European Journal of Environmental and Civil Engineering Prediction

This article was downloaded by: [M. Abdideh] On: 28 April 2014, At: 23:51 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK

European Journal of Environmental and Civil Engineering Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/tece20

Prediction of geomechanical modeling and selection of suitable layer for hydraulic fracturing operation in oil reservoir (South West of Iran) a

a

Mohammad Abdideh & Arash Ahmadifar a

Department of Petroleum Engineering, Omidieh Branch, Islamic Azad University, Omidieh, Iran. Published online: 04 Oct 2013.

To cite this article: Mohammad Abdideh & Arash Ahmadifar (2013) Prediction of geomechanical modeling and selection of suitable layer for hydraulic fracturing operation in oil reservoir (South West of Iran), European Journal of Environmental and Civil Engineering, 17:10, 968-981, DOI: 10.1080/19648189.2013.840249 To link to this article: http://dx.doi.org/10.1080/19648189.2013.840249

PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms &

Downloaded by [M. Abdideh] at 23:51 28 April 2014

Conditions of access and use can be found at http://www.tandfonline.com/page/termsand-conditions

European Journal of Environmental and Civil Engineering, 2013 Vol. 17, No. 10, 968–981, http://dx.doi.org/10.1080/19648189.2013.840249

Prediction of geomechanical modeling and selection of suitable layer for hydraulic fracturing operation in oil reservoir (South West of Iran) Mohammad Abdideh* and Arash Ahmadifar Department of Petroleum Engineering, Omidieh Branch, Islamic Azad University, Omidieh, Iran

Downloaded by [M. Abdideh] at 23:51 28 April 2014

(Received 26 October 2012; accepted 29 August 2013) Hydraulic fracturing operation is a methodused to improve productivity index of reservoirs with considerable oil in place and suitable porosity but low permeability or flow capacity. In the beginning of this study, geomechanical model, which includes dynamic and static Young’s modulus and in situ stresses, is calculated by poroelastic methods. Furthermore, normal stress regime (σν > σH > σh) is diagnosed for the reservoir rock. Secondly, induced stresses after drilling operation are determined and a safe mud window for selecting a safe mud pressure is designed, so the window helps to avoid problems like pipe sticking or fishing operations. Finally, based on the crucial factors such as in situ stress, porosity, water saturation and uniaxial compressive strength, best layers for hydraulic fracturing operation are selected and their fracture pressures are estimated. Keywords: EOR; hydraulic fracturing; geomechanical modeling; UCS; petrophysics; water saturation

1. Introduction Reservoir geomechanics has a key role in the evaluation and developing of the oil and gas reservoirs. Basically, geomechanics is a knowledge that investigates and interprets the earth reactions against stresses. These stresses might be natural stresses which exist inside the earth or induced stresses which are produced by human activities such as drilling operations. Consequently, based on the definition of the Geomechanics, the key solution for physical and mechanical problems, which are caused by interaction between materials in different depths and stresses, is in this field. But still, it is obvious that to study about the chemical anomalies and related problems in the drilling industry, we should use other sciences beside the Geomechanics (Amadie & Stephansoon, 1997). Always natural production from the layers which have sufficient and acceptable porosity and low permeability or flow capacity is not profitable and economic. So in this condition, EOR or enhanced oil recovery methods should be applied. Hydraulic fracturing operation is one of the most effective methods experienced ever in order to make the reservoir commercially valuable (Economides & Nolte, 2008; Hibbeler & Rae, 2005; Legarth, Huenges, & Zimmermann, 2005; Pak and Chan, 2008; Queipo, Verde, Canelon, & Pintos, 2002). In this task, an induced fracture is created inside wellbore interval by injection of high pressure flow of fluid; consequently, a channel *Corresponding author. Email: [email protected] Ó 2013 Taylor & Francis

