SPE 132352 (Currie) Continuous EUR (wPres)

7/29/2019 SPE 132352 (Currie) Continuous EUR (wPres)

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SPE 132352

Continuous Estimation of Ultimate RecoveryS.M. Currie, Texas A&M University, D. Ilk, Texas A&M University, and T.A. Blasingame, Texas A&M University

Copyright 2010, Society of Petroleum Engineers

This paper was prepared for presentation at the SPE Unconventional Gas Conference held in Pittsburgh, Pennsylvania, USA, 2325 February 2010.

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

Gas in place/reserves estimation in unconventional (low/ultra-low permeability) reservoirs has become a topic of increasedinterest as more of these resources are being developed domestically and internationally. Production data from these

unconventional gas reservoirs exhibit extended periods of transient/transition flow behavior that often lead to the over-estimation of gas in place/reserves with the use of simple rate-time extrapolation techniques.

In this work we show that the analysis of production data (particularly rate-time data) before the onset of boundary

dominated flow for these unconventional gas reservoirs leads to significant overestimation of gas in place/reserves.Consequently, we introduce the concept of "continuous estimation of ultimate recovery" (or "continuous EUR") where

estimation of reserves from a single gas well is performed in a dynamic fashion in other words we continuously estimate

the reserves for selected time intervals throughout the producing life of the well.

We have applied the "continuousEUR" method by using simple rate-time relations such as the Arps'"hyperbolic" rate declinerelation and the power-law exponential rate decline relation along with the straight line extrapolation technique, which

provides a lower limit forEUR. We present the application of the "continuousEUR" method with a simulated tight gas dataset and four (tight gas) field data sets. Our analyses show that the distinction in the flow behavior is more evident and the

uncertainty in reserves estimation decreases significantly when reserves are evaluated continuously.

Introduction

Estimation of petroleum reserves is one of the most important petroleum engineering areas of research since 1910's. The use

of only production data (i.e., rate-time data) to estimate the reserves has been an industry practice since the introduction of

the Manual for the Oil and Gas Industry under the Revenue Act of 1918 by the United States Internal Revenue Service[1919]. Lewis and Beal [1918] provides initial guidance on the extrapolation of future production of oil wells. Cutler [1924]

presents a detailed review of the oil reserves estimation procedures in 1920's. Johnson and Bollens [1928] introduce the lossratio and the loss ratio derivative definitions which lay the basis for the exponential and the hyperbolic rate decline relations.Arps [1945] presents the empirical exponential and hyperbolic rate decline relations, which are still the widely used relations

for production extrapolations of oil and gas wells, and can be assumed as valid for a variety of producing conditions for

practical purposes. Arps' relations are only applicable for the boundary-dominated flow regime and the improper use of Arps'

equations can yield inconsistent results and erroneous reserve estimates.

Rushing et al[2007] presents a study which was designed to assess the validity of estimating reserves using the hyperbolic


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2 S.M. Currie, D. Ilk, and T.A. Blasingame SPE 132352

The interested reader is referred to the works by Anderson et al[2006] and Ilket al[2007] for a detailed description andliterature survey for modern production data analysis. We note that we only use the rate-time relations for our purposes in

this work.

To obtain a theoretically based rate-time relation (without the use of bottomhole pressures), Ansah et al[2000] use a simple

linearization scheme, and develop a semi-analytical direct solution for determining average reservoir pressure, rate and

cumulative production for gas wells produced at a constant bottomhole pressure during reservoir depletion. Blasingame andRushing [2005] extend the applicability of Ansah et alrelations by developing new plotting functions for direct estimation of

contacted gas-in-place using only production data. It should be noted that these relations are applicable for the boundary-

dominated flow regime. Again we note that Ansah et alrelations are not utilized in this work.

The most important objectives of this work are to reduce the uncertainty in reserves estimation, and to define a consistent and

systematic methodology for production extrapolation in unconventional reservoirs using simple rate-time equations. The

estimation of reserves in unconventional reservoir systems is problematic due to the extremely complex geology, and becauseof the very low permeability of the reservoirs, longer transient flow periods are being exhibited throughout the producing life

of the well. Under these circumstances the uncertainty in reserves estimation is high and usually the reserves are over-estimated with the use of conventional rate-time relations.

From a practical standpoint, Arps' rate-time relations are used in order to estimate reserves in unconventional reservoirsystems. These relations (i.e., Arps' rate-time relations) are very convenient to use, but they usually over-predict the reserves

as they are only applicable for the boundary-dominated flow regime whereas unconventional reservoirs exhibit very long

transient flow periods (years or even decades).

In this work we propose the use of the simple rate-time relations and a straight line extrapolation technique in a dynamic

(continuous) manner to reduce the uncertainty in reserve estimates. We specify a time interval amongst the productionsequence, and for each interval we perform extrapolation of the simple rate-time relations to obtain the maximum production

(i.e., the estimation of ultimate recovery). For example, for 500 days of production data (i.e., rate-time data) we may select a100-day time interval and the maximum production would be estimated using 100 days, 200 days, 300 days, 400 days, and

500 days of production data (in principle, the interval is arbitrary it could even be daily, but such a small interval would

require an automated procedure, which is not addressed in this paper). In addition we use the straight line extrapolation

technique to provide a conservative estimate for reserves which we use as a "lower" limit forEUR.

We choose to call this procedure the continuous estimation of reserves or continuous EUR approach. For our purposes weonly use the Arps' hyperbolic rate-time and the power-law exponential rate-time relations in addition to the straight line

extrapolation technique for the continuous estimation of reserves. In the following subsections we provide short descriptionson the rate-time decline models that are being used in this work.

