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Stimulation for minimizing the total skin factor in carbonate reservoirs
Journal of Natural Gas Science and Engineering 21 (2014) 326e331
Contents lists available at ScienceDirect
Journal of Natural Gas Science and Engineering journal homepage: www.elsevier.com/locate/jngse
Stimulation for minimizing the total skin factor in carbonate reservoirs Jianchun Guo, Yong Xiao*, Heng Wang State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu, 610500, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 23 June 2014 Received in revised form 19 August 2014 Accepted 21 August 2014 Available online
Carbonate reservoir is characterized by natural fractures and vugs. Reservoir damage can be easily caused by drilling and completion processes that bring high total skin factor and additional pressure drop. To improve the well productivity, it is necessary to decompose the total skin factor and implement mechanism oriented actions to minimize the skin factor. To eliminate the reservoir damage, this work first aims at optimizing drilling and well completion technologies. Then, a fracture network acidizing technique that can remove “non-radial & network-like” damage by making full use of natural fractures and minimizing the skin factor is proposed to maximize the well productivity. © 2014 Elsevier B.V. All rights reserved.
Keywords: Reservoir damage Skin factor Carbonate reservoir Acid stimulation
1. Introduction In recent years, with the continuous exploration and development of deep marine carbonate reservoirs, China has ensured great oil and gas resources, such as the Puguang gas field and Longwangmiao gas reservoirs in Sichuan province. Due to the wide distribution of natural fractures and vugs, carbonate reservoirs easily suffer from reservoir damage caused by drilling and completion. The high total skin factor and additional pressure drop depress fluid conductivity around the wellbore. The total skin factor of oil and gas wells is controlled by many factors, which typically includes petrophysical properties, fluid properties, degree of formation damage and stimulation, well geometry, well completion, number of fluid phases, and fluid flow velocity (Darcy or non-Darcy). There are plenty of models studying the total skin factor. Odeh (1980) considered skin factor as restricted entry caused by plugged perforations or insufficient number of perforations; Vrbik (1991) thought that pseudo-skin factor arises because only a portion of the pay zone allows the flow of oil into the wellbore, i.e. the so-called partial well completion. Samaniego (1996), Economides et al. (2000) and Yildiz
* Corresponding author. Tel./fax: þ86 28 83032024. E-mail addresses: [email protected], [email protected] (Y. Xiao). http://dx.doi.org/10.1016/j.jngse.2014.08.017 1875-5100/© 2014 Elsevier B.V. All rights reserved.
(2006) presented how to put the individual skin factors together and correctly predict the total skin factor. Previous researches on skin factor mainly studied the reservoir damage, perforation and completion theoretically. Studies integrating field application to discuss how to minimize total skin factor are very rare. Problems including decomposition of total skin factor from the perspective of production stimulation and proper methods to reduce them, as well as effective engineering solutions for high skin factor need to be solved. All of these will be discussed in the following sections. In this paper, based on the binomial deliverability equation, the authors prove that it is feasible to increase production by minimizing the skin factor from a few aspects. Specifically, on one hand, the total skin factor is decomposed into components associated with drilling and well completion techniques which can be further optimized to prevent damage from the root; on the other hand, in view of the preexisting natural fractures and vugs in carbonate reservoirs, fracturing and acidizing techniques are optimized to reduce the skin factor by connecting the hydraulic fractures with them to form high conductive networks. 2. Stimulation mechanisms in reducing skin factor For oil and gas wells drilled in carbonate reservoirs, the total skin factor before stimulation represents the overall degree of damage and seepage resistance in the near wellbore area. The
J. Guo et al. / Journal of Natural Gas Science and Engineering 21 (2014) 326e331
greater the skin factor, the more serious damage and the more seepage pressure drop are. According to the binomial deliverability equation, Li et al. (2003) and Guo et al. (2014) described the relationship between total skin factor and productivity as follows. 2 Pe2 Pwf ¼ AQ g þ BQ 2g
(1)
327
Table 1 Expressions of total skin factor and its components (Yildiz, 2006). Vrbik (1991) Daltaban and Wall (1998) McLeod (1983) Bell et al. (1995)
St ¼ Sd þ Spp þ Sp þ Sq þ Sf St ¼ Sd þ Spp þ Sq Spdc ¼ Sd þ Spp þ Sq St ¼ Sd þ Spp þ Sq S h S St ¼ Spp þ hh pdc q g þ 9 þ 11 h p
where,
8:48 104 mg ZTPsc r lg i þ 0:434S A¼ KhTsc rw B¼
2 1:966 108 bgg ZTPsc
2R h2 Tsc
b ¼ 1:873 108
1 1 rw ri
(2)
hrw mg Tsc R D gg Psc K
(3)
(4)
Based on the field data of an oilfield in Sichuan basin in China, the IPR (inflow performance relationship) curves with different skin factors are drawn in Fig. 1. Every drop of 5 in the skin factor adds more than 20% in the open-flow capacity. When the reservoir is damaged with total skin factor of 15, the production is 480 104 m3/d. If the total skin drops to 0 through optimized design of drilling and completion, then the production will increase by over 65%. Acid fracturing is able to further reduce the skin factor to 15, in that case, the production will increase by more than 80%. Therefore, by optimizing the drilling and completion design and implementing acid fracturing treatment, the skin factor can be significantly reduced and thus high productivity can be achieved. The total pressure drop in completed wells can be expressed as.
