the state-of-the-art in natural gas production

lable at ScienceDirect

Journal of Natural Gas Science and Engineering 1 (2009) 14–24

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Journal of Natural Gas Science and Engineering

journal homepage: www.elsevier .com/locate/ jngse

The state-of-the-art in natural gas production

Xiuli Wang*

XGAS Ltd., 800 Gessner Rd, Suite 240, Houston, TX 77204, United States

a r t i c l e i n f o

Article history:Received 18 August 2008Accepted 6 March 2009Available online 30 May 2009

Keywords:Natural gas productionTurbulenceHydraulic fracturingVertical fractured gas wellsTransversely fractured horizontal gas wells

* Tel.: þ1 7136470916; fax: þ1 7136470940.E-mail address: [email protected]

1875-5100/$ – see front matter � 2009 Elsevier B.V.doi:10.1016/j.jngse.2009.03.001

a b s t r a c t

This paper summarizes the fundamentals of natural gas production, especially in moderate- to high-permeability reservoirs and shows the key issues in natural gas wells by performing studies in thepermeability range of 0.1–100 md. Emphasis is given on the impact of turbulence and the importance ofhydraulic fracturing on well deliverability for both vertical and horizontal gas wells. In addition, a designprocedure for hydraulic fractures in a gas well is provided. A sample of economic evaluation is alsopresented to emphasize that production enhancement requires both physical and economicoptimization.

� 2009 Elsevier B.V. All rights reserved.

1. Introduction

Natural gas is playing an increasing role in meeting world’senergy demands because of its abundance, versatility, and its cleanburning nature. As a result, lots of new gas exploration, fielddevelopment and production activities are under way. Newly foundreservoirs are primarily offshore and in developing nations and, incontrast to very low-permeability reservoirs in mature environ-ments such as the United States and continental Europe, they are ofmoderate- to high-permeability, i.e., 1–100 md.

As the well deliverability increases, turbulence becomes increas-ingly dominant in the production of gas wells. For reservoirs whosepermeability is more than 5 md, turbulence effects may account fora 20–60% reduction in the well production rate of an openhole well(when laminar flow is assumed). Turbulence in such cases practicallyoverwhelms all other factors, including damage (Wang and Econo-mides, 2004). In vertical gas wells, turbulence can be greatly reducedthrough hydraulic fracturing because the flow pattern through thehydraulic fracture towards the well is different than that in radial flow.

Early on, from the 1950s to the 1980s, hydraulic fracturingtechnology was applied to low-permeability reservoirs exploitedprimarily in North America (Economides et al., 2001). The perme-ability of these ‘‘typical’’ natural gas wells is 0.1 md or as low as0.001 md. Such wells can only be economically attractive bymassive hydraulic fracturing. It is estimated that over 90% of newgas wells, internationally, are hydraulically fractured.

In the past few years following the invention of the tip screenout(TSO) technique, hydraulic fracturing of high-permeability

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formations (also referred to as frac-pack) has become a common-practice in petroleum engineering and is absolutely essential inhigh-permeability gas wells. For a gas well, fracturing is not justdesigned to bypass damage near a wellbore and prevent formationsand production. Instead it is the great reduction in the turbulenceeffect through the modification of the flow pattern towards the wellthat makes fracturing an absolute must.

Although hydraulic fracturing is necessary for stimulation andreduction of turbulence in vertical wells in these moderate- tohigh-permeability reservoirs, this is not always true in transverselyfractured horizontal gas wells. On the contrary, turbulence effectsare enhanced in the latter because of the very small contact areabetween the well and the fracture. The limited communicationbetween the transverse fracture and the wellbore generates anadditional pressure drop and a choking effect. But more importantis that the increased turbulence affects greatly the performance oftransversely fractured horizontal gas wells whose permeability isabove 1 md and, perhaps, even much lower values of permeability.Their desirability is subjected to project economics (Wei, 2006).

In this paper, the turbulence effects in radial flow gas wells arediscussed first, then turbulence effects and the importance ofhydraulic fractures on the productivity of both vertical and hori-zontal gas wells are studied. In addition, a design procedure forhydraulic fractures in a gas well is provided. Economic evaluation isalso presented to emphasize that production enhancementrequires both physical and economic optimization.

2. Fundamentals of turbulent flow

Fluid flow in porous media is affected by the competing inertialand viscous effects, combined by the well-known Reynolds Number

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Fig. 1. A sketch of an openhole vertical well and its cross section.

Table 1

X. Wang / Journal of Natural Gas Science and Engineering 1 (2009) 14–24 15

whose value delineates laminar from turbulent flow (Wang, 2000).For small permeability values (i.e., 0.1 md), the production rate isgenerally small and flow is laminar near the crucial sandface (Yaoand Holditch, 1993). The well deliverability can be developed fromeither an extension of the oil production rate expressions or fromfundamental principles. Under a steady state, the production rate isproportional to the pressure squared difference between thereservoir pressure (pe) and the flowing bottomhole pressure (pwf)and is given by Eq. (1) (in oilfield units):

qðMscf=dÞ ¼kh�p2

e � p2wf

�1424 mZT

hln� re

rw

�þ si (1)

which can be rearranged as

p2e � p2

wf ¼1424 qmZT

kh

�ln�

re

rw

�þ s

(2)

where k is reservoir permeability, h is the reservoir net height, Z isthe gas deviation factor, T is the absolute temperature, re is thereservoir radial extent, rw is the effective wellbore radius, and s, theskin effect. The gas flow in reservoir under pseudo-steady state andtransient conditions can be found in Chapter 2 in the book ‘‘ModernFracturing-Enhancing Natural Gas Production’’ edited by Econo-mides and Martin (2007).

