spe 123298 (johnson) simple methodology direct est gas in place y reserves (wpres)

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SPE 123298

A Simple Methodology for Direct Estimation of Gas-in-place and ReservesUsing Rate-Time DataN.L. J ohnson, S.M. Currie, D. Ilk, and T.A. Blasingame, Texas A&M University

Copyright 2009, Society of Petroleum Engineers

This paper was prepared for presentation at the 2009 SPE Rocky Mountain Petroleum Technology Conference held in Denver, Colorado, USA, 14–16 April 2009.

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 beenreviewed 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, itsofficers, 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 toreproduce 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

Estimation of contacted gas-in-place/reserves in unconventional (low/ultra-low permeability) gas reservoirs is a problematic

issue, and the uncertainty associated with the estimate is relatively higher. In this work we provide a robust methodology for estimating gas reserves in tight gas/shale gas systems based (primarily) on the use of an integrated approach which makes use

of the following models:

1. Semi-analytical formulation — "Quadratic" rate-cumulative relation type curve (Blasingame and Rushing [2005]).

2. Empirical formulation — "power-law exponential" rate decline model (Ilk et al [2008a] and [2008b]).

A dimensionless quadratic rate-cumulative type curve is derived using the rate-cumulative relation proposed by Blasingame

and Rushing (2005) and is given by:

2

21

pD pD DGGq

α α +−= (where q

D=q

g /q

gi, G

pD=G

p/G, and α =G/( q

gi/ D

i) by definition)

A "reverse solution" for the α -parameter enables the analyst to establish the existence of boundary-dominated flow —

directly from the data. Our experience using synthetic and field data suggests that, for the Blasingame and Rushing model,the α -parameter is equal to two (2) for full boundary-dominated flow.

We have also written the "power-law exponential rate decline relation" in dimensionless rate-time form and we employ the

type-curve procedures for the analysis of a given set of rate-time data. The dimensionless power-law exponential rate declinerelation is given as:

]~

exp[ n

Dd Dd Dd t t Dq −−= ∞

We have validated our analysis procedure for this model using a two numerical gas simulation cases and we have applied this procedure to several tight gas and shale gas cases. Our results show that when gas production data are analyzed using the

integrated approach described in this work then the uncertainty in reserves estimates is reduced. Specifically, expressing the

rate-cumulative production data functions in dimensionless forms provides a direct diagnostic of the boundary-dominated

flow regime. Power law exponential rate decline type curves help the analyst to identify the features (character) in the ratedata.



2 N.L. J ohnson, S.M. Currie, D. Ilk, and T.A. Blasingame SPE 123298

throughout the production life of unconventional (low/ultra-low permeability) gas reservoirs. Rushing et al (Rushing et al

[2007]) presents a study which was designed to assess the validity of estimating reserves using the hyperbolic rate decline

relation. Their approach showed that the errors in reserve estimates based on the hyperbolic rate decline relation were

substantially higher (over 100 percent error) when the hyperbolic rate decline relation is applied during transient/transitionflow regimes.

The works by Fetkovich (Fetkovich [1980]) and Fetkovich et al (Fetkovich et al [1987]) discuss the use of the Arps'hyperbolic relations along with a semi-analytical result for gas flow behavior. The hyperbolic relations were utilized as rate-

time decline type curves. The type curves show a behavior of actual gas rate changing from one "hyperbolic" model to

another with time (i.e., the value for the b-parameter is not constant). This issue is attributed to pressure-dependent gas

properties (i.e., gas viscosity, z -factor, compressibility as functions of reservoir pressure). Carter (Carter [1981]) presented anew set of decline type curves for gas reservoir systems to address the changes in fluid properties with reservoir pressure.

But, this method (also the Fetkovich method) suffers from the requirement of a constant flowing bottomhole pressure.

Additionally, the analysis of rate and rate cumulative production data are not addressed in these methods.Knowles (Knowles [1999]) presented an approach for linearizing the gas flow equation — the nonlinear term, μ g c g , islinearized by using a straight line linearization scheme. The approach yields a p/z -squared form of the stabilized gas flow

equation. When this is coupled with the gas material balance equation, a semi-analytic quadratic gas flow equation is

obtained. Ansah et al (Ansah et al [2000]) generalized the concept (linearization of the gas flow equation) proposed byKnowles and developed semi-analytical, direct solutions for determining average reservoir pressure, rate, and cumulative

production for gas wells produced at a constant bottomhole pressure during reservoir depletion. Blasingame and Rushing

(Blasingame and Rushing [2005]) extended the applicability of Ansah et al relations by developing a new technique and

plotting functions for direct estimation of contacted gas-in-place using only production data — the "quadratic rate-

cumulative" relation was the key relation in their work. It should be noted that these relations are applicable for the boundarydominated flow regime. The quadratic rate-cumulative relation is given as:

2

2

1 p

i pi gi g G

G

DG Dqq +−= .............................................................................................................................................. (1)

The "power-law exponential" rate decline relation has recently been introduced in a series of publications by Ilk et al [2008aand 2008b]. For reference the power-law exponential rate decline relation is given as:

]ˆexp[ˆ ni gi g t Dt Dqq −−= ∞ ............................................................................................................................................... (2)

The definitions of the so called "loss-ratio" and the "loss-ratio derivative" as presented formerly by Johnson and Bollens[1927] and Arps [1945] describe the basis of the "power-law exponential" rate equation. The "power-law exponential" ratedecline relation is obtained by assuming that the D-parameter in the definition of the "loss-ratio" exhibits power-law

behavior. Ilk et al apply the new model to various field cases (Ilk et al [2008b] and Mattar et al [2008]) as well as to

simulated data (see Mattar et al [2008]) and verify that the power-law exponential rate decline model is very flexible enoughto match transient, transition, and boundary-dominated flow data and give realistic reserve estimates.

