Material Balance Analysis Theory and Practice

7/23/2019 Material Balance Analysis Theory and Practice

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Material Balance Analysis Theory

Material Balance AnalysisMaterial balance analysis is an interpretation method used to determine original fluids-in-place

(OFIP) based on production and static pressure data The general material balance e!uation

relates the original oil" gas" and #ater in the reser$oir to production $olumes and current pressure

conditions % fluid properties The material balance e!uations considered assume tan& type

beha$ior at any gi$en datum depth - the reser$oir is considered to ha$e the same pressure and

fluid properties at any location in the reser$oir This assumption is !uite reasonable pro$ided that

!uality production and static pressure measurements are obtained

'onsider the case of the depletion of the reser$oir pictured belo# At a gi$en time after the

production of fluids from the reser$oir has commenced" the pressure #ill ha$e dropped from its

initial reser$oir pressure pi" to some a$erage reser$oir pressure p sing the la# of mass balance"

during the pressure drop (p)" the epansion of the fluids lefto$er in the reser$oir must be e!ual to

the $olume of fluids produced from the reser$oir

The simplest #ay to $isuali*e material balance is that if the measured surface $olume of oil" gas

and #ater #ere returned to a reser$oir at the reduced pressure" it must fit eactly into the $olume

of the total fluid epansion plus the fluid influ


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The general form of the e!uation can be described as net #ithdra#al (#ithdra#al - in+ection) ,

epansion of the hydrocarbon fluids in the system cumulati$e #ater influ This is sho#n in the

e!uation belo#

.ach term in the e!uation can be grouped based on the part of the system it represents The table

belo# sho#s the terms and a simplified $ersion of the general e!uation based on the terms

Summary of Terms in the Material Balance Equation

Term Description

/implifiedgenerale!uation

0olume of#ithdra#al(production ain+ection) atreser$oirconditions is

determined bthe oil" #atergas producedthe surface

Total epans

If the oil coluis initially at tbubble point"reducing the

pressure #illresult in therelease of gaand theshrin&age of The remainin#ill consist ofand theremaining ga


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still dissol$edthe reducedpressure

1as epansiofactor For

eample as treser$oirdepletes" thecap epandsreser$oir $olupre$iouslyoccupied by o

.$en though#ater has lo#compressibilithe $olume oconnate #atethe system is

usually largeenough to besignificant T#ater #ill epto fill theemptying porspaces as threser$oirdepletes As reser$oir isproduced" thepressuredeclines and

entire reser$opore $olume reduced due compaction change in$olume epean e!ual $oluof fluid asproduction anthereforeadditi$e in theepansion te

2atio of gas c

to original oil place A gas also implies tthe initialpressure in thoil column mbe e!ual to thbubble pointpressure


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If the reser$oconnected toacti$e a!uifethen once thepressure drocommunicate

throughout threser$oir" the#ater #illencroach intoreser$oirresulting in a#ater influ Tcalculate theamount of #ainflu" either Fet&o$ich" 'aTracey"

3ot all terms #ill be used at any one time" but the purpose of a complete e!uation is to pro$ide abasis from #hich to analy*e many types of reser$oirs4 gas epansion" solution gas dri$e" gas cap

dri$e" #ater dri$e" etc Terms that are not needed for a particular reser$oir type #ill cancel out of

the e!uation For eample" #hen there is no gas cap originally present" the 1 and Bgiterms are

*ero

Application of Material Balance

Material balance is an important concept in reser$oir engineering since it is a performance-based

tool used to establish the original $olume of hydrocarbons-in-place in a reser$oir that typically

contains many #ells Additionally" the process of matching pressure-based depletion trends

bet#een #ells gi$es the reser$oir engineer the ability to create a performance-based $ie# of the

connected pore $olume in the reser$oir 'onse!uently" it is important that4

5 All fluids ta&en from or in+ected into the reser$oir be measured accurately

6 Pressure" $olume" and temperature characteristics (P0T properties) be measured and

$alidated /ubsurface samples from se$eral properly conditioned #ells are preferred