DP ¼
141:2Qg mg Bg ½lnðre =rw Þ þ S Kh
(5)
which gives the productivity index,
Jc ¼
Kh 141:2mg Bg ½lnðre =rw Þ þ S
(6)
p
Jones and Slusser (1974)
Spdc ¼ Sd þ ðK=Kd ÞðSp þ Scz þ Sx Þ Spd ¼ Sd þ ðK=Kd ÞSp
Penmatcha et al. (1995)
St ¼ ðh=hp ÞSpd þ Spp þ Sp þ Scz þ Sq
Golan and Whitson (1991) Samaniego and Ley (1996)
St ¼ ðh=hp ÞðSd þ Sp Þ þ Spp þ Scz St ¼ ðh=hp ÞðSd þ Sp Þ þ Spp þ Sq þ Sf St ¼ Sd þ Sp þ Sqpp
St ¼ ðh=hp ÞSpd þ Spp
Economides et al. (2000)
factor, it is essential to decompose the total skin factor into components associated with the root causes of the damage. 3. Decomposition of total skin factor Combination of the mechanical skin, completion pseudo-skin, and perforation pseudo-skin and geometrical pseudo-skin makes the total skin factor for a well. Many studies expressed the total skin factor as a linear summation of the individual skin factors.
S ¼ Sd þ SPT þ SPF þ Sq þ Sb þ Stu þ SA
(7)
where S is the total skin factor, Sd is mechanical skin factor due to drilling damage, SPT is completion pseudo-skin due to partial penetration, SPF is perforation pseudo-skin factor, Sq is geometrical pseudo-skin due to well inclination, Sb is mobility change pseudoskin factor, Stu is non-Darcy pseudo-skin factor due to high velocity flow and SA is the pseudo-skin factor related to drainage area shapes. Aside from Equation (7), many other publications present the total skin equations in different forms, as listed in Table 1. 3.1. Mechanical damage skin factor
Total skin factor can be estimated from production well testing data. For the wells with high total skin factor, to minimize the skin
Also known as drilling and completion damage skin factor, mechanical damage around the wellbore leads to additional pressure drop and reduces fluid production. Hawkins (1956) proposed that the damaged zone can be considered as a concentric cylinder
Fig. 1. Gas well IPR curves under different total skin factors.
Fig. 2. Concentric damage zone around an open hole well.
328
J. Guo et al. / Journal of Natural Gas Science and Engineering 21 (2014) 326e331
pointed out that partial penetration creates a two-dimensional flow field in the near wellbore area where permeability anisotropy, penetration ratio and wellbore size are dominant parameters of partial penetration pseudo-skin, as illustrated in Fig. 4. In the past several decades, a few simple semi-analytical and empirical models were developed to predict the partial penetration pseudoskin and its influence on the well productivity, such as those of Odeh (1980), Vrbik (1991) and Guo et al. (2014). Once the SPT (Partial penetration skin factor) value is available, the additional pressure due to partial penetration can be computed. SPT is defined as.
SPT ¼
DP ¼ Fig. 3. Skin factor and open flow capacity change over permeability damage ratio (Guo et al., 2014).
around the wellbore, as shown in Fig. 2. The mechanical skin of the damaged zone can be written as a function of permeability Kd and radius rw.
Sd ¼
Ko 1 ln Ld ln rw Kd
(8)
h 1 hp
!"
h ln rw
!
Kh Kv
1=2
141:2Qg mg Bg SPT Kh
# 2
(9)
(10)
Fig. 5 shows the variation of pseudo-skin factor and open flow capacity under different opening degree. Every 10% increment in reservoir opening degree brings about 35% decrease of the corresponding completion pseudo-skin. Besides, the open-flow capacity increases with increasing opening degree and gradually tends to smooth out. 3.3. Perforation pseudo-skin factor
In vertical wells with partial penetration, only parts of the wellbore allow the fluid flow from the formation. Yildiz (2006)
Compared with open-hole completion, cased hole completion needs perforation to connect the wellbore with reservoir and form oil and gas flow channels. The parameters controlling the SPF are perforation depth, density, diameter and phasing angle. A number of numerical, experimental, semi-analytical and empirical models have been established to predict the perforation pseudo-skin. Vrbik (1991) presented nomographs to estimate SPF, but the nomographs are not practical for multiple calculations or software development. McLeod (1983) proposed a simple equation combining the effects of perforation pseudo-skin, formation damage, and rock compaction around the perforation tunnel. Jones and Slusser (1974) also worked out a perforation skin model, but it is only applicable to perforation tunnels completely confined inside the damaged zone. Based on the previous researches, a new correlation is developed for the calculation of perforation pseudo-skin factor in Equation (11). One advantage of this model is that it does
Fig. 4. Well of partial penetration subject to formation damage (Yildiz, 2006).
Fig. 5. Pseudo-skin factor and open flow capacity change with opening degree (Guo et al., 2014).
Drilling fluid invasion into reservoir is a complicated process, the depth of which depends on the factors including differential pressure between drilling fluid and the original formation (DP), drilling fluid property, reservoir properties and soak time, etc. Fig. 3 shows that skin factor increases exponentially with increasing permeability damage ratio. If permeability damage ratio increases from 20% to 80%, the open-flow capacity loses over 60%. Therefore, optimization of drilling operations is one of the most effective ways to reduce the mechanical skin factor. 3.2. Partial penetration pseudo-skin
J. Guo et al. / Journal of Natural Gas Science and Engineering 21 (2014) 326e331
not require the relationship between the perforation depth and the damage depth.
