Thermal approach

Journal of Petroleum Science and Engineering 112 (2013) 105–116

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A case study for HCL-based fracturing and stress determination: A Deformation/Diffusion/Thermal approach A.H. Haghi a,n, R. Kharrat b, M.R. Asef c a

Dept. of Petroleum Eng., Bahonar University of Kerman, Iran Petroleum University of Technology, Tehran, Iran c Kharazmi University, Tehran, Iran b

art ic l e i nf o

a b s t r a c t

Article history: Received 24 July 2012 Accepted 18 October 2013 Available online 4 November 2013

In this research, attempts were made to estimate the in-situ stresses acting on a hydrocarbon reservoir based on routine activities of acid fracturing in carbonate reservoir. A triple DDT (Deformation/Diffusion/ Thermal) full solution was introduced to the estimate maximum horizontal stress magnitude by using rock mechanics and poroelastic equations for the circular underground cavities, fluid diffusivity equation through porous media and thermal stress. To eliminate errors in recognition of the breakdown pressure, it was replaced by re-opening pressure with some modifications. Accordingly, for the first time in this study bilinear flow equation was presented to simulate acid flow through the fracture. Furthermore, this approach was introduced as a good indicator of stress direction in open hole wells while the chemical reaction between HCL-based acids and carbonates caused enlargements of induced fracture and wellbore. Accordingly, this new stress indicator promoted some weaknesses from the old fracturing technologies, such as less fracture initiation pressure by producing heat at the borehole wall, easily defining fractures with caliper and image logs, introducing a triple full solution for direct estimation of SH and so on. This study was then applied successfully to an offshore well, and completed in Triassic carbonate reservoir in Persian Gulf, South Iran. Vertical stress at 2900 m depth was found to be 7800 psi from density log. Maximum and minimum horizontal stresses were calculated by employing the presented method and they were 8730 and 7180 psi respectively. Calculated field stress, noticed fracture and fault's strike direction and maximum horizontal stress orientation worked together and proved strike–slip faulting regime as the present-day stress field. The significance of this approach may be distinguished at both the local and global scale by enabling better correlation and development of in-situ stress data in oil-rich states around the world. & 2013 Elsevier B.V. All rights reserved.

Keywords: acid stimulation reservoir geomechanics present day in-situ stress re-opening pressure bi-linear flow

1. Introduction In-situ stresses acting on a hydrocarbon reservoir are essential characteristics to be known before any geomechanical evaluation is completed. The matter is so important that a global endeavor for sharing practice to determine such expensive data is formed, and world stress maps are being developed based on the information provided by individuals around the world. Knowledge of stresses at smaller basin and field scales is of critical importance for petroleum applications such as wellbore stability, and reservoir compaction (Tingay et al., 2005, 2009; Haghi et al., 2011). Although some methods have been introduced for direct measurement of these stresses, practical limitations such as finance, time, and accessibility at the time data is required,

n

Corresponding author. Tel.: þ 98 9133062800; fax: þ 98 6114223352. E-mail address: [email protected] (A.H. Haghi).

0920-4105/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.petrol.2013.10.013

industries are encouraged to seek for alternative options. In general, two different approaches may be followed for this purpose. First approach is based on laboratory experiments on core specimens such as differential strain core analysis (DSCA), differential wave velocity analysis (DWVA), and anelastic strain recovery (ASR). These methods can be used if the direction of core specimens are known (Warpinski and Teufel, 1986). Secondly, field approaches of stress indicators such as borehole breakouts and drilling-induced fractures, earthquake focal mechanisms, young geologic data, and hydraulic fracturing seem to be more reliable, but more expensive . Further information on the subject could be viewed in the related literature such as Amadei and Stephansson (1997), Zoback (2007), and Fjaer et al. (2008). With respect to the hydraulic fracturing and hydraulic test on pre-existing fractures, a full explanation has been presented as ISRM suggestions by Haimson and Cornet (2003). However, because these techniques are best suited for relatively shallow

A.H. Haghi et al. / Journal of Petroleum Science and Engineering 112 (2013) 105–116

Nomenclature S1 and S3 maximum and minimum principle in situ stress Sh, SH and Sv minimum and maximum horizontal and vertical insitu stress s1 and s3 maximum and minimum effective stress sh, sH and sv minimum and maximum horizontal and vertical effective stress PR Productivity Ratio PIs stimulated productivity index Ks stimulated region permeability (Darcy) K reservoir permeability (Darcy) re reservoir radius (ft) rw well radius (ft) rs stimulated region radius (ft) sθθ tangential stress (psi) ΔP pressure difference (psi) PW injection pressure in the wellbore (psi) P0 reservoir pore pressure (psi)

holes where both stress and temperatures are low (generally about 2 km, or less), these techniques have very limited application in the petroleum industry. Reynolds et al. (2006) determined the magnitude of the in situ stresses in the Cooper–Eromanga Basins by using an extensive petroleum exploration database of over 40 years of drilling. They used leak-off test data for estimation of the lower bond of minimum horizontal stress magnitude, and closure pressures from a large number of minifrac tests for the estimation of the minimum horizontal stress. Raaen et al. (2006) promoted the current extended LOT for the estimation of minimum horizontal stress by adding a monitored flowback phase. However still fracturing technologies show inefficiency in SH estimation in oil fields (Zoback, 2007). In this research, HCL-based acid fracturing method in carbonate reservoirs is presented as a great full field stress indicator. Considering geomechanical definitions of stress distribution around wellbore, poroelasticity, fluid diffusivity equations through porous media, and steady state thermal stress, a direct triple DDT approach is developed to estimate maximum horizontal stress in oil fields. During HCL-based acid fracturing, the chemical reaction between the penetrated acid into the formation and the carbonates, releases heat at the borehole wall that increases the temperature difference between the injected fluid and the borehole. As illustrated in Fig. 1, an increase in the temperature difference at the bottom hole will decrease the minimum tangential stress around the wellbore (Wiprut et al., 1997). It means a lower pressure is needed for fracture initiation. One of the main difficulties that caused hydraulic fracturing to be unsuccessful for deep and stiff carbonate reservoir is high pressure equipments for fracture initiation. As illustrated in the stress polygon in Fig. 1, when the mud is 25 1C cooler than the formation and is of 6 MPa excessive mud weight, tensile wall fractures occur at lower values of SH (Zoback, 2007). The construction of such stress polygons is discussed by Zoback et al., (1987) and Moos and Zoback, (1990). Briefly, in stress polygons the vertical and horizontal lines intersecting at Sh ¼ SH ¼Sv, separate the stress fields associated with normal, strike–slip and reverse faulting stress environments as defined by Anderson (1951). The vertical line in the lower left of the polygon indicates the lowest value of Sh possible in a normal faulting environment. In other words, for the value of Sh shown by this line, a Mohr circle would exactly touch a frictional failure envelope with a slope of 0.6. Similarly, the horizontal line defining the top of the polygon corresponds to the value of SH at which