As the fluid converges towards the well and travels through thenear-wellbore region, the flow area is reduced substantially. Theflow velocity increases and exceeds the Reynolds Number forlaminar or Darcy flow. Inertial effects become important and resultin turbulent flow (also referred as non-Darcy flow).

Turbulent flow has been studied since the 1900s (Forchheimer,1914). Pioneer and prominent among a number of investigators inthe petroleum literature have been Katz and co-workers (Katz et al.,1959; Firoozabadi and Katz, 1979; Tek et al., 1962). They suggestedthat turbulence plays a considerable role in well performanceshowing that the production rate is affected by itself: the larger thepotential rate, the larger the relative detrimental impact would be.Since most turbulent flow takes place near the wellbore region, theeffect of turbulence provides an extra pressure drop as given by

p2e � p2

wf ¼1424 mZT

kh

�ln�

re

rw

�þ s

qþ 1424 mZTDkh

q2 (3)

which can be rearranged and accounted for by a rate-dependentskin effect, described by (Swift and Kiel, 1962):

q ¼kh�

p2e � p2

wf

�1424 mZT

hln� re

rw

�þ sþ Dq

i (4)

where D is the turbulence coefficient with the unit of reciprocalrate. It is usually determined by analysis of the multi-rate pressuretests (Economides et al., 1994; Kakar et al., 2004), or from corre-lations when well test data is not available (Wang, 2000; Li andEngler, 2001)

Well and reservoir characteristics.

pe 3000 psire 660 ftrw 0.359 fth 50 ftT 710 �Rgg 0.7Case 1 Case 2pwf 1500 psi pwf 2500 psim 0.0162 cp m 0.0186z 0.91 z 0.9

3. Turbulence in radial flow vertical gas well

Fig. 1 is a sketch of a vertical gas well and its cross section. It isobvious that when the flow is far away from the wellbore, the flowvelocity is small and the flow can be assumed as laminar. In thenear-wellbore area, fluid converges to the small diameter produc-tion tubing. Turbulence occurs especially when the permeability ishigh and the well deliverability increases.

In radial gas flow wells, well deliverability can be described by(Katz et al., 1959):

p2e � p2

wf ¼1424 mZT

kh

�ln�

re

rw

�þ s

q

þ3:16ð10Þ�12bggZT

�1

rw� 1

re

�h2 q2 (5)

where b is the effective non-Darcy coefficient to gas and can becalculated by using the following correlation:

b ¼ 2:704ð10Þ10

k1:1(6)

For an isotropic formation, k equals the horizontal permeability.However, many naturally occurring porous media are anisotropic(Wang et al., 1999). In that case, k is defined as the equivalentpermeability, keq,

keq ¼�

1� log�

kv

kh

� �kv

kh

�1=3

kh (7)

where kv is the vertical permeability while kh is the horizontalpermeability. Multiphase non-Darcy flow behavior in porous mediathat are anisotropic at the pore-scale is studied elsewhere (Wangand Mohanty, 1999; Wang, 2000).

To demonstrate the effects of turbulence on natural gasproduction, a number of calculations are conducted by using theKatz et al. (1959) approach for reservoirs with permeability in therange of 0.1–100 md. The well and reservoir data are listed in Table 1and the results are presented in Table 2.

In Table 2, Dp represents the drawdown. It is the differencebetween the reservoir pressure (pe) and flowing bottom pressure(pwf). The first two columns of Table 2 show the expectedproduction rates under laminar (in ideal openhole wells with b¼ 0,s¼ 0) and turbulent (in radial flow wells with b> 0, s¼ 0) condi-tions at two different drawdowns (1500 and 500 psi), respectively.At low-permeability of 0.1 md, as expected, the rate reduction dueto turbulence is negligible; however, at 10 md, the rate is reducedfrom 10.8 to 9.6 MMscf/d at Dp¼ 500 psi and from 30.1 to22.0 MMscf/d at Dp¼ 1500 psi. That translates to a rate reduction

Table 2Turbulence effect at different permeabilities and different drawdowns.

k, md qideal OH, MMscf/d(b¼ 0, s¼ 0)

qRadial flow, MMscf/d(b> 0, s¼ 0)

qNegative Skin, MMscf/d(b> 0, s< 0)

s

Case 1: Dp¼ 1500 psi (pwf¼ 1500 psi)0.1 0.3 0.3 1.1 �6.21 3.0 2.9 7.8 �5.75 15.1 12.5 22.2 �5.110 30.1 22.0 37.3 �4.825 75.3 45.9 60.0 �4.3100 301.2 121.7 138.0 �3.7

Case 2: Dp¼ 500 psi (pwf¼ 2500 psi)0.1 0.1 0.1 0.6 �6.21 1.1 1.1 3.6 �5.75 5.4 5.0 11.3 �5.110 10.8 9.6 15.4 �4.825 27.0 21.4 32.7 �4.3100 108.1 64.4 79.9 �3.7

X. Wang / Journal of Natural Gas Science and Engineering 1 (2009) 14–2416

of 11–27% for these two different drawdowns, respectively.At high-permeability of 100 md, the rate drops from 108.1 to64.4 MMscf/d at Dp¼ 500 psi and 301.2 to 121.7 MMscf/d atDp¼ 1500 psi. That means the rate reduction is up to 40–60% at thedrawdowns of 500 and 1500 psi, respectively.

