SPE 153072

Production Data Analysis in Eagle Ford Shale Gas Reservoir Bingxiang Xu, SPE, China University of Petroleum-Beijing, University of Adelaide; Manouchehr Haghighi, and Dennis Cooke, SPE, University of Adelaide; Xiangfang Li, SPE, China University of Petroleum-Beijing

Copyright 2012, Society of Petroleum Engineers This paper was prepared for presentation at the SPE/EAGE European Unconventional Resources Conference and Exhibition held in Vienna, Austria, 20-22 March 2012. This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.

Abstract Eagle Ford shale in South Texas is one of the recent shale play in US which the development began in late 2008. So far many horizontal wells have been drilled and put into production using hydraulic fracturing. Production behaviour in shale gas reservoirs unlike conventional reservoirs is different in various plays and there are no published reports for production data analysis in Eagle Ford shale. We have used the linear dual porosity type curve analysis technology to analyse the production behaviour and to estimate the essential parameters for this reservoir. This type curve was constructed based on transient production rate with constant well pressure in a closed boundary of stimulated reservoir volume (SRV) with double porosity approach. In order to analyse the early production data we used Bello’s and Nobakht’s approach to account for apparent skin. In this study, three flow regimes were identified consisting of 1- bilinear flow; 2- matrix linear flow; and 3- boundary dominated flow. For the analysis of early flow regime, two possibilities of transition flow and apparent skin have been considered. First, the fracture permeability was estimated to be around 820 nano Darcy based on transition flow analysis. Second, the matrix permeability was estimated to be either 181 or 255 nano Darcy based on two different approaches in matrix linear flow regime. Furthermore, original gas in place (OGIP) and SRV were estimated from the boundary dominated flow regime. To validate the estimated matrix permeability, a single porosity numerical model with high permeability transverse fractures was built to match the production history. The permeability from simulation was in a good agreement with type curve analysis. Production forecasting has also been carried out using different adsorption isotherms. The results showed that the effect of desorption depends on the reservoir pressure and the shape of adsorption isotherm curve. In early time of production, desorption is usually not effective, however, for long-term production forecasting, it is necessary to account for this phenomenon by providing an accurate isotherm. Introduction Decline curve analysis (DCA) has been used as an effective method for the production forecasting and reserves estimation in shale gas reservoirs. Since production of shale gas reservoirs is usually from a stimulated reservoir volume (SRV) generated by hydraulic fracturing in a horizontal well and also because the shale gas reservoirs have very different petrophysical properties from conventional gas reservoirs, the production data analysis is different from conventional DCA methods developed first by Arps (1945), and modified by other authors such as Fetkovich (1987), Palacio and Blasingame (1993), Agarwal et al. (1999). The petrophysical difference makes naturally fractured shale gas reservoirs generate more complex fracture network than traditional bi-wing fracture (Cipolla et al., 2009). This fracture network leads to a SRV region. The initial active region of a shale gas reservoir only exists in the SRV, which is usually monitored by micro-seismic technique (Inamdar et al., 2010; Bello and Wattenbarger, 2010). Due to ultra-low matrix permeability and high fracture conductivity, the flow does not follow the radial behaviour similar to the conventional gas reservoirs; however, it follows a linear flow instead (Bello and Wattenbarger, 2010; Al-Ahmadi et al., 2010). Also shale gas reservoirs contain both free gas in macro pores and adsorbed gas on matrix surface area.