ΔT

s T

thermal stresses (psi) formation temperature (1C) α Biot's coefficient υ Poisson's ratio q injection flow rate (bbl/min) μ acid viscosity (cp) h reservoir thickness (ft) Ct total compressibility (1/psi) Φ porosity S skin factor E Young's Modulus (GPa) sT rock tensile strength (MPa) Kfbf fracture conductivity (mD.ft) tcrit critical time (min) PS shut-in pressure (Psi) k parameter ratio of minimum horizontal stress sh to the maximum horizontal stress sH μ internal friction coefficient z depth below surface (m)

reverse faulting would occur. The diagonal line bounding the polygon on the upper left corresponds to the value of SH at which strike–slip faulting would occur for a given value of Sh (Zoback et al., 2003). Dissolving the lateral rocks inside the fracture enlarges the fracture thickness. This would simplify the reorganization of tensile fractures through caliper and image logs in comparison to drilling induced (DIF) and hydraulic fractures. At the next step, one of the most important reasons why hydraulic fracturing cannot be used to determine SH in oil and gas (or geothermal) wells is that it is essentially impossible to detect fracture initiation at the wall of wellbore during pressurization. In point of fact, depending on the stress state, the breakdown pressure may not be the fracture initiation pressure (Zoback, 2007). Through presented method in this research, breakdown pressure is substituted by re-opening pressure in order to eliminate inaccuracies in detecting breakdown pressure. Accordingly, bilinear flow theory is presented for flow equation during reopening cycle. 85 80 75 70

SHmax

106

65

RF

60 55

Sv

∆T=25 C ∆P=6 MPa

RF 50 45 40 40

45

50

55

60

65

70

75

80

85

Shmin Fig. 1. Stress polygon that defines possible magnitudes of SH and Sh at any given depth as defined by Anderson's faulting theory and Coulomb faulting theory for a given coefficient of friction and pore pressure (Zoback, 2007).

A.H. Haghi et al. / Journal of Petroleum Science and Engineering 112 (2013) 105–116

Knowledge of the present-day stress orientation is particularly important in Iran, which has an extensive and mature petroleum exploration and production industry. Yet, the 2008 World Stress Map database contains very little present-day stress information for Iran and no stress data from petroleum wells (Heidbach et al., 2009). Yaghoubi and Zeinali (2009) investigated a detailed profile of the stress orientation in two wells in the Cheshmeh Khush oilfield in SW of Iran. Later, Rajabi et al. (2010) examined resistivity image logs and determined the present-day stress orientation of the Abadan Plain in SW Iran. Recently, Haghi et al. (2013) conducted an analysis of the present day stress of the central Persian Gulf using full-bore FMI log, leak of test and density logs. By creating the first full stress tensor, they concluded a strike–slip stress regime in the studied area in south of Iran. These researches indicated that the stresses in south and south-west of Iran are linked to the resistance forces generated by the Arabia–Eurasia collision at the Zagros orogeny. In this paper, stress field is investigated based on the acid fracturing data for a carbonate reservoir in Persian Gulf, south Iran. For this purpose, first of all the re-opening pressure curve is simulated based on bilinear flow theory and the presented DDT solution. Then using simulated shut-in pressure through the curve, maximum and minimum horizontal stresses are calculated. The calculated minimum horizontal stress is compared with leak of pressure, and this comparison validates the accuracy of the introduced method. Finally, the predicted full field stress magnitude in this study is evaluated in order to discover faulting environment. The results are compared with fault and stress orientation data from the field, and both studies prove the existence of strike–slip faulting environment for the central part of the Persian Gulf.

107

Sh SH

SH Sh Fig. 2. Stages of starting hydraulic fracturing test and the position of main stresses to fracture plane.

index after and before stimulation for an oil well with radial steady state flow is given in Eq. (1). This definition could be found in classic literatures Dake (1978), as follows: PR ¼

PIs ðK s =KÞlnðr e =r w Þ ¼ PI lnðr s =r w Þ þ ðK s =KÞlnðr e =r s Þ

ð1Þ

in this equation PIs, Ks, K, re, rw, rs specify as stimulated productivity index, stimulated region permeability, reservoir permeability, reservoir radius, well radius and stimulated region radius, respectively. As a result of well stimulation, PR becomes greater than one, which implies better performance of the reservoir. In order to create a fracture, packers are used to isolate a limited length from the rest of the well. Then the fluid is injected in the section between the packers. Due to increasing of pressure, the rock will eventually break. The orientation of minimum principal stress is perpendicular to fracture plane as illustrated in Fig. 2. This process is repeated for second cycles at a lower pressure than the first breakdown pressure.