In this work our objective is to develop a simple but robust integrated methodology to estimate the gas reserves in tight gas

and shale gas reservoir systems using only rate-time data. The integrated methodology is based on Eqs. 1 and 2 — in

particular, Eqs. 1 and 2 are modified to yield relations in dimensionless forms. The resulting relations are evaluated

independently and consistent estimates of gas reserves are obtained. From a different point of view, the integrated approach proposed in this work reduces the uncertainty in reserve estimates.

Development of the Integrated Approach

Rate-Cumulative Relation: Our proposed integrated approach is twofold: first we make use of Eq. 1 and modify Eq. 1 to yield

a dimensionless relation which should provide a diagnostic value. Recalling the semi-analytical relation for rate-cumulative

production which is given by Eq 1:



SPE 123298 A Simple Methodology for Direct Estimation of Gas-in-place and Reserves Using Rate-Time Data 3

Multiplying through by G/G yields the desired ratio (G p /G):

2

2

11 ⎥⎥

⎦

⎤

⎢⎢⎣

⎡

+⎥⎦

⎤

⎢⎣

⎡

−= G

GG

q

D

G

GG

q

D

q

q p

gii p

gii

gi g ............................................................................................................................ (5)

Collecting terms and rearranging, we have:

2

)/(2

1

)/(1

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡+⎥

⎦

⎤⎢⎣

⎡−=

G

G

Dq

G

G

G

Dq

G

q

q p

i gi

p

i gi gi

g ............................................................................................................... (6)

Defining the α -parameter, we obtain:

)/( i gi Dq

G=α ...................................................................................................................................................................... (7)

Substitution of the α -parameter yields the final form:

2

2

11

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡+⎥

⎦

⎤⎢⎣

⎡−=

G

G

G

G

q

q p p

gi

g α α .......................................................................................................................................... (8)

Eq. 8 can also be written in dimensionless form as:

2

21 pD pD D GGq

α α +−= ................................................................................................................................................. (9)

Where q D=q g /q gi and G pD=G p/G. Solving for the α -parameter, we have:

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡−⎥

⎦

⎤⎢⎣

⎡

⎥⎥⎦

⎤

⎢⎢⎣

⎡−

=

2

2

1

1

G

G

G

G

q

q

p p

gi

g

α ................................................................................................................................................. (10)

At long times where q g → 0 (hence, G p → G); Eq. 3 becomes:

2)(2

1)()0( GG

G

DGG Dqq p

i pi gi g →+→−=→ ........................................................................................................ (11)

Reducing terms, we have:

2

2

10 G

G

DG Dq i

i gi +−= ................................................................................................................................................. (12)

G DG Dq ii gi2

1−= ........................................................................................................................................................... (13)




22

11

G DG Dq i

i gi =⎥⎦

⎤⎢⎣

⎡−= ................................................................................................................................................. (14)

Where lastly, we obtain:

)and0(as 2)/(

GGq Dq

G p g

i gi→→==α ............................................................................................................... (15)

Eq. 15 indicates that for complete boundary-dominated flow regime, α parameter is equal to two. We use the plotting

function as suggested by Blasingame and Rushing [2005] to initiate our analysis procedure. This plotting function is given by:

pi

i p

g giG

G

D D

G

qq

2

1−=

−................................................................................................................................................ (16)

Eq. 16 is in the form of a straight line equation with the decline parameter, Di as the intercept and slope equal to Di/2G if (q gi-

q g )/G p is plotted against G p. Extrapolation to (q gi-q g )/G p=0 gives G p,max=2G. Our procedure for the rate-cumulative relationincludes four plotting functions which are defined as:

Plotting Function 1: PF 1

(q gi-q g )/G p vs G p (data and model Eq. 16)


α vs G p/G (α is computed by Eq. 10)


q g /q gi vs G p/G (data and model Eq. 8)


q g vs G p (data and model Eq. 3)

We use the four plotting functions jointly to establish the best estimate for the G (contacted gas-in-place) value. In simple

terms we begin by making use of Eq. 16 to estimate a value for G (contacted gas-in-place) and using this estimate, α is

computed by Eq. 10. If α is equal to two, boundary-dominated flow is then established. We calibrate the values of q gi, and Di, to achieve the best match and the plotting functions provide additional resolution in the process. On the other hand,

computation of the α -parameter provides a diagnostic insight to the data as α =2, boundary-dominated flow regime is

established. In other words, we use a spreadsheet format with a graphical display of the model and the data — in thespreadsheet approach all analyses are integrated (i.e., the all four plotting functions) and each function is linked by a common

set of model parameters.