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To use production analysis technique for shale gas, Lee and Gatens III. (1985), Hazlet et al. (1986), constructed a set of type curves for the Devonian shales using a solution for constant pressure in a bounded dual-porosity reservoir based on the Warren-Root model. Lewis and Hughes (2008) proposed production data analysis for shale gas using a modified material balance time to account for desorption. However, these methods were based on radial flow. Matter et al. (2008) showed that using conventional type curve technique to analyse the shale gas well performance may result in “false” radial flow when the fracture conductivity is finite. It was found that the best-fit match with the Arps’ hyperbolic decline gives constant values (b) greater than 1 (Baihly et al., 2010). This can cause to have physically unreasonable properties (Lee and Sidle, 2010). As a result, Valkó and Lee (2010) developed a stretched exponential production decline model. Duong (2010) also introduced a derived decline model that is based on long-term linear flow in a large number of wells in tight and shale-gas reservoirs. Wattenbarger et al. (1998) presented a linear flow approach to analyse production of fractured tight gas wells. The model was based on homogeneous and linear reservoirs with infinite conductivity hydraulic fracture. El-Banbi (1998) developed a transient dual porosity model for linear reservoirs. Recently many authors developed and applied type curves based on the transient dual porosity model and analysed shale gas production data, such as Bello and Wattenbarger (2008; 2009; 2010), Moghadam et al.(2010), Nobakht et al.(2010), Al-Ahmadi et al.(2010), and Anderson et al.(2010). However, desorption was ignored in these literatures, and also production was assumed to be from SRV only. Ozkan et al. (2009), Brown et al. (2009) and Brohi et al. (2011) recently presented tri-linear flow solutions for tight gas and shale gas reservoirs. It was concluded that outer unstimulated reservoir is subject to supply gas in later times, which depends on the permeability of the outer region. In current study, we have used the same dual porosity linear flow type curves presented by Bello and Wattenbarger (2010) to analyse the Eagle Ford Shale gas production data. Different flow regimes have been identified and the reservoir properties such as matrix permeability and completion efficiency or SRV have been evaluated. Also we have predicted the estimated ultimate recovery (EUR) and the future gas rate based on different assumptions. Basic Theory and Methodology Most shale gas production data show a long-term transient linear flow regime. This linear flow can be detected by a one-half slope on log-log plot of rate versus time. Dual porosity transient linear flow type curves for multi-stage hydraulic fractured horizontal well for shale gas were developed by Bello and Wattenbarger (2010). Four flow regimes exist in these type curves as follows:

• Regime1: Early linear flow in fracture system • Regime2: Bilinear flow caused by both fracture and matrix system • Regime3: Linear flow in matrix system • Regime4: Boundary dominated flow

The combination of area with permeability can be calculated based on the following equations:

Early linear flow: ( ) 1

11262mC

TkAmft

fcw !=+"µ#

(1)

Bilinear flow: ( )[ ] 2

25.014070mCk

TkAmftm

fcw !=+"µ#

(2)

Matrix linear flow: ( ) 3

11262mC

TkAmft

mcm !=+"µ

(3)

Where m1, m3 are straight line slopes on the [ ] gwfi qpmpm /)()( ! vs t plot, and m2 is the straight line slope from the

[ ] gwfi qpmpm /)()( ! vs 25.0t plot. Following two approaches are available to include the apparent skin effects. Apparent skin is the result of flow convergence around a horizontal well (Bello and Wattenbarger, 2009); and an extra pressure drop caused by bottom-hole pressure calculation (Nobakht et al., 2010); or pressure drop within finite conductivity fractures (Anderson et al., 2010) in early linear flow or bilinear flow. 1. Bello’s approach Bello (2009) demonstrated that the effect of skin on the linear reservoir response diminishes gradually with time. When the effect of skin is considered, the straight line through origin becomes a curve with a nonzero intercept on the specified plot

[ ] gwfi qpmpm /)()( ! vs. t . The following empirical equation (Bello and Wattenbarger, 2009) was derived.

SPE 153072 3

btm

btmq

pmpm

g

wfi

33 45.01

)()(

+

+=!

(4)

2. Nobakht’s approach Nobakht et al. (2010) stated that the effect of skin yields a straight line with intercept as it is shown in equation (5).

btmq

pmpm

g

wfi +=!

3)()(

(5)

Eagle Ford Reservoir and Well Description Eagle Ford shale is a calcareous shale play located in South Texas, US, which lies beneath the Austin chalk and extends laterally all the way across Texas from the southwest to the northeast part of the state (Inamdar, 2010; Stegent et al., 2010; Mullen et al., 2010). Its depth ranges from 2,500 to 14,000 ft; the thickness ranges from 50 to more than 300 ft, the pressure gradients are between 0.4 and 0.8 psi/ft, and TOC ranges from 2 to 9% (Stegent et al., 2010). Core data analysis shows that the gas saturation is between 83% and 85%, permeability varies between 1 to 800 nd (Inamdar, 2010). Fig. 1 displays the general areas where the reservoir produces oil (top), high liquids or condensate (middle), and predominately dry gas (bottom). In late 2008 the first few exploration wells in the Eagle Ford were drilled in LaSalle County in the gas window of the play (Stegent et al., 2010).