Downloaded by [M. Abdideh] at 23:51 28 April 2014

European Journal of Environmental and Civil Engineering

969

would be produced in low permeable zone. Generally, the main goals of this operation are first increasing of flow area for fluids in better words increasing permeability and second reducing the distance hydrocarbons should pass before reaching the wellbore. Furthermore, hydraulic fracturing helps to remove damaging area around borehole that is caused by drilling and completion activities. So, applying of this method rise the productivity of well significantly in comparison with the time well is produced under natural condition. Selection of suitable or target layer for hydraulic fracturing operation has its special challenges. Presentation of an accurate geomechanical model which saves the time and reduces the field attempts makes the selection of suitable layer possible. In order to prepare a geomechanical model, we need a wide range of data such as wire line logs, image logs, rock mechanics tests, drilling reports and data frac analysis selection of suitable layer is done based on rock and fluid properties for instance porosity, water saturation and in situ stress; in this study; we add the effect of uniaxial compressive strength (UCS) and the difference between horizontal stresses in order to accurate interval selection process. The field under study consists of three reservoirs of Asmari, Bangestan and Khami, of which the first two are oil reservoirs and the latter, a gas reservoir. Located in a flat plain, the studied field has no surface outcrop. This field, which is located in Zagros thrust-fold belt, has the same trend as the Zagros, namely the north-west and south-east. The Bangestan limestone unit consists of two formations, Ilam and Sarvak. The Sarvak formation is part of middle Cretaceous calcareous rocks. Lithology of the Ilam formation consists of limestone rocks with a regular stratification, in which there are thin interlayers of shale in some intervals. 2.

Workflow and methodology

The work flow that is designed for preparing the following study was divided in five main steps that include important factors influence the process of selection of the best layer for hydraulic fracturing operation in the Bangestan reservoir rock: (1) Calculation of the elastic properties of rock such as dynamic and static Young’s modulus and Poisson’s ratio. The equations that are used in this section are fed by compressive and shear transient times. The transient times is calculated by sonic log data. (2) Determination of main in situ stresses such as vertical stress or overburden stress, maximum and minimum horizontal stresses and make decision what type of stress regime exist in understudying area. Based on Anderson (1951), there are three different stress regimes exist: (a) Normal stress regime (rV
rH
rh ) (b) Reverse stress regime (rH
rH
rV ) (c) Strike-slip stress regime (sigmaH
rV
rh ) (3) Safe mud window design. Undoubtedly, most of the problems we are faced during drilling operation (such as fishing, pipe sticking) are related to the inappropriate mud weight selection. This window helps that the best mud weight select and reduces the cost of drilling beside the time that is saved.

970

M. Abdideh and A. Ahmadifar

(4) There are stresses in different directions such as radial, axial and tangential directions that are created after engineering constructions. The mentioned stress causes different types of failure in the borehole. In fourth step, these stresses are calculated and the type of failure is predicted also the minimum necessary pressure for hydraulic fracturing in layers is determined. (5) Final step is selection of the suitable layers for hydraulic fracturing. In this step, first, rock and fluid properties for instance UCS, water saturation, porosity and difference between in situ horizontal stresses are determined. Afterwards, based on above profiles, zonation is done and each zone is evaluated separately. In this condition, two different kinds of layers exist as follows: (1) target layer (2) obstacle layer.

Downloaded by [M. Abdideh] at 23:51 28 April 2014

2.1.

Determination of elastic properties

Elastic properties such as static Young’s modulus and Poisson’s ratio are the main data we need to convert the vertical stress to horizontal stresses in better word poroelastic correlations are fed by this data. There are two references for calculation of elastic coefficient in Equations (5) and (6): (a) logging data, (b) empirical correlations. The two following correlations are specifically used to calculate the dynamic Young’s modulus and Poisson's ratio base on the transient times that are gained by sonic log data: m¼

1 DtC 2 ð Þ 1 2 DtS C 2 ðDt Þ 1 DtS

ð1Þ

DtS qb ½3  4ðDt Þ C 2

EDynamic ¼

DtS2  DtC2

ð2Þ

In the above equations, primary and secondary transient times are in km/s, and dynamic Young’s modulus is in Gpa. Generally, in the Bangestan reservoir rock, the range of Poisson ratio is 0.3–0.37 and for the understudying section Poisson’s ratio is 0.3. Since we could not use dynamic data in geomechanical models, it is essential to convert them to the static condition. Based on the existing empirical correlations for the under studying area: EStatic ¼ 0:4145EDynamic  1:0593

ð3Þ

The difference between dynamic and static Young’s modulus is shown by Figure 1 (A)). 2.2.