Hyperbolic Rate Decline Function:

The most common method of well performance (i.e. rate-time data) analysis involves the empirical rate-time relations

presented by Arps [1945]. As mentioned before these equations were developed to analyze data exhibiting boundary-dominated flow behavior. Arps' equations are widely used to forecast production behavior and estimate reserves. The

decline behavior is described by the loss ratio, 1/D, and the derivative of the loss ratio, b, given by:

dtdq

q

D g

g

/

1

= ...................................................................................................................................................................... (1)

=

=

dtdq

q

dt

d

Ddt

db

g

g

/

1................................................................................................................................................ (2)

When the derivative of the loss ratio, b is constant then the hyperbolic rate decline relation is obtained and this relation is


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SPE 132352 Continuous Estimation of Ultimate Recovery 3

The decline parameter, b, is defined as the derivative of the "loss-ratio" with respect to time (i.e.d/dt[1/D]). The b-parameteris constant for the hyperbolic rate-decline relation and should lie between 0 and 1, but we often observe values greater than 1

especially during the transient and transition flow periods for unconventional gas reservoirs. Extrapolation of the rate-time

model prior to the onset of boundary-dominated flow results in the overestimation of reserves (see Rushing et al[2007] fordetails).

We integrate Eq. 3 to obtain a cumulative production relation and the result is given as:

])1(1[)1(

)( )/1(1 bii

gip tbD

Db

qtG +

= ............................................................................................................................. (5)

For the calculation of maximum production (Gp,max), we take the limit of Eq. 5 to infinite time.

+=

])1(1[)1(

Lim )/1(1, bii

git

maxp tbDDb

qG .................................................................................................................. (6)

When the b-parameter is bounded between 0 and 1 (i.e., 0


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Eq. 12 indicates that maximum gas production is obtained when the flowrate approaches to zero ( i.e., qg(t) 0, Gp(t)

Gp,max). In fact Eq. 12 can rigorously be derived for the black oil (slightly compressible liquid) case by combining the black

oil material balance and black oil pseudosteady-state flow relation with constant flowing bottomhole pressure assumption

(see Blasingame and Rushing [2005] and Reese et al[2007] for details on the derivation). We note that Eq. 12 should not beconsidered applicable for the gas flow case as nothing but a "very late transient" or "onset of boundary-dominated flow"

approximation. Therefore, we may use Eq. 12 for the purpose of finding a lower-limit for maximum gas production (or

estimated ultimate recovery). It is also important to state that neitherEUR norGp,max is the fluids-in-place, but rather thequantity of fluids that will be produced at infinite time.

Development of the Methodology

We develop the continuousEUR procedure to identify the error associated with the long transient flow periods when reserves

are being estimated in unconventional gas reservoirs at early times. From this approach we are able to quantify the change in

EUR estimates as a function of time. In this section we describe the details about our workflow on the continuous estimationof ultimate recovery.

Fig. 1 shows the first two steps of the workflow for the "Continuous EUR" procedure. We start by obtaining rate-time datafor an individual well. Prior to performing analysis, the rate-time data is edited and any points off trend from the dominant

production profile are removed. The data editing process is critical since the noise in the production data is significantly

amplified in theD-parameter and the b-parameter calculations (recall thatD-parameter and b-parameter calculations requirenumerical differentiation of the data set and the Bourdet algorithm [1989] is used for numerical differentiation purposes in

this work.).

The next step in the workflow is to create subsets of the production data ( i.e. flowrate versus time). Each subset starts from

the beginning of the production history (i.e. t = 0 days) and is analyzed individually with a rate-time relation (e.g.,"hyperbolic" and power-law exponential).


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Fig. 2 presents the next step, which is the rate-time analysis procedure in our workflow. Each subset of the data is matched

with the "hyperbolic" and power-law exponential relations and an EUR value is estimated by extrapolating the rate-timemodel to a specified time limit or abandonment rate. We note that for all the cases in this work, we have specified a time

limit of 30 years when calculatingEUR. In this work we have analyzed the flowrate data with the "hyperbolic" and power-law exponential rate decline relations, but this concept can be implemented with other rate-time relations as well.

In addition to the "hyperbolic" and power-law exponential relations, we use the straight line extrapolation technique to

estimate a "lower" limit forEUR. We plot gas flowrate versus cumulative gas production for an individual well on a

Cartesian scale. And for each previously specified interval, we fit a straight line through the part of the data exhibiting linear

trend. Thex-axis intercept of the line yields an estimate forGp,max. As mentioned earlier this method can be used to estimate

the maximum oil production for oil wells under the boundary-dominated flow regime. It is important to note that by applying

this technique a conservative estimate forGp,max can be obtained which yields a lower limit estimate forEUR. When short

period intervals (say 30 days, 60 days etc.) are selected then Gp,max estimates are observed to increase with time particularly

for the case of unconventional gas reservoirs.

On the other hand, Gp,max estimate can also be obtained by limiting the interval to only two points. The derivative of flowrate

(i.e., Eq. 12) is taken with respect to cumulative production. This provides theDi term in Eq. 12 in other words slope ofthe straight line passing through the two points is found. Next the qgi term in Eq. 12 is solved for and finally we extrapolate

the straight line to thex-axis (i.e., qg 0) for the Gp,max value.


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The final step in the procedure is shown by Fig. 3. TheEUR values obtained from the extrapolation of the rate-time relations

and the straight line extrapolation technique are plotted together as a function of time and this EUR versus time plot

provides a range for where the trueEUR value should lie. We suggest that theEUR estimate from the power law exponential

model can be used as an upper limit and theEUR estimate from the straight line extrapolation can be used as a lower limit forreserves. We also note that with increasing time the difference between upper and lower limits would reduce.

Fig. 3 Final step of the continuous EURprocedure: EURand Gp,maxvalues are plotted versus time and upper and lower limitsforEURare established.

Validation of New Analysis Methodology Numerical Simulation Study

In this section we verify our methodology by applying the continuous estimation concept to a numerically simulated case.