SPF ¼ SP þ SG þ Sdp ¼ Sh þ Sv þ Swb þ SG þ Sdp
(11)
where Sp is perforation pseudo-skin factor, SG is pseudo-skin factor due to linear flow through perforation tunnels, Sdp is pseudo-skin factor due to rock compaction, Sh is pseudo-skin due to flow convergence in the horizontal plane, Sv is pseudo-skin due to flow convergence in the vertical plane, Swb is pseudo-skin due to cylindrical wellbore. First, the pseudo-skin due to flow convergence in the horizontal plane (Sh) is computed.
Sh ¼ ln
rw 0 rw 4
r N
a1 log P2
K
1þ KV
# þa2
Sv ¼ 10
"
rffiffiffiffiffi!# rp N Kv 1þ K 2 "
b1
rffiffiffiffiffiffi b1 1 KV NLP K ! p ffiffiffi ffi r N K P 2
1þ
V K
rP N 2
K
1þ KV
þb2 1
#
þb2
(13) where, a1, a2, b1 and b2 are coefficients given as a function of the phasing angle, as shown in Table 2. Afterwards, the pseudo-skin due to cylindrical wellbore (Swb) is calculated. w C2 rwrþL p
Swb ¼ C1 e
(14)
The perforation pseudo-skin factor is determined as.
SP ¼ SH þ SV þ Swb
(15)
The pseudo-skin factor due to linear flow through perforation tunnels (SG) is.
SG ¼
SPF
2khLP KG rp2 N
8 rffiffiffiffiffiffib1 " rffiffiffiffiffiffi!#b k < ln rw 1 KV rP N KV a þ 10 1þ ¼ 0 kd :rw NLP 2 K K 44 9 0 1 = 2khL kdp r kh @ C rw P Aln dp 1 þ C1 e 2 rw þLp þ ;KG rp2 N kdp LP N kd rd
(18)
If the well is partially penetrated with damaged reservoir, then the perforation pseudo-skin factor can be expressed as.
SPF
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
"
Now, by summing up Equations 15e17, perforation pseudo-skin factor is achieved. If the well is completely penetrated with damaged reservoir, the proposed perforation pseudo-skin factor can be expressed as.
(12)
0 ð4Þ is effective wellbore radius tabuwhere 4 is phasing angle, rw lated as a function of the phasing angle. 0 ð4Þ ¼ L =4; otherwise, r 0 ð4Þ ¼ 24ðr þ L Þ. When 4¼0, rw w P P w Then, the pseudo-skin due to flow convergence in the vertical plane (Sv) is evaluated.
329
8 rffiffiffiffiffiffib1 " rffiffiffiffiffiffi!#b kh < rw 1 KV rP N KV 1þ þ 10a ¼ ln 0 kd hP : rw ðfÞ NLP 2 K K 9 0 1 = 2khL kdp r kh @ C rw P Aln dp 1 þ C1 e 2 rw þLp þ ;KG rp2 N kdp LP N kd rd (19)
Fig. 6 shows the variations of perforation pseudo-skin factor inside and beyond the damaged zone around wellbore. Along with the increase of perforating depth, skin factor decreases exponentially and finally levels out as negative. Provided that the mud damaged zone is not penetrated, perforation parameters affecting the skin factor in the descending order of significance are: perforation length, density, diameter and phasing angle. On the other hand, if perforation penetrates through the mud damaged zone, the perforation parameters affecting the skin factor in the descending order of significance are: perforation density, length, phasing angle and diameter. 3.4. Other forms of skin factor In addition to the three main skin factors above, researchers (Samaniego and Ley, 1996; Economides et al., 2000) also put forward other forms of skin factor, such as geometrical pseudo-skin due to well inclination (Sq), pseudo-skin factor associated with mobility change (Sb), non-Darcy pseudo-skin factor due to high velocity flow (Stu) and skin factor related to drainage area shapes
(16)
The pseudo-skin factor due to rock compaction (Sdp) is obtained from.
Sdp ¼
! kdp rdp kh ln 1 kdp LP N kd rd
(17)
Table 2 a1, a2, b1 and b2 related to phasing angle. 4
a1
a2
b1
b2
C1
C2
0 (360 ) 180 120 90 60 45
2.091 2.025 2.018 1.905 1.898 1.788
0.0453 0.0943 0.0634 0.1038 0.1023 0.2398
5.1313 3.0373 1.6136 1.5674 1.3654 1.1915
1.8672 1.8115 1.7770 1.6953 1.6490 1.6392
1.6E-1 2.6 E-2 6.6 E-3 1.9 E-3 3.0 E-4 4.6 E-5
2.675 4.532 5.320 6.155 7.509 8.791
Fig. 6. Perforation pseudo-skin factors under different perforation lengths.