2. Acid stimulation technology Acids are used as the fracturing fluids, scale removal as well as matrix treatments. Acids are also used to clean up gravel packs once they are positioned, or as cleansing agents to preflush the formation prior to administering a near-wellbore chemical treatment. However, an understanding of chemical reactions of different acids with minerals is necessary, to be able to select the appropriate acid for a specific application. Acid systems in current use can be classified as mineral acids, dilute organic acids, powdered organic acids, hybrid (or mixed) acids and retarded acids. All acids with the exception of hydrochloric–hydrofluoric and formic–hydrofluoric acid mixtures are used to treat carbonate formations (Newell, 1985). In addition to HCL, other organic acids are also used in the treatment of carbonate formation, but HCL is one of the most popular acid in acidizing (Gua et al., 2007). 2HCl þ CaCO3 ðcalsiteÞ2CaCl2 þ H2 O þ CO2 4HCl þ CaMgðCO3 Þ2 ðdolomiteÞ2MgCl2 þ CaCl2 þ 2H2 O þ 2CO2 Acid fracturing is a well stimulation method in which conductive fractures are created in the formation around the wellbore, and reached far into the formation. Fractures are created by applying pressure to the wellbore exceeding the fracturing pressure of the formation. Pressure is applied from the surface by pumping acids at a high rate into the rock matrix. Accordingly, creating a fracture by acid fluid in an area around the well will effectively remove skin effect. As a result, hydrocarbon will bypass damage zone through the fractures rather than crossing through rock pores. Therefore, the permeability near the borehole increases, and consequently the well productivity index (PI) increases. Productivity Ratio (PR) that compares productivity

3. Acid fracturing as stress indicator Several methods have been introduced as standard stress indicators in World Stress Map Project (Heidbach et al., 2008). The correlation between SH orientations derived from breakouts herein and earthquake focal mechanism solutions in the WSM project are scientifically significant. Earthquake focal mechanism solutions make up 72% of the 2008 WSM database (Heidbach et al., 2010). Few direct methods are introduced to estimate stress magnitude and orientation with acceptable certainty in hydrocarbon reservoirs. Zoback (2007) indicated that hydraulic fracturing was not an efficient method to estimate maximum horizontal stress magnitude due to the difficulties in reorganization of fracture initiation pressure. However, the need of high-pressure equipment for fracture initiation in deep tight reservoirs also caused difficulties in the estimation of maximum horizontal stress. Herein, we introduce HCL-base acid fracturing technology as a more relevant technique for stress estimation in carbonate reservoirs. 3.1. Stress magnitude by DDT solutions To set up a complete Deformation/Diffusion/Thermal solution for stress magnitude determination, first at all, we apply the solution proposed by Kirsch (1898) regarding tangential stress sθθ distribution for vertical well in polar coordinate (Fig. 3). Further equations could be viewed as well in the related literature such as Fjaer et al. (2008) and also Hudson and Harrison (1997). ! ! 1 R2 1 3R2 sθθ ¼ ðSH þ Sh  2P 0 Þ 1 þ 2  ðSH  Sh Þ 1 þ 2 2 2 r r

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A.H. Haghi et al. / Journal of Petroleum Science and Engineering 112 (2013) 105–116

Sh

σr

σθ

τrθ r

θ

SH

a

SH

Induced Fractue plane

Fig. 4. Two different flow regimes during HCL fracturing, (a) radial flow before fracturing and step (b) bilinear flow after fracturing.

Sh

(acid) is given as follows (Dake, 1978; Ahmed and Mckinney, 2005): ! ! 162:6qμ K log ðtÞ þ log ΔP ¼ P w  P 0 ¼  3:23 2S ð5Þ Kh μC t ΦR2

Fig. 3. Stress distribution around a circle drilling.

 cos 2θ 

ΔPR2 r2

 sΔT

Sθθ ð1Þ ¼ sθθ þ P 0

ð2Þ

where θ is measured from the azimuth of SH and ΔP is the difference between the injection pressure in the wellbore, PW, and Δ the reservoir pore pressure, P0. s T represents thermal stresses arising from the difference between the injected fluid temperature and formation temperature (T). Provided the formation is permeable to the injected fluid, the pressure difference causes an outward redial flow. If the injected and formation fluid have similar properties, the theory of poroelasticity holds and the second field of stresses are obtained as (Amadei and Stephansson, 1997)  Z   αð1  2νÞ 1 r Sð2Þ ΔPðrÞrdr  ΔPðrÞ ð3Þ θθ ¼ 2 ð1  νÞ r R where α is Biot's coefficient and υ is the Poisson's ratio. Through fracturing at the borehole wall (r¼ R), acid injection pressure should overcome the tangential stress in the direction of maximum horizontal stress which has least stress concentration (θ ¼ 0 and 180). The distribution of tangential stresses around the borehole is then obtained by superposition of two stress fields, ð1Þ

ð2Þ

Sθθ ¼ Sθθ þ Sθθ

  αð1  2ϑÞ Sθθ ¼ ðð3Sh  SH  2P 0  ΔP  sΔT Þ þ P 0 Þ þ ΔP ð1  ϑÞ   αð1  2ϑÞ ¼ 3Sh  SH P 0  sΔT  ΔP 1  ð1  ϑÞ

ð4Þ

To set up a complete solution for the diffusion–deformation– thermal phenomena which exists in petroleum-saturated porous media, the fluid diffusivity and thermal effect should be added (Zoback, 2007). Before fracture initiation a radial flow is supposed to move from the well to the formation. After that, the flow regime changes to bilinear flow through the fracture and from the fracture to the reservoir (Fig. 4). At the first step of pressure build up period during acid injection test with a constant flow rate (q), the bottomhole pressure increases with time. Here, considering a time dependent transient flow from bottom hole to the formation, the diffusivity equation of acid stimulation before fracture initiation (first cycle) with specification of radial flow of slightly compressible fluid

where μ, K, h, Ct, Φ and S are defined as the acid viscosity (cp), formation permeability (Darcy), reservoir thickness (ft), total compressibility (1/psi), porosity and skin factor, respectively. Thermal stress could be calculated with the steady state assumption from the following equation where αt is the linear coefficient of thermal expansion and E is the static Young's modulus (Fjaer et al., 2008). During HCL-based fracturing the value of thermal stress is not negligible due to the heat production near the borehole wall. sΔT ¼