In situ stress and stress field

To get the geomechanical model, firstly, calculate the magnitude of the main stresses, which are those vertical stresses on the plane that their shear stresses are zero. They are defined as maximum main stress (S1), intermediate main stress (S2) and minimum main stress (S3). The vertical stress (σv) is one of those, so the two other main stresses are minimum horizontal stress (σh) and maximum horizontal stress (σH).

European Journal of Environmental and Civil Engineering

971

(I) Vertical stress or overburden stress is determined by the below formula: Z

z

gz qðzÞgdz ffi q

rv ¼

ð4Þ

Downloaded by [M. Abdideh] at 23:51 28 April 2014

0

ρ (z) is the rock density and the function of depth. The average magnitude of density has been equalled by 2.56 (gr/cm3). Finally, overburden or vertical pressure is calculated by integrating all available density logs. It is estimated around 85.57 Mpa. (II) Knowledge of vertical profile of the minimum horizontal stress is one of the most important parameters in a hydraulic fracturing (Willis, Fontaine, Paugh, & Griffin, 2005; Wright, Weijers, Davis, & Mayerhofer, 1999).The minimum horizontal stress (σh) can be determined by different methods such as hydraulic fracture method, leak-off test method, macro-fracture test method and mini-fracture test method. However, the leakoff test method is much more common in comparison with the other methods. (Hubbert & Willis, 1957) presented a comprehensive study on hydraulic fracturing; they found that not only the induced fracture propagates perpendicular to the minimum horizontal stress [10], but also the work had done to keep a fracture open is appropriate to the stress, which is perpendicular to the fracture plane and try to close the fracture. In this study, poroelastic correlations have been done instead of the mentioned tests, in order to calculate the magnitude of horizontal stresses (Zoback, Barton, & Wiprut, 2003): rh ¼

m m E Em rv  aPp þ Pp þ ex þ ey 2 1m 1m 1m 1  m2

ð5Þ

rH ¼

m m Em E rv  aPp þ Pp þ ex þ ey 1m 1m 1  m2 1  m2

ð6Þ

where σh is minimum horizontal stress in Mpa, σH is maximum horizontal stress in Mpa, ν is Poisson’s ratio and dimensionless, σv is vertical stress in Mpa and α is Bayot factor. ɛx and ɛy are the strains in the direction of minimum and maximum horizontal stresses and equal 1.5 and 1, respectively. Based on two above calculation, the magnitude of two horizontal stresses is computed 62.45 Mpa for maximum horizontal stress and 52.47 Mpa for minimum horizontal stress, respectively. (III) Pore pressure gradient is considered as 10.85 Kpa/m. Furthermore, the temperature is around 104–118 °F in reservoir depths. After conclusion of the minimum and maximum horizontal stresses, normal stress regime (σν > σH > σh) was diagnosed as the main stress regime for the Bangestan reservoir rock. Figure 1(B)) shows minimum and maximum horizontal stresses. 2.3.

Safe mud window design

Now, in this step, it is possible to design and sketch the mud window by using the pore pressure and minimum horizontal stress data. The window helps us to select suitable mud weight. Safe mud window shows that if the mud pressure is lower than pore pressure then the well will kick and fluid flow into the hole. Also if the mud pressure is higher than minimum horizontal stress, then induced tensile failures will occur during drilling operation and minor mud loss will happen.

M. Abdideh and A. Ahmadifar

Downloaded by [M. Abdideh] at 23:51 28 April 2014

972

Figure 1(A).

Dynamic and static Young’s modulus.