330
J. Guo et al. / Journal of Natural Gas Science and Engineering 21 (2014) 326e331
Table 3 Comparison between matrix acidizing, massive acid fracturing and network fracture acidizing (applied statistics in carbonate reservoir in Sichuan basin in China). Technical features
Matrix acidizing
Massive acid fracturing
Network fracture acidizing
Pumping rate, m3/min Acidizing scale, m3 Acid system Formation characteristics
1e2 <100 Hydrochloric acid, gelled acid Polluted formation with high permeability
2e5 100e250 Crosslinked acid, authigenic acid Less fractures and caves, good matrix permeability
5e7 250e450 Steering acid, drag-reducing acid Development with natural fracture and cave systems
(SA). But these skin factors are not dominant in oil and gas well production, thus they are not described here. 4. Fracture network acidizing technology Total skin factor forms after drilling and well completion, and then appropriate acid fracturing treatment needs to be selected to minimize the skin factor. Due to the existence of enormous natural fractures and vugs within carbonate reservoirs, satisfactory effectiveness cannot be achieved with ordinary acidizing treatment. The reason is, in carbonate reservoirs with naturally developed fractures, mud invades deep into reservoirs by the aid of differential pressure between drilling fluid and reservoir; thus it is difficult for acid to remove the deep contamination. Matrix of carbonate is relatively tight, while fractures and vugs are effective porous space for oil and gas migration. Therefore, how to fully connect the fractures and vugs system far from the well bore is an urgent problem to be solved in acid fracturing treatment. In consideration of the acidizing fluid filtration and wormhole formation in natural fractures, a fracture network acidizing technique combining volume fracturing is proposed to achieve the goal of removing “non-radial, network-like” damage. Specifically, bulk
of drag reduction acid is pumped at high rate to improve the net pressure inside the natural fractures and open them. Meanwhile, contaminants, primary and secondary fillings are dissolved and heterogeneous etchings occurred. As time goes on, wormholes with certain conductivity interconnect with each other as well as natural fractures and vugs, achieving far distance networks with high effective permeability. Successful implementation of this technique requires large volume of acid to ensure adequate acid reaction to link up the fractures and vugs system at a far distance. Besides, during the operation, preflush acid is preferentially injected at low rate to remove the damaged zone; afterwards, large amount of acid is pumped at high rate to increase the effective acidizing distance. Table 3 compares the details of matrix acidizing, massive acid fracturing and fracture network acidizing in Sichuan basin in China. Fig. 7a shows a damaged zone near the wellbore causing additional pressure drop and a lot of natural fractures and many independent high permeability vugs in the neighborhood region. Fig. 7b presents the damage plugs near the wellbore are effectively cleaned by matrix acidizing. Also the permeability of the near wellbore region is increased; Fig. 7c indicates that, with the deep acid fracturing technique, a high permeability fracture is created to further contact the far field area, promoting the inflow of oil and gas;
Fig. 7. Acidizing stimulation effects with different techniques (Guo et al., 2014).
J. Guo et al. / Journal of Natural Gas Science and Engineering 21 (2014) 326e331
Fig. 7d describes the principles of fracture acidizing technique that is characterized by the formation of a high permeability fracture network. In this case, acid corrodes reactive minerals to form wormholes which connect the natural fractures and vugs of the reservoir. Eventually, a fracture network interconnected by high conductivity acid wormholes is established in a certain area around the wellbore. 5. Conclusions This work first details the methods for prediction of the total skin factor for perforated and damaged wells. Then, the total skin factor is decomposed into a few components corresponding different damage mechanisms. Finally, practical drilling and well completion optimization method and acid stimulation plan are put forward based on field operations. 1. Analysis of binomial productivity equation proves that oil and gas well production can be improved by minimizing the total skin factor. 2. Total skin factor for carbonate wells mainly results from drilling fluid damage, imperfect perforation and open degree. Optimizing drilling and completion technology is one of the effective means to minimize the skin factor. 3. Carbonate reservoir is characteristic of natural fractures and vugs systems. A fracture network acidizing technology that aims at removing the “non-radial & network-like” damage plugs by making use of natural fractures is of great advantage. Nomenclature Pe Pwf Qg
mg
Z T Psc k h Tsc
formation pressure, MPa bottom hole pressure, MPa production rate, m3/d viscosity of gas, cp natural gas deviation factor temperature, K standard pressure, MPa permeability, md formation thickness, m standard temperature, K
ri rw S DP Bg re Jc Kd hp kH kV N Lp KG
331
radius at i, m wellbore radius, m skin factor total pressure drop, MPa compressibility coefficient of gas reservoir radius, m productivity index permeability of damaged zone, md the length of the completed interval, m permeability in lateral direction, md permeability in vertical direction, md number of shots per foot perforation length, m gravel pack permeability, md
References Bell, W.T., Sukup, R.A., et al., 1995. Perforating. Henry L. Doherty Memorial Fund of AIME, Society of Petroleum Engineers. Daltaban, T.S., Wall, C.G., 1998. Fundamental and Applied Pressure Analysis. World Scientific. Economides, M.J., Nolte, K.G., et al., 2000. Reservoir Stimulation. Wiley, Chichester. Golan, M., Whitson, C.H., 1991. Well Performance. Prentice Hall, Englewoods Cliffs. Guo, Jianchun, Lu, Cong, et al., 2014. Reservoir stimulation techniques of minimizing the skin factor of the Lonwangmiao Fm gas reservoir in the Sichuan Basin. Nat. Gas Ind. 34 (3), 97e102. Hawkins Jr., M.F., 1956. A note on the skin effect. J. Petrol. Technol. 8 (12), 65e66. Jones, L.G., Slusser, M.L., 1974. The estimation of productivity loss caused by perforations-including partial completion and formation damage. In: SPE Midwest Oil and Gas Industry Symposium, Society of Petroleum Engineers. Li, X., Huang, B., et al., 2003. The establishment and application of binomial deliverability equation for horizontal gas well. J. Can. Petrol. Technol. 42 (10), 8e10. McLeod Jr., H.O., 1983. The effect of perforating conditions on well performance. J. Petrol. Technol. 35 (01), 31e39. Odeh, A.S., 1980. An equation for calculating skin factor due to restricted entry. J. Petrol. Technol. 32 (06), 964e965. Penmatcha, R., Fayers, J., et al., 1995. Skin Factor Calculations for Vertical, Deviated, and Horizontal Wells (Task 2). Productivity and Injectivity of Horizontal Wells, Annual Project Report, DOE/BC/14862-10. Stanford University, CA. Samaniego, V.F., Ley, H.C., 1996. Well test analysis in carbonate reservoirs. Dev. Petrol. Sci. 44, 549e681. Vrbik, J., 1991. A simple approximation to the pseudoskin factor resulting from restricted entry. SPE Form. Eval. 6 (04), 444e446. Yildiz, T., 2006. Assessment of total skin factor in perforated wells. SPE Reserv. Eval. Eng. 9 (01), 61e76.