The ratio of actual (radial flow with b> 0, s¼ 0) to ideal open-hole (b¼ 0, s¼ 0) rate at different drawdowns at a range ofpermeability, shown in Fig. 2, is perhaps the most telling. Whenpermeability is less than 1 md, the rate reduction is less than 5 % forboth cases. As permeability increases, the ratio between theturbulence-affected production (qRadial Flow) and the one calculatedunder the assumption of openhole laminar flow (qIdeal OH) declinesprecipitously. Turbulence takes over and the production rate is nolonger a linear relationship with the drawdown in both cases(Dp¼ 500 and 1500 psi). The higher the drawdown is, the higherthe well deliverability is, the stronger the turbulence is, andtherefore a larger reduction in the production occurs. Turbulenceeffects become so significant at high-permeability that theyoverwhelm practically all other factors, including damage or near-well stimulation. This is also demonstrated in the third column inTable 2 shown as qNegative Skin (b> 0, s< 0).

The calculation is done for gas wells when hypothetical negativeskin effects are used. Results are shown inTable 2. The values are thosethat would have resulted from a hydraulic fracture treatment withoutconsidering the improvement in the overall turbulence effects. Theseskins (the last column in Table 2) would be in e.g., oil wells withcomparable fracture treatments (Wang and Economides, 2004).

Fig. 2. Turbulence effect for a permeability range and different drawdowns.

Results show that when k< 1 md (i.e., when turbulence effects inradial flow are not significant), the impact of the negative skin effect isvery large. At 0.1 md and Dp¼ 1500 psi, the production rate atnegative skin of �6.2 is 1.1 MMscf/d which is 3.7 times higher thanthat in radial flow with zero skin (b> 0, s¼ 0) and 6 times higher(0.6 versus 0.1 MMscf/d) at Dp¼ 500 psi. When the permeability is10 md, the production from the negative skin (�4.8) is 37.3 MMscf/dwhich is 1.7 times higher than the zero skin case for Dp¼ 1500 psi. Itis 15.4 MMscf/d and about 1.6 times higher than the zero skin case forDp¼ 500 psi. When the turbulence effects are great as in the 100 mdcase, the production ratio between the negative skin (�3.7) and thezero skin is far less, e.g., around 1.2 under both drawdowns. Thisimplies that, when permeability is high (>1 md for this case), theproduction impediment from turbulence is much higher than thatfrom near-wellbore skin damage or stimulation (Wang and Econo-mides, 2004). This would also mean that while an acid job in e.g.,a carbonate reservoir, can impose a near-wellbore negative skin it cando little about the turbulence. To reduce turbulence in vertical gaswells, hydraulic fracturing is essential. By changing the flow profile inthe well, turbulence will be reduced considerably. It is important tonote that Eq. (4) can no longer be used for a fractured gas wellperformance. In words, the term Dq, accounting for radial turbulenceeffects, will no longer be present.

4. Turbulence in hydraulically fractured vertical gas well

Hydraulic fracturing is the most effective technique to increasethe well productivity index. As shown in Fig. 3, when a gas well isfractured, the flow pattern is no longer radial. Gas will first flow intothe propped fracture and then along the fracture to the wellbore.While fracturing has proven very beneficial compared to theprevious state of the well, it is essential that the performance of thewell considers the new turbulence effects – those inside the frac-ture itself.

Several studies have been done on turbulence effects inhydraulically fractured gas wells (Wang and Economides, 2004; Gilet al., 2001; Lolon et al., 2004; Kakar et al., 2004; Miskimins et al.,2005; Ouyang, 2007; Huang and Ayoub, 2007; Friedel et al., 2007;Nashawi, 2007) and gas condensate wells (Wang et al., 2000; Indriatiet al., 2002; Ravari and Ibrahim, 2005; Ravari et al., 2007; Mahdiyaret al., 2008). Studies (Gil et al., 2001; Ubani and Evans,1982) showedthat significant turbulence flow can exist in a fracture at any time inthe life of a vertically fractured gas well. On the average, about 10% ofthe total fracture pressure drop can be attributed to turbulenceeffects (Kakar et al., 2004). If substantial non-Darcy flow is occurringin the fracture, the calculation of the apparent fracture length usingconventional techniques will result in values that are far too small(Holditch and Morse, 1976).

Since turbulence effects in a fracture depend on fracturegeometry, it is possible to reduce turbulence flow in a hydraulicallyfractured vertical well by optimizing the fracture length, width, andfurther achieving the maximum productivity index. With the tipscreenout (TSO) treatment, medium (0.5–5 md) and high- (morethan 5 md) permeability formations can be fractured (Economideset al., 2001). A physical optimization technique was introduced byValko and Economides and co-workers as in Romero et al. (2003)and is called the ‘‘Unified Fracture Design (UFD)’’ approach.

4.1. Unified Fracture Design (UFD)

In the UFD approach, Economides et al. (2002a,b) introduced theconcept of the dimensionless Proppant Number, Nprop, given by:

Nprop ¼ I2xCfD ¼

4 kf xf wkx2

e¼ 4 kf xf whp

kx2ehp

¼ 2 kf Vp

kVr(8)

Table 3Constants a and b.

Proppant size a b

8–12 1.24 17,42310–20 1.34 27,53920–40 1.54 110,47040–60 1.6 69,405

Fig. 3. Sketch of a hydraulically fractured vertical well and its cross section.


where Ix is the penetration ratio and CfD is the dimensionlessfracture conductivity, Vr is the reservoir drainage volume, and Vp isthe volume of the proppant in the pay. It is equal to the total volumeinjected times the ratio of the net height to the fracture height.