The best domain for the safe mud window is between pore pressure and the minimum horizontal stress. From the geomechanical point of view, safe mud window allows the well to avoid tensile failures or pipe sticking that is caused by mud weight. Furthermore, it prevents the shear failures to occur because of low mud weight (Al-Ajmi & Zimmerman, 2006). Figure 2(A)) shows safe mud window which includes pressure in domain between 37 and 61.72 MPa (37 < Pw < 61.72). 2.4. Calculation of drilling-induced stresses and fracture pressure limit Underground structures are always under pressure because of vertical and tectonic stresses. When a borehole is drilled inside a structure, some parts of (rock) materials are

973

Downloaded by [M. Abdideh] at 23:51 28 April 2014

European Journal of Environmental and Civil Engineering

Figure 1(B).

Minimum and maximum horizontal stresses.

missed. Borehole’s side walls are maintained only by fluid pressure. Since this fluid pressure is not consistent with in situ structure stresses; new stress redistribution occurs around borehole that may lead to rock fracture .Therefore, identification of stresses existent around a borehole is of great importance to examine borehole problems. There two common types of borehole fracture: first one is drilling induced tension fracture and the second one, with 90° of difference, is called breakout. In a substance with linear elastic behaviour, centralisation of bigger stress occurs on borehole wall, so borehole fracture is expected to start from this area. First, it is crucial to calculate the tangential, radial and axial induced stresses which would be produced after drilling operation:

Downloaded by [M. Abdideh] at 23:51 28 April 2014

974

M. Abdideh and A. Ahmadifar

Figure 2(A).

Safe mud windows.

rhh Max ¼ 3rH  rh  Pw  Pp

ð7Þ

rhh Min ¼ 3rh  rH  Pw  Pp

ð8Þ

rzz Max ¼ rv þ 2mðrH  rh Þ  Pp

ð9Þ

rzz Min ¼ rv  2mðrH  rh Þ  Pp

ð10Þ

rrr ¼ Pw  Pp

ð11Þ

975

Downloaded by [M. Abdideh] at 23:51 28 April 2014

European Journal of Environmental and Civil Engineering

Figure 2B.

Drilling-induced stresses.

In above equation, the wellbore pressure can be easily calculated by using mud weight and depths. Depending on the status of the three components of stresses, 6 modes of shear failure and 3 modes of tensile failure may occur around the wellbore (Table 1) (Fjaer, Holt, Horsrud, Raaen, & Risnes, 2008). Because of the typical depth of oil reservoirs, the most common types of failure are of breakout and vertical tensile failure. Induced stresses in different directions are shown in Figure 2(B). Finally, shear failure model with the name “shear failure shallow knockout (SSKO)” is diagnosed as the main shear failure for the mentioned reservoir rock. So, if mud pressure is selected lower than 30.71 Mpa, shear failure will happen on the wellbore and, if mud pressure is selected higher than 78.28 Mpa, tensile failure will happen on the wellbore.

976 3.

M. Abdideh and A. Ahmadifar Determination of rock and fluid properties profiles

Generally, in order to determine the suitable layer for hydraulic fracturing operation, we need three necessary logs: (1) In situ stress variation vs. depth. The magnitude of the in situ stresses is calculated by poroelastic equations which are fed by sonic and density log data. (2) Porosity log which shows how porosity change along depth. (3) Water saturation log which is drew based on Archie’s formula. This formula is fed by porosity, resistivity data. For hydraulic fracturing operation, we should consider three crucial conditions:

Downloaded by [M. Abdideh] at 23:51 28 April 2014

(a) The candidate layer should have low in situ stress. (b) The candidate layer should have high porosity. (c) The candidate layer should have low water saturation. If the under studying layer has the three mentioned conditions at the same time, it will be a perfect candidate for our purpose. If any of the conditions were not true, we cannot select this layer as a suitable layer because of the near future problems that might be faced like water production problem. In the recent studies, all three of the above conditions had been used (Table 2), but we also included the effect of other geomechanical factors, for example, UCS (Perumalla et al., 2012) or the difference between the minimum and maximum horizontal in situ stresses. UCS, which is the capacity of rock to withstand axially directed pushing forces, was calculated by the following empirical equation: UCS ¼ 135:9Expð4:8  uÞ