Dimensionless Power-Law Exponential Relation: Our next step is to convert the power-law exponential relation into a

dimensionless form and develop type curves. The dimensionless form of the power-law exponential relation is given by:

]

~

exp[

n

Dd Dd Dd t t Dq−−=

∞ ............................................................................................................................................ (17)

It is noted that all of the parameters in this equation are dimensionless. The dimensionless rate and time are defined as:

gi g Dd qqq ˆ/= ................................................................................................................................................................... (18)

nni Dd t Dt )ˆ( /1= ................................................................................................................................................................ (19)




In Eq. 21 the ∞ D~

parameter is set to zero. Fig. 1 illustrates the type curve for several values of the exponent, n, as the family

parameter. We note that Fig. 1 provides significant characteristic value as it helps the analyst to establish the value of the

exponent, n, without computing D- and b-parameters by numerically differentiating the rate-time data. Once the value of n isestablished, the second set of type curves, which are developed to incorporate the effect of ∞ D~ parameter, can be used. The

second set of type curves are designed to incorporate the effect of boundary-dominated flow and hence a lower limit for the

reserves estimate can be achieved. In Figs. 2-11, we present the second set of type curves for a specific value of the

exponent, n with ∞ D~

as the family parameter. Once the sought parameters — giq̂ , i D̂ , n and D∞

are obtained from match

points, Eq. 2 can be used and reserves extrapolation can be performed. It should also be noted that the values from match

points can also be fine tuned to yield a better match of the power-law exponential rate decline model with the rate data. We

emphasize that the value of the type curves developed in this work lie in understanding the character of the rate data insteadof blindly performing an equation fitting process. We observe that smaller values of n (i.e., n<0.2) indicate longer

transitional flow regimes whereas, higher values of n (i.e., n>0.7) indicate flow regimes similar to exponential decline.

Validation of New Analysis Methodology

Synthetic Example 1: In this section we validate our proposed methodology using two synthetic examples. The first exampleincludes production data of a horizontal well having four transverse fractures generated by a numerical simulator. The

detailed information on the simulation and the properties of this well and reservoir system can be found in the work by

Mattar et al [2008]. We also note that the production data from this well was previously analyzed using the power-law

exponential rate decline model. Our objective is to verify the previous result (i.e., the reserves estimate) using the type curveapproach proposed in this work.

Fig. 12 presents the rate and cumulative production data of this well for almost two years. Our first task is to employ the typecurve approach and find the value of the exponent, n. When the data is projected on to the type curve, it is seen that there isan outstanding match of the data with the model where n=0.15 (see Fig. 13). We proceed and use the type curve for n=0.15

and establish the lower limit for the gas reserves of this well. In Fig. 14 we present the type curve match; the best match is

obtained on the trend where ∞ D~

=10-5. For this case we establish the lower and upper bound of the gas reserves for this well

to be 2.5 BSCF and 3.1 BSCF, respectively.

Our next step is to use the "rate-cumulative" relations to estimate the contacted gas-in-place of this well. Before describingthe procedure, we have to state that in this work, contacted gas-in-place estimate, G, from "rate-cumulative" relation is equal

to the reserves estimate, G p,max from the power-law exponential rate decline relation by definition. Using the values from the PF 1 ((q gi-q g )/G p versus G p) as the starting values, we match the multiple model functions with the data functions. Fig. 15

presents the (q gi-q g )/G p versus G p plot, and the straight line is the indicative of the boundary-dominated flow regime. Fig. 16 ( PF 2) presents the computed α parameter versus G p/G plot and α =2 indicates the complete boundary-dominated flow regime.

Figs. 17 and 18 (( PF 3) and ( PF 4)) present the matches of the quadratic models with the data. It is worth to mention that all

analyses are linked and Figs 15-18 illustrate the best matches obtained in this example. The contacted gas-in-place is

estimated to be 2.55 BSCF using the linked analysis procedure. The analysis results for this case are summarized in Table 1

below. The values of the parameters in the power-law exponential rate decline model can be adjusted to yield 2.55 BSCF aswell.

Table 1 — Analysis results for the numerical simulation case 1 (horizontal well with four transverse fractures).

"Quadratic Rate-Cumulative" Analysis:Initial gas production rate, q gi = 6500 MSCF/D

Decline constant, Di = 5.1x10-3 1/D

Contacted gas-in-place, G = 2.55 BSCF

" Power-Law Exponential Rate Decline Model ":

Initial gas production rate q̂ = 6x105 MSCF/D




This case was also evaluated using the power-law exponential rate decline model in the work by Ilk et al [2008b]. Fig. 19

presents the production data obtained by the simulator. Fig 20 presents the type curve match to find the value for the time

exponent, n. Once the value of n is established, we obtain the match in Fig. 21 which is the type curve with n=0.1 and the

parameter is found to be ∞ D~ =10-8. In this example the effects of the boundaries are obvious (i.e., change of the rate data

trend at late times). The lower limit for the reserves of this well is found to be 2.5 BSCF.

Our next step is to use the "rate-cumulative" relations to estimate the contacted gas-in-place of this well. Using the values

from the PF 1 ((q gi-q g )/G p versus G p) as the starting values, we match the multiple model functions with the data functions.

Fig. 22 presents the (q gi-q g )/G p versus G p plot, and the apparent straight line strongly suggests the boundary-dominated flow

regime. Fig. 23 ( PF 2) presents the computed α parameter versus G p/G plot and α =2 trend indicates the complete boundary-

dominated flow regime. Figs. 24 and 25 (( PF 3) and ( PF 4)) present the matches of the quadratic models with the data. We

note that in all of the plots outstanding matches are obtained with the models and data (where the boundary dominated flow

regime is established). The contacted gas-in-place is estimated to be 2.65 BSCF using the linked analysis procedure. Theanalysis results for this case are summarized in Table 2 below. As mentioned before the values of the parameters in the power-law exponential rate decline model can be adjusted to yield to match 2.65 BSCF as well.

Table 2 — Analysis results for the numerical simulation case 2 (East Tx gas well (Pratikno et al [2003])).





