TIPS TRICKS AND TRAPS OF MATERIAL BALANCECALCULATIONS

M.R. CARLSON

this article begins on the next page FFTips, Tricks and Traps of Material Balance Calculations M.R. Carlson Applied Reservoir Engineering Ltd. Abstract The author has encountered a number of situations where drastically different interpretations are possible from oil material balances. The paper focusses on two of these field situations. In the first case, a gas cap could be interpreted which subsequent analysis disproved. In the second case, regression techniques converged to a total of three different combinations of gas cap and oil leg sizes. The existence of multiple solutions was not readily apparent. The discussion isapproached from three different perspectives, which are referenced to the two different field examples: 1. How production, geological, PVT (oil, gas and water) and historical information may be used to screen results and to apply the mathematical technique. 2. A new mathematical approach to error analysis for the Havlena and Odeh material balance has been developed, which the author has not seen elsewhere in the literature. Additionally, graphical interpretation can identify situations where multiple interpretations are likely. 3.

A spreadsheet has been used to implement the Havlena and Odeh material balance. Using some simple macros it is possible to quickly generate all of the diagnostic plots. This is a cost effective alternative to purchase of a specialty program. Aquifers are also included as well as statistical regression. Convergence is demonstrated as a criteria for confidence in material balance calculations. The new interpretations were significant. In the first case, it was an important factor in deciding to proceed with a string of successfulworkovers designed to recover attic oil. In the second case, the new interpretation cut short a field extension drilling program which was resulting in unexpected dry holes. Introduction This paper is based on half a dozen material balance studies that the author has prepared on a consulting basis. Four were for carbonate reservoirs and two were for sandstone reservoirs. The contents are based on this experience and thus represent a mixture of field case, theoretical analysis (developed during projects) and an evolving approach to material balance calculations. Two examples are given,however, they represent the combined experience on all of the above reservoirs. Scales have, for the most part, been removed; since the data is from actual studies. The paper has been structured as follows: 1. A quick summary is made of the material balance equations. These are used for the derivation of the error analysis. No derivation of the equations was made since this is comprehensively covered in many reservoir engineering textbooks. A summary of the various Havlena and Odeh plots is also made, since this material is discussed in the paper. 2.

An analysis of the effects of errors in pressure measurement is presented. The author uses this for weighting data points. 3. Some practical observations are made on statistical minimization. 4. The general approach used by the author is outlined. 5. Two typical material balance situations are described, which highlight error analysis and data screening. The paper differs slightly from the norm for a technical paper. The -conclusions+ are presented as -tips+ and -traps+ since, in many cases, they represent matters of style. For instance, the author chooses to keep some pressure points based on his error analysis, where others might choose to use this (or similar) analysis to weight each point individually. Material Balance Equation The author prefers the method of Havlena and Odeh. Although favoured for its graphical interpretation, it also forces one to think in terms of reservoir conditions, a major benefit. The Havlena and Odeh material balance equation is as follows:

(1) The above terms are expanded upon as follows: (2) (3) (4) (5) These symbols are in fairly common usage and may also be found at the end of this paper under Nomenclature.

II

M.R. CARLSONApplied Reservoir Engineering Ltd.

Tips, Tricks and Traps ofMaterial Balance Calculations

The Journal of Canadian Petroleum Technology

F= N[Eo+m Eg + E/,",] + WeB",...................................................(1)

The author prefers the method of Havlena and Odeh. Althoughfavoured for its graphical interpretation, it also forces one to thinkin tenns of reservoir conditions, a major benefit. The Havlena andOdeh material balance equation is as follows:

(C..S" + C/ ) ( )Efio,=U+m)Boi (l-S) p;-p

.~ (5)

Eg

=Bo;r=:; -ll (4)

Eo = (Bo - Bo;) + (RSi - Rs)Bg (3)

F =N p[Bo +(Rp - Rs )B.]+ WpB., (2)

Material Balance Equation

hensively covered in many reservoir engineering textbooks.A summary of the various Havlena and Odeh plots is alsomade, since this material is discussed in the paper.

2. An analysis of the effects of errors in pressure measurementis presented. The author uses this for weighting data points.

3. Some practical observations are made on statistical mini­mization.

4. The general approach used by the author is outlined.

5. Two typical material balance situations are described, whichhighlight error analysis and data screening.

The paper differs slightly from the nonn for a technical paper.The "conclusions" are presented as "tips" and "traps" since, inmany cases, they represent matters of style. For instance, theauthor chooses to keep some pressure points based on his erroranalysis, where others might choose to use this (or similar) analy­sis to weight each point individually.