7 At least one static pressure from each #ell prior to production and se$eral after production

has commenced are re!uired to achie$e good results

The establishment of original-in-place fluid $olumes and connected pore $olume are critical to the

de$elopment of ongoing depletion plans" especially #here secondary or tertiary reco$ery methods

are being considered


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Gas Material Balance

1as material balance is a simplified $ersion of the general material balance e!uation 8hen the

general e!uation is reduced to its simplest form containing only gas terms" it appears as sho#n

belo#4

In this e!uation" it is assumed that gas epansion is the only dri$ing force causing production This

form is commonly used because the epansion of gas often dominates o$er the epansion of oil"

#ater" and roc& Bg is the ratio of gas $olume at reser$oir conditions to gas $olume at standard

conditions This is epanded using the real gas la#

The reser$oir temperature is considered to remain constant The compressibility factor (9) for

standard conditions is assumed to be 5 The number of moles of gas do not change from reser$oir

to surface /tandard temperature and pressure are &no#n constants 8hen Bgis replaced and the

constants are cancelled out" the gas material balance e!uation then simplifies to4

8hen plotted on a graph of p%9 $ersus cumulati$e production" the e!uation can be analy*ed as a

linear relationship /e$eral measurements of static pressure and the corresponding cumulati$e

productions can be used to determine the -intercept of the plot - the original gas-in-place (O1IP)"

sho#n as 1 in the e!uation


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Advanced Gas Material Balance

For a $olumetric gas reser$oir" gas epansion (the most significant source of energy) dominates

depletion beha$iour: and the general gas material balance e!uation is a $ery simple yet po#erful

tool for interpretation ;o#e$er" in cases #here other sources of energy are significant enough to

cause de$iation from the linear beha$iour of a p%9 plot" a more sophisticated tool is re!uired For

this" a more ad$anced form of the material balance e!uation has been de$eloped" and the

standard p%9 plot is modified to maintain a linear trend #ith the simplicity of interpretation

In his #or& on 'BM" to replace p%9 By modifying 9" parameters to

incorporate the effects of adsorbed gas #ere incorporated so the total gas-in-place is interpreted

rather than +ust the free gas-in-place: and a straight line analysis techni!ue is still used This

concept has been etended to additional reser$oir types #ith Fe&ete?s p%9>> method (Moghadam

et al 6@@=)

The reser$oir types considered in the ad$anced material balance e!uation are4 o$erpressured

reser$oirs" #ater-dri$e reser$oirs" and connected reser$oirs The total 9>> e!uation is sho#n belo#

#ith the modified material balance e!uation


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Overpressured Reservoir

At typical reser$oir conditions" gas compressibility is orders of magnitude greater than that of the

formation roc& or residual fluids In reser$oirs at high initial pressures the gas compressibility is

much lo#er" in the same order of magnitude as the formation A typical eample of this #ould be

an o$erpressured reser$oir" #hich is a reser$oir at a higher pressure than the hydrostatic column

of #ater at that depth - in other #ords" a higher than epected initial pressure gi$en the depth In

this situation" ignoring the formation and residual fluid compressibility #ill result in o$er-prediction

of the original gas-in-place The initial depletion #ill sho# effects of both depletion and reser$oir

compaction and the slope of a p%9 plot #ill be shallo#er Once the pressure is much lo#er than the

initial pressure" gas epansion is dominant and a steeper slope is obser$ed on the p%9 plot 8hen

matching on the shallo#er slope of this bo#-shaped trend" all later pressure data #ill be lo#er

than the analysis line" and the estimated original gas-in-place #ill be higher than the true original

gas-in-place The plot belo# sho#s an o$erpressured reser$oir matched on the initial data and the

analysis line of the ad$ance material balance method


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Based on the definition of compressibility" the follo#ing e!uation represents the total effect of

formation and residual fluid compressibility4

The approimate form of this e!uation" found by considering compressibility for oil" #ater" and the

formation as constant: and e as 5 " is4

In order to use this compressibility in the material balance e!uation" the change in pore $olume is

ta&en relati$e to the initial pore $olume The rigorous and approimate forms are sho#n belo#

2igorous form4

Approimate form4

WaterDrive Reservoir

/ome gas reser$oirs may be connected to a!uifers that pro$ide pressure support to the gas

reser$oir as it is depleted In this case" the pressure decrease in the gas reser$oir is balanced by

