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Copyright 2007, Society of Petroleum Engineers

This paper was prepared for presentation at the 2007 SPE Hydrocarbon Economics andEvaluation Symposium held in Dallas, Texas, U.S.A., 13 April 2007.

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Abst ractDecline curve analysis is one of the most commonly used

techniques to estimate reserves from production data. In tightformations that have been stimulated, especially when there

are multiple layers that communicate only at the wellbore, the

uncertainty in reserves estimates from this technique is quite

large because forecasting future performance is quite difficult.This uncertainty can affect the classification of reserves, and

could limit what we should call proved developed reserves.

In this paper, we present new procedures to mitigate thecomplexity of decline curve analysis in multilayer tight gas

wells. Using synthetic and field examples, we demonstratehow reserves can be estimated more reliably.

For tight and multilayer gas wells, it is not uncommon that

decline curve analysis yields an Arps decline-curve parameterb larger than 1. Single-layer hydraulically fractured tight gas

wells also appear to have bvalues greater than one. Different

practices are used to handle such complexity. For forecasts,

some analysts simply use the b value obtained frommatching production data, while others force the b value to

be 1. Still others use the hyperbolic decline and the matched

value of b, but, when the decline rate reaches a

predetermined limit, they switch to exponential decline for theremainder of the forecast. Thus, forecasted performance

differs significantly when different analysts analyze the data.

Consequently, the reserves estimate has large uncertainty,which can, in turn, affect its classification.

In this paper, we first present an in-depth investigation of

decline behavior of tight, single-layer and multilayer gas wells

by analyzing depletion characteristics using simulated datasets. We illustrate the long-duration transient effects present in

single-layer stimulated tight gas wells and the complex flow

regimes present when wells in layered reservoirs are produced

commingled. Our work indicates that, as observed in field

data, transient effects and coexistence of different flow

regimes between layers lead to abnormal decline behavior

(b>1.0) in multilayer tight gas wells, which leads to errors in

production forecasts. Our new procedure provides a method tominimize these errors.

Introduction

Decline curve analysis is one of the most commonly used

techniques to predict future production performance andestimate reserves from routinely available production data

Although Arps decline equations were developedempirically,1 the parameter b in the decline equations was

proved to be related to fluid properties and production

conditions.2-3 Conventional decline curve analysis inherently

assumes a single-layer reservoir, the well producing a

constant bottomhole pressure, and stabilizedflow conditions.In addition, use of Arps equations implies that there are no

changes in completion and operating conditions. It is wel

documented that the decline exponent should range between

zero and 1.0 when these assumptions are satisfied.1,3

Tight gas reservoirs are characterized by permeabilities

less than 0.1 md. Gas wells in tight formations usually requirehydraulic fracturing of multiple layers to be commercially

viable. Therefore, analysis of decline behavior in tight gaswells presents unique technical challenges.4-5 It is often very

difficult, if not impossible, to estimate reserves accurately in a

timely and consistent fashion with decline curve analysis

Long times, often years, are required to reach so called

pseudo-steady state flow (actually, boundary-dominated flowsince the term pseudo-steady state strictly applies only to

constant-rate production). The production data available fordecline curve analysis are, therefore, typically not stabilized

As a result, it is not uncommon for tight gas wells to exhibi

Arps decline constants, b, that exceed 1.0.6 With b-value

greater than 1.0, future performance and remaining reserveswill be greatly overestimated. In conventional practice, some

analysts simply use the b value obtained from matching of

production data, while others force the b value to be 1.0. Stil

others use the hyperbolic decline and the matched value of b

but, when the decline rate reaches a predetermined limit, theyswitch to exponential decline for the remainder of the forecast

However, this procedure has no physical basis. This type of

decline behavior is highly unlikely in nature.

Another complication in analysis of decline data in tight

gas wells is that, in most cases, production is commingled

from multilayered formations that are hydraulically fractured

with multiple stages. Due to variations in formation

SPE 108176

Improving Reserves Estimates From Decline Curve Analysis of Tight and MultilayerGas WellsY. Cheng, SPE, W.J. Lee, SPE, and D.A. McVay, SPE, Texas A&M U.