Initial gas production rate, iq̂ = 2.57x105 MSCF/D

Decline constant, i D̂ = 2.86 1/D

Decline constant, D∞ = 2.3x10-4 1/D

Time exponent, n = 0.10

Maximum gas production, G p,max = 2.5 BSCF ( D∞≠0) Maximum gas production, G p,max = 13.10 BSCF ( D∞=0)

Application to Field Data

Field Example 1: In this section we analyze gas production data obtained from tight gas and shale gas reservoirs using theintegrated approach described in this work. Our first example includes production data from a hydraulically fractured gas

well in a tight gas reservoir. Fig. 26 presents the rate and cumulative production data of this well. We note that this well has

been analyzed before in the works by Ilk et al [2008b] and Ilk et al [2008c]. We also note that daily production data areavailable for this well — and the rate data seem affected by liquid loading.

In Fig 27, we match the rate data with the n=0.2 trend and obtain a very good match of the data with the type curve. It is

noted that all of the rate data are matched with the power-law exponential model. Fig 28 presents the type curve match when

∞ D~ ≠0. It is noted ∞ D

~=10-3.75 gives the lower bound for the reserves estimate (2.01 BSCF) for this well.

We use the "rate-cumulative" relations on the other hand, to estimate the contacted gas-in-place for this well. Figs 29-32exhibit outstanding matches of the data with the models (during the boundary-dominated flow regime). The contacted gas-

in-place estimate of 1.98 BSCF verifies the consistency of our approach. Table 3 summarizes our results for this case.

Table 3 — Analysis results for field example 1 (tight gas well).

"Quadratic Rate-Cumulative" Analysis:

Initial gas production rate, q gi = 2500 MSCF/D

Decline constant, Di = 2.52x10-3

1/D




Field Example 2: Our second example also includes production data from a hydraulically fractured gas well in a tight gas

reservoir. Fig. 33 presents the rate and cumulative production data of this well. The production data of this well has also been analyzed before in the works by Ilk et al [2008b] and Ilk et al [2008c]. We observe that daily production data are of

qood quality —except for the erratic rate performance between 260 and 1100 days.

In Fig 34, we match the rate data with the n=0.2 trend and obtain an outstanding match of the data with the type curve. It is

observed that all of the rate data are matched with the power-law exponential model. When ∞ D~

≠0, we obtain the match as

seen in Fig 35. Interestingly, we obtain the same trend — ∞ D~

=10-3.75 — for the lower bound for the reserves estimate

(G p,max=2.78 BSCF) for this well. This should not be surprising as both of the wells are in the same reservoir anddimensionless relations provide a unique character.

The "rate-cumulative" relations are used in an integrated fashion, to estimate the contacted gas-in-place for this well. Figs

36-39 exhibit outstanding matches of the data with the models (during the boundary-dominated flow regime). The contacted

gas-in-place estimate of 2.78 BSCF verifies that our analysis is consistent. Table 4 summarizes our results for this example.

Table 4 — Analysis results for field example 2 (tight gas well).

"Quadratic Rate-Cumulative" Analysis:

Initial gas production rate, q gi = 1400 MSCF/DDecline constant, Di = 1.008x10-3 1/D





Decline constant, D∞ = 6x10-5 1/D


Maximum gas production, G p,max = 2.78 BSCF ( D∞≠0)

Maximum gas production, G p,max = 7.38 BSCF ( D∞=0)

Field Example 3: In this example we analyze the publicly available monthly production data acquired from a gas well located

in the Barnett shale. Previously the production data of this well has been analyzed using the power-law exponential rate

decline model by Mattar et al [2008]. Almost 3 years of production data are available (see Fig. 40). We suspect that

fluctuations in the rate profile are caused by liquid loading. Visual inspection of the rate data suggests that boundary-dominated flow regime has been established.

We obtain a good match of the data with the n=0.3 trend in Fig. 41. Fig 42 presents the type curve match in order to

establish the lower bound for the reserves. However, in this case the upper and lower bound of the reserves are very close toeach other. This can also be confirmed by the type curve match in Fig. 42.

Figs 43-46 present the matches obtained using the "rate-cumulative" relations and we observe very good matches of the datawith the models. This procedure yields the contacted gas-in-place estimate as 0.33 BSCF which is the same as the value

obtained from power-law exponential model. Table 5 summarizes our results for this case.

Table 5 — Analysis results for field example 3 (shale gas well).








Field Example 4: Our last example is also an analysis of a publicly available monthly production data acquired from a gas

well located in the Barnett shale. Same production data of this well has also been analyzed using the power-law exponentialrate decline model by Mattar et al [2008]. Approximately 5.5 years of production data are available (see Fig. 47). Rate data

look smooth with minor fluctuations.

The data is matched with the n=0.2 trend in Fig. 48. In Fig 49 ∞ D~

=10-3.5

gives the lowest value of the reserves for this well.

Also, in this case the upper and lower bound of the reserves are close to each other.

Figs 50-53 present the matches obtained using the "rate-cumulative" relations and we observe very good matches of the data

with the models. This procedure yields the contacted gas-in-place estimate as 0.33 BSCF which is essentially the same as the

value obtained from power-law exponential model. Table 6 summarizes our results for this case.

Table 6 — Analysis results for field example 4 (shale gas well).