#ater encroaching into the reser$oir As this happens" the pore $olume of gas is decreasing and

the a$erage reser$oir pressure is maintained Often this reser$oir #ill sho# a flat pressure trend

after some depletion An eample of this beha$iour on a p%9 plot is sho#n belo#


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The change in reser$oir $olume due to net encroached #ater can be determined from the

follo#ing e!uation4

To use this in the material balance" the change in pore $olume is ta&en relati$e to the initial pore

$olume" sho#n belo#

8hen dealing #ith this e!uation" the ma+or un&no#n $alue to be determined is #ater

encroachment from the a!uifer (8e) T#o a!uifer models are pro$ided to determine net

encroached #ater4 /chilthuis /teady-/tate Model and Fet&o$ich Model


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Schilthuis Steady-State Model

This is the simplest a!uifer model and assumes the rate of #ater influ is proportional to pressure

dra#do#n In this model it is assumed that the a!uifer $olume is much larger than the gas

reser$oir and remains at the initial pressure

sing this model" the only parameter to sol$e for is the transfer coefficient ()

Fetkovich

In the Fet&o$ich a!uifer" the a!uifer is assumed to be in pseudo-steady state and deplete

according to the material balance e!uation In this model" both the a!uifer $olume and transfercoefficient must be determined The e!uations are sho#n belo#

8hile the transfer coefficient is defined" the re!uired inputs to calculate the transfer coefficient are

often not &no#n More commonly the transfer coefficient is determined as part of matching the p%9

plot

!onnected Reservoir

Another scenario #hich #ill appear as pressure support on the p%9 plot is the connected reser$oir

model The generic description is that t#o gas reser$oirs are connected" described by a transfer

coefficient bet#een them" and gas feeds from one tan& to the other as one of the tan&s is

depleted This can be obser$ed #ith t#o gas reser$oirs #ith some communication" t#o *ones in a

reser$oir #ith different permeability or some barrier bet#een them" or e$en another #ay of


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considering the situation of free and adsorbed gas in a reser$oir Because both #ater-dri$e and

connected reser$oirs sho# pressure support" it can be easy to mista&e #hich model should be

used In a connected reser$oir" the influ into the main reser$oir is gas as compared to influ of

#ater in #ater-dri$e /o the pressure support #ill be accompanied by more gas in the reser$oir

rather than a shrin&ing reser$oir as in #ater-dri$e Typically if the initial p%9 trend points to an

original gas-in-place smaller than the cumulati$e production" a connected reser$oir #ill be the

appropriate model to use

For a connected reser$oir" the material balance e!uation is #ritten as sho#n belo# to account for

gas influ

This can be con$erted into a dimensionless term similar to the terms describing relati$e change inpore $olume (c#ip" cep" and cd) for other models" as sho#n belo#


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/imilar to the #ater-dri$e model" the influ of gas from the second reser$oir (1 T) is li&ely not a

&no#n $alue" and so must be determined based on the si*e of the connected reser$oir and the

transfer coefficient bet#een the reser$oirs The e!uation for gas influ is sho#n belo#

Oil Material Balance

As seen in the general material balance e!uation there are many un&no#ns" and as a result

finding an eact or uni!ue solution can be difficult ;o#e$er" using other techni!ues to help

determine some $ariables (for eample" m or original gas-in-place from $olumetrics or seismic)"

the e!uation can be simplified to yield a more useful ans#er 0arious plots are a$ailable to conduct

an oil material balance rather than calculating an ans#er from indi$idual measurements of

reser$oir pressure The primary analysis plot is the

"avlenaOdeh #All Reservoir Types$

/imilar to the interpretation of gas material balance" oil material balance uses plotting techni!ues

;o#e$er" unli&e the e!uation for single-phase gas epansion" the standard form of the material

balance e!uation for oil reser$oirs does not easily yield a linear relationship The e!uation can be

organi*ed to sho# linear beha$ior Based on the rearrangement belo#" the large combinations of

terms are used as and y #hile 1 is the slope and 3 is the intercept This of course implies that#ater influ term for each data point is a &no#n $alue" or the simpler scenario that there is no

#ater influ Additionally" if the #ater influ is neglected in calculating the terms the result #ill be

non-linear beha$ior on the plot This can be a diagnostic to determine the presence of #ater dri$e

In practice" the scatter in the data may be great enough and the signature of #ater dri$e subtle

enough that de$iation from linear beha$ior on the ;a$lena-Odeh plot may go unnoticed