Fig. 1: Lateral extent of Eagle Ford shale in south Texas (Mullen, 2010)

Well A is a horizontal dry gas producer which was completed with a ten stages proppant fracture stimulation treatment in a 4,000 ft lateral. Each 400 ft stage was perforated with four, two-foot clusters spaced 75 ft apart. According to the results of production log and radioactive log, only 20 transverse fractures are effective on production. Stimulated reservoir volume (SRV) of 169 MMft3 was estimated by fracturing modelling. The pay zone height is 283 ft. Summary of reservoir and fluid properties data in Table 1 is from Bazan et al. (2010).

Table 1: Properties Data for Well A (Bazan et al., 2010) Well radius (ft) 0.333 Lateral length (ft) 4000 Pay zone height (ft) 283 Depth, TVD (ft) 10875 HC* porosity (%) *(!hc = !eff (1-Sw)) 5.76 Reservoir pressure (psi) 8,350 Temperature (oR) 745 Gas compressibility(10-5psi-1) 6 Viscosity(cp) 0.03334 Effective fracture number 20 SRV (MMft3) 169

The daily gas rate in Fig. 2 and original bottom-hole flowing pressure (BHFP) in Fig. 3 for 250 days are also from Bazan et al. (2010). In order to minimize the effect of data fluctuation, BHFP was smoothed using an exponential smoothing algorithm (Lewis and Hughes, 2008). The equation used in the smoothing is

( ) ( ) ( ) ( )11 !"!+"= txtxtx smthsmth ## (6)

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The dampening factor (!) is 0.25. From the smoothed plot (Fig. 3), the BHFP can be assumed constant after 50 days. Therefore, the type curve with constant BHFP can be used to analyse the data.

Fig. 2: Gas rate and cumulative production (Bazan et al., 2010) Fig. 3: Original and smoothed bottom-hole flowing pressure Flow Regimes Identification Based on Fig. 4 and Fig. 5, three following flow regimes were identified: 1-bilinear flow or apparent skin effect, 2- matrix linear flow, and 3- boundary dominated flow. Fig. 4 is a log-log plot of normalized rate [ ])()(/ wfi pmpmq ! versus time. In the very early times the data exhibits a negative " slope indicating either a bilinear flow or apparent skin effect, while in the later times the data exhibits negative one-half slope indicating matrix linear flow.

Fig. 4: Normalized rate vs time Fig. 5: Normalized pseudo-pressure vs square root of time

Fig. 5 is the normalized pseudo-pressure [ ] qpmpm wfi /)()( ! versus t . In this figure, we observed a deviation of early time

data from straight line and having an intercept on the axis of normalized pseudo-pressure. This behaviour indicates to have a non-linear flow such as skin effect, while in later times; the data indicate a straight line, which is a typical characteristic of linear flow. In very late times, the data begin to derivate from the straight line at about 225 days indicating the boundary effect. Since this time period is relatively short, the boundary effect cannot be identified from the log-log plot. Linear Flow Parameters Analysis The half-width of the drainage area (rectangular geometry) can be calculated from in following simple calculation (Fig. 6). We have assumed bi-wing hydraulic fracture geometry and slab matrix bulk. The half-width is equivalent to SRV divided by 2xeh.

ft7528340002

101692

6!

""

"==

hxSRVye

e

It is noted that ye can also be estimated from OGIP if SRV is not known. Average fracture spacing L was calculated from well length 4,000 ft divided by the number of effective fractures which is 20.

ft200204000

==L

Well-face cross-sectional area to flow is: 26ft10264.2283400022 !=!!=""= hxA ecw

Total matrix-fracture surface area in a double porosity slab model was calculated from the below equation: 26ft10698.12022 !=!!!= hyA ecm

SPE 153072 5

Fig. 6: Reservoir geometry for dual porosity slab model

Based on the flow regimes identification two possibilities were analysed below. Bilinear Flow Followed by Matrix Linear Flow We have plotted [ ] qpmpm wfi /)()( ! vs 25.0t and [ ] qpmpm wfi /)()( ! vs t in Figs. 7a and 7b respectively to obtain m2 =

283333 and m3 = 111250.