α t E ΔT 1ϑ

ð6Þ

Based on the given information on diffusivity and thermal equations, Eq. (4) could be rewritten as follows: ! α t E ΔT 162:6qμ Kt log  Sθθ ¼ sθθ þ P 0 ¼ 3Sh  SH  P 0  KH 1ϑ μC t ΦR2   αð1  2ϑÞ  3:23  2SÞÞ 1  ð1  ϑÞ

ð7Þ

As we know, fracture initiation takes place when the tangential effective stress becomes equal to the rock tensile strength and bottom hole pressure becomes equal to breakdown pressure (injecting acid for tcrit time with constant flow rate) which induces a vertical fracture perpendicular to Sh. sθθ ¼  st

α t E ΔT 162:6qμ Kt crit log SH  3Sh ¼  2P 0 þ st   KH 1ϑ μC t ΦR2   αð1  2ϑÞ  3:23  2SÞÞ 1  ð1  ϑÞ

!

ð8Þ

The above equation gives a triple DDT (Deformation/Diffusion/ Thermal) solution for a linear function of maximum and minimum horizontal stresses based on the acid fracturing data from the first opening pressure curve (breakdown pressure) in carbonates reservoirs. After the creation of initial fracture at the wellbore through the second injection cycle, the flow diffusivity equation changes to a bilinear flow equation as follows (Cinco-Ley and

A.H. Haghi et al. / Journal of Petroleum Science and Engineering 112 (2013) 105–116

where Freopening (DDT) is the time-dependent Deformation/Diffusion/Thermal function for stress estimation within re-opening cycle of HCL-based fracturing test. Using k parameter as the ratio of minimum horizontal stress sh to the maximum horizontal stress sH, we have   1 ℱreopening ðDDTÞ ¼ ℍℱreopening ðDDTÞ sH ¼ ð13Þ 3k  1

Samaniego, 1981; Ahmed and McKinney, 2005):

ΔP frac ¼ P w  P frac ¼

44:1qμ

hðK f bf Þ1=2 ðΦμct KÞ

p ffiffi 4 t 1=4

ð9Þ

where Kfbf is the fracture conductivity (mD ft) which could be easily defined from pressure transient curves. Comparing Eq. (9) with Eq. (5), reservoir pore pressure P0 is substituted by fracturing pressure Pfrac in order to simulate bilinear flow instead of radial flow in porous media. In the second cycle, bottom hole pressure increased with time and after tcrit it exceeded to the re-opening pressure. At this moment, the preexist fracture from the first cycle re-opened, the fracture conductivity increased and this caused a tangible pressure drop at the bottom hole (Deng et al., 2011). Accordingly, pressure drop curves versus time for the first and second cycles simulate precisely the natural phenomenon of acid stimulation technology in this study. For the second opening pressure curve, Eq. (8) is replaced with Eq. (9). In this state tensile strength is neglected due to existence of a fracture from the first cycle (sT ¼0). As in the re-opening cycle, the permeability of the existing fracture is much more than the original formation permeability and the second field of stress based on Eq. (3) is negligible (Sθθ(2) E 0). In other words, the fluid preferably moved across the fracture and would not follow the radial flow equation based on theory of poroelasticity. ! p ffiffiffiffiffiffiffiffi α t E ΔT 44:1qμ 4 t SH  3Sh ¼  2P 0   ð10Þ crit 1ϑ hðK f bf Þ1=2 ðΦμcKÞ1=4

 sh ¼

 k ℱreopening ðDDTÞ ¼ 3k  1

s1 ¼ f ðμÞ ¼ ½ðμ2 þ 1Þ1=2 þ μ2 s3

ð16Þ

Considering the state of stress in a strike–slip faulting environment in which s2 ¼sv, the difference between sH and sh is limited by the frictional strength of the pre-existing faults. In other words, sH increases with respect to sh. As soon as the faults start to slip, further stress increases of sH with respect to sh cannot occur (Townend and Zoback, 2000; Zoback et al., 2003). Now Eq. (16) and Anderson's faulting theory are used to estimate an upper bound for the ratio of the maximum and minimum effective stresses, s1/s3 rf(m), (or lower limit for the ratio of the minimum and maximum effective stresses, 1/f(m)rs3/s1) for all faulting environments (Anderson, 1951)     s s Normal faulting ðsh r sH r sv Þ 0:33 r K h ¼ h r k ¼ h sv sH ð17Þ

3.1.1. Stress equation analysis and interpretation Recovering DDT formulas with effective stress specification (s), Eq. (10) changes as follows: ! p ffiffiffiffiffiffiffiffi α t E ΔT 44:1qμ 4 3sh  sH ¼ t crit ¼ ℱreopening ðDDTÞ þ 1ϑ hðK f bf Þ1=2 ðΦμcKÞ1=4

Strike  slip faulting ðsh r sv r sH Þ

ð12Þ

H Function 2

3

5

0

0.6

0.7

1

2

3

4

0.3

SS

SS

0.4

k=Kh

k value

k value

0.5

0:33 r k ¼

h Function 4

0.3

0.4

ð15Þ

s1 ¼ 3:1 s3

Vertical stress Sv directly estimated based on density of overburden layers.