An eample of the plot is sho#n belo# The scatter sho#n in the data points demonstrates the

difficulty in determining trends in the reser$oir beha$iour


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This method #or&s for most reser$oir types In the case of an undersaturated reser$oir (abo$e

bubble point) the .g Bgi> .f#term #ill be *ero and this plot #ill not be as useful The standard

;a$lena-Odeh plot can be substituted for one that ecludes free gas terms

"avlenaOdeh % vs& Et#'o (nitial Gas !ap$

If the reser$oir to be analy*ed has no initial free gas" the free gas terms of the e!uation can be

eliminated This e!uation is no# much simpler to lineari*e In the e!uation sho#n belo#" the total

epansion term is split into the oil and #ater % formation epansion terms Once again" the

inclusion of #ater influ is such that it is assumed to be &no#n

In this form of the e!uation" 3 is the slope on a plot of epansion terms $ersus #ithdra#al and

influ terms There is no intercept so the analysis line is typically forced through *ero /imilar to

the ;a$lena-Odeh plot that includes gas terms" if #ater influ is neglected and a non-linear trend

results" this can be a diagnostic for obser$ing #ater dri$e effects An eample of the plot is sho#n

belo#


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' vs& Time

sing plots of $arious terms in the material balance e!uation can be used for o$erall analysis" but

each pressure measurement can be independently used for material balance calculation'omparing the results of o$erall analysis and single-point calculations demonstrates #hether there

is consistency bet#een the methods It is epected that the single-point calculations #ill remain in

a trend around the original oil-in-place determined from the o$erall analysis This comparison can

be plotted as a series of original oil-in-place results displayed at the point in time of the pressure

measurement" #ith a continuous line at the $alue of original oil-in-place from the o$erall analysis

The plot is sho#n belo#

This plot is also useful as a diagnostic to determine if the correct reser$oir type has been

assumed" and also to assess the data !uality An inconsistent trend usually indicates that the

!uality of the pressure measurements are not good" or the definition of the #ells in the reser$oir

should be re$ie#ed A consistent up#ard trend indicates that another dri$e mechanism may be

present" #hereas a do#n#ard trend indicates that not all #ells in the reser$oir ha$e been included

in the analysis


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)ressure "istory Match

The pressure match method employs an iterati$e procedure that uses the $alues of original oil-in-

place" original gas-in-place" and 8 to calculate the reser$oir pressure $ersus time The pressure

match is then plotted against the real measured static reser$oir pressures and compared This is

by far the most robust and easily understood material balance techni!ue" as4

Pressure and time are easily understood $ariables" and so sensiti$ity analysis can be

conducted relati$ely easily

C se of time allo#s the analyst to see directly the impact of4

'hanging #ithdra#al rates" especially shut-ins on reser$oir pressure decline

In+ection operations on pressure response

8ater dri$e and connected reser$oirs on reser$oir depletion" especially since

these are both cumulati$e #ithdra#al and time-based processes

D A relati$ely simple" iterati$e process is used to achie$e a uni!ue solution #herein4

/tart #ith the simplest solution (oil and%or gas depletion only) and then

proceed to more comple models only if demonstrated to be re!uired

.mploy a left-to-right matching techni!ue (early-time to late-time)" #herein

initial reser$oir pressure is matched first" follo#ed by early-time depletionresponse" and then late-time responses /ince #ater dri$e and connectedreser$oir models are cumulati$e #ithdra#al and time-based" their responsesare minimal at early-times and maimi*ed at late-times

E Ma+or changes to depletion" such as con$ersion to storage or blo#do#n" can be both

segregated (time) and integrated in a single analysis method

An eample of a pressure history match is sho#n belo#4


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Drive (ndices

ri$e indices for oil reser$oirs indicate the relati$e magnitude of the $arious energy sources acting

in the reser$oir A simple description of a dri$e inde is the ratio of a particular epansion term to

the net #ithdra#al (hydrocarbon $oidage) These dri$e indices are cumulati$e and #ill change as

the reser$oir is produced A plot of dri$e indices and the details of specific dri$e indices are sho#n

belo#

Summary of Drive (ndices

Drive (nde* Description

epletion ri$e Inde

/egregation (1as 'ap) ri$e Inde

8ater ri$e Inde

Formation and 'onnate 8ater 'ompressibility Inde

If the dri$e indices do not sum to unity (or $ery close to 5)" the correct solution to the material

balance has not been obtained

Dia+nostics Da,e and !amp-ell

a&e and 'ampbell plots are used as diagnostic tools to identify the reser$oir type based on the

signature of production and pressure beha$iour The plots are established based on the