They also found that for a given value of Nprop there is an optimaldimensionless fracture conductivity, CfDopt, at which the produc-tivity index, JD, is maximized. The maximized productivity index,JDmax, as a function of Nprop, can be calculated by

JDmax�Nprop

�

¼

8><>:

10:990�0:5lnNprop

if Nprop�0:1

6p�exp

�0:423�0:311Nprop�0:089ðNpropÞ2

1þ0:667Npropþ0:015ðNpropÞ2

if Nprop>0:1ð9Þ

Similarly, correlations were presented for CfDopt for the entirerange of Nprop.

CfDopt�Nprop

�

¼

8>><>>:

1:6 if Nprop<0:1

1:6þexph�0:583þ1:48lnNprop

1þ0:142lnNprop

iif 0:1�Nprop�10

Nprop if Nprop>10

ð10Þ

Once the CfDopt is known, the optimal fracture length xfopt, andwidth, wopt, can be readily determined:

xfopt ¼

kf Vf

CfDoptkh

!0:5; wopt ¼

CfDoptkVf

kf h

!0:5(11)

where Vf is the volume of one propped wing, Vf¼ Vp/2.At ‘‘low’’ Proppant Numbers (i.e., Nprop< 0.1), the optimal

conductivity, CfDopt equals 1.6. As the Proppant Number increases,the absolute maximum for JD is 6/p¼ 1.909 (this value is theproductivity index for a perfect linear flow in a square reservoir).When the propped volume increases or the reservoir permeabilitydecreases (i.e., large Proppant Numbers), the CfDopt compromisehappens at larger dimensionless fracture conductivities, becausethe penetration cannot exceed unity and hence the width has toincrease (Economides et al., 2001). In moderate- to high-perme-ability and facpack-treated formations, it is difficult to achievea Proppant Number larger than 0.1 (usually 0.0001<Nprop< 0.01).Therefore in such cases the CfDopt is always 1.6. In ‘‘tight gas,’’ on theother hand, it is possible to achieve large Nprop.

In the case of a potentially high-rate natural gas well, theimportant issue is that the effective proppant-pack permeability(that is used to calculate the Proppant Number and the dimen-sionless fracture conductivity) depends on the production rate,because of the turbulence effects.

The fractured vertical gas well deliverability can be calculated bythe combination of the UFD method with Gidley’s (1990) adjust-ment to the proppant-pack permeability and the Cooke’s (1973)

correlations for flow in the fracture. The calculation procedure issummarized below:

1. An initial Reynolds Number (such as zero) is assumed.2. The effective permeability using the in-situ Reynolds Number

is calculated by

kf ;e ¼kf;n

1þ NRe(12)

3. Proppant Number is calculated by using Eq. (8). From which themaximum JDV (Eq. (9)) and the optimum dimensionlessconductivity (Eq. (10)) are calculated. The latter allows thedetermination of the indicated fracture dimensions using Eq. (11).

4. From the dimensionless productivity index and the drawdown,the actual production rate is calculated by

qðMscf=dÞ ¼kh�

p2e � p2

wf

�1424 mZT

JDV (13)

5. Reynolds Number is calculated by

NRe ¼bkf;nnr

m(14)

where kf,n is the nominal permeability (under Darcy flow condi-tions) in m2, b is in 1/m, v is the fluid velocity at reservoir conditionsin m/s. It is determined as the volumetric flow rate in the fracturenear the well divided by the fracture height times the fracturewidth (both determined from the design in each iteration). m is theviscosity of the fluid at reservoir conditions in Pa and r is thedensity of the flowing fluid in kg/m3. The value of b is obtained from

b ¼�1� 108� b�

kf ;ne�a (15)

where a and b are obtained from Cooke (1973) (Table 3):The procedure ends when the assumed and calculated Reynolds

Numbers are close enough.

4.2. Constraints

It is worth noting that the fracture optimization outlined above isa physical optimization without constraints. It may not be practicalor achievable in reality (Demarchos et al., 2004, Economides et al.,

Table 4Results from hydraulic fractured vertical gas wells. (kf¼ 60,000 md, proppantmass¼ 400,000 lbm).

k, md qfractured, MMscf/d kf,e, md xf, ft

Case 1: Dp¼ 1500 psi (pwf¼ 1500 psi)0.1 2.8 11,540 5611 13.1 9251 2185 43.5 7950 9110 75.5 7019 6125 160.3 6670 36100 524.0 5525 16

Case 2: Dp¼ 500 psi (pwf¼ 2500 psi)0.1 1.2 16,244 5691 5.8 12,493 2505 18.9 10,770 10810 32.3 9638 7125 69.2 8980 44100 224.0 7494 20

0

2

4

6

8

10

12

14

0.1 1 10 100

Pro

du

ctivity R

atio

Permeability, md

Negative Skin/Radial Flow

Fractured/Radial Flow

Fractured (premium)/Radial Flow

Fig. 4. Comparison of production ratio of wells with negative skin and fracture overwells without fracture (Dp¼ 1500 psi).


2002a). For example, at low formation permeability, optimizationmay indicate a fracture which is very long and very narrow so that ithas the maximum exposure to the reservoir. In reality, if the fractureis too narrow, it could cause premature screenout due to proppantbridging. Therefore, a constraint is added in the calculation proce-dure, e.g., the minimum fracture width must be not less than threeproppant diameters.

A second constraint may involve the net pressure, whichemerges in high-permeability reservoirs. For such reservoirs thetheoretical optimization may point towards a fracture with a largepropped width. During execution, a large hydraulic width wouldyield an unrealistically large net pressure. Therefore a secondconstraint may be added in the calculation procedure, e.g., the netpressure should be less than 1000 psi.

A third constraint may be that the total pumping time should beless than a number of hours to comply with regulations or safety.Other constraints may be envisioned such as logistical and localconditions, etc. However, in all cases while the actual design willdepart from the theoretical optimization, this should be done ina reasonable manner and the adjustment should be no more thannecessary (Economides et al., 2002a). The three constraints describedabove are used in the fracture design for the rest of this study.