1

ð14Þ

Such that assuming internal friction coefficient μ ¼ 0.6, the ratio of maximum and minimum effective stresses became

ð11Þ

0

ℱreopening ðDDTÞ

coefficients are functions of k ¼sh/sH parameter. where ℍ and As we know in the Mohr–Coulomb diagram for any given values of minimum effective stress s3, there is a maximum value of maximum effective stress s1 established by the frictional strength of the pre-existing faults. Jaeger and Cook (1979) showed that the values of s1 and s3 that correspond to the situation where a critically oriented fault is at the frictional limit are given by

these equations could be solved successively for maximum horizontal stress by substituting minimum horizontal stress with shut-in pressure. Sh ¼ P S

109

0.6

0.7

0.8

0.8

0.9

0.9

1

1 Fig. 5. Variation of H and h functions with k value for different faulting environments.

5

sh sH

ð18Þ

110

A.H. Haghi et al. / Journal of Petroleum Science and Engineering 112 (2013) 105–116

 Reverse faulting ðsv r sh r sH Þ

0:33 r

   1 sv s ¼ r k¼ h K H sH sH ð19Þ

where KH ¼sH/sv, Kh ¼sh/sv and the value 0.33 is the frictional limit for μ ¼0.6 (1/f(l ¼0.6)E0.33). Fig. 5 illustrates variation of ℍ and functions with k value. As it is shown, diminishing k value to the lower limit defined by frictional fault theory (Eqs. (17)–(19)), ℍ and functions increase sharply which could be related to the rock failure. With respect to the upper bound for k value for various faulting environment, we have Normal faulting ðsh r sH r sv Þ

0:33 r K h r k r 1 r

Strike  slip faulting ðsh r sv r sH Þ Reverse faulting ðsv r sh r sH Þ

ð20Þ

1 r1 KH

1 r k r 1 r Kh KH

k=0.6

k=0.8

ð21Þ ð22Þ

k=0.9

k=1

1/KH increase

RF SS

1/KH=1

NF Kh=1

Kh increase

45°

0 0

h(k) function

k increase

Fig. 6. Semi stress polygon that shows the range of allowable values for ℍ and functions in the earth's crust for normal, strike–slip and reverse faulting environments at a particular depth for a given pore pressure.

where z (m) is the depth below surface and E (GPa) is the average deformation modulus of the upper part of the earth's crust measured in a horizontal direction. Using Eq. (23), ℍ and functions are related to Young's Modulus to find the lower bounds of ℍ and functions for strike–slip faulting environments for a certain depth z¼2900 m (Fig. 7). Finally, the relation between ℍ and functions and depth is evaluated by using several worldwide case studies. Table 1 gives several equations of horizontal stress magnitudes with depth reported in the literature for various regions of the world and the resulted k values. Fig. 8 provides the variation of ℍ and functions with depth based on empirical equations from Table 1 for different regions of the world. From these curves, the average values for ℍ and functions for depth between 2000 and 5000 m are determined equal to 1.5 and 0.85, respectively.

H Function

Young Modulus (GPa)

0

1

2

3

h Function 4

5

0

10

10

20

20

30

30

40 50 60 70

Young Modulus (GPa)

H(k) function

0:33 r k r K h r

0:33 r

k=0.33

1 KH

Several physical and empirical approaches in literatures which specified the relation between minimum horizontal and vertical stresses, could be used to find the upper bound of the k parameter and the corresponding lower bound for ℍ and functions for strike–slip and reverse faulting environments. As illustrated in Fig. 5, for instance, for a Kh value equal to 0.45, ℍ ¼2.6 and ¼1.2 points are the lower bounds for strike slip (SS) faulting or upper bound for normal faulting (NF) environment. For reverse faulting environment, Kh is greater than one. As discussed early, stress polygons define possible magnitudes of SH and Sh in the earth's crust for normal, strike–slip and reverse faulting environments at any given depth as defined by Anderson's faulting theory and Coulomb faulting theory for a given coefficient of friction and pore pressure (Zoback et al., 1987; Moos and Zoback, 1990). Fig. 6 illustrates semi stress polygon that shows the range of allowable values for ℍ and functions in the earth's crust for normal, strike–slip and reverse faulting environments using Eqs. (17)–(22) at a particular depth for a given pore pressure and assumed coefficient of friction (here taken to be 0.6). Sheory (1994) developed an elasto-static thermal stress model of the earth. This model considers curvature of the crust and variation of elastic constants, density and thermal expansion coefficients through the crust and mantle for the depth lower than 3000 m. He provided a simplified equation that can be used for estimating the horizontal to vertical stress ratio. This equation is   1 K h ¼ 0:25þ 7E 0:001 þ ð23Þ z

1

2

3

4

5

40 50 60 70

80

80

90

90

100

100

Fig. 7. Lower Bounds of H and h functions for strike–slip faulting versus young modulus based on the Sheorey theory.

A.H. Haghi et al. / Journal of Petroleum Science and Engineering 112 (2013) 105–116

111

Table 1 Variation of horizontal stress components with depth and the resulted k values. Ref

Relation

k equation

Field

Haimson (1977)

sH ¼4.6 þ 0.025z sh ¼1.4 þ0.018z

k¼ sh/sH

Michigan basin (0–5000)

Rummel (1986)

KH ¼ 0.98 þ250/z Kh ¼ 0.65 þ 150/z

k¼ Kh/KH

World data (5000-3000)

Herget (1987)

KH ¼ 1.46 þ 357/z Kh ¼ 1.10þ 167/z

k¼ Kh/KH

Canadian shield(0–2200)

Pine and Kwakwa (1989)

sH ¼15þ 0.028z sh ¼6 þ0.012z

k¼ sh/sH

Carnmenellis granite Cornwall, UK(0–2000)

Baumgaetner et al. (1990)

sH ¼30.4 þ 0.023z sh ¼16þ 0.011z

k¼ sh/sH

KTB hole(800–3000)

Te Kamp et al. (1995)

sH ¼15.83 þ 0.0302z sh ¼6.52 þ0.01572z

k¼ sh/sH

KTB hole (0–9000)

H function 0

1

2

3

h Function 4

5

0

0

0

1000

1000

2000

2000

1

2

3

3000 World data

Canadian Shield

5000 Carnmenellis granite Cornwall, UK

Depth (m)

Depth (m)

World data

4000

4000 Canadian Shield

5000 Carnmenellis granite Cornwall, UK

6000

KTB pillot Hole

KTB pillot Hole

7000

5

Mishigan Basin

Mishigan Basin

3000

6000

4

KTB hole

7000

8000

8000

9000

9000

KTB hole

Fig. 8. H and h functions versus depth based on worldwide empirical equation.