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permeability and fracture half length, different flow regimes

may co-exist in different layers. Lower permeability zones

may be in transient flow while higher permeability zones haveestablished stabilized, boundary-dominated flow. The profile

of production contribution by individual layers constantly

changes with time. Given these complications, decline curve

analysis of multilayer tight gas wells is especially difficult,

particularly with regard to estimating long-term productionand reserves.

The objective of this study is to develop methodology toimprove reserve estimates from decline curve analysis of tight

and multilayer gas wells. We first generated simulated data

sets representing two synthetic cases a single-layer gas well

and a multilayer gas well. We then analyzed the characteristicsof decline equation parameters resulting from fitting the

simulated rate data. Since the true reserves for the simulated

cases are known, we determined the errors in projecting future

performance and estimating reserves using current analysis

techniques. We show that decline curve analysis usingstabilized data is sufficient to produce accurate reserves

estimates. However, given the fact that, in most tight wells, wehave to work with transient flow data to estimate reserves

from early-time production data, we propose an improved

analysis technique to effectively handle such cases.

Improvement in reserves estimates for synthetic and field

examples are illustrated using the proposed technique.

Analysis of Decline Behav iorWe generated two synthetic cases using a commercial

reservoir simulator. These two synthetic cases illustrate thedecline behavior of a fractured, single-layer well and a

fractured multilayer well.

Synthetic casesSynthetic Case 1.In this case, a gas well produces from a

hydraulically fractured single-layer reservoir. The well is

centered in a square reservoir with a drainage area of

1867*1867 ft2 (80 ac). Basic reservoir, fracture and fluid

properties are listed below:

Reservoir and fracture propertiesReservoir temperature = 250 oF

Initial reservoir pressure = 5,000 psi

Net pay thickness = 150 ft

Gas porosity = 0.06Gas permeability = 0.006 md

Fracture half-length = 450 ft

Fracture conductivity = 100 mdftBottom-hole flowing pressure = 1,000 psi

Fluid properties

Gas gravity (air=1) = 0.65Initial gas viscosity = 0.025 cp

Initial gas compressibility = 1.2*10-4psi-1

Initial gas production rate = 2,000 Mscf/d

The decline performance of this gas well during a 30-year

history is shown in Fig. 1. The time to achieve stabilized,

boundary-dominated flow is about 1,600 days. However, from

simulation results, the time at which production response

feels the boundary effects is much earlier than the

stabilization time. After 4 months of production, the pressureat the nearest boundaries (from the hydraulic fracture tips)

dropped 10 psia. Therefore, although the flow regime is

transient before stabilized flow is reached, boundaries begin to

affect production data prior to complete stabilization. Thus

the possibility exists of predicting long-term behavior withunstabilized data.

Synthetic Case 2. In this case, a gas well produces from

three layers with three hydraulic fracture treatment stages

These three layers communicate only at the wellbore. As in

Case 1, the well is centered in a square reservoir with adrainage area of 1867*1867 ft2. The permeabilities of the three

productive formations are 0.02 md, 0.006 md and 0.002 md

The adjacent productive layers are separated by shale zones 50

ft thick. Each productive formation has 50 ft of net pay and a

fracture half-length of 450 ft. Other basic reservoir, fractureand fluid properties are the same as in synthetic Case 1.

The 30-year decline behavior of this gas well is shown inFig. 2. The production rates from each of the three layers are

also displayed in this figure. Because of the differences in

layer permeabilities, the production rates in the different layers

vary significantly. The higher permeability layer has a

relatively high early-time production rate and a steeperdecline. Lower permeability layers decline less rapidly and

dominate the later time production. Due to permeability

differences, the time required to establish boundary-dominated

flow is very different in the different layers. For the 0.02-mdlayer, 480 days, or 1.3 year, were required to reach stabilized

flow while the 0.002-md layer required 4,800 days, or 13

years.

Dynamics of decline curves and forecast errorsDecline behavior of oil and gas wells is often described

by Arps decline curve equations. Arps equation for a

hyperbolic decline is

bbtDqq ii1

)1(

+= (1)

where qis production rate at time t, qiis the initial productionrate,Diis the initial decline rate, and bis the decline exponent

When bapproaches 0, the decline becomes exponential; when

bapproaches 1, the decline becomes harmonic.In tight reservoirs, determination of b has often been

problematic. Some analysts simply take the bvalue obtainedfrom matching of production data (which is often greater than1), while others force the b value to be 1. The value of b

significantly affects the projection of future rates.