It is also worth noting that in the original UFD, the drainage areawas assumed as square. When it is not, the UFD still can be used,but the Proppant Number needs to be adjusted by using the Dietzshape factors (Daal and Economides, 2006). With modified UFD,the performance of a fractured gas well and reserves recovery canbe predicted at different infield drilling scenarios with square orirregular drainage configurations (Economides and Martin, 2007;Marongiu-Porcu and Economides, 2008).

4.3. Results and discussion

Results for the fracture designs and expected production ratesfor the range of permeability used for the non-fractured wells aresummarized in Table 4. These designs assume sand as proppantwith kf¼ 60,000 md and the proppant mass (for two fracturewings) is 400,000 lbm. For comparison purposes, the followingproductivity ratios are plotted in Fig. 4: qNegative Skin (b> 0, s< 0, inTable 2)/qRadial Flow (b> 0, s¼ 0, in Table 2) and qFractured (in Table 4)/qRadial Flow (b> 0, s¼ 0, in Table 2).

Results show that, at drawdown of 1500 psi and at 0.1 md, theradial flow well would deliver 0.3 MMscf/d (Table 2). For a wellwith an equivalent skin of �6.2 the production rate (qNegative Skin)would be 1.1 MMscf/d, near a four-fold increase (Fig. 4). Thisproduction increase would be the one expected in an oil well,flowing at laminar conditions. The production increase froma fractured well, on the other hand, is over nine-fold which isshown in Fig. 4. At 10 md, the fold of increase between qNegative Skin

and qRadial Flow is near 1.7 while the ratio between qFractured andqRadial Flow is over 3.4.

As the permeability increases further, the trends diverge. Theratio of qNegative Skin and qRadial Flow decreases continuously due toturbulence effects that dominate radial flow and affect wellperformance. The ratio of qFractured and qRadial Flow, on the other hand,starts increasing. At a permeability of 100, the ratio of qNegative Skin

and qRadial Flow decreases to about 1 while the ratio of qFractured andqRadial Flow reaches 4.3. As mentioned earlier, this is becausehydraulic fracture alters the fluid flow path (see Fig. 3) in thewellbore area and reduces turbulence substantially in the reservoirnear the wellbore. Therefore, hydraulic fracturing is a must forvertical gas wells at all permeability range. It is not only forbypassing near-wellbore damage, but also for reducing turbulence.Otherwise, the gas well will be greatly handicapped in terms ofproduction (Marongiu-Porcu and Economides, 2008).

If premium proppants are used (kf¼ 600,000 md), shown inFig. 4 the fractured well will be even more prolific: ‘‘pushing thelimits of hydraulic fracturing’’ (Demarchos et al., 2004). (For inter-pretation of the references to colour in this text, the reader isreferred to the web version of this article.)

5. Transversely fractured horizontal gas wells

Depending on the horizontal well orientation with respect tothe state of stress, two limiting fracture geometries may be created:longitudinal or transverse (Soliman and Boonen, 1997; Mukherjeeand Economides, 1991; Eirafie and Wattenbarger, 1997; Crosbyet al., 1998; Emanuele et al., 1998; Soliman et al., 1999; Minner et al.,2003; Fisher et al., 2004). The longitudinal configuration is gener-ated when the well is drilled along the expected fracture trajectory(Valko and Economides, 1996; Soliman et al., 1999; Economideset al., 1994). The performance of such a well is almost identical toa fractured vertical well when both have equal fracture length andequal conductivity. Therefore, existing solutions for vertical wellfractures can be applied to a longitudinally fractured horizontalwell (Economides et al., 2002a; Soliman et al., 1999; Villegas et al.,1996; Valko and Economides, 1996; Wei, 2006).

As discussed in the previous section, in vertical gas wellsturbulence can be greatly reduced through hydraulic fracturing,because the flow pattern (shown in Fig. 3) through the hydraulicfracture towards the well is different from that in radial flow(shown in Fig. 1). For transversely fractured horizontal gas wells,turbulence effects inside the fracture are enhanced because of thevery small contact area between the well and the fracture, seeFig. 5. The limited communication between the transverse fractureand the wellbore generates an additional pressure drop, causes

Fig. 5. Sketch of a transversely fractured horizontal well and its cross section.

0

2

4

6

8

10

12

14

0.1 1 10 100

Pro

du

ctivity R

atio

Permeability, md

Ideal Openhole VerticalRadial Flow Vertical/Ideal OHFractured Vertical/Ideal OHTransversely Fractured/Ideal OH4Transversely Fractured/Ideal OH

Fig. 6. Folds of increase in productivity ratio.


choking effects for all transversely fractured horizontal gas wells,and further increases turbulence. This precludes application toessentially any well whose permeability is above 1 md and,perhaps, to even much lower values of permeability, all subjected toproject economics (Wei, 2006).

For a single transversely fractured horizontal well, as shown inFig. 5, the cross section of the contact between a transverse fractureand a horizontal well is 2p rww, where w is the width of the fracture(which can be obtained by using a design procedure such as theUFD approach described in the previous section but now the flowvelocity, the Reynolds Number, and the resulting reduction in theeffective proppant-pack permeability must be calculated based onthe much smaller area of flow), and rw is the radius of the hori-zontal well. This notion shows the flow from the reservoir into thefracture is linear while the flow inside the fracture is convergingradial (Economides et al., 1994). The combination of flows results inan additional pressure drop which can be accounted for by a skineffect, denoted as sc (Mukherjee and Economides, 1991):

sc ¼kh

kf w

�ln�

h2rw

�� p

2: (16)

Mukherjee and Economides (1991) assumed that the horizontalwell is at the vertical center of a reservoir (see Fig. 5), and the flow isfrom the reservoir into the fracture and then from the fracture intothe wellbore. The produced fluid enters the wellbore only throughthe fracture, no matter whether the remaining part of the well isperforated or not. These assumptions are also valid in this study.