3.2. Stress orientation As it is indicated early, tensile fractures propagate vertically on the plane perpendicular to Sh. Accordingly, it would be easy to determine stress orientations if the direction of the induced fracture is known. However, HCL based acid fracturing differs from other fracturing technologies due to the chemical reaction between acids and the carbonate rocks, which put HCL-based acid fracturing on the better position. HCL preliminary dissolves rocks on the wellbore and this yields well enlargement and skin removal. As the fracture initiates, HCL flows across the fracture and starts to react with the carbonates inside the fracture (Fig. 9). This causes a thicker fracture which could be easily detected by Straddle-packers, image or caliper logs in open hole completion wells. 3.2.1. HCL-based acid fracture by image and caliper logs During HCL treatment in carbonate reservoirs, fracturing and wellbore enlargement take place simultaneously. Accordingly, HCL

Fig. 9. HCL chemical reaction with carbonate inside the fracture.

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A.H. Haghi et al. / Journal of Petroleum Science and Engineering 112 (2013) 105–116

Both pads record enlargement

Fig. 10. HCL fractures on Formation Micro Imager Log. As it illustrated in the model FMI both calipers record deviations from bit size and on the other hand the dark parallel lines are thick lines which specify the direction of SH.

fractures would be distinguished from other types of tensile fractures (DIF, HF) and shear failures (Borehole Breakouts). As a result of chemical reaction, the inner width of the fracture increases to the amount that caliper pads could detect the fracture. As it is illustrated in the schematic FMI log on Fig. 10, HCL fractures are thick dark lines (like borehole breakouts) which separate 1801 and specify the direction of maximum horizontal stress. However, these lines could be recognized from Borehole breakout by considering the wellbore enlargement induced by HCL-based acid fracturing (like washouts). However, in some cases where wide HCl-based fractures exposed on the wellbore, it could be confused with borehole breakouts on image logs (Plumb and Hickman 1985).

4. Case study: field “A”, central part of Persian Gulf The Persian Gulf and its coastal areas are the world's largest single source of crude oil and related industries dominating the region. In 2002, this strategic area produced about 25% of the world's oil, held nearly two-thirds of the world's crude oil reserves, and about 35% of the world natural gas reserves. As it is illustrated in Fig. 11, field “A” located in Persian Gulf in the south of Iran. The structural context is complex in the neighborhood of the Oman Mountains and the Zagros orogenies. It is characterized by two main features: (1) a N20–N40 basement based trend that corresponds to the field major dome axis in the prolongation of the Qatar peninsula and (2) a conjugated NW–SE and NE–SW strike–slip system rejuvenated by the Zagros movement; the NW–SE direction is the more frequent one. According to WSM project database released by Heidbach et al. (2010) (Fig. 11b), strike–slip and reverse faulting regime are the dominant tectonic regime in northern margin of the field region based on focal mechanism solution with quality C. However, no

published stress data has been recorded by WSM project for the region of Persian Gulf. Fault vicinity often has a great impact on the fracture density and orientation. The NW–SE main fracture set direction (Fig. 11c) is a common regional direction interpreted as a strike–slip component of the Zagros orogeny. But its orientation nearly perpendicular to the regional present day maximum horizontal stress (defined from Image log) is not a priori in favor of fracture aperture in this direction unless a strike–slip fault regime still prevails as present day in situ stress field. The Kangan/Dalan reservoir of the field is dated from the large scale transgressive regressive cycle of the middle upper Permian to lower Triassic. This formation is divided in four layers (K1–K4) where three main lithologies (limestone, dolomite and anhydrite) are alternating (Fig. 12). The initial reservoir pressure estimated 5290 psi at the datum depth about 2900 m. To verify the accuracy of the DDT solution presented in this study, Eqs. (13) and (14) are used in order to find field stress based on the acid stimulation data of the vertical well no. 13. The stress information could be used to determine the nature of mud loss and wellbore instability in the region. Well no. 13 is completed in layers K1–K4 produce gas and gas condensate. With production over time, skin effect and wellbore damage decrease the production rates of the wells. Accordingly, acid stimulation process was employed to increase the production rate. Table 2 gives details about the acid stimulation for this well. HCL-based acid was injected with constant flow rate equal to 10 bbl/min inside the well. Through acid stimulation, matrixacidizing process for skin removal was fulfilled successfully but fracturing process did not function precisely due to equipment disabilities. However, after great modification in facilities and acid dissolving power, the pressure curve versus injection fluid encountered a slightly deviation of tangent due to pressure increase to the level of 7690 psi at the depth of 2900 m. Zoback

A.H. Haghi et al. / Journal of Petroleum Science and Engineering 112 (2013) 105–116

113

0 330

20 % 15 %

300

30

60

10 % 270

90

120

240

Fault strike 210

330

300

150 180 0 20 % 15 %

Persian Gulf

30

60

10 % 90

270

120

240

210

150 180

Fig. 11. (a) Location of Field “A” in Persian Gulf, southern part of Iran and (b) maximum horizontal stress orientations in South–SW of Iran from the World Stress Map database (Heidbach et al., 2007) and for the studied area. Symbols and different colors indicate the method of measurement and the stress regime (NF¼ normal faulting stress regime me; SS ¼ strike-slip faulting stress regime; TF¼ thrust faulting stress regime; black¼undefined stress regime) and (c) NW–SE as the main strike direction of the fracture set.