Use of b-value obtained from best fit with transient data

included. We first determine the b-values and other declineequation parameters from the best fit to simulated rate data, in

which transient data are included, with varying fraction of the

total production history starting from time zero. The regressed

parameters are then used to forecast the production for a totawell life of 30 years. Table 1 gives regressed values of the

parameters (qi, b,Di) for the single-layer case. As we can see

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the b-values decrease as more production data are used in

regression, but they are all larger than 1. We also notice thatDi is positively correlated with b. Fig. 3 shows a set ofproduction forecasts using the b-values and corresponding qi

andDi from best curve fits of one year, ten years and twenty

years of production data. Note that the quality of the matches

is good for 1-year production data, but deteriorates as longer

production data (such as 10 years and 20 years) are matched.Fig. 3 clearly indicates that future production is greatly

overestimated in all cases. The b-values greater than 1 leads tothese overestimated future production values.

For the multilayer commingled production case, the b-

values obtained from history matching are also all greater than

1, as shown in Table 2. Again,Diis positively correlated withb. Fig. 4 is a set of production forecasts with these b-values

and other regressed parameters. Future projections are

overestimated for all scenarios investigated.

As a conclusive observation, for both single-layer and

multiple layer cases, decline curve fitting with transient flowdata included leads to b-value greater than 1, and forecasting

using b-values1.0 overestimates remaining reserves.

Use of b-value forced to be 1 with transient data included.

With bconstrained between 0 and 1 during history matching,

we obtained other sets of production forecasts. Table 3 gives

regressed values of the decline parameters (qi, b, Di) forsynthetic Case 1.Dicontinuously decreases as production time

increases whereas b is constant at 1 for all history match

periods. Fig. 5 shows the forecasted production rates. When

one year of rate data is used in history matching, futureproduction is greatly underestimated. When 5 years of rate

data are used for history matching, projected performance

approaches the actual performance at late times, but most ofthe projection is still less than actual. History matching and

forecasted production change only slightly when historymatching duration increases from 5 years to 10 years. The

projected rate curve crosses the actual rate curve and leads to

an overestimated prediction.For synthetic Case 2, multilayer production, Table 4

provides the regressed values of the decline parameters (qi, b,

Di) for various senarios. Future production is alsounderestimated for short history match periods, but is much

closer to the true value than the single-layer case (Fig. 6). The

projections almost overlap for history matching durations of 5years and 10 years.

These observations indicate that b constrained to be less

than or equal to 1 can result in either underestimated or

overestimated production forecasts. With values of qi and Diobtained from history matching of very early-time data (suchas one year), future production would typically be

underestimated. When more late-time data are included,

forecasts approach and surpass the true values. Forecasts tend

to become more stable as more late-time data are included inthe analysis. Note that as b is constrained to be less than 1.0,

the quality of the matches becomes worse (as we compare the

matches from the best curve fit).

Use of b-value obtained from best fit of only stabilized

data. We also examined b-value variation when only

stabilized data during boundary-dominated flow are used in

the analysis and transient flow or unstabilized data are

excluded from history matching.

For the single-layer case, boundary-dominated flow isreached at about 1,600 days, or 4.4 years. We discarded the

data for the first five years to exclude transient data and began

history matching starting at 1,825 days, or 5 years. Table 5

provides the regressed values of the three decline parameter

based on history matching to the end of the 6th through the10th year. The value of bgenerally decreases as we include

more late-time data in history matching, but all are less than1.0. Dialso decreases as bdecreases. Future production was

forecasted using the regressed parameters (as shown in Fig. 7)

and the relative errors in estimated remaining reserves are

presented in Table 5. The range of relative errors is from 1%to 4%.