(a) [ ] qpmpm wfi /)()( ! vs t (b) [ ] qpmpm wfi /)()( ! vs 25.0t

Fig.7: Specialized plot analysis Then mcm kA was determined based on the following calculation:

( )0.524

3mdft1049.2

1112501

03334.00.000060576.0745126211262

!"=!""

"=!=

+mC

TkAmft

mcm#µ

Since the fracture porosity can be negligible compared to the matrix porosity, ( )mtC!µ was assumed to be equal to ( ) mftC +!µ . Due to high reservoir average pressure in early production, the gas desorption is negligible. And also the rock compressibility is ignored. Therefore, the total compressibility Ct was assumed to be equal to Cg. Matrix permeability was evaluated from the following calculation:

md1015.210!1.69810!2.49 4

2

6

42

!"=##$

%&&'

(=

))*

+

,,-

.=

cm

mcmm A

kAk

Fracture permeability Kf was estimated from the following:

( )[ ]

[ ]0.524

25.044

225.0

mdft1048.6

2833331

03334.00.000060576.01015.2100.3

7454070

14070

!"=

"""""""

"=

!=

##

+mCk

T

kA

mftm

fcw

$µ%

6 SPE 153072

Where matrix block shape factor, for slab model is 242 ft100.312 !!"==L

#

md102.810!2.26410!6.48 4

2

6

42

!"=##$

%&&'

(=

))

*

+

,,

-

.=

cw

fcwf A

kAk

This fracture permeability is low because the well-face cross-sectional area has been used. Matrix Linear Flow with Apparent Skin

Bello’s Approach

In this approach, two parameters of m3=111250 and intercept b=2.1#105 were obtained from Fig.7a, and then substituted into the equation (4). The initial relation of production rate versus time accounting for apparent skin is given:

5

5

101.211125045.01

101.2111250)()(

!

!+

!+=

"

tt

qpmpm wfi (7)

We used above equation to match the production data and fortunately obtained acceptable results by initial guess (Figs. 8a and 8b). In case of not good matching, we need to assume m3 and b as matching parameters to reach reasonable results. Based on m3 = 111250, we estimated the matrix permeability as 2.15#10-4 md.

(a) Log-Log plot (b) Square root of time plot

Fig. 8: Fitting the results with Equation 7.

Nobakht’s Approach From the plot of [ ] gwfi qpmpm /)()( ! vs t , (Fig. 9), a straight line has been drawn through the data points and the intercept

5105.1 !=b was obtained.

Fig. 9: Specialized plot to obtain intercept b for Nobakht’s approach

SPE 153072 7

Then calculating modified normalized pressure as follow:

bq

pmpmq

pmpm wfi

m

wfi !!

="#

$%&

' ! )()()()( (8)

Plotting [ ]{ }mwfi qpmpm )()( ! versus time on log-log plot, as shown in Fig. 10, indicated a one-half slope even in the early

time. Plotting [ ]{ }mwfi qpmpm )()( ! vs t , as shown in Fig.11, the slope is m3=93750.

( )41095.2

937501

03334.00.000060576.0745126211262

!="!!

!#"=

+mC

TkAmft

mcm$µ

So the estimated matrix permeability was calculated below.

md1002.310!1.69810!2.95 4

2

6

42

!"=##$

%&&'

(=

))*

+

,,-

.=

cm

mcmm A

kAk

In Fig. 11, we also found out the time at the end of straight line has been changed, which is at 132 days.

Fig. 10: Modified normalized rate vs time on log-log plot Fig. 11: Modified [ ] qpmpm wfi /)()( ! vs t

Estimation of OGIP The approach for estimating OGIP has been previously presented by Wattenbarger et al (1998). This method is based on the assumption that boundary dominated flow begins when the pressure at the centre of the matrix block starts to decline. The formula is given in Equation (9).

( ) 3

6.200OGIP

mt

BCTS esl

igt

gi !=µ

(9)

In our case we have

30032.000006.003334.07456.200OGIP

mtesl!