The simulated data is obtained from the work by Ilk et al[2008], which is given as the simulated East Tx gas well example.

This case is for a vertical well with a single vertical hydraulic fracture of finite conductivity which produces from a tight gasreservoir. The model parameters including reservoir and fluid properties were obtained from the work by Pratikno et al

[2003] and are provided in Table 1. The synthetic gas flowrate data is generated using a numerical simulator by Ilket al

[2008]. We present the flowrate data and the cumulative production data in Fig. 4 (the entire simulation run, approximately 6

years of data, are presented).

Our first task is to match the subsets of the flowrate data with the "hyperbolic" rate decline relation. In Fig. 5 we present the

"hyperbolic" model matches imposed on the flowrate data, and the D- and b-parameter trends. For this case, we note that the


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Table 1 Reservoir and fluid properties for numerical simulation case (single layer tight gas well with hydraulicfracture).

Reservoir Properties:

Wellbore Radius, rw = 0.333 ftEstimated net pay thickness, h = 170 ft

Average porosity, = 0.088 (fraction)Average irreducible water saturation, Swirr = 0.131 (fraction)

Permeability, k = 0.005 md

Fluid Properties:

Gas formation volume factor atpi,Bgi = 0.5498 RB/MSCF

Gas viscosity atpi, gi = 0.0361 cp

Gas compressibility atpi, cgi = 5.1032x10-5

psi-1

Production Parameters:

Initial reservoir pressure,pi = 9,330 psia

Original gas-in-place, OGIP = 2.65 BSCF

Our next task is to match the subsets of the flowrate data with the power-law exponential rate decline relation. In Fig. 7 we

present the power law exponential model matches imposed on the flowrate data, andD- and b-parameter trends. We observe

that the model match stabilizes and becomes identical for each interval after 1,000 days of production. We attribute this

result to the boundary-dominated flow regime effects in fact, we expect that once complete boundary-dominated flow

regime is established, rate-time model match would be identical for each additional interval. Also we observe that the power-

law exponential rate decline relation matches the transient, transition, and boundary-dominated flow behavior very well.We use the straight line extrapolation technique to estimate a lower limit forEUR. In Fig. 8 we show the results of thestraight line extrapolation for this case. Thex-axis intercept of the lines (i.e., continuous estimation of the Gp,max) increase

with time resulting in an increasing estimate ofGp,max. Again it is worth to mention that during the boundary-dominated flow

regime Gp,max estimates do not seem to change significantly over time.

The last step in our workflow is to calculate theEUR based on the matches obtained with the "hyperbolic" and the power-lawexponential rate decline relations. In Fig. 9 we present the calculatedEUR values versus production time. We observe that

theEUR values obtained from the "hyperbolic" model matches decrease significantly at early times and then converge at latetimes to a value of 2.55 BSCF. TheEUR values obtained from the power-law exponential model matches also decrease at

early times but become constant at a value of 2.41 BSCF after 750 days of production. From the reservoir simulation model,the gas produced at 30 years is 2.42 BSCF, which is consistent with the EUR estimated using the power-law exponential

model. The EUR values estimated from the power-law exponential model matches are more conservative than the valueestimated from the hyperbolic model matches. We also observe that the EUR values obtained from both models converge or

become constant once boundary-dominated flow has been established.

The Gp,max values obtained from the straight line extrapolation technique are shown to increase with time and never reach the

actual cumulative production (Gp) value (2.42 BSCF) during the 2,000 days of production. This result confirms that thestraight line technique may not be applicable for gas flow however; it can be used to provide a "lower" limit forEUR for

practical purposes. Finally we present all of the model parameters and theEUR and Gp,max values for each interval in Table

2.

Application of the Continuous Estimation of Ultimate Recovery Methodology to Field Data

In this section we present four field examples on the application of the proposed continuous EUR methodology. The field

data include rate-time data of hydraulically fractured wells completed in a low permeability (tight) gas reservoir (k


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In Fig. 12 we observe that the value of the b-parameter continues to decrease over the entire production history and does not

appear to stabilize. We observe every subset (or interval) which is matched with a "hyperbolic"b-parameter greater than 1indicates that the boundary-dominated flow regime has not been established yet. Specifically the b-parameter value

decreases from 2.20 to 1.57 during the production history this result may indicate that transient flow effects are stilldominant in the production behavior. However, the effects of transition to boundary-dominated flow regime start to be seen.

Our next task is to match the subsets of the flowrate data with the power-law exponential rate decline relation. In Fig. 13 the

power law exponential model matches imposed on the flowrate data andD- and b-parameter trends are shown. We note that

for all matches aD value is not used indicating that boundary-dominated flow character is not observed (the behavior of thecalculatedD-parameter data trend may serve as a validation for not using the D

parameter in the power law exponential

relation as it exhibits only power law behavior for this case). We observe that the model matches stabilize and become

relatively stable after about 1,500 days of production for each additional interval.

We use the straight line extrapolation technique to estimate Gp, max. In Fig. 14 we show the lines fit through the end portionof the data for each interval. Thex-axis intercept of the lines increase with time resulting in an increasing estimate ofGp,max

or "lower" limit estimate ofEUR. All of the model parameters for this example are presented in Table 3.

The last step in our workflow is to plot the EUR based on the matches obtained with the "hyperbolic" and the power-lawexponential rate decline relations versus time. In Fig. 15 we present the calculatedEUR values versus production time. Weobserve that theEUR estimates obtained from the "hyperbolic" relation significantly overestimate reserves at early times and

converge at late times to a value of 3.10 BSCF. The estimates provided by the power law exponential model appear to be

constant at 3.05 BSCF after 1,500 days. We expect lowerEUR values to be estimated by the rate-time relations when

complete boundary-dominated flow regime is established later in the life of this well.