(2007) indicated in oil and gas wells it was straightforward to show that it is essentially impossible to detect the pressure at which the fracture initiates at the wellbore wall. Also in our case, the first injection cycle do not provides any clear points for stress analysis. Hence, the process repeats for the second cycle by injecting acid with a constant rate of 10 bbl/min. After 22 min, surface pump's pressure decreases sharply from the pick value at 3164 psi. This pressure is noticed clearly as the surface re-opening pressure. Fig. 13 illustrates the simulated process of fracture re-opening curve with time using bilinear flow assumption of the presented complete DDT solution in Section 3.1. Based on the field data provided in Table 2, DDT formula shows an increase of ΔPfrac to the maximum value of ΔPreopening ¼2074 psi at tcrit ¼22 min. After

this moment because the augmentation of the fracture conductivity, shown in Fig. 14, ΔPfrac subsides sharply and then becomes constant at a level equal to ΔPshut-in ¼ 1897 psi (Fig. 13). Fig. 15 shows variations of F function (Eqs. (13) and (14)) with time for the well no. 13 based on the flow diffusivity and thermal parameters. Also, Fig. 15 proves the sensitivity of Freopening(DDT) function with thermal stress (ΔT) in the wellbore. For ΔT ¼30 1c in Fig. 15, Freopening(DDT) gets 2248.53 psi at the average depth equal to 2900 m. Assuming equal values for minimum principle horizontal stress, Sh, and simulated shut-in pressure, Ps, on the basis of Eq. (11), we have ½Sh ¼ sh þ P o  ¼ ½P s ¼ ΔP shutin þ P o  δ

ð24Þ

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Fig. 12. Reservoir model layering prepared by E300 simulation software.

Value

Parameter

Value

Ave. porosity Ave. permeability Well redious Compressibility

0.15 42 mD 0.51 in. 10  10–6 1/psi

Poisson ratio Youngs modulus Acid viscosity ΔT

0.2 38 GPa 2 cp 30 1C

2100 2000 1900 1800 1700 1600 1500 1400 1300 1200 1100 1000 900 800 700 600 500 400 300 200 100 0

Simulated ΔPfrac by DDT solution

7235 7230 7225 7220 7215 7210 7205 7200 7195 7190 7185 7180 130

4

3

2

y = 1E-05x -0.0076x + 2.1133x - 261.35x + 19308

140

150

160

170

180

190

200

Fracture Conductivity (mDarcy.ft) Fig. 14. Bottom hole pressure versus fracture conductivity in acid injection test. As it is shown increasing the fracture conductivity, bottom hole pressure decreases due to fluid deflation from the fracture.

ΔPshut-in point of Shut-in Pressure

2400

ΔPreopening

0

10

20

30

Simulated Freopening by DDT solution

2200

40

50

60

70

80

90

100

Time (min) Fig. 13. Simulated ΔPfrac curve versus time on the basis of bilinear flow theory.

F function (Psi)

ΔPfrac (Psi)

Parameter

Bottom Hole Pressure (Psi)

Fracture Conductivity

Table 2 Acid stimulation data for well no. 13.

2000

F(ΔT=50°C)

1800

F(ΔT=40°C)

1600

F(ΔT=30°C)

1400

F(ΔT=20°C)

1200

F(ΔT=10°C)

F=Freopening

1000 800 600 400 200 0

where δ is the difference between ΔPshut-in and the point of shutin pressure. Accordingly, sh approximates 1890 psi. Inserting calculated values of Freopening(DDT) and sh into Eq. (14), function and k value at the depth of 2900 m are estimated as 0.84 and 0.55, respectively. These data are projected in the semi-stress polygon in Fig. 16 to present the stress data for the field at the depth of 2900 m. According to Young's Modulus presented in Table 2 for

0

10

20

30

40

50

60

70

80

90

100

Time (min) Fig. 15. Ffunction with time.

the field, the magnitude of Kh based on the Sheorey equation is about 0.6. As 0.33okr Kh o1, strike–slip faulting environment is predicted for the region. Principle horizontal stress for field “A” at

A.H. Haghi et al. / Journal of Petroleum Science and Engineering 112 (2013) 105–116

GR/MD(m)

5

k=0.33

4.5

k=0.55

k=1

4

Minor Fault

3.5

H function

115

2844

3 2.5

SS

2

Stress for Field “A” in Persian Gulf

H=1.53

1/KH=1 1

2845

0.5

Kh=1

Displaced strata Along minor fault

0

0.5

h=0.8 4

0 1

1.5

2

2.5

3

3.5

4

4.5

5

h function

Fig. 16. H and h functions for field “A” and the predicted faulting environment for the region. 2846

Pressure (Psi)

Depth (m)

0 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 3000 3100

1000

2000

3000

4000

5000

6000

7000

8000

9000

Fig. 18. Noticed minor fault through FMI log at depth 2844–2846 for field “A” in Persian Gulf (Haghi et al., 2013).

hydrostatic Pressure

SH

0 20%

330

Sv SH

30

15%

Sh

60

300 10%

Formation Pressure From RFT LOT

90

270

120

240

SH

Fault strike 210

150 180

Fig. 19. Investigation of strike–slip faulting environment for field “A” by evaluating the relation between fault strike and maximum horizontal stress direction obtained from drilling induced fracture orientation.

K reservoir 1.74

2.03

2.32

2.61 2.9psi/m

Fig. 17. Principle stress and formation pressure with depth for field “A”.

depth of 2900 m are estimated as follows: SH ¼ sH þ P o ¼ ℍℱreopening ðDDTÞ þP 0 ¼ 8730 psi ¼ 60 MPa Sh ¼ sh þ Po ¼ fx15ℱreopening ðDDTÞ þ P o ¼ 7180 psi ¼ 49 MPa Offshore principle vertical stress on the basis of average overburden density ρ and water density ρW is calculated as follows: Sv ¼ ρgðz  hÞ þ ρW gh ¼ 7800 psi ¼ 53 MPa

ð25Þ

Subsurface pressure data versus depth for the field and producing reservoir Kangan/Dalan are illustrated in Fig. 17. Also, the results of RFT and LOT test for the well are inserted for comparison.

