Material Balance for Oil Reservoirs

• Why do it?

• Basic Principle

• Data available for performing material balance

• Derivation of the material balance equation

Uses of material balance

1 Provide insight into the production characteristics of the reservoir

2 History matching, reservoir drive mechanisms

3 Determination of initial oil in place

Linearized form of material balance equationused to estimate the initial oil in place (the intercept of thestraight line) - Havlena and Odeh procedure applied in:“Reservoir characterization, geological modeling and reservoir simulation of the N’Sano field - G.R. King 1998

Basic Principle

p1 > p2 p3 p4> >

Undersaturatedoil

Bubblepoint

ExpandingGas Cap

Liquid shrinkingdue to liberationof dissolved gas

Oil

+dissolved

gas

Initial gas cap Expanded gas cap

Expanded of oil +dissolved gas

Reduction in PV due to increased grain packing and connate water expansionPinit P>

In this lecture we will derive the material balance as a volumetric balance. Material balance is also a critical step in modern reservoir simulation where a mass balance of components within the different fluid phases is generally performed.

Pinit P>

A

BOil +

dissolvedgas

Gas cap

C

Withdrawl = Expansion of oil+originally(rb) dissolved gas (B) (rb)

+ Expansion of gascap gas(A)(rb)+ Reduction in PV due to expansion of connate water

and tighter grain packing(C)(rb)

NOTE that the volume balance is written in terms of fluid at reservoir conditions or as underground withdrawl and fluid expansion.

Another interpretation:

compressibility or

In this case since dV is production and VdP is volume expansion, the negative sign is removed: i.e. Production is directly related to the volume expansion of fluids. Parameters related to the PVT behaviour of fluids and the fluid phases present are rolled into a equivalent compressibility ce

dPdV

Vce

1 VdPcdV e

VdPcdV e

Data available to do material balanceProduction DataNp = Cummulative oil volume produced (stb)Rp = Cummulative gas-oil ratio

=

PVT propertiesBo = Oil FVF (bbl/STB)Bg = Gas FVF (cu.ft/SCF)Bw = Water FVF(bbl/STB)Cw = Compressibility of water (psi-1)Rso = Solution Gas-Oil RatioReservoir propertiesCf = Rock CompressibilitySwi = Connate water saturation

(stb) produced oil of volume Cum.(scf) produced gas of volume Cum.

Other parameters

N = Initial volume of oil in reservoir (rb)

= (stb)

m = Initial gas cap

=

These are listed as other parameters because these may either be known by wireline logs, reservoir modeling etc. Or they may be the objective of the material balancecomputation.

(rb) oil of volume nhydrocarbo Initial(rb) gap gas of volume nhydrocarbo Initial

oiwc BSV /)1(

Derivation of the material balanceExpansion of the oil + liberated gas

Two components:

1. Expansion of oil:Initial Oil = N (stb)Initial oil at reservoir conditions = N Boi (rb)Volume of oil at reduced pressure p = N Bo (rb)Net oil expansion = N(Bo-Boi) (rb)

2. Expansion of liberated gas:Gas dissolved at initial condition = NRsi (scf)Gas dissolved at reduced pressure p = NRs (scf)Liberated gas = N(Rsi-Rs) (scf)Volume of gas at reservoir conditions = N(Rsi-Rs)Bg (rb)

Volume change due to expansion of oil and liberated gas:= N(Bo-Boi) + N(Rsi-Rs)Bg (rb)

Let us consider a material balance accounting for just thisvolume change term (ignoring gas cap expansion, waterinflux or pore volume reduction):

Withdrawl:Amount of oil produced = Np (stb)Oil produced at reservoir conditions = NpBo (rb)Volume of gas produced = NpRp (scf)Let us look at this quantity of gas at the reduced pressure pVolume of gas dissolved in Np vol. of oil at p = NpRs (scf)Remainder gas is the subsurface gas withdrawl in the form ofexpanding liberated gas and expanding free gasSubsurface withdrawl of gas = Np(Rp-Rs) (scf)Subsurface withdrawl of gas in reservoir bbls = Np(Rp-Rs)Bg (rb)

Therefore, the total subsurface fluid withdrawl := NpBo + Np(Rp-Rs)Bg (rb)

Now writing the material balance:

NpBo + Np(Rp-Rs)Bg = N(Bo-Boi) + N(Rsi-Rs)Bg

Recovery :

If the initial oil in place is unknown and the reservoir drive mechanism is strictly solution gas:

(stb)

Alternatively denoting the withdrawl term as F and the expansion term [(Bo-Boi) + (Rsi-Rs)Bg] = Eo, the material balance becomes:

F = NEo

gspo

gssioiop

BRRBBRRBB

NN

)()()(

gssioio

BgRsRpBop

BRRBBN

N)()(

)(

Material balance : F = NEo

i.e. a plot of F (withdrawl) vs. expansion Eo should be a straight line with slope N (the initial oil in reservoir).

If the plot is not a straight line - other reservoir drive mechanisms are presentRemarks:• The recovery is determined once Np, N and the PVT

properties are known.• The material balance equation shows no explicit

dependence on pressure. The influence of the pressure drop is implicitly introduced through the PVT parameters.

• The material balance as derived above is zero dimensionali.e. the entire reservoir volume is assumed to be concentrated at a point. The pressure specification istherefore at that point.

Remarks (cont’d)

• For a undersaturated reservoir, all the produced gas Rp canbe dissolved in the oil at reservoir conditions I.e. Rp=Rs=Rsi

The recovery in such a reservoir is simply:

Recovery : o

oiop

BBB

NN )(