With the calculated sc from Eq. (16), the dimensionlessproductivity index of transversely fractured horizontal gas well canbe calculated (Wei and Economides, 2005):

JDTH ¼1�

1JD

�þ sc

(17)

where JD is the dimensionless productivity index of a transverselyfractured horizontal well without taking into account of the chokeeffects. It is calculated by using the same UFD model and proceduredescribed earlier. Further, the actual production rate from a singletransversely fractured horizontal well can be obtained:

qðMscf=dÞ ¼kh�

p2e � p2

wf

�1424 mZT

JDTH (18)

5.1. Single transversely fractured horizontal wells

For comparison purposes, the same parameters used in thefractured vertical well design (listed in Table 1) are used in thehorizontal well fracture design. Proppant-pack permeability is600,000 md, proppant mass is 400,000 lbm, and the drawdownis 1500 psi. Results are compared with the ideal openhole case(b¼ 0, s¼ 0) and presented in Fig. 6. The results from radial flow(b> 0, s¼ 0) and fractured vertical wells are also presented inFig. 6. (For interpretation of the references to colour in this text,the reader is referred to the web version of this article.)

Results show that when permeability is 0.1, turbulence isnegligible. The fold of increase (FoI) from a single transverselyfractured horizontal well (Fig. 6) is about 3.4. FoI from a fracturedvertical well is w13. That is almost 4 times higher than that in thetransversely fractured horizontal well. Once the permeability ishigher than 1 md, the choke effects in the transversely fracturedhorizontal well become dominating. The skin, sc (described in Eq.(16)), increases from 0.6 at 0.1 md to 6.7 at 1 md and 137 at 100 md(Fig. 7). This causes the FoI from the single transversely fracturedhorizontal well to be less than 1, which means its performance isworse than that in an ideal openhole well (b¼ 0, s¼ 0). Whenpermeability is 100 md, the FoI drops to 0.05 which is worse thanfrom a (non-fractured) radial flow vertical well (Fig. 6). The FoI from

0

20

40

60

80

100

120

140

0.1 1 10 100

sc

Permeability, md

Fig. 7. Skin versus permeability in the single transversely fractured horizontal well.


the vertical fractured well is over 2. This means that single trans-versely fractured horizontal wells simply cannot compete withvertical fractured wells at the given permeability range even whenthe premium proppant (600,000 md) is used. Can multiple trans-versely fractured horizontal wells compete with vertical wells? Ifyes, how many transverse fractures need to be added? (For inter-pretation of the references to colour in this text, the reader isreferred to the web version of this article.)

0.5

1.0

1.5

2.0

2.5

3.0

0.01 0.1 1

Pro

du

ctivity R

atio

Permeability, md

600,000md/60,000md

Fig. 8. Proppant-pack permeability impact on productivity in a transversely fracturedhorizontal well (proppant mass¼ 150,000 lbm).

5.2. Multiple transversely fractured horizontal wells

If assuming the drainage zone is isolated evenly and theformation is isotropic, qt is the total production rate from mtransverse fractures, and the production from each transversefracture is equal (Economides and Martin, 2007), then

qt ¼ mqjðj ¼ 1;2;.;mÞ (19)

The production of a horizontal well with 4 transverse fracturesis plotted in Fig. 6. Results show that at permeability of 0.1, theperformance of the horizontal well with four transverse fractures isslightly better than that from the fractured vertical well (13.6versus 13.0). Clearly, more than 4 successful treatments will add tothe production and current industry practices point towards a largenumber of treatments in low to very low-permeability formations.Once the permeability is larger than 0.1 md, the horizontal well(with 4 transverse fractures) productivity drops significantly. At1 md, the productivity ratio drops to 2.9 while the vertical well is6.6. When the permeability is above 10 md, the productivity ratio ofhorizontal well with 4 transverse fractures drops below 1 and it isequivalent to a radial flow vertical (non-fractured) well. (Forinterpretation of the references to colour in this text, the reader isreferred to the web version of this article.)

The conclusion from this study is that when formation perme-ability is lower than 0.1 md, horizontal wells are acceptable ifmultiple transverse fractures can be generated. When the perme-ability is higher than 1 md, a transversely fractured horizontal wellsimply cannot compete with a fractured vertical well even if thehorizontal well has multiple fractures (in this particular case,m¼ 4). When the formation permeability is 10 md or more, theturbulence caused by the choke effects is so huge that theproductivity from the horizontal well with multiple transversefractures (such as the 4 here) is worse than that from a non-frac-tured vertical well. This is a striking example on how a wellcompletion such as hydraulic fracturing which is a must fora vertical well may be misapplied in horizontal wells.

5.3. Factors affecting the productivity of transversely fracturedhorizontal wells

Some parameters play roles in increasing the productivity oftransversely fractured horizontal wells. Studies (Wei, 2006) showthat increasing the proppant-pack permeability increases theproductivity slightly in the single transversely fractured horizontalwell. For example, when proppant-pack permeability increases 10times from 60,000 to 600,000 md (proppant mass¼ 150,000 lbm),at the given permeability range (0.01–1 md), the productivityincreases as the permeability increases as shown in Fig. 8. At 1 md,the productivity ratio between proppant-pack permeability of600,000 and 60,000 md is about w2.5 times. This is because thechoke skin is a function of the proppant-pack permeability, asshown in Fig. 9. The higher the proppant-pack permeability is, thelower the choke skin is. At permeability of 1 md, the choke skin isreduced from 36.7 (Fig. 9) to 10.6, which is about 71% reduction.(For interpretation of the references to colour in this text, thereader is referred to the web version of this article.)