For the multilayer production case, we also used only data

after the fifth year for decline curve analysis. Recall that the

two layers with higher permeabilities have reached boundary-

dominated flow while the bottom layer with the smallespermeability is still in transient flow at the end of the fifth

year. Nevertheless, the total well production appears to bestabilized after five years of production. The regressed

parameters obtained from history matching of one year

production data (from the end of the fifth year to the end of the

sixth year) through five years of data (from the end of the fifth

year to the end of the tenth year) are shown in Table 6. The b

value changes slightly, but remains near 0.6. The error in the

forecast is quite small, varying from 0.2% to 1.2%. In contras

to the single-layer case, the forecast errors decrease steadily as

more data are available for history matching. The forecastedfuture production is shown in Fig. 8.

Results from this section demonstrate that decline curve

analysis using only stabilized data is sufficient to produceaccurate reserves estimates.

Improved Analysis TechniqueFor tight gas wells, transient flow may last many years. We

often have to forecast future production and estimateremaining reserves when we have only transient data

Methodology to improve the reliability of decline curve

analysis based on only transient flow data would be ofsignificant value to the industry.

MethodologyIn the previous section, we saw that b-values obtained from

regression are all greater than 1 when transient data are

included in the history match. Use of b-values greater than 1

leads to a significantly overestimated production forecastConstraining b-values to be less than or equal to 1 also fails to

provide accurate projections. To project future performance

accurately, the b-value that represents stabilized flow is

required. Unfortunately, such a b-value cannot be obtained

from analysis of transient flow data.We propose an improved technique to analyze transient-

flow-dominated production data. There are two key

components in our proposed method. First, we estimate apriori a b-value that can reasonably represent stabilized

(boundary-dominated) flow. Second, we fix this b-value in

history matching of production data to determine other decline

parameters (qiand Di) in a backward data fitting fashion. The

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parameters qiand Diare extrapolated backward to time zero,

and the resulting set of decline parameters including the

predetermined b-value is then used for future projections.For a gas well producing from a single layer, the

representative b-value for stabilized flow has been shown to

be related to the reservoir drive mechanism,3and also to the

fluid properties and reservoir conditions.2-3bis not a constant

but decreases as the reservoir depletes at constant BHP.Although instantaneous values of bcan be larger than 1 under

some conditions, the average b during the entire depletionphase will be less than 1.2 As bis a variable, but depends on

the time segment used for history matching, Chen2proposed a

model to estimate an average bas a best approximation during

boundary-dominated depletion. From commonly availablereservoir properties, Chen proposed that we calculate an

average b, called bE, using pseudopressure7:

)()(

)()(1

wf

wf

i

i

wfpip

i

gii

E

z

p

z

p

pppp

z

cpb

= ...(2)

For a gas well producing from multiple layers, finding the

representative value of b is more difficult. Table 7 gives therange of b-value obtained from matching the remaining well

life at different production stages using data from synthetic

Case 2. This table provides insight to help us identify thebest representative value of b for the duration of the

projection because we obtained b directly by matching the

data in the projection period. As we can see, bdemonstrated aquite stable value of about 0.6 during most stages of depletion.

Therefore, we suggest using b= 0.6 for multilayer production

cases. We will further validate the choice of this b-value later,

and we note that this value is supported by the work ofFetkovich et al.8

When b is determined, we need to find appropriate

values of qi and Di for forecasting. We used a backward

analysis scheme.9In this approach, we start at the latest point

of available production data and go back a selected timeinterval to obtain a segment of data for history matching. We

obtain one set of parameters from fitting the selected data

segment. If we start at the end and go back further to another,earlier time point, we can obtain another segment of data for

history matching and thus obtain another set of parameters. In

this way, we obtain multiple sets of regressed parameters with

available data. Each set of parameters (qiand Di) correspond

to a given backward time interval. If we then plot log Divs.backward time interval and extrapolate the plot to time zero,

we obtain theDicorresponding to the latest time for which we

have production data. The same procedure is also applied to qito obtain the value of qi corresponding to the latest time.

Forecasting is then initiated at the latest point of production

data with extrapolated values of qiandDi, and the preselectedb-value.

Validation with synthetic cases

We used the two synthetic cases given in the previous

section to validate the proposed method.

Synthetic Case 1. We assume that only the production data

from the first three years of well life are available for the

analysis, and that we need to forecast the productionperformance for the remaining 27 years.