Contents lists available at ScienceDirect
Journal of Natural Gas Science and Engineering journal homepage: www.elsevier.com/locate/jngse
Stimulation for minimizing the total skin factor in carbonate reservoirs Jianchun Guo, Yong Xiao*, Heng Wang State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu, 610500, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 23 June 2014 Received in revised form 19 August 2014 Accepted 21 August 2014 Available online
Carbonate reservoir is characterized by natural fractures and vugs. Reservoir damage can be easily caused by drilling and completion processes that bring high total skin factor and additional pressure drop. To improve the well productivity, it is necessary to decompose the total skin factor and implement mechanism oriented actions to minimize the skin factor. To eliminate the reservoir damage, this work first aims at optimizing drilling and well completion technologies. Then, a fracture network acidizing technique that can remove “non-radial & network-like” damage by making full use of natural fractures and minimizing the skin factor is proposed to maximize the well productivity. © 2014 Elsevier B.V. All rights reserved.
Keywords: Reservoir damage Skin factor Carbonate reservoir Acid stimulation
1. Introduction In recent years, with the continuous exploration and development of deep marine carbonate reservoirs, China has ensured great oil and gas resources, such as the Puguang gas field and Longwangmiao gas reservoirs in Sichuan province. Due to the wide distribution of natural fractures and vugs, carbonate reservoirs easily suffer from reservoir damage caused by drilling and completion. The high total skin factor and additional pressure drop depress fluid conductivity around the wellbore. The total skin factor of oil and gas wells is controlled by many factors, which typically includes petrophysical properties, fluid properties, degree of formation damage and stimulation, well geometry, well completion, number of fluid phases, and fluid flow velocity (Darcy or non-Darcy). There are plenty of models studying the total skin factor. Odeh (1980) considered skin factor as restricted entry caused by plugged perforations or insufficient number of perforations; Vrbik (1991) thought that pseudo-skin factor arises because only a portion of the pay zone allows the flow of oil into the wellbore, i.e. the so-called partial well completion. Samaniego (1996), Economides et al. (2000) and Yildiz
* Corresponding author. Tel./fax: þ86 28 83032024. E-mail addresses: [email protected], [email protected] (Y. Xiao). http://dx.doi.org/10.1016/j.jngse.2014.08.017 1875-5100/© 2014 Elsevier B.V. All rights reserved.
(2006) presented how to put the individual skin factors together and correctly predict the total skin factor. Previous researches on skin factor mainly studied the reservoir damage, perforation and completion theoretically. Studies integrating field application to discuss how to minimize total skin factor are very rare. Problems including decomposition of total skin factor from the perspective of production stimulation and proper methods to reduce them, as well as effective engineering solutions for high skin factor need to be solved. All of these will be discussed in the following sections. In this paper, based on the binomial deliverability equation, the authors prove that it is feasible to increase production by minimizing the skin factor from a few aspects. Specifically, on one hand, the total skin factor is decomposed into components associated with drilling and well completion techniques which can be further optimized to prevent damage from the root; on the other hand, in view of the preexisting natural fractures and vugs in carbonate reservoirs, fracturing and acidizing techniques are optimized to reduce the skin factor by connecting the hydraulic fractures with them to form high conductive networks. 2. Stimulation mechanisms in reducing skin factor For oil and gas wells drilled in carbonate reservoirs, the total skin factor before stimulation represents the overall degree of damage and seepage resistance in the near wellbore area. The
J. Guo et al. / Journal of Natural Gas Science and Engineering 21 (2014) 326e331
greater the skin factor, the more serious damage and the more seepage pressure drop are. According to the binomial deliverability equation, Li et al. (2003) and Guo et al. (2014) described the relationship between total skin factor and productivity as follows. 2 Pe2 Pwf ¼ AQ g þ BQ 2g
(1)
327
Table 1 Expressions of total skin factor and its components (Yildiz, 2006). Vrbik (1991) Daltaban and Wall (1998) McLeod (1983) Bell et al. (1995)
St ¼ Sd þ Spp þ Sp þ Sq þ Sf St ¼ Sd þ Spp þ Sq Spdc ¼ Sd þ Spp þ Sq St ¼ Sd þ Spp þ Sq S h S St ¼ Spp þ hh pdc q g þ 9 þ 11 h p
where,
8:48 104 mg ZTPsc r lg i þ 0:434S A¼ KhTsc rw B¼
2 1:966 108 bgg ZTPsc
2R h2 Tsc
b ¼ 1:873 108
1 1 rw ri
(2)
hrw mg Tsc R D gg Psc K
(3)
(4)
Based on the field data of an oilfield in Sichuan basin in China, the IPR (inflow performance relationship) curves with different skin factors are drawn in Fig. 1. Every drop of 5 in the skin factor adds more than 20% in the open-flow capacity. When the reservoir is damaged with total skin factor of 15, the production is 480 104 m3/d. If the total skin drops to 0 through optimized design of drilling and completion, then the production will increase by over 65%. Acid fracturing is able to further reduce the skin factor to 15, in that case, the production will increase by more than 80%. Therefore, by optimizing the drilling and completion design and implementing acid fracturing treatment, the skin factor can be significantly reduced and thus high productivity can be achieved. The total pressure drop in completed wells can be expressed as.