ð12Þ

where UCS is in Mpa. Based on experimental studies, rocks with the high UCS in the range of 159–207 Mpa have high strength against failure (Perumalla et al., 2011). Where UCS is weaker it means that rock has low level of strength and fracture formation is easier and vice versa. In other words, high UCS not only restricts fracture initiation but also makes some problems on the way to identify the suitable layer for hydraulic fracturing operation. One other use for UCS is when there is no tensile strength. In this case, if UCS is estimated accurately, the tensile strength is equal to1/10 to 1/12 times UCS. Furthermore, the difference between minimum and maximum horizontal stresses is another critical factor that even a small diversity between these two stresses makes some problems in the controlling of stress orientation. In other words, we cannot make fracture in a desirable direction. In other words in homogeneous media, where horizontal stresses are very close to each other, control the direction of the fracture is difficult and this media are stable. This is very useful in wellbore stability issue. More the wellbore is homogeneous so more that is stable. It is generally accepted that stress variation between pay zone and adjacent layers is the most important controlling factor for creating fracture height containment (Rahim, Bartko, & Al-Qahtani, 2005). Both the target layer and adjacent layers have critical role in layer selection process because if adjacent layers are weak, it will causes fracture propagate into them which results in the water production problem. Water cut is defi-

Modes Wide breakout (WBO): Conventional breakout Low angle echelon (LAE): Requires high mud weights. Failed rock will not fall into the wellbore as σrr ≡ σ2 σzzHigh angle echelon (HAE): Forms on opposite side of well as a conventional breakout but the failed rock will not fall into the wellbore as σrr ≡ σ2 Shallow knockout (SKO): Results in failure all the way around the wellbore Narrow breakout (NBO): Requires unreasonably high mud weights Deep knockout (SDKO): Requires unreasonably high mud weights

Multiple modes of compressive failure

Cylindrical (CYL)

Vertical (VER)

Horizontal (HOR)

Modes

Notes: σ1, σ2 and σ3: maximum, mean and minimum stresses, σH and σh: maximum and minimum horizontal stresses, h: angle measured from the azimuth of σH, PP and Pm: pore and mud pressure, σhh, σrr and σzz: tangential, redial and vertical effective stresses.

σhh σrr σzz σhh σhh σzz

σzz σrr σrr

σ3 σzz σzz σhh

σ2 σrr σrr σrr

Δ = σzz T > 0 Pm > [σV + σh (2υ3) + σH (2υ3)] Δ = σhh T > 0 Pm 0 Pm>PP+T

Multiple modes of tensile failure

Multiple modes of wellbore failure.

σ1 σhh σhh σzz

σrr = σ3

σhh = σ3

σzz = σ3

Table 1.

Downloaded by [M. Abdideh] at 23:51 28 April 2014

European Journal of Environmental and Civil Engineering 977

978

M. Abdideh and A. Ahmadifar

Table 2. Layer characterisation for selection of suitable layers for hydraulic fracturing operation. Layer Layer Layer Layer Layer Layer

no. no. no. no. no.

6 9 12 14 18

Layer

Downloaded by [M. Abdideh] at 23:51 28 April 2014

Layer Layer Layer Layer Layer

no. no. no. no. no.

6 9 12 14 18

Depth (M)

Thickness (M)

In situ stress (M)

Horizontal stresses difference (M)

3260–3295 3330–3342.5 3380–3392.5 3430–3457.5 3587.5–3600

35 12.5 12.5 27 12.5

57.6 60.4 62.3 61.5 65.4

0.5626 0.7177 0.8137 0.6562 0.7598

Porosity (%)

Water saturation (%)

UCS (Mpa)

27 13 11 17 15

20 43 21 25 45

52.87 73.68 90.82 65.44 75.93

Fracturing pressure > (Mpa) 73.7 76.6 78 78.5 83.4

nitely undesirable since two to three separator phases are needed for its treatment that causes more expenses with a non-profitable production. Basically, adjacent layers should be characterised by high in situ stress and low porosity so that they can act as barrier layers. 4.