As it is illustrated in Fig. 18, a minor fault has been interpreted for the sub-vertical open fracture at 2844–2846 m because the layers are displaced by about 10 cm along its plane. The dip of the feature is 661 NNE. As the maximum horizontal stress oriented NEE (Fig. 19), the nearly vertical minor fault demonstrates the existence of a strike–slip faulting environment for the present day stress field. This knowledge and the previous study by Haghi et al. (2013) confirm the predicted faulting environment by DDT solution for the Persian Gulf. As no image log ran after acid stimulation in the well, it was not possible to investigate stress orientation based on induced fracture inclination in the wellbore. However, stress orientation is determined from other stress indicators for the field including drilling induced tensile fractures and borehole breakouts.

5. Discussion and conclusions An efficient methodology was presented to estimate the full field in-situ stresses on the basis of a complete Deformation/

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Diffusion/Thermal solution. This method improves some weaknesses of other fracturing methods: (1) less breakdown pressure by producing heat at the bottom hole, (2) easily define fractures with caliper and image logs for stress orientation, (3) simulating re-opening pressure with bilinear flow assumption instead of using inaccessible breakdown pressure in deep petroleum reservoirs, (4) taking into account thermal stress effects in order to consider undeniable effect of heat production due to chemical reactions at the bottom hole, and (5) introducing a triple full solution for direct estimation of SH. Herein, we considered well accepted Kirsch equations for stress distribution around the wellbore for the first and second cycles of acid fracturing as in both cycles pressure is applied to a circular borehole with similar criteria (Amadei and Stephansson, 1997; Zoback, 2007). However, in the second cycle a narrow fracture is exposed on the wellbore wall that tends to get close in the fracture closure pressure. With respect to the effect of tensile strength in the stress distribution equation, the existence of the fracture made it negligible. Furthermore, comparing the high permeability of the narrow pre-exist fracture with rock permeability, in the second cycle the radial flow equation did not satisfy the pressure build up equation on the borehole and it must be changed with bi-linear flow equation. Considering these two modifications in the equation of stress around the wellbore, made it appropriate for the second cycle of acid fracturing. For the case of Field “A” in Persian Gulf, HCL-based acid employed for well stimulation and stress estimation. Normally it would be difficult to create hydraulic fractures through tight deep carbonate reservoirs in Iran due to the high value of fracture initiation pressure. Using this method, breakdown pressure decreased to 7690 psi. Minimum and maximum horizontal stress approximates by DDT solution with assumption of bilinear flow in reopening cycle equal to 7180 and 8730 psi, respectively. Simulated minimum horizontal stress adjusted greatly with the leak of Pressure (LOP). Regarding the calculated principle stresses, strike– slip faulting environment is predicted for the field. According to the field observations related to the presence of strike–slip regimes, this result demonstrates the accuracy of the predicted faulting environment in this paper. Maximum horizontal stress oriented NEE which is deviated from the observed minor fault strike. References Ahmed, T., Mckinney, P.D., 2005. Advanced Reservoir Engineering. Gulf Proffessional Publishing, Elsevier, United State of America. (isbn:0-7506-7733-3). Amadei, B., Stephansson, O, 1997. Rock Stress and Its Measurement. Chapman & Hall, 2-6 Boundary Row, London. (SE18HN). Anderson, E.M., 1951. The Dynamics of Faulting, 2nd ed. Oliver and Boyd, White Plains, N.Y. Baumgartner, J., Rummel, F., Zoback, M.D., 1990. Hydraulic fracturing in situ stress measurements to 3 km depth in the KTB pilot hole VB. A summary of a preliminary data evaluation. In: Bram, K., Draxier, J.K., Kessels, W., Zoth, G., (Eds.), KTB Report 90–6a, NLfB-KTB, Hannover, pp. 353–399. Cinco-Ley, H., Samaniego, F.V., 1981. Transient pressure analysis for fractured wells. J. Pet. Technol. (JPT), 1749–1766. (paper SPE 7490). Dake, L.P., 1978. Fundamentals of Reservoir Engineering. Elsevier Ltd, London. (WCIX 8RR). Deng, J., Hill, A.D., Zhu, D., 2011. A theoretical study of acid-fracture conductivity under closer stress. J. SPE Prod. Oper., 9–17. Fjaer, E., Holt, R.M., Horsrud, P., Raaen, A.M., Risner, R., 2008. Petroleum Related Rock Mechanics, 2nd ed. Elsevier Science Publishers B.V, UK. (isbn 978-0-44450260-5). Gua, B., Lyons, W.C., Ghalambor, A., 2007. Petroleum Production Engineering: A Computer-Assisted Approach. Elsevier Science and Technology Publishing Ltd., UK. (isbn 075068270). Haghi, A.H., Kharrat, R., Asef, M.R., 2011. Simulation and analysis of production induced compaction using geomechanical formulation of fracturing technology for stress prediction. In: Proceedings of the SPE/IPTC. Bangkok, Thailand, 14832 pp. Haghi, A.H., Kharrat, R., Asef, M.R., Rezazadegan, H., 2013. Present-day stress of central Persian Gulf: implications for drilling and well performance. J. Tectonophys. 608c, pp. 1429–1441. (10.1016/j.tecto.2013.06.001). Heidbach, O., Tingay, M., Barth, A., Reinecker, J., Kurfeß, D., Müller, B., 2008. The World Stress Map database release 2008. http://dx.doi.org/10.1594/GFZ.WSM. Rel2008.

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