Decline constant, D∞ = 1.22x10-3 1/D


Maximum gas production, G p,max = 0.81 BSCF ( D∞≠0) Maximum gas production, G p,max = 1.41 BSCF ( D∞=0)

Summary and Conclusions

Summary: In this work we propose a new integrated approach for the direct estimation of contacted gas-in-place and reservesusing only rate-time data. We utilize two methods that have been previously introduced to literature — a semi-analytical

"quadratic rate-cumulative" formulation and the empirical "power-law exponential" rate decline relation. We modify the

"quadratic rate-cumulative" formulation based on the work by Blasingame and Rushing [2005] and develop four plottingfunctions for the analysis procedure. The basis of this method is the integration of the four plotting functions derived from a

base model (i.e., quadratic rate-cumulative formulation). This procedure yields the contacted gas-in-place.

We also convert the "power-law exponential" rate relation as proposed by Ilk et al [2008b] into a dimensionless form and

generate two different sets of type curves. These type curves are designed to distinguish the character exhibited by the rate

data function — particularly to identify the value of the time exponent, n, and the lower and upper bound for reserves,

∞ D~

parameter value. We validate our methodology using two numerical simulation cases and estimate the reserves/contacted

gas-in-place of several tight gas and shale gas wells using the procedure proposed in this work.

Conclusions: We state the following conclusions based on this work:

1. The spreadsheet approach, in which we simultaneously match multiple independent plotting functions, guarantees

consistent evaluations of the production data. The computation of the α -parameter (as described by Eq. 10) provides a diagnostic value in terms of confirming the establishment of the boundary-dominated flow regime. We

believe the proposed analysis procedure and plotting functions are simple but robust.

2. The significance of the type curves is that certain features of the rate data can be distinguished by using the type

curves such as the time exponent, n and the boundary-dominated flow parameter, ∞ D~

. This has particular as it

prevents the analyst to use statistical methods to obtain the parameter values in the "power-law exponential" rate

d li l i bli dl I ddi i h i f h D d b b i l diff i i




Nomenclature

Field Variables

b = Arps' decline exponent, dimensionlessc g = Gas compressibility, psi-1

D = Arps' "loss ratio," D-1 Di = Initial decline constant, D-1

D∞

= Decline constant at "infinite time" [i.e., D(t =∞)], D-1

i D̂ = Decline constant, D-1

G = Original (contacted) gas-in-place, MSCF

G p = Cumulative gas production, MSCF

G p,max = Maximum gas production, MSCF

n = Time exponent p = Pressure, psia pi = Initial reservoir pressure, psia pwf = Flowing bottomhole pressure, psiaq g = Gas production rate, MSCF/D

q gi = Gas initial production rate, MSCF/D or STB/D

giq̂ = Rate "intercept" [i.e., q g (t =0)], MSCF/D

t = Time, days

z = Gas compressibility factor

Dimensionless Variables

∞ D~

= Dimensionless Decline constant at "infinite time" ( )ˆ/(~ /1 n

i D D D ∞∞ = )

G pD = Dimensionless cumulative production, (G pD=G p/G) q D = Dimensionless rate (quadratic "rate-cumulative" relation), (q D=q g /q gi)

q Dd = Dimensionless rate, (power-law exponential relation) (q Dd =q g / giq̂ )

t Dd = Dimensionless time, (power-law exponential relation) ( nni Dd t Dt )ˆ( /1= )

Greek Variables

α = Boundary-dominated flow characteristic parameter, α =G/(q g i/ Di) by definition μ g = Gas viscosity, cp




References

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Calgary, Alberta, Canada, 17-19 June. (in preparation)

Ilk, D., Perego, A.D., Rushing, J.A., and Blasingame, T.A. 2008b. Exponential vs. Hyperbolic Decline in Tight Gas Sands —

Understanding the Origin and Implications for Reserve Estimates Using Arps' Decline Curves. Paper SPE 116731 presented

at the SPE Annual Technical Conference and Exhibition, Denver, Colorado, 21-24 September.

Ilk, D., Perego, A.D., Rushing, J.A., and Blasingame, T.A. 2008c. Integrating Multiple Production Analysis Techniques To

Assess Tight Gas Sand Reserves: Defining a New Paradigm for Industry Best Practices. Paper SPE 114947 presented at theSPE Gas Technology Symposium, Calgary, Alberta, Canada, 17-19 June.

Knowles R.S. 1999. Development and Verification of New Semi-Analytical Methods for the Analysis and Prediction of Gas

Well Performance. M.S Thesis, Texas A&M University, College Station, Texas.

Pratikno, H., Rushing, J.A., and Blasingame, T.A. 2003. Decline Curve Analysis Using Type Curves: Fractured Wells. Paper

SPE 84287 presented at the SPE Annual Technical Conference and Exhibition, Denver, CO., 05-08 October.

Rushing, J.A., Perego, A.D., Sullivan, R.B., and Blasingame, T.A. 2007. Estimating Reserves in Tight Gas Sands at HP/HTReservoir Conditions: Use and Misuse of an Arps Decline Curve Methodology. Paper SPE 109625 presented at the 2007

Annual SPE Technical Conference and Exhibition, Anaheim, CA., 11-14 November.




Fig. 1 — (Log-log Plot): Type curve for the power-law exponential rate decline model for various values of n. ( ∞ D

~

=0)




Fig. 3 — (Log-log Plot): Type curve for the power-law exponential rate decline model for various values of ∞ D~

. (n=0.15)





. (n=0.3)





. (n=0.5)





. (n=0.7)





. (n=0.9)




Fig. 13 — (Log-log Plot): Type curve match for the power-law exponential rate decline model. This type curve match isperformed to obtain the value for the time exponent, n. (n=0.15)




Fig. 15 — (Cartesian Plot): (q gi-q g )/G p versus G p. Extrapolation of the straight line trend yields G=2.55 BSCF.