""

"=

For Bello’s approach: m3=111250, tesl=225 days, then OGIP= 3.15 Bscf

For Nobakht’s approach: m3=93750, tesl=132 days, then OGIP= 2.87 Bscf When OGIP is known, the SRV can be obtained using the following equation:

gi

gi

SB

!

"=OGIP

SRV (10)

Then Bello’s approach: SRV=175 MMft3; Nobakht’s approach: SRV=159 MMft3. Comparing the estimated SRV with previous given value of 169 MMft3, Bello’s approach overestimates 6 MMft3 in SRV, while Nobakht’s approach underestimates 10 MMft3. However, both methods give a reasonable value.

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Numerical Simulation and Discussion A numerical simulation has been designed to validate the results from type curve matching. We have developed a single porosity single phase model. In this model, 20 transverse fractures have been defined as very high permeable path along the horizontal wellbore evenly (Fig. 12). The well is placed in the centre of the reservoir. The reservoir area is assumed to be equal to the area of SRV. Other parameters for simulation are shown in Table 1.

Fig. 12: Simulation model for well A, 20 transverse fractures

Fig. 13: History matching of well A

Fig. 13 shows the good matching of simulated data with actual production history except some points in the initial data which is affected by the fracture system. The matching matrix permeability was 1.25 #10-4 md. Comparing this matching permeability from simulation with the above results from type curve analysis indicates the permeability from type curve is higher especially 172% of Bello’s and 242% of Nobakht’s (Table 2). Ibrahim & Wattenbarger (2006) stated that the effect of

drawdown on transient linear flow could lead to overestimation of mcm kA and OGIP, and developed the following empirical equation to estimate the correction factor.

20857.00852.01 DDcp DDf !!= (11) Where DD is the drawdown parameter defined by the following equation:

)(

)()(

i

wfiD pm

pmpmD

!= (12)

We used an average bottom-hole pressure of 1500 psi and obtained DD=0.941, then the correction factor of 0.884 is determined as following:

844.0941.0941.00857.0941.00852.01 =!!"!"=cpf

The correction factor was applied to modify matrix permeability, OGIP and SRV. The results are shown in Table 2. The modified matrix permeability is still higher than the permeability from simulation. We believe this difference is related to the assumption of dual-porosity flow behaviour in type curve analysis while we have used a single porosity model in reservoir simulation. The reason a single porosity model was used is that we could not get good results by using matrix shape factor " of 3.0#10-4 ft-2 in double porosity simulation. Also in Bello’s approach, only the effect of convergence skin was considered, and the pressure drop in horizontal wellbore was not included. In overall, the permeability from simulation was in the range of acceptable agreement with type curve analysis. Since the effect of skin exhibits a curve deviated from the straight line with having an intercept (Fig. 9), Bello’s approach is closer to the numerical simulation result (Table 2).

SPE 153072 9

Table 2: Parameters estimation and modification

Approach OGIP, Bscf SRV, MMft3 Matrix permeability, 10-4md

Original Modified Original Modified Original Modified Numerical simulation

Bello’s 3.15 2.66 175 148 2.15 1.81 1.25

Nobakht’s 2.87 2.42 159 134 3.02 2.55 It is needed to mention that the modified SRV are lower than the SRV reported from hydraulic fracture modelling, especially 86% for Bello’s case and 79% for Nobakht’s case (Table 2). However, these results are also in the acceptable range of estimation. The modified OGIP is either 2.66 or 2.42 Bscf, which represents the total free gas in SRV region because the adsorbed gas has not been included in the calculation. Production Forecasting Dual porosity linear flow model can be used to predict the shale gas production. However, many parameters are required and this would lead to uncertainties of the results. For boundary dominated flow in this case, material balance and pseudo-steady flow equation were combined and used for production forecasting. The material balance for volumetric gas reservoirs accounting for desorption (King, 1990) is given:

!!"

#$$%

&'=GG

zp

z

p p

i

i 1** (13)

pzRTCzz

E

!+

=1

* (14)

Where, CE is equilibrium isotherm. The rock and water compressibility is assumed to be negligible. Pseudo-steady flow equation for gas reservoir is given below.