The Gp,max values obtained from the straight line extrapolation seem to increase with time are always less than the estimatesprovided by the rate-time relations. TheEUR of this well should be in between 2.58 BSCF (the "lower" limit given by the

straight line extrapolation technique at 2,000 days) and 3.05 BSCF (the "upper" limit given by the power law exponentialestimate at 2,000 days).

Field Case 2:

We apply our proposed methodology to a second field data set acquired from a hydraulically fractured well completed in atight gas reservoir. We present the flowrate data and the cumulative production data which spans almost 5.5 years in Fig. 16.

In this case we observe the effects of liquid loading and operational changes (specifically at 1,000 days of production) on the

flowrate profile as well.

The subsets of the flowrate data are matched with the "hyperbolic" rate decline relation initially. In Fig. 17 we present the

"hyperbolic" model matches imposed on the flowrate data, and D- and b-parameter trends. We use the same matchingtechnique as previously described and hold qgi constant while matching the end portion of the data where boundary-

dominated flow regime assumption may be made. We observe every subset of the data is matched with a "hyperbolic"b-parameter greater than 1 indicating that complete boundary-dominated flow regime effects are not established yet. In Fig. 18

we observe that the b-parameter is relatively stable after about 250 days of production with a slight inconsistency occurring

after about 1,000 days of production. We believe that this issue can be attributed to the changing production profile notedearlier. The b-parameter value seems to decrease from 2.37 to 1.90 during the entire production history.

Next we match the selected subsets of the flowrate data with the power-law exponential rate decline relation. In Fig. 19 wepresent the power law exponential model matches imposed on the flowrate data, and D- and b-parameter trends. We notethat for all matchesD

value is not used in the model as dictated by the data character (i.e., power-lawD-parameter trend).

We observe that the model matches are for the most part identical during the entire production history. In particular, we note

that the character of the data specifically the computedD-parameter trend for the smallest interval (or subset) is almost

identical to the character of the data for the largest interval resulting in almost identical power-law exponential rate model

matches. Therefore,EUR estimates from the power law exponential model would be relatively constant for this case.


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The Gp,max values obtained from straight line extrapolation are shown to increase with time, and they are always less than the

estimates provided by the rate-time relations. Also we observe that Gp,max values obtained from straight line extrapolation

still appear to increase at late times Gp,max values appear not to stabilize. Consequently, theEUR of this well should be in

between 3.57 BSCF (the "lower" limit given by the straight line extrapolation technique at 1,930 days) and 4.06 BSCF (the"upper" limit given by the power law exponential estimate at 1,930 days). We summarize all the model parameters in Table

4 for this well.

Field Case 3:

The third field data set also includes the daily rate-time data a hydraulically fractured well completed in a tight gas reservoir.

We present the flowrate data and the cumulative production data which spans almost 5.5 years in Fig. 22.


"hyperbolic" model matches imposed on the flowrate data, and D- and b-parameter trends. We observe that every subset of

the data is matched with a "hyperbolic"b-parameter greater than 1 indicating that complete boundary-dominated flow has notbeen established yet. In Fig. 24 we observe that the b-parameter value changes over time and is relatively stable after about

1,000 days of production in particular, b-parameter value decreases from 4.79 to 1.66 during the production history. This

change corresponds to the final EUR estimate, which is three times less than the initial EUR estimate as predicted by the

"hyperbolic" equation using the initial value of the b-parameter in the first subset of the data.

Next we employ the power-law exponential rate decline relation for rate-time extrapolations for each interval (or subset). InFig. 25 we present the power law exponential model matches imposed on the flowrate data andD- and b-parameter trends as

well. Again for this case we note that for all matches, a D, value is not used indicating that boundary-dominated flowcharacter is not observed. We observe that the model matches stabilize and become relatively constant after about 1,000 days

of production for each additional interval.In Fig. 26 we show the results of the straight line extrapolation technique for this case. The x-axis intercept of the

extrapolated lines increases with time resulting in an increasing estimate of Gp,max over time. Table 5 presents the modelparameters along with theEUR estimates for each interval using all the rate-time models and straight line extrapolation.

The last step in our workflow is to calculate theEUR based on the matches obtained with the "hyperbolic" and the power-lawexponential rate decline relations. In Fig. 27 we present the calculatedEUR values versus production time. We observe that

theEUR values obtained from the "hyperbolic" and power-law exponential model matches decrease at early times but appearto stabilize after about 1,000 days of production. TheEUR values estimated from the "hyperbolic"model matches convergeat late times to a value of 2.39 BSCF, and the power-law exponential model matches also converge at late times to a value of2.28 BSCF. TheEUR of this well should be in between 2.04 BSCF (the "lower" limit given by the straight line extrapolation

technique at 2,000 days) and 2.28 BSCF (the "upper" limit given by the power law exponential estimate at 2,000 days).

Field Case 4:

We apply our proposed methodology to the production data acquired from a hydraulically fractured well completed in a tight

gas reservoir. We present the flowrate data and the cumulative production data which spans over 6 years in Fig. 28.


"hyperbolic" model matches imposed on the flowrate data, andD- and b-parameter trends. In all of the model matches usingthe "hyperbolic" relation, we obtain b-parameter values greater than 1 again indicating that transient flow regime effects are

still dominant. In Fig. 30 we observe that the b-parameter value decreases significantly over the production history and doesnot appear to stabilize at late times (for longer intervals). Specifically, the b-parameter value decreases from 3.66 to 1.70during the production history (from the shortest subset of 50 days to entire production history).