Fig. 17 — (Cartesian Plot): q g /q gi versus G p/G. α=2→ complete boundary-dominated flow regime.




Fig. 19 — (Semi-log Plot): Production history plot — flowrate (qg) and cumulative production (Gp) versus production time. Tightgas well with a vertical hydraulic fracture (Ilk et al [2008b]).




Fig. 21 — (Log-log Plot): Type curve match for the power-law exponential rate decline model. This type curve match is

performed to obtain the lower and upper bound for the reserves. ( ∞ D~

=10-8)




Fig. 23 — (Cartesian Plot): Computed α-parameter versus Gp /G. α=2→ complete boundary-dominated flow regime.




Fig. 25 — (Log-log Plot): qg versus Gp. Model validation plot — data is matched with the model across the boundary-dominatedflow regime.




Fig. 29 — (Cartesian Plot): (qgi-qg)/Gp versus Gp. Extrapolation of the straight line trend yields G=1.98 BSCF.




Fig. 31 — (Cartesian Plot): qg /qgi versus Gp /G. α=2→ complete boundary-dominated flow regime.

SPE 123298 A Si l M th d l f Di tE ti ti f G i l d R U i R t Ti D t 27




Fig. 33 — (Semi-log Plot): Production history plot (field example 02) — flowrate (qg) and cumulative production (Gp) versusproduction time. Tight gas well with a vertical hydraulic fracture (Ilk et al [2008c]).

28 N L J ohnson S M Currie D Ilk andT A Blasingame SPE 123298






=10-3.75

)

SPE 123298 A Simple Methodology for DirectEstimationof Gas-in-place and Reserves Using Rate-TimeData 29



SPE 123298 A Simple Methodology for Direct Estimation of Gas in place and Reserves Using Rate Time Data 29


30 N.L. J ohnson, S.M. Currie, D. Ilk, andT.A. Blasingame SPE 123298



p gy p g





Fig. 43 — (Cartesian Plot): (qgi-qg)/Gp versus Gp. Extrapolation of the straight line trend yields G=0.33 BSCF.




Fig. 45 — (Cartesian Plot): qg /qgi versus Gp /G. α=2→ complete boundary-dominated flow regime.




Fig. 47 — (Semi-log Plot): Production history plot (field example 04) — flowrate (qg) and cumulative production (Gp) versusproduction time. Shale gas well (Barnett shale) (Mattar et al [2008]).






=10-3.50

)





SPE 123298



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2009 SPE Rocky Mountain Petroleum Technology Conference — Denver, CO — 14–16 April 2009

SPE 123298 — A Simple Methodology for Direct Estimation of Gas-in-place and Reserves Using Rate-Time Data

(Johnson/Currie/Ilk/Blasingame)

N. Johnson — Texas A&M University (16 April 2009)

N.L. Johnson, Texas A&M University

S.M. Currie, Texas A&M UniversityD. Ilk, Texas A&M University

T.A. Blasingame, Texas A&M University

Department of Petroleum EngineeringTexas A&M UniversityCollege Station, TX 77843-3116

+1.979.845.4064 — [email protected]

SPE 123298 A Simple Methodology for Direct Estimation

of Gas-in-place and Reserves Using Rate-Time Data

Presentation Outline ●



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●Rationale for this Work●Literature Review/Orientation●Development of the Integrated Approach■Rate-Cumulative Production Relation■ Power-Law Exponential Model Type Curves

●Validation: (Numerical Simulation Cases)■Horizontal Well with Multiple Fractures■ Tight Gas Well (SPE 84287 Data)

●Illustrative Examples:■ Field Data Case — Tight Gas Well (Bossier)■ Field Data Case — Barnett Shale Gas Well

●Summary and Conclusions

( O u

t l i n e )

Rationale For This Work

R E i i i O l R Ti D●

○



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●Reserves Estimation using Only Rate-Time Data:■ Arps' Decline Curves. [effect of the b-parameter]

■ Reciprocal Rate Method [Reese et al (2007)]. [only for oil wells]■ Blasingame and Rushing (2005). ["q g -G p

2" relation for gas flow]■ Power-Law Exponential Relation [Ilk et al (2008)]. [D(t ) and b(t )] ( R

a t i o n a l e ) ●

Rationale For This Work●

●

●Obj ti



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( R a t i o n a l e ) ●

●Objectives:■ To use the "q g -G p

2" relation as a basis for analysis/interpretation.

■ To develop rate-time type curves and plotting functions.■ To develop an integrated methodology to reduce uncertainty in

reserves estimation.

Orientation: Rate-Cumulative Production Relation●

○



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( O r i e n t a

t i o n ) ●

●Discussion: Rate-Cumulative Gas Flow Relation (SPE 98042)■ Based on a semi-analytical quadratic rate-cumulative relation.■ Derived using gas material balance and ( p /z )2-form gas flow equation.■ Yields a direct estimation of gas-in-place/reserves.

F r o m : B l a s i n g a m e

, T . A . a n d R u s h i n g , J . A . 2 0 0 5 . A P r o d u c t i o n - B a s e d

M e t h o d f o r

D i r e c t E s t i m a t i o n o f

G a s - i n - p l a c e a n d R e s e r v e s .

S P E p a p e r 9 8 0 4 2 p r e s e n t e d a t t h

e S P E E a s t e r n R e g i o

n a l

M e e t i n g , M o r g a n t o w n , W e s t V i r g

i n i a . 1 4 - 1 6 S e p t e m b e r .