[ ])()( wfcpg pmpmJq != (15)

Where, Jcp is the production index for the constant bottom-hole pressure. For well A, the latest production data were used to calculate an average Jcp. This value depends on average pressure or OGIP. Then two results can be obtained for two different OGIP values of Bello’s and Nobakht’s cases. Fig.14 is the production forecasting of 15 years for well A at constant bottom-hole pressure 1500 psi. Due to the larger OGIP value in Bello’s approach, we have obtained a little higher production rate than Nobakht’s case. The gas rate decline with time and the decline rate gradually close to a constant value after 15 years. It is noted that the production forecasting in our calculation is underestimated because the contribution of un-stimulated zone to production was not considered.

Fig. 14: 15 years production forecasting, no desorption Fig. 15: Adsorption isotherms Barnett Shale (Bartenhagen, 2009); Woodford Shale (Jack Breig, 2010) In order to investigate the effect of desorption, two adsorption isotherms (Fig. 15) were used for production forecasting (adsorption isotherm for Eagle Ford was not available), Isotherm 1 has a low Langmuir pressure which is around 300 psi, while isotherm 2 has the value of 1500 psi. Fig. 16 is the production forecasting of 15 years for different adsorption isotherms at constant bottom-hole pressure of 500 psi. It is illustrated that the higher Langmuir pressure releases more adsorbed gas and results in higher gas production. However, the effect of desorption using isotherm 1 is not significant due to the relative high average reservoir pressure not allowing gas desorption in this case. However, for long-term production forecasting, it is always needed to account for desorption. As seen in Table 3, gas desorption can make the EUR to be up to 27% higher.

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Fig.16: Production forecasting for different adsorption isotherms

Table 3: EUR comparison

!EUR at 30 years, Bscf

Bello Nobakht

No desorption 2.38 2.22

Isotherm 1 2.58 2.42

Isotherm 2 3.00 2.82

Conclusions • Three flow regimes of bilinear flow; matrix linear flow; and boundary dominated flow are found in Eagle Ford shale

production data. • Fracture permeability was calculated to be around 820 nd based on bilinear flow analysis and the assumption of slab

model. • The effect of apparent skin has been considered based on two different approaches of Bello and Nobakht methods. • OGIP was estimated by boundary dominated flow to be 2.42 or 2.66, and SRV was estimated to be 134 or 148 MMft3

which is close to the reported value of SRV in hydraulic fracture modelling. • Matrix permeability was estimated to be 181 or 255 nd by matrix linear flow analysis. The results are validated by

numerical simulation. The permeability from simulation was in the range of acceptable agreement with type curve analysis.

• Production forecasting has been carried out with different adsorption isotherms. The results showed that the effect of desorption depends on both reservoir pressure and adsorption isotherm. In early times when the reservoir pressure is high the gas desorption is usually not important; however, for long-term production forecasting, it is needed to account for desorption based on a laboratory measured isotherm.

Nomenclature Acw = well face cross-sectional area to flow, ft2 Acm = total matrix surface area draining into fracture system, ft2 Bg = formation volume factor at initial reservoir pressure, rcf/scf b = intercept of field data on the [m(pi) – m(pwf)]/qg vs. t 0.5 plot, psi2/cp/Mscf/day Cf = hydraulic fracture conductivity, md-ft

Ct = total compressibility at initial reservoir pressure, psi-1

CE=equilibrium isotherm, 1b-moles/ft3 DD=drawdown parameter, fraction fCP = drawdown correction factor, dimensionless G = gas in place, scf Gp = cumulative gas production, scf h = reservoir thickness, ft Jcp= production index for the constant bottomhole pressure, Mscf/day/psi2/cp kf = fracture permeability, md km = matrix permeability, md L = fracture spacing for slab model, ft m1= slope of the line matching the early linear flow data and passing through the origin on the square root of time plot m2= slope of the line matching the bilinear flow data and passing through the origin on the quarter root of time plot