Table 8 provides multiple sets of regressed parameters (q

and Di) by backward analysis. Note that b is fixed at 0.433

which is estimated using Eq. 2. We then plot log qiand logD

vs. backward time interval, respectively, as shown in Figs. 9and 10. Extrapolating these two plots to time zero, we obtain

the values of qi and Di at the end of the third year, 494MSCF/D and 0.000284 1/D, respectively. Taking the end o

the third year as the initial time for prediction, we used qi =

494 MSCF/D, b = 0.433 and Di = 0.000284 1/D to predic

production performance for the remaining 27 years, as shownin Fig. 11. The production performance predicted using

conventional practices of decline curve analysis (1) using the

b-value from the best fit regardless of the value, or (2)

constraining b to less than or equal to 1, as discussed

previously are also presented in Fig. 11 for comparison. Therelative errors in estimated remaining reserves are -2.8% using

our method, compared to 56.2% and -35.2% usingconventional practices.

This synthetic case indicates that our method significantly

improves future projection with decline analysis for single-

layer, hydraulically fractured tight gas wells.

Synthetic Case 2. In this case, we assume that only the firs

years production data are available for decline analysis, and

production performance for the remaining 29 years needs to be

forecasted. We fixed bat 0.6 and history matched the data todetermine qiand Di. With the backward scheme, we obtained

multiple sets of qiand Di, as summarized in Table 9. Plotting

log qiand log Divs. backward time interval, we obtained thevalues of qiandDiat the end of the first year by extrapolation

Using b = 0.6 and the extrapolated values qi= 861 MSCF/Dand Di = 0.000815 1/D, we projected future production

performance (Fig. 12). The predicted performance from two

conventional practices used in decline curve analysis is alsopresented in Fig. 12. The relative errors of estimated

remaining reserves are -14.7% from our method, compared

with 109.9% and -28.3% from other methods. It is obviousthat our method provides much better estimation than

conventional practices of decline analysis.

We examined the effectiveness and superiority of ourmethod when more production data are available. Fig. 13

presents the forecasts for 28 and 27 years. The 28-yea

projection corresponds to two years of production data

available for analysis, while the 27-year projectioncorresponds to three years of production data available foranalysis. The 29-year projection is also included in Fig. 13

The error in the production forecast is reduced significantly

when more production data are available. Using decline

analysis of two years of production data, we obtained theestimated remaining reserves with a relative error of -4.5%

compared to -14.7% when only one year of data was available

Using decline analysis of three years of production data, weobtained the estimated remaining reserves with a relative error

of -2.0%.

Synthetic Case 2 indicates that our method greatly

improved production forecasts and reserves estimates for

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multilayer tight gas wells when only transient flow data are

available for the analysis. It is superior to conventional

practices used in decline analysis. This new methodconsistently provides more accurate forecasts when more

production data are available.

Field example

We next apply our new method to a field example anddemonstrate its applicability to typical well data.

This field example is a gas well producing from a tight gasreservoir with permeabilities ranging from 0.002 to 0.02 md.

The initial reservoir pressure was about 4,500 psi and the net

pay is estimated to be 150 ft. Three staged hydraulic fracture

treatments were implemented on multiple productive zones.The fracture half-lengths are estimated to range between 300 ft

and 600 ft. This well was plugged after 20 years of production.

Fig. 14 shows the monthly gas rate history over the well life.

We applied our decline analysis method to the first three

years of data and then predicted performance for theremaining 17 years. Fig. 15 is the plot of log qivs backward

time interval. The value of qi extrapolated to time zero is

7,315 MSCF/mo. Fig. 16 is the plot of log Di vs backward

time interval. The value of Di extrapolated to time zero is

0.0087 1/mo. Note that outliers were removed for

extrapolation because we need to characterize the overall

decline trend instead of localized variation. We took the end ofthe third year as the initial point of projection, and used the set

of parameters qi= 7,315 MSCF/mo, b = 0.6 and Di= 0.0087

1/mo for forecasting. The projected performance is shown in

Fig. 14, along with the actual production performance. Fig. 14shows that the predicted decline behavior is very consistent

with the observed behavior. The relative errors of estimated

remaining reserves and ultimate reserves are -2.97% and -1.97%, respectively. Our method led to a forecast that is a

good representation of actual production history.Fig. 17 presents the projections obtained using

conventional practices in decline analysis, with the same

production data as we used in our method, i.e, the first threeyears of production data. One forecasts far too much future

production, and the other forecasts far too little future

production. The relative errors in estimated remaining reservesare 36.50% and -47.18%, respectively, for these other

methods.