An interesting observation here is that at low-permeability of0.01 md, the productivity ratio shown in Fig. 8 is less than 1. Thereason behind this is because of the constraint of fracture width. Asmentioned earlier under Unified Fracture Design, the minimumfracture width has to be 3 times the maximum proppant diameters.For this particular case at proppant-pack permeability of600,000 md, the optimized fracture width happens to be smallerthan 3 times the proppant diameter. Therefore, the actual designhas to depart from the optimized physical design and further, theproductivity is not optimum.

The impact of proppant mass on productivity is shown in Fig. 10.At the same proppant permeability of 60,000 md and formationpermeability of 0.01 md, the incremental productivity is 51% and8.2% when the proppant mass is doubled from 75,000 to150,000 lbm (Fig. 10) and from 150,000 to 300,000 lbm, respec-tively. It drops dramatically to 3.6 and 0.8%, respectively whenpermeability is 0.1 md. When the formability permeability is higherthan 0.1 md, increasing proppant mass does not increase produc-tivity even when the proppant mass is increased 4 times from75,000 to 300,000 lbm (Fig. 10). This raises another question: Is itworth investing money on fracture execution with expensivepremium proppant and conduct a massive job to gain very littleincremental production? Where should one draw the line? Thiswill require economic optimization to answer those questions. (Forinterpretation of the references to colour in this text, the reader isreferred to the web version of this article.)

0

5

10

15

20

25

30

35

40

0.01 0.1 1

sc

Permeability, md

600,000md

60,000md

Fig. 9. Proppant-pack permeability impact on choke skin in a transversely fracturedhorizontal well (proppant mass¼ 150,000 lbm).

Proppant Mass, lbm

NP

V, M

illio

n $

Maximum NPV

Fig. 11. NPV versus proppant mass for a given reservoir permeability.


6. Economic optimization of fractured gas wells

So far the discussion has been focused on physical optimizationby taking into account of all the logistic, equipment, and technologyconstraints. To make a project attractive, it must be economic at thegiven circumstance as well. Several factors have to be taken intoaccount such as: the incremental production from hydraulic fracturetreatment, treatment costs, risks associated to the mechanicalproblems that could cause the treatment to be unsuccessful, and thesensitivity of the geopolitical locations, etc. Marongiu-Porcu andEconomides (2008) used the Net Present Value (NPV) as the criterionfor the economic optimization and the evaluation of the desirabilityof the specific hydraulic fracture treatments at different perme-abilities and locations. NPV is defined as

NPV ¼X Rn

ð1þ iÞn� I (20)

where I is a given investment to generate the revenue flow, i isa discount rate (the interest rate used in determining the presentvalue of future cash flow), and a project is to be assessed for a timespan of n years.

Their studies show that, for a given formation permeability,there is a proppant mass that gives the maximum NPV (indicated inFig. 11) for a fractured vertical well (based on the productionforecast). The higher the permeability is, the smaller the proppantmass (that gives the maximum NPV) is. This agrees with the finding

0

10

20

30

40

50

60

70

0.01 0.1 1

In

cre

men

tal P

ro

du

ctivity, %

Permeability, md

150,000lbm/75,000lbm300,000lbm/150,000lbm300,000lbm/75,000lbm

Fig. 10. Proppant mass impact on productivity in a transversely fractured horizontalwell (proppant-pack permeability¼ 60,000 md).

mentioned earlier in this study. That is low-permeability reservoirsneed larger fractures of much larger length to have maximumaccess to the reservoir. High-permeability reservoirs, on the otherhand, need smaller fractures but much larger widths to increaseproductivity and reduce turbulence.

For the same hydraulic fracture treatment at different locations,the cost can be significantly different. Some of the cost comparisonresults are shown in Fig. 12. Results show that to drill and completea well overseas are very expensive. Sometimes it can be 3 timesmore expensive than that in the USA. As shown in Fig. 12, thepumping job, fracturing fluid and proppant are about 1.7–2 timesmore expensive in overseas than in the USA. Mobilization anddemobilization of equipment are about 2.3 times higher. That iswhy the NPVs are different, as shown in Fig. 13. In this study, the gasprice is assumed as $7/Mscf. The discount rate is assumed to be 10%in the calculation for the USA and 25% for some overseas countries(to reflect higher risk). Four different infield drilling scenarios areconsidered (shown in Fig. 14): one non-fractured vertical gas well,one fractured vertical gas well, four non-fractured vertical gaswells, and four fractured vertical gas wells.

0

0.5

1

1.5

2

2.5

3

3.5

Well C

on

stru

ctio

n

(D

rillin

g &

C

om

pletio

n)

Pu

mp

in

g C

harg

es

Eq

uip

men

t M

ob

ilizatio

n

/D

em

ob

ilizatio

n

Pro

pp

an

t C

ost

(20/40 C

eram

ic)/lb

m

Fractu

rin

g F

lu

id

C

ost

(X

-L

in

ked

G

el)/g

al

Co

st R

atio

Overseas/USA

Fig. 12. Comparisons of capital investments between the USA and overseas (Datasource: Marongiu-Porcu and Economides, 2008).