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m3= slope of the line matching the matrix linear flow data and passing through the origin on the square root of time plot m(p) = pseudopressure (gas), psi2/cp pi = initial reservoir pressure, psi pwf = wellbore flowing pressure, psi p = average reservoir pressure, psi

qg = gas rate, Mscf/day R = gas constant, J!K$1!mol$1 Sgi = initial gas saturation, fraction T = absolute temperature, oR t = time, days tesl = time to end of straight line on the square root of time plot, days xe = drainage area length (rectangular geometry), ft ye = drainage area half-width (rectangular geometry), equivalent to fracture half-length, ft z = compressibility factor, fraction z*=modified compressibility factor account for gas desorption, fraction Greek symbols ! = dampening factor, dimensionless % = dimensionless interporosity parameter µ = viscosity, cp & = dimensionless storativity ratio " = porosity '=shape factor, ft-2

Subscript i = initial f = fracture m = matrix f+m = total system (fracture + matrix) References Agarwal, R.G., Gardner, D.C., Kleinsteiber, S.W., et al. 1999. Analyzing Well Production Data Using Combined-Type-Curve and Decline-

Curve Analysis Concepts. SPE Reservoir Res Eval. & Eng 2 !5"# 478-486. SPE-57916-PA. http://dx.doi.org/10.2118/57916-PA. Al-Ahmadi, H.A., Almarzooq, A.M. and Wattenbarger, R.A. 2010. Application of Linear Flow Analysis to Shale Gas Wells-Field Cases.

Paper SPE 130370 presented at the SPE Unconventional Gas Conference held in Pittsburgh, Pennsylvania, USA, 23–25 February. http://dx.doi.org/10.2118/130370-MS.

Anderson, D.M., Nobakht.M., Moghadam, S., et al. 2010. Analysis of Production Data from Fractured Shale Gas Wells. Paper SPE 131787 presented at the SPE Unconventional Gas Conference held in Pittsburgh, Pennsylvania, USA, 23-25 February. http://dx.doi.org/10.2118/131787-MS.

Arps, J.J. 1945. Analysis of Decline Curves. Trans., AIME, 160: 228-247. Baihly, J., Altman, R., Malpani, R., et al. 2010. Shale Gas Production Decline Trend Comparison over Time and Basins. Paper SPE 135555

was presented at the SPE Annual Technical Conference and Exhibition held in Florence, Italy, 19-22 September. http://dx.doi.org/10.2118/135555-MS.

Bartenhagen, K. 2009. Evaluation of Shale Gas Reservoirs Focus on Haynesville, http://etgpa.org/wp-content/uploads/2010/07/20090310-%E2%80%93-Evalutation-of-Shale-Gas-Reservoirs-with-Focus-on-the-Haynesville-Shale-%E2%80%93-Schlumberger.pdf (downloaded 12 December 2010).

Bazan, L.W., Larkin, S.D., Lattibeaudiere, M.G., et al. 2010. Improving Production in the Eagle Ford Shale with Fracture Modeling, Increased Conductivity and Optimized Stage and Cluster Spacing Along the Horizontal Wellbore. Paper SPE138425 presented at the SPE Tight Gas Completions Conference held in San Antonio, Texas, USA, 2–3 November. http://dx.doi.org/10.2118/138425-MS

Bello, R.O. and Wattenbarger, R.A. 2008. Rate Transient Analysis in Naturally Fractured Shale Gas Reservoirs. Paper SPE 114591 presented at the CIPC/SPE Gas Technology Symposium 2008 Joint Conference, Calgary, Alberta, Canada, 16 -19 June. http://dx.doi.org/10.2118/114591-MS

Bello, R.O. and Wattenbarger, R.A. 2009. Modeling and Analysis of Shale Gas Production with a Skin Effect. Paper CIPC 2009-082 presented at the Canadian International Petroleum Conference, Calgary, Alberta, Canada, 16 -18 June. http://dx.doi.org/10.2118/2009-082.

Bello, R.O. 2009. Rate Transient Analysis in Shale Gas Reservoirs with Transient Linear Behaviour. PhD Dissertation, Texas A &M U., College Station, Texas (May 2009).

Bello, R.O. and Wattenbarger, R.A. 2010. Multi-stage Hydraulically Fractured Shale Gas Rate Transient Analysis. Paper SPE 126754 presented at the SPE North Africa Technical Conference and Exhibition held in Cairo, Egypt, 14 - 17 February. http://dx.doi.org/10.2118/126754-MS.

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