This field example indicates that our method cansignificantly improve the reliability of decline curve analysis

in multilayer tight gas wells, since the error of reserves

estimation and production forecast is greatly reduced.

Conclusions1. Conventional practices of decline curve analysis in tight

gas wells are problematic in forecasting long-term

performance, and typically provide quite inaccurate

reserves estimates.2. We have developed a new method to accurately project

production performance and reliably estimate remaining

reserves from decline analysis of the early-timeproduction data.

3. The proposed method mitigates the complexity of declinecurve analysis in tight gas wells. Our method was

validated using synthetic examples for single-layer andmultilayer gas wells. Accurate reserves estimates and

performance forecasts were obtained.

4. Practical applicability of our method was demonstratedwith an actual tight gas well producing from multiple

zones fractured with multistage treatments. The forecast isquite consistent with the actual behavior. Similar to the

synthetic examples, an accurate reserves estimate andperformance forecast were obtained.

5. The new method provides a useful tool to estimatereserves and forecast future performance from decline

analysis of the early-time production data in tight gaswells. Althrough there are some limitations, it should stil

be far better than conventional practices.

Nomenclatureb = Arps decline exponentbE = average decline exponent

cgi = initial gas compressibility, 1/psia

Di = initial decline rate, 1/D or 1/mo

p = initial pressure, psia

pp = pseudopressure, psia2/cp

pwf = bottom-hole flowing pressure, psiaq = gas production rate, MSCF/Dqi = initial gas production rate, MSCF/D

t = time, days or months

zi = initial gas compressibility factor, 1/psi

zwf = gas compressibility factor at BHP, 1/psi

References1. Arps, J.J.: Analysis of Decline Curves, Tran., AIME (1945

160, 228.

2. Chen, Her-Yuan.: Estimating Gas Decline-Exponent beforeDecline-Curve Analysis, SPE 75693 presented at the 2002 SPE

Gas Technology Symposium, Calgary, Alberta, Canada, 30April-2 May.

3. Fetkovich, M.J., Fetkovich, E.J. and Fetkovich, M.D.: UsefuConcepts for Decline-Curve Forecasting, Reserve Estimation

and Analysis, SPERE (Feb. 1996) 13.4. Cox, S. A.: Reserve Analysis for Tight Gas, paper SPE 78695

presented at the 2002 SPE Eastern Regional MeetingLexington, KT, 23-25 October.

5. Neal, D.B. and Mian, M. A..: Early-Time Tight Gas ProductionForecasting Technique Improves Reserves and ReservoiDescription, SPEFE (Mar. 1989) 25.

6. Maley, S.: The Use of Conventional Decline Curve Analysis inTight Gas Well Applications, paper SPE/DOE 13898 presented

at the 1985 SPE/DOE Low Permeability Gas ReservoirsSymposium, Denver, CO, 19-22 May.

7. Lee, W.J., Rollins, J.B., and Spivey, J.P.: Pressure TransienTesting, Textbook Series, SPE Richardson, TX (2003) Vol. 9.

8. Fetkovich, M.J. et al: Depletion Performance of LayeredReservoirs without Crossflow, SPEFE (Sept. 1990) 310.

9. Cheng, Y., Wang, Y., McVay, D.A. and Lee, W.J.: PracticalApplication of a Probabilistic Approach to Estimate ReservoirsUsing Production Decline Data, SPE 95974 presented at the2005 Annual Technical Conference and Exhibition, Dallas, 9-12

October.