Following our procedure, we next use the power-law exponential model to match the subsets of the flowrate and estimate the

EUR values. In Fig. 31 we present the power-law exponential model matches imposed on the flowrate data, andD- and b-

parameter trends. Once again D value is not used in the power-law exponential model which suggests that boundary-dominated flow regime effects have not started to evolve We observe that the model stabilizes and becomes relatively


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TheEUR values seem to somewhat stabilize but still decrease at late times at a slower rate. TheEUR values obtained from

the power-law exponential model matches decrease significantly at early times and stabilize after about 750 days of

production. As mentioned earlier the EUR values estimated from the power-law exponential model matches are more

conservative the than value estimated from the hyperbolic model matches. After 2,384 days of production, both modelsconverge to anEUR value of 3.78 BSCF. TheEUR of this well should be in between 3.39 BSCF (the "lower" limit given by

the straight line extrapolation technique at 2,000 days) and 3.78 BSCF (the "upper" limit given by the power law exponential

estimate at 2,000 days). For reference the model parameter values and theEUR values for each interval are presented inTable 6.

Summary and Conclusions

Summary: In this work we propose the continuous EUR method to reduce the uncertainty in reserves estimation particularly

for unconventional gas reservoirs. We utilize rate time functions and a simple extrapolation technique in a dynamic manner

to offer a profile ofEUR versus time. The proposed method is found to be especially useful to provide "upper" and "lower"limits forEURprior to the onset of boundary-dominated flow.

Conclusions:

We state the following conclusions based on this work:

1. The uncertainty in reserves estimation for unconventional reservoirs is relatively high. A systematic methodologyis needed to reduce the uncertainty associated with reserves estimation for unconventional gas reservoirs. The

proposed continuous EUR method offers an effective way to reduce the associated uncertainty with reserves

estimation by performing dynamic rate-time analysis/extrapolation throughout the producing life of the well.

2. The proposed "continuousEUR method evaluatesEUR as a function of time and shows thatEUR estimates stabilizewhen boundary dominated flow is established.

3. In this work we use the "hyperbolic", power law exponential with the proposed continuousEUR method. Other rate

decline relations can also be implemented with this approach.

4. The straight line extrapolation technique offers a "lower" limit forEUR and can be used to establish a range for the

reserves as well as to prevent the overestimation of reserves.

Nomenclature

Field Variables

b = Arps' decline exponent, dimensionlessD = Loss ratio, D-1

Di = Initial decline constant for hyperbolic rate relation, D-1

D

= Decline constant at "infinite time" for power-law exponential relation [i.e.,D(t=)], D

-1

iD = Decline constant for power-law exponential relation, D-1

EUR = Estimate of ultimate recovery, BSCFEURLL = Lower limit for estimate of ultimate recovery, BSCFEURUL = Upper limit for estimate of ultimate recovery, BSCFG = Original (contacted) gas-in-place, MSCFGp = Cumulative gas production, MSCFGp,max = Maximum gas production (t), MSCFk = Formation permeability, mdn = Time exponent for power-law exponential relation, dimensionlessqg = Gas production rate, MSCF/D

qgi = Gas initial production rate for hyperbolic rate relation, MSCF/D

R t "i t t" f l ti l l ti [i (t 0)] MSCF/D


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Lewis, J.O., and Beal, C.H.. 1918. Some New Methods for Estimating the Future Production of Oil Wells. Trans. AIME 59, 492-525.

Manual for The Oil and Gas Industry Under The Revenue Act of 1918, Treasury Department United States Internal Revenue Service.1919.

Pratikno, H., Rushing, J.A., and Blasingame, T.A. 2003. Decline Curve Analysis Using Type Curves Fractured Wells. Paper SPE 84287presented at the SPE Annual Technical Conference and Exhibition, Denver, Colorado, 5-8 October.

Reese, P.D., Ilk, D., and Blasingame, T.A. 2007. Estimation of Reserves Using the Reciprocal Rate Method. Paper SPE 107981 presentedat the 2007 SPE Rocky Mountain Oil & Gas Technology Symposium, Denver, Colorado, 16-18 April.

Rushing, J.A., Perego, A.D., Sullivan, R.B., and Blasingame, T.A. 2007. Estimating Reserves in Tight Gas Sands at HP/HT ReservoirConditions: Use and Misuse of an Arps Decline Curve Methodology. Paper SPE 109625 presented at the 2007 Annual SPE TechnicalConference and Exhibition, Anaheim, California, 11-14 November.


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Fig. 4 (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[2008]).


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Fig. 6 (Cartesian Plot): Hyperbolic b-parameter values obtained from model matches with production data.


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Fig. 8 (Cartesian Plot): Rate Cumulative Plot flowrate (qg) versus cumulative production (Gp) and the linear trends fitthrough the data.


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Fig. 10 (Semi-log Plot): Production history plot flowrate (qg) and cumulative production (Gp) versus production time.Hydraulically fractured tight gas well.


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SPE 132352 C ti E ti ti f Ulti t R 27


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Table 2a Analysis results for numerical simulation case (fractured tight gas well) "hyperbolic" model parameters.

Time Interval,days

qgi(MSCFD)

Di(D-1)

b(dimensionless)

EURhyp(BSCF)

50 4,400 0.01000 2.80 9.46

100 4,400 0.01380 2.60 7.67

250 4,400 0.01600 2.15 5.80

500 4,400 0.01000 1.50 3.90

750 4,400 0.00713 1.10 3.09

1,000 4,400 0.00600 0.90 2.82

1,250 4,400 0.00540 0.85 2.72

1,500 4,400 0.00500 0.78 2.60

1,750 4,400 0.00497 0.75 2.552,000 4,400 0.00497 0.75 2.55

Table 2b Analysis results for numerical simulation case (fractured tight gas well) power-law exponential model parameters.

Time Interval,days

giq

(MSCFD)iD

(D-1)n

(dimensionless)

D

(D-1)EURPLE(BSCF)

50 6,292,146 6.216 0.05 0 6.74

100 7,325,965 6.361 0.05 0 6.37

250 1,132,541 4.440 0.07 0 4.99

500 812,662 4.158 0.07 0.000421 4.02

750 812,662 4.158 0.07 0.000440 2.41

1,000 812,662 4.158 0.07 0.000460 2.41

1,250 812,662 4.158 0.07 0.000460 2.41

1,500 812,662 4.158 0.07 0.000460 2.41

1,750 812,662 4.158 0.07 0.000460 2.41

2,000 812,662 4.158 0.07 0.000460 2.41

Table 2c Analysis results for numerical simulation case (fractured tight gas well) straight line extrapolation.