DP ¼
141:2Qg mg Bg ½lnðre =rw Þ þ S Kh
(5)
which gives the productivity index,
Jc ¼
Kh 141:2mg Bg ½lnðre =rw Þ þ S
(6)
p
Jones and Slusser (1974)
Spdc ¼ Sd þ ðK=Kd ÞðSp þ Scz þ Sx Þ Spd ¼ Sd þ ðK=Kd ÞSp
Penmatcha et al. (1995)
St ¼ ðh=hp ÞSpd þ Spp þ Sp þ Scz þ Sq
Golan and Whitson (1991) Samaniego and Ley (1996)
St ¼ ðh=hp ÞðSd þ Sp Þ þ Spp þ Scz St ¼ ðh=hp ÞðSd þ Sp Þ þ Spp þ Sq þ Sf St ¼ Sd þ Sp þ Sqpp
St ¼ ðh=hp ÞSpd þ Spp
Economides et al. (2000)
factor, it is essential to decompose the total skin factor into components associated with the root causes of the damage. 3. Decomposition of total skin factor Combination of the mechanical skin, completion pseudo-skin, and perforation pseudo-skin and geometrical pseudo-skin makes the total skin factor for a well. Many studies expressed the total skin factor as a linear summation of the individual skin factors.
S ¼ Sd þ SPT þ SPF þ Sq þ Sb þ Stu þ SA
(7)
where S is the total skin factor, Sd is mechanical skin factor due to drilling damage, SPT is completion pseudo-skin due to partial penetration, SPF is perforation pseudo-skin factor, Sq is geometrical pseudo-skin due to well inclination, Sb is mobility change pseudoskin factor, Stu is non-Darcy pseudo-skin factor due to high velocity flow and SA is the pseudo-skin factor related to drainage area shapes. Aside from Equation (7), many other publications present the total skin equations in different forms, as listed in Table 1. 3.1. Mechanical damage skin factor
Total skin factor can be estimated from production well testing data. For the wells with high total skin factor, to minimize the skin
Also known as drilling and completion damage skin factor, mechanical damage around the wellbore leads to additional pressure drop and reduces fluid production. Hawkins (1956) proposed that the damaged zone can be considered as a concentric cylinder
Fig. 1. Gas well IPR curves under different total skin factors.
Fig. 2. Concentric damage zone around an open hole well.
328
J. Guo et al. / Journal of Natural Gas Science and Engineering 21 (2014) 326e331
pointed out that partial penetration creates a two-dimensional flow field in the near wellbore area where permeability anisotropy, penetration ratio and wellbore size are dominant parameters of partial penetration pseudo-skin, as illustrated in Fig. 4. In the past several decades, a few simple semi-analytical and empirical models were developed to predict the partial penetration pseudoskin and its influence on the well productivity, such as those of Odeh (1980), Vrbik (1991) and Guo et al. (2014). Once the SPT (Partial penetration skin factor) value is available, the additional pressure due to partial penetration can be computed. SPT is defined as.
SPT ¼
DP ¼ Fig. 3. Skin factor and open flow capacity change over permeability damage ratio (Guo et al., 2014).
around the wellbore, as shown in Fig. 2. The mechanical skin of the damaged zone can be written as a function of permeability Kd and radius rw.
Sd ¼
Ko 1 ln Ld ln rw Kd
(8)
h 1 hp
!"
h ln rw
!
Kh Kv
1=2
141:2Qg mg Bg SPT Kh
# 2
(9)
(10)
Fig. 5 shows the variation of pseudo-skin factor and open flow capacity under different opening degree. Every 10% increment in reservoir opening degree brings about 35% decrease of the corresponding completion pseudo-skin. Besides, the open-flow capacity increases with increasing opening degree and gradually tends to smooth out. 3.3. Perforation pseudo-skin factor
In vertical wells with partial penetration, only parts of the wellbore allow the fluid flow from the formation. Yildiz (2006)
Compared with open-hole completion, cased hole completion needs perforation to connect the wellbore with reservoir and form oil and gas flow channels. The parameters controlling the SPF are perforation depth, density, diameter and phasing angle. A number of numerical, experimental, semi-analytical and empirical models have been established to predict the perforation pseudo-skin. Vrbik (1991) presented nomographs to estimate SPF, but the nomographs are not practical for multiple calculations or software development. McLeod (1983) proposed a simple equation combining the effects of perforation pseudo-skin, formation damage, and rock compaction around the perforation tunnel. Jones and Slusser (1974) also worked out a perforation skin model, but it is only applicable to perforation tunnels completely confined inside the damaged zone. Based on the previous researches, a new correlation is developed for the calculation of perforation pseudo-skin factor in Equation (11). One advantage of this model is that it does
Fig. 4. Well of partial penetration subject to formation damage (Yildiz, 2006).