Analysis of stress and rock properties profiles and selection of suitable interval

Firstly, in order to interpret the layers, zonation is needed; the interval, which starts in 3187 m and finishes in 3628 m, is divided into 19 separated zones or layer (Figure 3): Layer no. 1: The layer with high level of in situ stress around 57.5 Mpa and high water saturation beside low percent of porosity near 10% can be selected as obstacle layer. Layer no. 2: This layer has in situ stress equal to 54 Mpa because of high water saturation. However, the mentioned layer is not a smart choice for hydraulic fracturing operation since it has a potential for water production that causes problem. In addition, low stress level and high water saturation in lower layer leads the fracture towards itself and makes water production problem again. Layer no. 4: This layer has three factors for making safe fracture. But due to having a weak layer above it (layer No. 3), making fracture will cause water production problem in this layer. Layer no. 5: High level of in situ stress and low porosity makes this layer a good candidate as a barrier layer. Layer no. 6: This layer has low stress and water saturation besides having high porosity of around 23% shows that it is a smart choice for hydraulic fracturing. Adjacent layers have high stress level and low porosity, so they can prevent fracture propagation in undesirable directions. Layer no. 9: This layer has 15% porosity, 45% water saturation and low stress level in comparison with its neighbouring layers .So, this is a perfect layer for hydraulic fracturing. Adjacent layers have all the necessary conditions as barrier layers. Layers no. 10 and no. 11: These two layers are obstacle layers of the other layers for having low percentage of porosity and high water saturation and in situ stress.

Downloaded by [M. Abdideh] at 23:51 28 April 2014

European Journal of Environmental and Civil Engineering

Figure 3.

979

Profiles of stress, porosity, water saturation and UCS of the well.

Layer no. 12: It has narrow thickness but suitable porosity, low water saturation and acceptable stress level. Furthermore, the barrier layers in its neighbourhood prepare an ideal condition for hydraulic fracturing operation. Layer no. 13: This layer has all required condition as a barrier layer. Layer no. 14: It has 15% porosity, 62 Mpa in situ stress and 25% water saturation which make it to become another good candidate for hydraulic fracturing. Layer no. 16: This layer has all the conditions for hydraulic fracturing operation but due to the existence of weak layers above and below it, it cannot prevent fracture propagation in itself. So in the case of carrying out the operation, the water production problem would be predicted. Layer no. 18: This layer and the layer No. 16 are at the same hall, and they both are good for hydraulic fracturing. All three key factors are true for this layer, and there is no way for the fracture to propagate in the adjacent layers (layers no. 17, and no.19 are the obstacle layers). 5.

Conclusion (1) Normal stress regime (σν > σH > σh) has been diagnosed for the under studied reservoir rock.

980

M. Abdideh and A. Ahmadifar

(2) After prediction of safe mud window, it is recommended that mud pressure should be selected in the range between 37 and 61.72 Mpa. In this condition, pressure is high enough to avoid wellbore kick and also low enough to prevent tensile failures. (3) Based on failure models that had been selected, shear failure shallow knockout (SSKO), the upper and lower failure pressures have been predicted. If mud pressure is selected lower than 30.71 Mpa, shear failure will happen in the wellbore. Also, if mud pressure is selected higher than 78.28 Mpa, tensile failure will happen in the wellbore. (4) After putting the in situ stress, porosity, water saturation and UCS logs into consideration, they were divided to 19 separate zones or layers. Finally, five layers became candidates as suitable layers for hydraulic fracturing. Table 1 shows various properties of the candidate layers.

Downloaded by [M. Abdideh] at 23:51 28 April 2014

Nomenclature S1 S2 S3 σv σH σh ρ z ν Pp α ɛx ɛy Δtc Δts E EDynamic EStatic UCS Φ σhhMax σhhMin σzzMax σzzMin σrr

Maximum main stress (MPa) Intermediate main stress (Mpa) Minimum main stress(Mpa) Overburden stress (Mpa) Maximum horizontal stress (Mpa) Minimum horizontal stress (Mpa) Density (gr/cm3) Depth (Metre) Poisson’s ratio (Dimensionless) Pore pressure (Mpa) Bayot factor (dimensionless) Strain in the direction of the maximum horizontal stress Strain in the direction of the minimum horizontal stress Primary transient time (Sec/ft) Secondary transient time (Sec/ft) Young’s modulus (Gpa) Dynamic Young’s modulus (Gpa) Static Young’s modulus (Gpa) Uniaxial compressive strength (Mpa) Porosity (dimensionless) Maximum tangential induced stress (Mpa) Minimum tangential induced stress (Mpa) Maximum axial induced stress (Mpa) Minimum axial induced stress (Mpa) Radial induced stress (Mpa)