Time Interval,days

Slope,10-6 D-1

Intercept,MSCF/D

Gp,max(BSCF)

50 15,250 6,891 0.45

100 3,648 3,912 1.07

250 2,478 3,352 1.35

500 1,724 2,814 1.63

750 1,294 2,381 1.84

1,000 1,176 2,245 1.91

1,250 922 1,894 2.05

1,500 818 1,733 2.12

1,750 738 1,601 2.17

2,000 738 1,601 2.17

28 S M Currie D Ilk and T A Blasingame SPE 132352


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Table 3a Analysis results for field example 1 (fractured tight gas well) "hyperbolic" model parameters.

Time Interval,days

qgi(MSCFD)

Di(D-1)

b(dimensionless)

EURhyp(BSCF)

50 4,100 0.0094 2.20 6.04

100 4,100 0.0094 2.05 5.84

250 4,100 0.0131 1.98 4.92

500 4,100 0.0146 1.94 4.53

750 4,100 0.0146 1.83 4.12

1,000 4,100 0.0146 1.75 3.82

1,250 4,100 0.0158 1.68 3.42

1,500 4,100 0.0158 1.63 3.24

1,750 4,100 0.0152 1.59 3.172,000 4,100 0.0152 1.57 3.10

Table 3b Analysis results for field example 1 (fractured tight gas well) power-law exponential model parameters.

Time Interval,days

giq

(MSCFD)iD

(D-1)n

(dimensionless)

D

(D-1)EURPLE(BSCF)

50 72,500 1.785 0.14 0 3.10

100 67,426 1.684 0.15 0 3.09

250 67,426 1.684 0.15 0 3.09500 67,426 1.684 0.15 0 3.09

750 67,426 1.684 0.15 0 3.09

1,000 67,426 1.684 0.15 0 3.09

1,250 67,426 1.684 0.15 0 3.09

1,500 66,500 1.684 0.15 0 3.05

1,750 66,500 1.684 0.15 0 3.05

2,000 66,500 1.684 0.15 0 3.05

Table 3c Analysis results for field example 1 (fractured tight gas well) straight line extrapolation.

Time Interval,days

Slope,10-6 D-1

Intercept,MSCF/D

Gp,max(BSCF)

50 22,385 8,248 0.37

100 21,845 9,881 0.45

250 3,915 4,045 1.03

500 1,843 2,714 1.47

750 819 1,738 2.12

1,000 728 1,558 2.14

1,250 605 1,356 2.24

1,500 569 1,310 2.30

1,750 454 1,139 2.51

2,000 443 1,145 2.58



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Time Interval,days

qgi(MSCFD)

Di(D-1)

b(dimensionless)

EURhyp(BSCF)

50 3,495 0.0160 2.37 5.05

100 3,495 0.0153 2.25 4.75

250 3,495 0.0141 2.14 4.57

500 3,495 0.0140 2.11 4.44

750 3,495 0.0140 2.10 4.34

1,000 3,495 0.0140 2.09 4.28

1,250 3,495 0.0130 1.95 4.18

1,500 3,495 0.0120 1.90 4.11

1,750 3,495 0.0121 1.90 4.111,930 3,495 0.0121 1.90 4.11


Time Interval,days

giq

(MSCFD)iD

(D-1)n

(dimensionless)

D

(D-1)EURPLE(BSCF)

50 26,695 1.58 0.12 0 4.54

100 28,606 1.61 0.12 0 4.43

250 30,654 1.65 0.12 0 4.32500 32,849 1.69 0.12 0 4.20

750 35,200 1.73 0.12 0 4.08

1,000 40,421 1.93 0.11 0 4.06

1,250 40,421 1.93 0.11 0 4.06

1,500 40,421 1.93 0.11 0 4.06

1,750 40,421 1.93 0.11 0 4.06

1,930 40,421 1.93 0.11 0 4.06


Time Interval,days

Slope,10-6 D-1

Intercept,MSCF/D

Gp,max(BSCF)

50 12,459 3,805 0.31

100 3,068 2,544 0.83

250 1,762 2,082 1.18

500 1,023 1,686 1.65

750 625 1,401 2.24

1,000 421 1,127 2.68

1,250 354 1,023 2.89

1,500 288 930 2.23

1,750 268 910 3.39

1,930 242 863 3.57



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30 S C , , g S 3 35


Time Interval,days

qgi(MSCFD)

Di(D-1)

b(dimensionless)

EURhyp(BSCF)

50 1,900 0.01920 4.79 6.19

100 1,900 0.01470 4.20 5.75

250 1,900 0.01430 2.93 3.88

500 1,900 0.00862 2.16 3.12

750 1,900 0.00825 1.97 2.82

1,000 1,900 0.00737 1.81 2.64

1,250 1,900 0.00755 1.75 2.50

1,500 1,900 0.00700 1.71 2.46

1,750 1,900 0.00700 1.66 2.421,995 1,900 0.00713 1.66 2.39


Time Interval,days

giq

(MSCFD)iD

(D-1)n

(dimensionless)

D

(D-1)EURPLE(BSCF)

50 424,256 4.82 0.05 0 3.34

100 92,676 3.25 0.07 0 3.27

250 185,041 3.97 0.06 0 3.16500 23,247 1.84 0.11 0 2.86

750 30,654 2.17 0.10 0 2.56

1,000 23,247 1.77 0.12 0 2.43

1,250 20,244 1.73 0.12 0 2.35

1,500 21,966 1.77 0.12 0 2.30

1,750 18,632 1.58 0.13 0 2.29

1,995 22,928 1.54 0.14 0 2.28


Time Interval,days

Slope,10-6 D-1

Intercept,MSCF/D

Gp,max(BSCF)