The above tenns are expanded upon as follows:

These symbols are in fairly common usage and may also befound at the end of this paper under Nomenclature.

rAb~tr~~t:'" ._~ ..: _.., ~ '~.,-: ; . .jI' , ' ',' ,,'. j , . 1, The author has encountered a number of situations wherelIdrastically different interpieta~ons 'are possible from oil material

Ibalances. The, paper focusses on;two ,of these field situations. Inthe first case, a gas cap could be'interpreted which subsequentl

tanalysis disproved. In the second case,- regression techniques I

I,converged to a tot,al of ~~e different combinations of gas cap Iand oil leg sizes. The 'existence ofmultiple: solutiqns.was not,

!readily apparent. ". '.' . .": .:::;,~.'<'"! The discussion is approached froii-t three diffeient;'piis~ec~~itives, which are re~erenced to ~he'tW9 diffe~entfiel(ft<x~m~fe~~<,jI 1. How productIon, geologIcal; PVT (011, gas an<i w~tertahq1I historical infonnation mayoeused'to screenJ~sultfa~d<~p.~! apply the mathematical technique.,', '.' " . ';".: .... ,<,i 2. A new mathematical ap~roach to eri:oranaly~is:f()r:tIie1J Havlena and Odeh matenal balancehas'been.aevelope~,.'J

I which the author has not seen elsewhere jn'the'literatuie~;! Additionally, graphical interpretation can identifY ~ifua/I tions where multiple interpretations are likely.. '" .... '. : ;I 3. A spreadshe~t has been used. to implem~nt.the Havl.ena':~n.~ ,I Odeh matenal balance, Usmg some SImple macros 'It 18·i possible to quickly generate all of the diagnostic',plots"

This is a cost effective alternative to purchase of a special- i

ty program. Aquifers are also included as welt"as 'statistical~regression. Convergence is demonstrated as a'criteria fot;

I confiden'ce in material balance calculations. '. :. '.• ' ~,'iI The new interpretations were significant. In the first c~s~,jt,Iwas an important factor in deciding to proceed with a string ofIsuccessful workovers designed to recover attic oil. In the second:case, the new interpretation cut short a field extension drilling,!program which was resulting in unexpected dry holes.L .._._ .._ ....:._. .._.__ _... '.

IIIIIIrI In~::~~:::~~aSed on half a dozen material balance studies

Ithat the author has prepared on a consulting basis. Four were for

,. carbonate reservoirs and two were for sandstone reservoirs. The

contents are based on this experience and thus represent a mixtureI of field case, theoretical analysis (developed during projects) and111 an evolving approach to material balance calculations. Two exam-

ples are given, however, they represent the combined experience

Ion all of the above reservoirs. Scales have, for the most part, beenremoved; since the data is from actual studies. The paper has beenstructured as follows:

II 1. A quick summary is made of the material balance equations., These are used for the derivation of the error analysis. NoI derivation of the equations was made since this is compre-

~r-_,~_~_

i\,I!!\I1

a[Eo+mEg+EjW]

N ap[Eo + mEg + EjW]

aFaN apap = [Eo + m Eg+ EjU' ]

Then dividing through by N,

Dividing by the drive indices term yields.

aF1 aN apNap:= N[Eo+mEg+EJ-.]

Re-arranging we get:

aF_aN[ ] a[Eo+mEg+EjW]--- Eo+mEg+EJ-. +N aap ap 'P

F E-:=N+mN....!..Eo Eo

F

F:=N Eo

This will yield a straight line plot with a slope of mN and anintercept of N, the original oil-in-place. For reservoirs that havewater influx:

If F is plotted against Eo, a straight line of slope N is obtained.For a reservoir with gas cap and solution gas drive the followingcombination may be plotted:

Graphical Interpretation/

This form of the equation can be interpreted graphically in anumber of different ways(l). The fIrst is for a solution gas drive inwhich there is no gas cap nor any water influx:

which yields a straight line with a slope of Bw and an intercept ofN.

Substituting the Right Hand Side "RHS" of Equation (1) for theLHS in the fIrst term of the RHS of the above equation,

This is a handy form since it shows the change in aOlP isrelated to the percentage change in underground withdrawals anddrive indices.

Aquifer Mathematical Technique

'The author has used the approximate water influx theory ofFetkovitch for fInite aquifers in all of the cases described. Themethod is not quite as accurate as the Van Everdingen and Hursttechnique. The largest error is during early times, as demonstratedin the example calculation outlined in Dake(2). In general, thiserror is not signifIcant.

1 aN 1 aF--:=

Nap F ap.............................................(6)

Error Analysis

1.16

1.2 .-------------------,

... \

:0: I1I

IjI,I

"i II

:·1I!

'iI\

f1j!I

Iii

~.,

35

FIGURE 2: PVT data used in error analysis.

Rs (m3/m3)00.--'--'---'-------------.,

Pressure (kPa)

-i- ..

.0

PVT DataAlmost all the variables (Eo, Eg, and Efw) are functions of pres­

sure. In order to solve this problem it is necessary to make somesimplifying assumptions regarding PVT properties. Based on theauthor's experience on data from numerous studies, black oil PVTdata can usually be reasonably approximated by straight lines.

10

11..-__-'-__-'-__--1. '--_---'

o

December 1997, Volume 36, No. 11

1.1

-.,

Pressure (kPa)

FIGURE 1: PVT data used in error analysis.

In this section, the accuracy and precision of the material bal­ance calculation are examined. There will be two parts to the dis­cussion. The fIrst describes sensitivity to pressure measurementsand the second describes sensitivities to values of m.

The fIrst step is differentiating Equation (1) with respect to thepressure. Note that the water term has been excluded from thisanalysis. Using the product rule:

Bo

I'---r_-..,.':':••..,.,...77........."'.<:--..,..",.-.~-...