Orientation: Power-Law Exponential Rate Decline●

●

e



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( O r i e n t a

t i o n )

F r o m : I l k , D . , P e r e g o , A . D . , R u s h i n g , J . A . , a n d B l a s i n g a m e , T . A .

2 0 0 8 . E x p o n e n t i a l v s . H y p e r b o l i c D e c l i n e i n T i g h t G a s

S a n d s —

U n d e r s t a n d i n g t h e

O r i g i n a n d I m p l i c a t i o n s f o r

R e s e r v e E s t i m a t e s U s i n g A r

p s ' D e c l i n e C u r v e s . P

a p e r S P E

1 1 6 7 3 1

p r e s e n t e d a t t h e S P E

A n n u a l T e c h n i c a l C

o n f e r e n c e

a n d E x h i b i t i o n , D e n v e r , C o l o r a d o , 2 1 - 2 4 S e p t e m b

e r .

●Discussion:■ b(t ) and D(t ) are evaluated continuously using numerical differentiation.■ D(t ) trend indicates "power-law" behavior converging to a constant at

late times.■ Very flexible model that can be used to match transient, transition, and

boundary-dominated flow data.

]ˆ exp[ˆ nii t Dt Dqq −−=

∞

Development: q g -G p Relation ○ ○

●Q d ti t l ti d ti l ti b



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( D e v e l o p m e n t

) ● ○ ○●Quadratic rate-cumulative production relation can be

rearranged to yield a plotting function as:

●The plotting function (q gi -q g )/G p versus G p yields anintercept in the x -axis of 2G — i.e., use to estimate G .

pi

i p

g giG

G

D D

G

qq

2

1−=

−

●B d d i t d fl i b id tifi d

Development: q g -G p Relation○

○ ○



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●Boundary-dominated flow regime can be identifiedusing the α-parameter through the modification of therate-cumulative production relation:

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

⎥⎦

⎤

⎢⎣

⎡

−⎥⎦

⎤

⎢⎣

⎡

⎥⎥⎦

⎤

⎢⎢⎣

⎡−

=2

2

1

1

G

G

G

G

q

q

p p

gi

g

α

●The plotting function, α versus G p /G has a diagnosticvalue in establishing the boundary-dominated flowregime (i.e., α = 2 as q g → 0 and G p→ G ).

( D e v e l o p m e n t ) ● ● ○

●Th l tti f ti / G /G d

Development: q g -G p Relation●

○ ○



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●The plotting functions q g /q gi versus G p /G and q g versus G

p

are used in conjunction with the previousplotting functions to yield the best estimate for G .

●q gi , Di , G parameters are calibrated using the plottingfunctions.●We iterate on all plots until the best match is obtained.

( D e v e l o p m e n t ) ● ● ●

●We convert the "power law exponential" rate decline

Development: Rate Decline Model Type Curves●

● ○



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●We convert the power-law exponential rate declinemodel into a dimensionless form.

]~

exp[n Dd Dd Dd t t Dq −−= ∞]ˆ exp[ˆ n

ii t Dt Dqq −−=∞

( D e v e l o p m e n t ) ● ● ●

●We develop type curves using the dimensionless form

Development: Rate Decline Model Type Curves●

● ●



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●We develop type curves using the dimensionless formof the "power-law exponential" rate decline model.

]~exp[n Dd Dd Dd t t Dq −−= ∞

( D e v e l o p m e n t ) ● ● ●

● ○ ○

Validation: Numerical Simulation Case 1



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( N u m e r i c a l S i m u l a t i o n C a s e 1 ) ●

●Numerical Simulation: Horizontal Well with Multiple Fractures■ Almost two years of production data of a horizontal well having four

transverse fractures generated by numerical simulator (ref. Mattar et al (2008)).

■ Our objective is to obtain the gas-in-place input in the simulation usingthe integrated approach proposed in this work (k =0.1 md, G inp=2.55BSCF).

Validation: Numerical Simulation Case 1●

● ○



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a. Plotting Function 1: (MFHW Gas Well ) (q gi -q g )/G p vs G p Plot(Cartesian scale).

b. Plotting Function 2: (MFHW Gas Well ) "α" Diagnostic Plot— reverse solution for the α- parameter (Cartesian scale).

c. Plotting Function 3: (MFHW Gas Well ) Model Validation Plot— q g /q gi versus G p /G (Cartesian scale).

d. Plotting Function 4: (MFHW Gas Well ) Model Validation Plot— q g (data and model) versus G p (log-log format).

( N u m e r i c a l S i m

u l a t i o n C a s e 1 ) ●

Validation: Numerical Simulation Case 1●

● ●



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2009 SPE Rocky Mountain Petroleum Technology Conference — Denver, CO — 14–16 April 2009SPE 123298 — A Simple Methodology for Direct Estimation of Gas-in-place and Reserves Using Rate-Time Data



●Discussion: Horizontal

Well with Multiple

Fractures■ Outstanding match of

the data with the typecurve for n=0.15.

■ G p,max is estimated by thesecond type curvematch.

■ G p,max =2.55 BSCF. Thisresult is consistent withthe value obtained usingthe rate-cumulativeproduction relation.

510

~ −∞ = D


u l a t i o n C a s e 1 )

● ○ ○




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( N u m e r i c a l S i m u l a t i o n C a s e 2 )

●Numerical Simulation: East Tx Gas Well (SPE 84287)

■ Previously obtained model parameters (see Pratikno et al (2003) wereused to generate the synthetic rate performance (with constant flowingwellbore pressure).

■ Tight gas well having a vertical fracture with finite conductivity (k =0.005md, F cD=10, and G inp=2.65 BSCF).