50 15,589 2,351 0.15

100 2,436 1,614 0.66

250 2,010 1,421 0.71

500 1,043 1,114 1.07

750 833 1,036 1.24

1,000 525 789 1.50

1,250 465 755 1.62

1,500 368 669 1.82

1,750 348 659 1.89

1,995 292 595 2.04



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y


Time Interval,days

qgi(MSCFD)

Di(D-1)

b(dimensionless)

EURhyp(BSCF)

50 8,315 0.8310 3.66 7.29

100 6,704 0.2800 3.28 6.34

250 5,606 0.1100 2.81 5.24

500 5,280 0.0810 2.65 4.93

750 4,852 0.0560 2.52 4.71

1,000 4,500 0.0390 2.36 4.44

1,250 4,000 0.0250 2.21 4.24

1,500 3,932 0.0251 2.19 4.15

1,750 3,905 0.0242 2.16 4.072,000 3,932 0.0230 2.10 4.02

2,250 3,669 0.0151 1.90 3.85

2,384 2,880 0.0070 1.70 3.78


Time Interval,days

giq

(MSCFD)iD

(D-1)n

(dimensionless)

D

(D-1)EURPLE(BSCF)

50 688,395 4.77 0.05 0 5.88100 243,999 3.79 0.06 0 5.55

250 344,776 4.08 0.06 0 5.08

500 522,057 4.46 0.06 0 4.40

750 261,467 3.74 0.07 0 4.02

1,000 300,246 3.82 0.07 0 3.98

1,250 344,776 3.91 0.07 0 3.92

1,500 354,446 3.93 0.07 0 3.90

1,750 57,116 2.28 0.10 0 3.82

2,000 80,706 2.44 0.10 0 3.81

2,250 75,314 2.41 0.10 0 3.78

2,384 75,314 2.41 0.10 0 3.78


Time Interval,days

Slope,10-6 D-1

Intercept,MSCF/D

Gp,max(BSCF)

50 15,697 4,033 0.26

100 5,449 2,908 0.53

250 2,064 2,066 1.00

500 1,086 1,635 1.51

750 705 1,379 1.95

1,000 552 1,236 2.24

1 250 392 1 030 2 63


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2010 SPE Unconventional Gas Conference Pittsburgh, PA 2325 February 2010

SPE132352 Continuous Estimation of Ultimate Recovery

(Currie/Ilk/Blasingame)

Stephanie M. CURRIE Texas A&M University (23 February 2010)

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 University

College Station, TX 77843-3116+1.979.845.4064 [email protected]

SPE 132352Continuous Estimation of Ultimate

Recovery

Presentation Outline


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Rationale for this WorkLiterature Review/OrientationDevelopment of the MethodValidation: (Numerical Simulation Case) East Tx Gas Well (SPE 84287)

Illustrative Examples: Field Example East Tx Gas Well (SPE 84287) Field Example Fractured Gas Well

Summary and Conclusions

(Ou

tline)

Rationale For This Work


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Uncertainty in Reserves Estimation for UnconventionalGas Reservoirs: Very low permeability. [longer transient flow periods] Arps' Decline Curves. [boundary-dominated flow only] (R

ationale)

Objectives: To show that the analysis of production data before the onset of

boundary-dominated flow will lead to significant overestimation ofreserves.

To reduce uncertainty in reserves estimates by applying thecontinuous EURapproach.

Orientation: "Hyperbolic" Rate Decline Relation


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(Orientation)

Discussion: "Hyperbolic" Rate Decline Relation "Hyperbolic" relation is the mostly used relation for reserves estimation. b-parameter should lie between 0 and 1 but is greater than 1 during

transient or transition flow regimes. Extrapolation of "hyperbolic" model prior to the onset of BD flow will

result in overestimation of reserves (Rushing et al[2007]).

Arps' HyperbolicRate-Time Relation

)/1()(1

)(b

i

i

tbD

qtq

+=

dtdqq

D g

g

/1

dtdq

q

dt

d

Ddt

dbg

g

/

1

"Loss-ratio" derivative

Definition of "Loss-ratio"

Orientation: Power-Law Exponential Rate Decline


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(Orientation)

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 basis for the power-law exponential relation. Very flexible model that can be used to match transient, transition, and

boundary-dominated flow data.

From:Ilk,D.,P

erego,A.D.,Rushing

,J.A.,andBlasingam

e,T.A.

2008.Exponentialvs.HyperbolicDeclineinTight

Gas

Sands

Understandingthe

OriginandImplicationsfor

Reserve

EstimatesUsingArps'DeclineCurves.P

aperSPE

116731presentedattheSPE

AnnualTechnicalConference

andExh

ibition,Denver,Colo

rado,21-24Septemb

er.

]exp[n

ii tDtDqq =

Development: Continuous EUR Method


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(Developme

nt)Review and Edit Data

50 days 250 days 2000 days...

Specify Time Intervals

Development: Continuous EUR Method

Analyze All Intervals Using the Find Lower Limit Using q


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50 days

250 days

2000 days

.

.

.

