Production Decline Analysis

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Introduction

Production decline analysis is a traditionalmeans of identifying well production problemsand predicting well performance and life based

on real production data.

It uses empirical decline models that have littlefundamental justications. These modelsinclude the following:

Exponential decline constant fractionaldecline!

"armonic decline

"yperbolic decline

Production Decline Analysis


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#lthough the hyperbolic decline model is moregeneral$ the other two models are degenerations of

the hyperbolic decline model. These three modelsare related through the following relative declinerate e%uation #rps$ &'()!:

where b and d are empirical constants to be

determined based on production data. *hen d + ,$E%. -.&! degenerates to an exponential declinemodel$ and when d + &$ E%. -.&! yields a harmonicdecline model.

*hen , d &$ E%. -.&! derives a hyperbolic


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Exponential Decline

The relative decline rate and productionrate decline e%uations for the exponential

decline model can be derived fromvolumetric reservoir model.

/umulative production expression isobtained by integrating the production

rate decline e%uation.


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Relative Decline Rate

/onsider an oil well drilled in a volumetric oilreservoir.

0uppose the well1s production rate starts to declinewhen a critical lowest permissible! bottom2hole

pressure is reached. 3nder the pseudo4steady2state 5ow condition$ the production rate at a givendecline time t can be expressed as


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The cumulative oil production of the well after theproduction decline time t can be expressed as

The cumulative oil production after the productiondecline upon decline time t can also be evaluated basedon the total reservoir compressibility:


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Ta6ing derivative on both sides of this e%uationwith respect to time t gives the di7erentiale%uation for reservoir pressure:

8ecause the left2hand side of this e%uation is %and E%. -.9! gives


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Production rate decline

E%uation -.! can be expressed as


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0ubstituting E%. -.&;! into E%. -.9! gives the wellproduction rate decline e%uation:

which is the exponential decline model commonlyused for production decline analysis of solution2gas2drive reservoirs. In practice$ the following form of E%.-.&)! is used:


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Cumulative production

Integration of E%. -.&! over time gives an

expression for the cumulative oil production sincedecline of


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Determination of decline rate

The constant b is called the continuous decline rate.

Its value can be determined from production historydata.

If production rate and time data are available$ the b

value can be obtained based on the slope of thestraight line on a semi2log plot. In fact$ ta6inglogarithm of E%. -.&! gives

which implies that the data should form a straightline with a slope of b on the log%! versus t plot$ ifexponential decline is the right model. Pic6ing up

any two points$ t&$ %&! and t9$ %9!$ on the straight


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If production rate and cumulative production dataare available$ the b value can be obtained based onthe slope of the straight line on an


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=epending on the unit of time t$ the b can havedi7erent units such as month4& and year4&.

The following relation can be derived:

where ba$ bm$ and bd are annual$ monthly$ and

daily decline rates$ respectively.


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Eective decline rate

8ecause the exponential function is not easy touse in hand calculations$ traditionally thee7ective decline rate has been used.

0ince e4x > &4x for small x2values based onTaylor1s expansion$ e4b &4b holds true for smallvalues of b.

The b is substituted by b1$ the e7ective declinerate$ in eld applications. Thus$ E%. -.&!

becomes

# ain$ it can be shown that


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=epending on the unit of time t$ the b1 can havedi7erent units such as month4& and year4&. Thefollowing relation can be derived:


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Example Problem 8.1 ?iven that a well has

declined from &,, stb@day to ' stb@dayduring a &2month period$ use the exponentialdecline model to perform the following tas6s:

&. Predict the production rate after &&more months

9. /alculate the amount of oil producedduring the rst year

;. Project the yearly production for thewell for the next ) years


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olution

&. Production rate after && moremonths:


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In summary$


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!armonic Decline

*hen d + &$ E%. -.&! yields di7erentiale%uation for a harmonic decline model:

which can be integrated as

where %0is the production rate at t + ,.

Expression for the cumulative production isobtained by integration:


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!yperbolic Decline

*hen , d &$ integration of E%. -.&! gives


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Expression for the cumulative production isobtained by integration:


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"odel Identi#cation

Production data can be plotted in di7erentways to identify a representative declinemodel.

If the plot of log%! versus t shows a straight

line Aig. -.&!$ according to E%. -.9,!$ thedecline data follow an exponential declinemodel.

If the plot of % versus


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If the plot of


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$i%ure 8.1 A semilo% plot of & versus t indicatin% an

exponential decline.


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$i%ure 8.' A plot of (pversus & indicatin% an

exponential decline.


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$i%ure 8.) A plot of lo%*&+ versus lo%*t+

indicatin% a


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$i%ure 8.- A plot of (p

versus lo%*&+ indicatin%

a ,armonic


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$i%ure 8. A plot of relative decline rate versus

production rate.


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$i%ure 8./ Procedure for determinin% a0 and


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Determination of "odel Parameters

Bnce a decline model is identied$ the modelparameters a and b can be determined by ttingthe data to the selected model.

Aor the exponential decline model$ the b value canbe estimated on the basis of the slope of the

straight line in the plot of log%! versus t E%.C-.9;D!.

The b value can also be determined based on the

slope of the straight line in the plot of % versus


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The b value can also be estimated basedon the slope of the straight line in the plotof


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Illustrative Examples

Example Problem 8.' Aor the data given inTable -.&$ identify a suitable decline model$determine model parameters$ and projectproduction rate until a marginal rate of 9)stb@day is reached.


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olution# plot of log%! versus t is presentedin Aig. -.$ which shows a straight line.

#ccording to E%. -.9,!$ the exponentialdecline model is applicable. This is furtherevidenced by the relative decline rate shownin Aig. -.-.


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$i%ure 8. A plot of lo%*&+ versus t s,o2in% an

exponential


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$i%ure 8.8 Relative decline rate plot s,o2in%

exponential


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0elect points on the trend line:


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$i%ure 8.3 Pro4ected production rate by aexponential

decline model.


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Example Problem 8.) Aor the data given inTable -.9$ identify a suitable decline model$

determine model parameters$ and projectproduction rate until the end of the fth year.


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olution # plot of relative decline rate isshown in Aig. -.&,$ which clearly indicates a

harmonic decline model.

Bn the trend line$ select

%,+ &,$,,, stb+day at t + ,

%&+ )$-, stb+day at t + 9 years:

Therefore$ E%. -.(,! gives

Projected production rate prole is shown in

Aig. -.&&.


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$i%ure 8.15 Relative decline rate plot s,o2in%,armonic


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$i%ure 8.11 Pro4ected production rate by a


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Example Problem 8.- Aor the data given inTable -.;$ identify a suitable decline model$

determine model parameters$ and projectproduction rate until the end of the fth year.


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olution # plot of relative decline rate is shown


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olution # plot of relative decline rate is shownin Aig. -.&9$ which clearly indicates a hyperbolicdecline model.


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$i%ure 8.1' Relative decline rate plot s,o2in%


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$i%ure 8.1) Relative decline rate s,ot s,o2in%


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Projected production rate prole is shown in Aig.-.&(.


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Documents

Production Decline Analysis