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assumption of a $olumetric reser$oir" and de$iation from this beha$iour is used to indicate the

reser$oir type

In the a&e plot" the simplest oil case of solution gas % depletion dri$e (no gas cap" no #ater dri$e)

is used to determine the aes of the plot The material balance e!uation is rearranged as sho#n

belo#

In a $olumetric reser$oir producing due to depletion dri$e only" production is balanced by the oil

and #ater%formation epansion and the original oil-in-place is constant If a plot of cumulati$e oil

production $ersus the net #ithdra#al o$er epansion is created #ith this reser$oir type?s data" the

points #ill remain along a hori*ontal line

If a gas cap is present" there #ill be a gas epansion component in the reser$oir?s production As

production continues and the reser$oir pressure decreased" the gas epansion term increases

#ith an increasing gas formation $olume factor To balance this" the #ithdra#al o$er

oil%#ater%formation epansion term must also continue to increase Thus in the case of gas cap

dri$e" the a&e plot #ill sho# a continually increasing trend

/imilarly" if #ater dri$e is present the #ithdra#al o$er oil%#ater%formation epansion term must

increase to balance the #ater influ 8ith a $ery strong a!uifer the #ater influ may continue to

increase #ith time" #hile a limited or small a!uifer may ha$e an initial increase in #ater influ that

e$entually decreases


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The 'ampbell plot is a $ery similar diagnostic to a&e" #ith the eception that it incorporates a gas

cap if re!uired In the 'ampbell plot" the #ithdra#al is plotted against #ithdra#al o$er total

epansion" #hile the #ater influ term is neglected If there is no #ater influ" the data #ill plot as a

hori*ontal line If there is #ater influ into the reser$oir" the #ithdra#al o$er total epansion term

#ill increase proportionally to the #ater influ o$er total epansion The 'ampbell plot can be more

sensiti$e to the strength of the a!uifer In this $ersion of the material balance" using only . T

neglects the #ater and formation compressibility (compaction) term The 'ampbell plot is sho#n

belo#


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.oida+e Replacement Ratio

8ater in+ection is a secondary reco$ery techni!ue that is often employed as a means for pressure

maintenance to re-energi*e a reser$oir There are many easy-to-use techni!ues for monitoring a

#ater in+ection%#aterflood pro+ect" (;all plot" 8O2"

0oidage replacement ratio is defined as the ratio of in+ected reser$oir $olume to produced

reser$oir $olume


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Typically" #aterflooding commences after a period of primary production The purpose of

#aterflooding is to enhance reco$ery by maintaining reser$oir pressure" or #hen necessary"

increasing reser$oir pressure so that it approaches the bubble point pressure to maintain solution

gas 'onse!uently" instantaneous $oidage replacement ratio often commences at $alues greater

than one" and then declines gradually to one as the target reser$oir pressure is achie$ed On the

other hand" cumulati$e

0oidage replacement calculations are often conducted on the entire reser$oir /ince reser$oirs are

more heterogenous than homogenous" e$en though the

se of $oidage replacement calculations is an ecellent #ay to better understand connecti$ity#ithin a reser$oir

.olatile Oil Walsh %ormulation

0olatile oil is also called high shrin&age crude oil" or near-critical oil It contains relati$ely fe#er

hea$y molecules and more intermediates than blac& oils It has a higher API (typically greater than

)" and is typically lighter in color

A small reduction in pressure belo# the bubble point causes the release of a large amount of gas

in the reser$oir An additional property is used to the describe $olatile oil - the $olatile oil ratio 2$

The $olatile oil ratio describes the amount of $olatili*ed oil in the reser$oir gas phase and is

typically epressed in


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2egular material balance does not account for $olatile oil In a reser$oir containing $olatile oil" the