Fig. 5. Pseudo-skin factor and open flow capacity change with opening degree (Guo et al., 2014).
Drilling fluid invasion into reservoir is a complicated process, the depth of which depends on the factors including differential pressure between drilling fluid and the original formation (DP), drilling fluid property, reservoir properties and soak time, etc. Fig. 3 shows that skin factor increases exponentially with increasing permeability damage ratio. If permeability damage ratio increases from 20% to 80%, the open-flow capacity loses over 60%. Therefore, optimization of drilling operations is one of the most effective ways to reduce the mechanical skin factor. 3.2. Partial penetration pseudo-skin
J. Guo et al. / Journal of Natural Gas Science and Engineering 21 (2014) 326e331
not require the relationship between the perforation depth and the damage depth.
SPF ¼ SP þ SG þ Sdp ¼ Sh þ Sv þ Swb þ SG þ Sdp
(11)
where Sp is perforation pseudo-skin factor, SG is pseudo-skin factor due to linear flow through perforation tunnels, Sdp is pseudo-skin factor due to rock compaction, Sh is pseudo-skin due to flow convergence in the horizontal plane, Sv is pseudo-skin due to flow convergence in the vertical plane, Swb is pseudo-skin due to cylindrical wellbore. First, the pseudo-skin due to flow convergence in the horizontal plane (Sh) is computed.
Sh ¼ ln
rw 0 rw 4
r N
a1 log P2
K
1þ KV
# þa2
Sv ¼ 10
"
rffiffiffiffiffi!# rp N Kv 1þ K 2 "
b1
rffiffiffiffiffiffi b1 1 KV NLP K ! p ffiffiffi ffi r N K P 2
1þ
V K
rP N 2
K
1þ KV
þb2 1
#
þb2
(13) where, a1, a2, b1 and b2 are coefficients given as a function of the phasing angle, as shown in Table 2. Afterwards, the pseudo-skin due to cylindrical wellbore (Swb) is calculated. w C2 rwrþL p
Swb ¼ C1 e
(14)
The perforation pseudo-skin factor is determined as.
SP ¼ SH þ SV þ Swb
(15)
The pseudo-skin factor due to linear flow through perforation tunnels (SG) is.
SG ¼
SPF
2khLP KG rp2 N
8 rffiffiffiffiffiffib1 " rffiffiffiffiffiffi!#b k < ln rw 1 KV rP N KV a þ 10 1þ ¼ 0 kd :rw NLP 2 K K 44 9 0 1 = 2khL kdp r kh @ C rw P Aln dp 1 þ C1 e 2 rw þLp þ ;KG rp2 N kdp LP N kd rd
(18)
If the well is partially penetrated with damaged reservoir, then the perforation pseudo-skin factor can be expressed as.
SPF
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
"
Now, by summing up Equations 15e17, perforation pseudo-skin factor is achieved. If the well is completely penetrated with damaged reservoir, the proposed perforation pseudo-skin factor can be expressed as.
(12)
0 ð4Þ is effective wellbore radius tabuwhere 4 is phasing angle, rw lated as a function of the phasing angle. 0 ð4Þ ¼ L =4; otherwise, r 0 ð4Þ ¼ 24ðr þ L Þ. When 4¼0, rw w P P w Then, the pseudo-skin due to flow convergence in the vertical plane (Sv) is evaluated.
329
8 rffiffiffiffiffiffib1 " rffiffiffiffiffiffi!#b kh < rw 1 KV rP N KV 1þ þ 10a ¼ ln 0 kd hP : rw ðfÞ NLP 2 K K 9 0 1 = 2khL kdp r kh @ C rw P Aln dp 1 þ C1 e 2 rw þLp þ ;KG rp2 N kdp LP N kd rd (19)
Fig. 6 shows the variations of perforation pseudo-skin factor inside and beyond the damaged zone around wellbore. Along with the increase of perforating depth, skin factor decreases exponentially and finally levels out as negative. Provided that the mud damaged zone is not penetrated, perforation parameters affecting the skin factor in the descending order of significance are: perforation length, density, diameter and phasing angle. On the other hand, if perforation penetrates through the mud damaged zone, the perforation parameters affecting the skin factor in the descending order of significance are: perforation density, length, phasing angle and diameter. 3.4. Other forms of skin factor In addition to the three main skin factors above, researchers (Samaniego and Ley, 1996; Economides et al., 2000) also put forward other forms of skin factor, such as geometrical pseudo-skin due to well inclination (Sq), pseudo-skin factor associated with mobility change (Sb), non-Darcy pseudo-skin factor due to high velocity flow (Stu) and skin factor related to drainage area shapes
(16)
The pseudo-skin factor due to rock compaction (Sdp) is obtained from.