● ● ○



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a. Plotting Function 1: (East Tx Gas Well ) (q gi -q g )/G p vs G p Plot(Cartesian scale).

b. Plotting Function 2: (East Tx Gas Well ) "α" Diagnostic Plot— reverse solution for the α- parameter (Cartesian scale).

c. Plotting Function 3: (East Tx Gas Well ) Model Validation Plot— q g /q gi versus G p /G (Cartesian scale).

d. Plotting Function 4: (East Tx Gas Well ) Model ValidationPlot — q g (data and model) versus G p (log-log format).




● ● ●



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●Discussion: East Tx Gas

Well

■ Very good match of thedata with the type curvefor n=0.1 (except for theboundary-dominatedflow regime).

■ G p,max is estimated by thesecond type curvematch.

■ G p,max =2.5 BSCF. Thisresult can be further

adjusted to yieldG p,max =2.65 BSCF bycalibrating power-lawexponential modelparameters.

810

~ −∞ = D



● ○ ○

Field Example: Tight Gas Well



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( T i g h t G a s W

e l l )

●Field Example: Tight Gas Well (Bossier )

■ Hydraulically fractured gas well in a tight gas reservoir. Thisproduction data well has been analyzed before using model basedanalysis earlier (see Ilk et al (2008)).

■ Daily pressure and flowrate data are available. Flowrate data seemaffected by liquid loading.


) ● ● ○



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a. Plotting Function 1: (Tight Gas Well ) (q gi -q g )/G p vs G p Plot(Cartesian scale).

b. Plotting Function 2: (Tight Gas Well ) "α" Diagnostic Plot —reverse solution for the α- parameter (Cartesian scale).

c. Plotting Function 3: (Tight Gas Well ) Model Validation Plot —q g /q gi versus G p /G (Cartesian scale).

d. Plotting Function 4: (Tight Gas Well ) Model Validation Plot— q g (data and model) versus G p (log-log format).

( T i g h t G a s W

e l l )


) ● ● ●



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●Discussion: Tight Gas

Well (Bossier )■ Excellent match of the

data with the type curvefor n=0.2 — this yieldsan upper bound for thereserves (≈ 5.34 BSCF).

■ The lower bound for thereserves (G

p,max ) is

estimated by the secondtype curve match.

■ G p,max =2.01 BSCF. Thisresult is consistent withthe G value obtainedfrom rate-cumulativeproduction relation(G =1.98 BSCF).

75.310

~ −∞ = D

( T i g h t G a s W

e l l )

) ● ○ ○

Field Example: Barnett Shale Gas Well



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( B a r n e t t S

h a l e G a s W

e l l )

●Field Example: Barnett Shale Gas Well ■ Monthly production data are available from public records (almost 5.5

years of production).■ Flowrate data seem smooth except for minor fluctuations.


) ● ● ○



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a. Plotting Function 1: (Barnett Shale Gas Well ) (q gi -q g )/G p vs G pPlot (Cartesian scale).

b. Plotting Function 2: (Barnett Shale Gas Well ) "α"Diagnostic Plot — reverse solution for the α- parameter (Cartesian scale).

c. Plotting Function 3: (Barnett Shale Gas Well ) ModelValidation Plot — q g /q gi versus G p /G (Cartesian scale).

d. Plotting Function 4: (Barnett Shale Gas Well ) Model Valida-tion Plot — q g (data and model) versus G p (log-log format).

( B a r n e t t S

h a l e G a s W

e l l


) ● ● ●



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●Discussion: Barnett

Shale Gas Well

■ Excellent match of thedata with the type curvefor n=0.2 — this yieldsan upper bound for thereserves (≈ 1.41 BSCF).

■ The lower bound for thereserves (G p,max ) isestimated by the secondtype curve match.

■ G p,max =0.81 BSCF. This

result is consistent withthe G value obtainedfrom rate-cumulativeproduction relation(G =0.82 BSCF).

5.310

~ −∞ = D

( B a r n e t t S h a l e G a s W

e l l

Summary and Conclusions:

o n s ) ●

●(Summary ):■ "Rate cumulative production" and the "power law exponential"



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( S u m m a r y

a n d C o n c l u

s i o■ Rate-cumulative production and the power-law exponential

rate decline relations are used in conjunction to yield anintegrated approach using only rate-time data.■Rate-cumulative production relation is incorporated into the

procedure by making use of four plotting functions.■Power-law exponential rate decline is converted into a

dimensionless form to obtain type curve solutions.●(Conclusions):■The use of the plotting functions not only guarantees

consistent evaluations of the production data but also

provides additional resolution into the analysis.■Certain features of the rate data can be identified using typecurves such as the time exponent, n, and boundary-dominatedflow parameter, .

■The procedure proposed in this work yields consistent

contacted gas-in-place/reserves estimates. The uncertainty issignificantly reduced if the integrated approach is used.■This methodology is well suitable for direct estimation of

contacted gas-in-place/reserves in tight gas and shale gasreservoir systems.

∞ D~

SPE 123298



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N.L. Johnson, Texas A&M University

S.M. Currie, Texas A&M UniversityD. Ilk, Texas A&M UniversityT.A. Blasingame, Texas A&M University

Department of Petroleum EngineeringTexas A&M UniversityCollege Station, TX 77843-3116

+1.979.845.4064 — [email protected]

A Simple Methodology for Direct Estimationof Gas-in-place and Reserves Using Rate-Time Data

End of Presentation

spe 123298 (johnson) simple methodology direct est gas in place y reserves (wpres)

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