8alsh formulation is used to calculate original oil-in-place The e!uations #hich are modified from

standard material balance are sho#n belo#

Terms Descrip

Modified#ithdra#term for$olatile o

Modifiedepansioterm for$olatile o

Modifiedgasepansio

term for$olatile o

!BM Material Balance

There are three forms of the material balance a$ailable for 'BM analysis4


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There are t#o sources of gas in 'BM reser$oirs" the gas adsorbed in the matri" and the gas

stored in the cleat space4

1total, 1adsorbed 1cleats

The gas adsorbed in the coal matri can be described by the Gangmuir isotherm4

As the abo$e e!uation epresses $olume in scf%ton" the total $olume of adsorbed gas in the

reser$oir can be found by the follo#ing e!uation4

8here4

A , area (acres)

h , net pay (ft)

1adsorbed, $olume of adsorbed gas (mmscf)

P , pressure (psia)

PG , Gangmuir pressure (psia)

0G , Gangmuir $olume (scf%ton)

b, bul& density (g%cm7)

The gas contained in the cleat $olume is described by the e!uation for $olumetric storage in the

pore space4

8here4

A , area (acres)

Bg, gas formation $olume factor (ft7%scf)

1cleats, $olume of gas stored in the cleats (mmscf)

h , net pay (ft)/#, #ater saturation

H , porosity

Adding the t#o gas $olumes results in the follo#ing epression for the total gas content4


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The abo$e e!uation can be used to calculate the initial gas in place (1 i) by using the pressure"

porosity" and #ater saturation at initial conditions The remaining gas (1r) can be calculated using

pressure" porosity" and #ater saturation at the current a$erage reser$oir pressure /ubstituting the

original gas in place" and the remaining gas at the current conditions into the general gas material

balance e!uation #ill yield4

In the abo$e e!uation" three terms change #ith pressure4

/#(#ater saturation)

H (porosity)

Bg(gas formation $olume factor)

The #ater saturation in the cleats" as #ell as the cleat $olume itself" changes #ith pressure and

#ater influ%efflu The #ater saturation in the cleats is affected by three mechanisms4

The epansion of #ater due to its compressibility

8ater influ (from an a!uifer)" and efflu (from production)

The change in pore $olume caused by the formation compressibility

In mathematical terms" this is epressed by the follo#ing e!uation4

8here4

A , area (ft6)

B#, #ater formation $olume factor (ft7%scf)

c#, #ater compressibility (5%psia)

cf, formation compressibility (5%psia)

h , net pay (ft)

p , pressure (psia)

pi, initial reser$oir pressure (psia)

, a$erage #ater saturation

/#i, initial #ater saturation

8e, encroached #ater (bbls)


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8p, produced #ater (bbls)

Hi, initial porosity

The porosity changes #ith pressure as a result of the formation compressibility" and can be

epressed by the follo#ing e!uation4

The gas formation $olume factor can be epressed using the gas real gas la# as follo#s4

/ubstituting these three e!uations into the gas material balance e!uation yields the follo#ing4

8ith 9> defined as4

O1IP can be calculated from the abo$e e!uation #hen p , @ (implying the pressure has been

completely depleted" and all the gas has been produced)4

i$iding the 1pe!uation by the epression for O1IP yields a more useful form of the material

balance e!uation4

Plotting P%9> $ersus 1pyields the familiar graphical representation of the material balance

e!uation" #ith a y-intercept at P i%9i>" and an -intercept at O1IP


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Seidle #0111$

/eidle (5===) suggested using a similar material balance as that de$eloped by is dominated by the ratio of sorbed to free gas in the

denominator Formation and #ater compressibilities are also assumed to be negligible These

assumptions result in the follo#ing epression for 9>4

This definition of 9> can be used in the same material balance e!uation deri$ed by the


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8here4

A , area (acres)

h , net pay (ft)

1adsorbed, $olume of adsorbed gas (mmscf)

P , pressure (psia)

PG , Gangmuir pressure (psia)

0G , Gangmuir $olume (scf%ton)

b, bul& density (g%cm7)

The gas material balance e!uation can be epressed as4

Gp= G Gr

#hich becomes"

i$iding by (57C=E 5@-7) 0GAhJb" and rearranging gi$es4

Plotting $ersus 1pyields a straight line #ith a y-intercept at " and an -intercept at the

O1IP


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'opyright K 6@56 Fe&ete Associates Inc

Documents

Material Balance Analysis Theory and Practice