EUR=

6.04 BSCF

EUR=

4.92 BSCF

EUR=

3.10 BSCF

EUR=

3.09 BSCF

Gp,max=

0.37 BSCF

Gp,max=

1.03 BSCF

Gp,max=

2.58 BSCF

EUR=

3.10 BSCF

EUR=

3.05 BSCF

Analyze All Intervals Using

the Hyperbolic Relation

Analyze All Intervals Using the

Power-Law Exponential

Relation

Find Lower Limit Using qgvs. Gp Straight Line

Extrapolation

(Developme

nt)

Development: Continuous EUR MethodPl G D d EUR E i f M d l Ti f All I l


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Plot Gp Data and EUR Estimates from Models vs. Time for All IntervalsEURhyp Gp,maxEURPLE

Identify the Upper Limit forEUR Using the Power Law

Exponential Model

Identify the Lower Limit for

EUR Using the Straight Line

Extrapolation Technique

(Developme

nt)

Validation: Numerical Simulation Case


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(Num

ericalSimu

lationCase)

Discussion: East Tx Gas Well(SPE84287) Previously obtained model parameters (see Pratikno et al(2003) were

used to generate the synthetic flowrate response (with constant flowingwellbore pressure).

Tight gas well having a vertical fracture with finite conductivity (k=0.005md, FcD=10, and Ginp = 2.65 BSCF Gp (t=30 years) = 2.42 BSCF).



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(Num

ericalSimu

lationCase)

Discussion: Continuous EURusing Arps' Hyperbolic Decline Subsets of data are matched using the Arps' hyperbolic decline relation. EURof each subset is estimated (qgi is fixed). b-parameter value decreases (as expected) over time.



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(Num

ericalSimu

lationCase)

Discussion: Continuous EURusing Power-Law Exponential Model EURof each subset of data is estimated progressively. We do not fix any model parameter for the power-law exponential model. EUR stabilizes when boundary-dominated flow regime is established.



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(Num

ericalSimu

lationCase

)

Discussion: Gp,maxusing Straight Line Extrapolation Gp,maxfor each interval is referred as the "lower-limit" forEURusing the

straight line extrapolation (boundary-dominated flow assumption). Gp,maxis expected to increase with time for unconventional reservoirs.



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(Num

ericalSimu

lationCase

)

Discussion: Continuous EUR Upper and lower limits ofEURare established. EURestimate decreases over time and stabilizes at late times. EURestimate using the power-law exponential model stabilizes earlier

and is more conservative.

Field Example: East Tx Gas Well(SPE84287)


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(TightGasWell1

)

Discussion: East Tx Gas Well Hydraulically fractured gas well completed in a tight gas reservoir

(Bossier field) (see Pratikno et al(2003) for well/reservoir properties). Off-trend data are removed prior to analysis.



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(TightGasWell1

)

Discussion: Continuous EURusing Arps' Hyperbolic Decline b-parameter value ranges between 1.57 (all data) and 2.2 (earliest

interval) for the subsets of data. No strong evidence of boundary-dominated flow is observed.



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(TightGasWell1

)

Discussion: Continuous EURusing Power-Law Exponential Model All of the matches for each part of the data set are almost outstanding. EURestimates from the hyperbolic and power-law exponential relations

are close. However, power-law exponential relation matches all data.



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(TightGasWell1

)

Discussion: Gp,maxusing Straight Line Extrapolation Straight line extrapolation yields the minimum value for the reserves

estimate as boundary-dominated flow assumption is made. Gp,max(t) does not stabilize at late times.



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(TightGasWell1

)

Discussion: Conclusions Almost 50 percent decrease is observed in the EURestimate when

power-law exponential and hyperbolic relations are used. Character of flowrate data do not seem to be influenced by the

boundary-dominated flow behavior.

Field Example: Fractured Gas Well


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(TightGasWell2

)

Discussion: Fractured Gas Well Hydraulically fractured gas well completed in a tight gas reservoir. 2000 days of daily production data are available. We edit the data prior

to analysis.


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2010 SPE Unconventional Gas Conference Pittsburgh, PA 2325 February 2010SPE132352 Continuous Estimation of Ultimate Recovery



(TightGasWell2

)

Discussion: Continuous EURusing Power-Law Exponential Model EURof each subset of data is estimated progressively. We do not fix any model parameter for the power-law exponential model. Boundary-dominated flow regime is not observed (straight line D(t) trend).



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(TightGasWell2

)

Discussion: Gp,maxusing Straight Line Extrapolation Gp,max(t) increases with time and does not appear to converge as

boundary-dominated flow is not established. Straight line extrapolation provides a conservative way to identify the

"lower-limit" for reserves.



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(TightGasWell2

)

Discussion: Conclusions EURestimate decreases over time and stabilizes at late times as the

effects of transition to boundary-dominated flow are being established. Production data exhibit transition to boundary-dominated flow behavior

EURestimate may decrease further at a lower rate of stabilization.

Summary and Conclusions:

s)

(Summary):


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(SummaryandConclusions

This work presents a new procedure for the estimation of

reserves particularly in unconventional reservoirs.We employ simple rate-time relations (i.e., hyperbolic and

power-law exponential) in a "dynamic" manner in ourprocedure.

Time intervals are specified and rate-time relations are

extrapolated for each interval to create a "time-dependent"profile ofEURvs. time.Straight line Gp,maxextrapolation is performed to obtain the

"lower-limit" for reserves. This process also yields a "time-dependent" Gp,max(t) vs. tprofile.

Summary and Conclusions:

s)

(Conclusions):


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(SummaryandConclusions

The uncertainty in reserves estimate for unconventional

reservoirs is relatively high and a systematic methodology isrequired to reduce the uncertainties associated with reservesestimation.

Continuous EURprocedure evaluates the EURas a function oftime, and eventually EURstabilizes when complete boundary-

dominated flow regime is established. In this work we use the hyperbolic and power-law exponential

rate decline relations in conjunction to estimate the EUR.However, additional rate-time relations may be implemented inthe procedure.

"Lower-limit" ofEUR(obtained by straight line extrapolation)can be used as a "safeguard" to prevent overestimation ofreserves for each interval.

SPE 132352


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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 132352

Continuous Estimation of Ultimate

RecoveryEnd of Presentation

SPE 132352 (Currie) Continuous EUR (wPres)

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Transcript of SPE 132352 (Currie) Continuous EUR (wPres)