini is associate professor of Mining Engineering in Isfahan University of Technology, Isfahan, Iran. He obtained his Ph.D. in mechanics of soil and structure in l'Institue National Polytechnique de Grenoble (INPG), Grenoble, France

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