-10

-5

0

5

10

15

20

25

30

35

40

1 UNFRACCED 1FRACCED 4UNFRACCED 4FRACCED

NP

V, M

illio

n $

A.S0U,d

m1

ASU,dm

1.0

ASU,dm

1.0

ASU,dm

1.0

ASU,dm5

ASU,dm5

ASU,dm5

ASU,dm5

saesrev

O,dm5

saesrev

O,dm5

saesrev

O,dm5

saesrevO,dm1.0

saesrevO,dm1.0

saesrevO,dm1.0

saesrev

O,dm

1.0

saesrevO,dm5

Fig. 13. NPV for both the USA and overseas scenarios (Data source: Marongiu-Porcu, 2007).


A few interesting findings from this study are:

� Hydraulically fractured vertical gas well can be attractiveeconomically in certain reservoirs in some areas (see the green,blue and black blocks in Fig. 13) but not attractive elsewhere(see red block in Fig. 13). (For interpretation of the references tocolour in this text, the reader is referred to the web version ofthis article.)� For a company with a large portfolio of reservoirs it is more

profitable to fracture a few high-permeability gas wells thana large number of low-permeability ones (see the differences ofthe NPV at 0.1 and 5 md in Fig. 13 for both the USA andoverseas).� Hydraulic fracturing is an integral part of well and reservoir

management and a mainstay of production.

Fig. 14. Four different drainage configurations (Marongiu-Porcu, 2007).

� The combination of the NPV and the modified UFD can be usedto predict the performance of fractured gas wells and reservesrecovery of a given reservoir at different infield drillingscenarios with square or irregular drainage configurations.

7. Remarks

A review paper in the allotted space is not possible to do justiceto all the issues related to gas production. The purpose of this paperis to identify the most important issues such as turbulence innatural gas wells and how to remediate it. The discussion is focusedon the productivities of vertical and horizontal wells with andwithout fractures. The turbulence effects in cased and perforated(C&P) gas wells can be found in published literature (Karakas andTariq, 1988; Ichara, 1987; Nguyen, 1986). Their studies show thathigh-perforation density of long-penetrating tunnels reducesturbulences. The results of turbulence effects in the perforationtunnels of cased-hole frac-packed (CHFP) gas wells can be found inthe studies performed by Lolon et al. (2004) and Ouyang (2007).The study by Ouyang (2007) shows that increasing proppantpermeability (i.e., using larger gravel for well completion)decreases the turbulence in the perforation tunnels of CHFP wells.The combination of high-velocity and multiphase flow hasconsiderable effects on productivity and stimulation effectivenessin hydraulically fractured wells (Barree and Conway, 2007; Su,2004). It is also important in near-well pressure drop in high-permeability retrograde condensate reservoirs and frac-pack orgravel pack completions. For unconsolidated formations, besideturbulence, sand production could be another hurdle in optimizinggas production. Operating sand control wells with screen by usingflux based guidelines (Tiffin et al., 2003) to prevent sand controlfailure due to screen erosion is recommended.

8. Conclusions

This paper summarizes the fundamentals of natural gas produc-tion, especially the key issues and challenges in moderate- to high-permeability reservoirs. Studies are performed in the permeabilityrange of 0.1–100 md. Emphasis is given on showing the impact ofturbulence and the importance of hydraulic fracturing on well deliv-erability for both vertical and horizontal gas wells. Results show that


� At moderate- to high-permeability reservoirs, turbulenceeffects overwhelm almost all factors including near-wellboredamage in vertical gas wells.� The answer to turbulence in vertical gas wells is hydraulic

fracturing. It is a must for vertical gas wells at all permeabilityranges as it is not only bypassing near-wellbore damage, butalso reducing turbulence. Otherwise, the gas well will begreatly handicapped in terms of production.� For transversely fractured horizontal gas wells, turbulence effects

inside the fracture are enhanced because of the very small contactarea (which causes additional pressure drop and choking effect)between the well and the fracture, and further increases turbu-lence. This precludes application to essentially any well whosepermeability is above 1 md and, perhaps, to even much lowervalues of permeability, all subjected to project economics.

In addition to the above studies, a Unified Fracture Design (UFD)procedure for hydraulic fractures in a gas well is provided. Economicevaluation is also presented to emphasize that productionenhancement requires both physical and economic optimization.

Nomenclature

a constant used to calculate b

b constant used to calculate b

CfD dimensionless fracture conductivityCfDopt optimal dimensionless fracture conductivityD turbulence coefficient with the unit of reciprocal rateh formation thickness, fthf height of the propped fracture, fti discount rateI investment, $Ix penetration ratioJD dimensionless productivity indexJDV dimensionless productivity index of fractured vertical

wellJDmax maximum productivity indexJDTH dimensionless productivity index of a transversely

fractured horizontal wellk reservoir permeability, mdkf proppant-pack permeability, mdkf,e effective fracture permeability, mdkf,n nominal fracture permeability, mdkeq equivalent permeability, mdkh horizontal permeability, mdkv vertical permeability, mdm number of transverse fractures in a horizontal welln time span of a project to be assessed, yearNPV Net Present Value, $NRe Reynolds NumberNprop Proppant Number, dimensionlesspe reservoir pressure, psipwf flowing bottomhole pressure, psiq gas flow rate, Mscf/dre drainage radius, ftrw well radius, fts skinsc choke skin in transversely fractured horizontal well,

dimensionlessT temperature, �RVf volume of one propped wingVp volume of the proppant in the payVr reservoir drainage volumew propped fracture width, in

xf propped fracture half length, ftxfopt optimum fracture half length, ftZ gas deviation factorb effective non-Darcy coefficient to gasgg gas gravity to air¼ 1m viscosity of the fluid at reservoir conditions, Pa or cpv fluid velocity at reservoir conditions, m/s,r the density of the flowing fluid, kg/m3

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