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Table 1. Regressed parameters from historymatching different duration periods for syntheticcase 1 (bobtained from best curve fit)

Start End

0 1 2025 2.93 0.0164

0 2 2030 3.01 0.0171

0 3 2031 3.02 0.01730 5 2023 2.96 0.0164

0 10 1945 2.59 0.0114

0 20 1675 1.90 0.0045

HM* period, yearq i , MSCF/D b D i , 1/D

* History matching

Table 2. Regressed parameters from historymatching different duration periods for syntheticcase 2 (bobtained from best curve fit)

Start End

0 1 2027.6 3.16 0.0100

0 2 2006.3 2.84 0.00860 3 1971.5 2.52 0.0071

0 5 1891.9 2.03 0.0050

0 10 1744.2 1.43 0.0029

0 20 1622.5 1.06 0.0019

HM period, yearq i , MSCF/D b D i , 1/D

Table 3. Regressed parameters from historymatching different duration periods for syntheticcase 1 (bconstrained to be < 1)

Start End

0 1 1745 1.0 0.0046

0 2 1581 1.0 0.00300 3 1474 1.0 0.0022

0 5 1348 1.0 0.0016

0 10 1229 1.0 0.0011

0 20 1199 1.0 0.0010


Table 4. Regressed parameters from historymatching different duration periods for syntheticcase 2 (bconstrained to be < 1)

Start End

0 1 1810 1.0 0.0033

0 2 1699 1.0 0.0024

0 3 1643 1.0 0.0020

0 5 1594 1.0 0.0018

0 10 1573 1.0 0.0017

0 20 1589 1.0 0.0018

HM period, year q i , MSCF/D b D i , 1/D

Table 5. Regressed parameters from historymatching of only boundary-dominated (stabilized)flow data for synthetic Case 1

Start End

5 6 428.5 0.362 0.0002620 1.0%

5 7 428.5 0.432 0.0002621 3.7%

5 8 428.5 0.432 0.0002620 4.1%

5 9 428.5 0.419 0.0002617 3.1%5 10 428.4 0.397 0.0002608 3.6%

Error*HM period, year

q i , MSCF/D b D i , 1/D

* Relative error in estimated remaining reserves

Table 6. Regressed parameters from historymatching only boundary-dominated (stabilized) flowdata for synthetic Case 2

Start End

5 6 401.4 0.615 0.000413 1.2%

5 7 401.4 0.606 0.000413 0.9%

5 8 401.3 0.598 0.000412 0.6%

5 9 401.3 0.592 0.000412 0.4%5 10 401.3 0.588 0.000412 0.2%

Error*HM period, year

q i , MSCF/D b D i , 1/D

* Relative error in estimated remaining reserves

Table 7. Regressed parameters from historymatching late-time data for synthetic Case 2

Start End

1 30 885 0.638 0.00071

2 30 687 0.605 0.000578

5 30 401 0.589 0.000412

10 30 215 0.594 0.000287

13 30 161 0.599 0.00024216 30 126 0.592 0.000208

19 30 102 0.571 0.000182

20 30 95 0.554 0.000175


Table 8. Regressed q iand Difor synthetic Case 1

Time interval q i b D i

Start End days MSCF/D 1/D

182 1095 913 864 0.433 0.00067

365 1095 730 733 0.433 0.00051

547 1095 548 658 0.433 0.00043

730 1095 365 605 0.433 0.00038

912 1095 183 564 0.433 0.00035

HM period, days

Table 9. Regressed q iand Difor synthetic Case 2

Time interval q i b D i

Start End days MSCF/D 1/D

91 365 274 1285 0.6 0.00152

182 365 183 1104 0.6 0.00119

273 365 92 989 0.6 0.00101

HM period, days

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SPE 108176 7

10

100

1000

10000

0 2,000 4,000 6,000 8,000 10,000 12,000

Time, days

Gasrate,

MSCF/D

Fig. 1Production performance for hydraulically fractured well in

single-layer reservoir (Case 1).

1

10

100

1000

10000

0 2,000 4,000 6,000 8,000 10,000 12,000

Time, days

Gasrate,

MSCF/D

Layer 1: k=0.02 mdLayer 2: k=0.006 mdLayer 3: k=0.002 mdTotal production

Fig. 2Production performance for hydraulically fractured well in

multil ayer reservoir (Case 2).

10

100

1000

10000

0 2,000 4,000 6,000 8,000 10,000 12,000

Time, days

Gasrate,M

SCF/D

True production1 year HM10 year HM20 year HM

Fig. 3Predicted performance resulting from conventionaldecline analysis techniques for synthetic Case 1 (bobtained from

best curve fit).