Sdp ¼
! kdp rdp kh ln 1 kdp LP N kd rd
(17)
Table 2 a1, a2, b1 and b2 related to phasing angle. 4
a1
a2
b1
b2
C1
C2
0 (360 ) 180 120 90 60 45
2.091 2.025 2.018 1.905 1.898 1.788
0.0453 0.0943 0.0634 0.1038 0.1023 0.2398
5.1313 3.0373 1.6136 1.5674 1.3654 1.1915
1.8672 1.8115 1.7770 1.6953 1.6490 1.6392
1.6E-1 2.6 E-2 6.6 E-3 1.9 E-3 3.0 E-4 4.6 E-5
2.675 4.532 5.320 6.155 7.509 8.791
Fig. 6. Perforation pseudo-skin factors under different perforation lengths.
330
J. Guo et al. / Journal of Natural Gas Science and Engineering 21 (2014) 326e331
Table 3 Comparison between matrix acidizing, massive acid fracturing and network fracture acidizing (applied statistics in carbonate reservoir in Sichuan basin in China). Technical features
Matrix acidizing
Massive acid fracturing
Network fracture acidizing
Pumping rate, m3/min Acidizing scale, m3 Acid system Formation characteristics
1e2 <100 Hydrochloric acid, gelled acid Polluted formation with high permeability
2e5 100e250 Crosslinked acid, authigenic acid Less fractures and caves, good matrix permeability
5e7 250e450 Steering acid, drag-reducing acid Development with natural fracture and cave systems
(SA). But these skin factors are not dominant in oil and gas well production, thus they are not described here. 4. Fracture network acidizing technology Total skin factor forms after drilling and well completion, and then appropriate acid fracturing treatment needs to be selected to minimize the skin factor. Due to the existence of enormous natural fractures and vugs within carbonate reservoirs, satisfactory effectiveness cannot be achieved with ordinary acidizing treatment. The reason is, in carbonate reservoirs with naturally developed fractures, mud invades deep into reservoirs by the aid of differential pressure between drilling fluid and reservoir; thus it is difficult for acid to remove the deep contamination. Matrix of carbonate is relatively tight, while fractures and vugs are effective porous space for oil and gas migration. Therefore, how to fully connect the fractures and vugs system far from the well bore is an urgent problem to be solved in acid fracturing treatment. In consideration of the acidizing fluid filtration and wormhole formation in natural fractures, a fracture network acidizing technique combining volume fracturing is proposed to achieve the goal of removing “non-radial, network-like” damage. Specifically, bulk
of drag reduction acid is pumped at high rate to improve the net pressure inside the natural fractures and open them. Meanwhile, contaminants, primary and secondary fillings are dissolved and heterogeneous etchings occurred. As time goes on, wormholes with certain conductivity interconnect with each other as well as natural fractures and vugs, achieving far distance networks with high effective permeability. Successful implementation of this technique requires large volume of acid to ensure adequate acid reaction to link up the fractures and vugs system at a far distance. Besides, during the operation, preflush acid is preferentially injected at low rate to remove the damaged zone; afterwards, large amount of acid is pumped at high rate to increase the effective acidizing distance. Table 3 compares the details of matrix acidizing, massive acid fracturing and fracture network acidizing in Sichuan basin in China. Fig. 7a shows a damaged zone near the wellbore causing additional pressure drop and a lot of natural fractures and many independent high permeability vugs in the neighborhood region. Fig. 7b presents the damage plugs near the wellbore are effectively cleaned by matrix acidizing. Also the permeability of the near wellbore region is increased; Fig. 7c indicates that, with the deep acid fracturing technique, a high permeability fracture is created to further contact the far field area, promoting the inflow of oil and gas;
Fig. 7. Acidizing stimulation effects with different techniques (Guo et al., 2014).
J. Guo et al. / Journal of Natural Gas Science and Engineering 21 (2014) 326e331
Fig. 7d describes the principles of fracture acidizing technique that is characterized by the formation of a high permeability fracture network. In this case, acid corrodes reactive minerals to form wormholes which connect the natural fractures and vugs of the reservoir. Eventually, a fracture network interconnected by high conductivity acid wormholes is established in a certain area around the wellbore. 5. Conclusions This work first details the methods for prediction of the total skin factor for perforated and damaged wells. Then, the total skin factor is decomposed into a few components corresponding different damage mechanisms. Finally, practical drilling and well completion optimization method and acid stimulation plan are put forward based on field operations. 1. Analysis of binomial productivity equation proves that oil and gas well production can be improved by minimizing the total skin factor. 2. Total skin factor for carbonate wells mainly results from drilling fluid damage, imperfect perforation and open degree. Optimizing drilling and completion technology is one of the effective means to minimize the skin factor. 3. Carbonate reservoir is characteristic of natural fractures and vugs systems. A fracture network acidizing technology that aims at removing the “non-radial & network-like” damage plugs by making use of natural fractures is of great advantage. Nomenclature Pe Pwf Qg
mg
Z T Psc k h Tsc
formation pressure, MPa bottom hole pressure, MPa production rate, m3/d viscosity of gas, cp natural gas deviation factor temperature, K standard pressure, MPa permeability, md formation thickness, m standard temperature, K
ri rw S DP Bg re Jc Kd hp kH kV N Lp KG
331
radius at i, m wellbore radius, m skin factor total pressure drop, MPa compressibility coefficient of gas reservoir radius, m productivity index permeability of damaged zone, md the length of the completed interval, m permeability in lateral direction, md permeability in vertical direction, md number of shots per foot perforation length, m gravel pack permeability, md
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