References Al-Ajmi, A. M., & Zimmerman, R. W. (2006). Stability analysis of vertical boreholes using the mogi-Coulomb failure criterio. International Journal of Rock Mechanics and Mining Sciences, 43, 1200–1211. Amadie, B., & Stephansoon, O. (1997). Rock stress and its measurement (1st ed.). London: Chapman & Hall. Anderson, E. M. (1951). The dynamic of faulting and dyke formation with applications to Britain. Edinburgh: Oliver and Boyd. Economides, M. J., & Nolte, K. G. (2002). Reservoir stimulation (3rd ed., pp. 1–6). Schlumberger: Wiley. Fjaer, E., Holt, R. M., Horsrud, P., Raaen, A. M., & Risnes, R. (2008). Petroleum related rock mechanics (2th ed.). Amsterdam: Elsevier.

Downloaded by [M. Abdideh] at 23:51 28 April 2014

European Journal of Environmental and Civil Engineering

981

Hibbeler, J., & Rae, P. (2005) Simplifying hydraulic fracturing-theory and practice. SPE 97311, SPE Annual Technical Conference and Exhibition, Dallas, Texas, USA, October 9–12, 2005. Hubbert, M. K., & Willis, D. G. (1957). Mechanics of hydraulic fracturing. Petroleum Transactions AIME, 2, 53–63. Legarth, B., Huenges, E., & Zimmermann, G. (2005). Hydraulic fracturing in a sedimentary geothermal reservoir: Results and implications. International Journal of Rock Mechanics Sciences, 42, 1028–1041. Pak, A., & Chan, D. H. (2008). Numerical modeling of hydraulic fracturing in oil sands”. ScientiaIranica, 15, 536–540. Perumalla, S., Moos, D., Bartoon, C., Finkbeiner, T., Al-Mahrooqi S., Weissenback M., … Al-syabi, H. (2011). Role of Geomechanics in appraisal of the a deep tight gas reservoir: A case history from Gas Conference and Exhibition, Muscat, Oman, January 31–February 2, 2011. Perumalla, S., Santagati, A., Addis, T., Al-Mahrooqi, S., Curtino, J., Briner A., … Qobi, L. (2012). Influence of rock properties and geomechanics on hydraulic fracturing: a case study from the Amin Deep Tight Gas Reservoir, Sultanate of Oman. SPE 153227, SPE Middle East unconventional Gas conference and Exhibition, Abu Dhabi, UAE, January 23–25, 2012. Queipo, N. V., Verde, A. J., Canelon, J., & Pintos, S. (2002). Efficient global optimisation for hydraulic fracturing treatment design. Journal of Petroleum Science and Engineering, 35, 151–166. Rahim, Z., Bartko, K., & Al-Qahtani, M. Y. Hydraulic fracturing case histories in carbonate and sandstone reservoir of khuff and prekhuff formations, Ghawar field, Saudi Arabia. SPE 77677, SPE Annual Technical Conference, San Antonio, Texas, USA, September 27, 2005. Willis, R. B., Fontaine, J., Paugh, L., & Griffin, L. (2005). Geology and geometry: A review of factors affecting the effectiveness of hydraulic fractures. SPE 97993, SPEEastern Regional Meeting, Morgantown, W.V., September 14–16, 2005. Wright, C. A., Weijers, L., Davis, E. J., & Mayerhofer, M. (1999). Understanding hydraulic fracture growth: Tricky but not hopless. SPE 56742, SPE Annual Technical Conference and Exhibition, Houston, Texas, USA, October 3–6, 1999. Zoback, M. D., Barton, C. D., & Wiprut, D. J. (2003). Determination of stress orientation and magnitude in deep wells”. International Journal of Rock Mechanics and Mining Sciences, 40, 1049–1076.