10

100

1000

10000

0 2,000 4,000 6,000 8,000 10,000 12,000

Time, days

Gasrate,

MSCF/D


Fig. 4Predicted performance resulting from conventionadecline analysis techniques for synthetic Case 2 (bobtained from

best curve fit).

10

100

1000

10000

0 2,000 4,000 6,000 8,000 10,000 12,000

Time, days

Gasrate,

MSCF/D


Fig. 5Predicted performance resulting from conventionadecline analysis technique for synthetic Case 1 (bconstrained to

be < 1.0).

1

10

100

1000

10000

0 2,000 4,000 6,000 8,000 10,000 12,000

Time, days

Gasrate,M

SCF/D

Total production1 year HM5 year HM10 year HM

Fig. 6Predicted performance resulting from conventionadecline analysis technique for synthetic Case 2 (bconstrained to

be < 1.0).

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8 SPE 108176

10

100

1000

10000

0 2,000 4,000 6,000 8,000 10,000 12,000

Time, days

Gasrate

,MSCF/D

Series1HM over 5 years to 8 yearsHM over 5 years to 7 yearsHM over 5 years to 6 yearsHM over 5 years to 9 yearsHM over 5 years to 10 years

Fig. 7Predicted performance resulting from stabilized flow for

synthetic Case 1.

10

100

1000

10000

0 2,000 4,000 6,000 8,000 10,000 12,000

Time, days

Gasrate,

MSCF/D

True productionHM over 5 years to 10 yearsHM over 5 years to 9 yearsHM over 5 years to 8 yearsHM over 5 years to 7 yearsHM over 5 years to 6 years

Fig. 8Predicted performance resulting from stabilized flow for

synthetic Case 2.

y = 494.3e0.0006x

R2= 0.9702

100

1000

10000

0 200 400 600 800 1,000

Backward time interval, days

qi,

MSCF/D

Fig. 9Extrapolating q i to the initial time of projection for

synthetic Case 1.

y = 0.000284e0.00087x

R2= 0.9497

0.0001

0.001

0.01

0 200 400 600 800 1,000

Backward time interval, days

D

i,1/day

Fig. 10Extrapolating Di to the initial time of projection fo

synthetic Case 1.

10

100

1000

10000

0 2,000 4,000 6,000 8,000 10,000 12,000

Time, days

Gasrate,

MSCF/D

True productionb=3.0 for best fit, error=56.2%b=1.0 for b1 constraint, error=-35.2%b=0.433, new method, error=2.8%

ForecastHM

Fig. 11Forecasts using different decline analysis techniques fo

synthetic Case 1.

10

100

1000

10000

0 2,000 4,000 6,000 8,000 10,000 12,000

Time, days

Gasrate,

MSCF/D

True productionb=3.16, best fit, error=109.9%b=1, constraint b1, error=-28.3%b=0.6, new method, error=-14.7%

Forecast

HM


synthetic Case 2.

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10

100

1000

10000

0 2,000 4,000 6,000 8,000 10,000 12,000

Time, days

Gasrate,

MSCF/D

True production1 year HM, error=-14.7%2 year HM, error=-4.7%3 year HM, error=-2.0%

Fig. 13Forecasts using our decline analysis technique for

synthetic Case 2.

100

1,000

10,000

100,000

0 50 100 150 200 250 300Time, months

Gasrate,

MSCF/mo

Actual data

Predicted performance

Fig. 14Product ion his tory and forecast for fi eld example.

y = 7315.1e0.025x

R2= 0.9723

1,000

10,000

100,000

0 5 10 15 20 25 30 35 40

Backward time interval, months

q

i,MSCF/mo

Fig. 15Extrapolating qi to the initial time of projection for field

example.

y = 0.0087e0.0375x

R2= 0.9483

0.001

0.01

0.1

0 5 10 15 20 25 30 35 40

Backward time interval, months

Di,1/mo

Outlier

Fig. 16Extrapolating Di to the initial time of projection for field

example.

100

1,000

10,000

100,000

0 50 100 150 200 250 300

Time, months

Gasrate,

MSCF/mo

Actual datab=0.6, new method, error=-2.97%b=1, constraint b1, error=-47.18%b=2.65, best fit, error=36.50%


field example.

spe-108176-ms-p

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