fluid properties_ comprehensive formation volume factor module

Dr. FP-Formation Volume Factor 1

Formation Volume FactorThe formation volume factoris an engineering variable developed to facilitate

material balance calculations and use of flowequations in reservoir engineering.

Since volume of the phases is varies greatly withP and T, defining the conditions at whichvolumes are reported is also necessary.

The reference conditions at which the volumesare reported are referred to as standard orbase conditions.

The oil and gas formation volume factors aredefined and ilustrated as follows..


Oil Formation Volume FactorThe early use of formation volume factor was

limited to dry gases and black oils. Thus theclassical material balance equations wasdeveloped and used for these two types ofreservoir fluids. Later in 1994, (almost 60years after the first introduction of MBE) themodern MBE equations were developed whichinvolved a new concept called volatilized oilgas ratio, Rv.

The following is a treatment of the oil and gasformation volume factors.


Oil Formation Volume FactorThe treatment of the FVFs will be dealt with in

stages. Starting with dry gas and black oil FVSand then illustrating the same concepts forvolatile oil and retrograde gases.


Gas Formation Volume FactorThe gas formation volume factor is defined asthe volume of an gas phase sample at reservoir

conditions divided by the volume of gas phaseyielded by the same sample at standardconditions. In equation form,

Bg = Volume of a gas phase sample in reservoir at reservoir Tand P Volume of gas phase yielded by the same sample at Tsc and Psc

The units are cuft of gas at reservoir conditions per cuft of gas at standard conditions, cuft/SCF.

The standard volume of gas is usually reported at 600F and 14.7 psia

Illustration of Bg for Dry Gases


• Consider a dry gas phase sample in a PVT cell of volume VGR at reservoir T and P. Let this sample be brought to surface conditions yielding a VGSC volume of gas. Note dry gases yield no liquid phase at surface conditions, hence, the dry gas formation volume factor is:

Example of a reservoir dry gas sample during its journey to surface


Derivation of Bg for dry gases

• From real gas low we have

• Rearranging


RR

GRR

SCSC

GSCSC

TzVP

TzVP

=

R

RR

SCSC

SC

GSC

GRg P

TzTz

PVVB ==

Gas Formation volume factor

But Tsc = 520oR and Psc= 14.65 psia, and for all practical purposes zsc = 1,

Then Bg= ZT (14.65)/(1.0)(520)P= 0.0282ZT/P cu ft/scf

Bg = (0.0282 zT/P cu ft/scf) (bbl/5.615 cu ft)= 0.00502 zT/P res bbl/scf.

T = Temp in R and P = pressure in psia. Dr. FP-Formation Volume Factor 8

Example 5-2 MCCain : Calculate a value of the formation volume factor of a. dry gas with a specific gravity of 0.818 at reservoir temperature of 2200F and reservoir pressure of 2100 psig.

Solution1. Estimate pseudocritical properties,

calculate pseudoreduced properties, andget a value of z-factor.

2. Tpc =4060R and Ppc = 647 psia at γg =0.818, Fig. 3.11 McCain

Tpr = (220+460)/406 = 1.68 andPpr = (2100+14.7)/ 647=3.27.z = 0.855, figure 3-7 MCCain


Example 5.2

2. Calculate Bg as follows:Bg = 0.00502 zT PBg = (0.00502)(0.855)(220+460)

(2100+14.7)= 0.00138 res bbl /scf


Class Work: Using the z values in example 5.2 answer the following based on the assumption that this gas is produced from reservoir where the reservoir gas volume is calculated to be 105 MMMcuft

If we can produce 80 percent of the totalreservoir gas what will be our ultimatesurface production in SCF

If we had produced 40 MMMSCF how muchmore gas can we produce.

What is the volume of the gas letf in thereservoir after producing 40 MMMSCF



Oil Formation Volume FactorThe oil formation volume factor is defined asthe volume of an oil phase sample at reservoir

conditions divided by the volume of oil phaseyielded by the same sample at standardconditions. In equation form,

B0 = Volume of an oil phase sample in reservoir at reservoir Tand P Volume of oil phase yielded by the same sample at Tsc and Psc

The units are barrels of oil at reservoir conditions per barrel of stock- tank oil, res bbl/STB.

The volume of stock-tank oil is mostly reported at 600F and 14.7 psia

Illustration of Bo for Black Oils


• Consider an oil phase sample in a PVT cell of volume VoR at reservoir T and P both are above bubble point values. Let this sample be brought to surface conditions yielding a VoSC volume of oil and VGSC volume of gas. Then oil formation volume factor is:

Example of a reservoir sample during its journey to surface


Factors influencing Oil FVF1. Change in pressure

1. Volume of an oil sample expands as pressure decrease from the reservoir conditions to surface conditions

2. Change in temperature– Volume of an oil sample decreases due to

temperature decrease from reservoir temperature to surface temperature

3. Change in dissolved gas– As p decreases dissolved gas is released from

solution resulting in volume shrinkage in oil phase

Dr. 16FP-Formation Volume Factor


Oil Formation Volume FactorNote thatas the reservoir oil phase includes dissolved gas, the oil

sample at reservoir conditions separates into an oilphase and gas phase as it is brought to surfaceconditions.

Therefore, volume of the oil phase yielded by a reservoiroil sample is much less than that of the oil phasesample in reservoir conditions due to liberation ofdissolved gas

Note also that Bo is always greater than 1, as explainedin next slide.

Assume PR=Patm, thus only T influence Bo. As TR > 60 F,and since volume at high T is greater Bo is always greaterthan one for an isothermal production phase.



Example 1:

A sample of reservoir liquid occupied a volume of 400 cc in a PVT cell under reservoir conditions. This sample was passed through a mini-separator system and finally allowed to flow into a stock tank at atmospheric pressure 14.7 psia and a temperature of 60 F.

The liquid volume in the stock tank was 274 cc. A total of 1.21 scf of gas was released during the jurneythrough separators.

Calculate the oil formation volume factor.


Solution

• B0 = 400 res cc = 1.46 res bbl274 ST cc STB

The reciprocal of the formation volume factor is called the shrinkage factor.

• b0 = __1_ B0


Example 2: ( Class C field is the one that has a reserves (feasibly recoverable oil) between 10-25 MM STB of oil)

A black oil reservoir contains 22 MM bbls of oil at reservoir conditions. If we can produce all this oil, how much oil do we get at our stock tanks.

Assume that the small sample from this oil yielded the results that have been calculated in example 1.


Solution• In example 1, the oil formation volume was calculated

to be Bo=1.46 bbl/STB• Then, let the amount of oil that we would have at

surface be represented by N and the total oil volume in the reservoir be VoR

• Note that our sample is the whole reservoir oil resources now and hence based on our definition of Bo, we can write

BO=VOR/N or N=VOR/BO=22/1.46=15.07 MMSTB

Note this value of total oil in reservoir, N, (expressed in STB) is called oil-in-place.


Example 3: ( Class A field is the one that has a reserves (feasibly recoverable oil) between 50-100 MM STB of oil)

A black oil reservoir contains 80 MM bbls of oil at reservoir conditions. It has been estimated that we can produce only 60% this oil economically with the available technology. The reservoir has been under production for 10 years now and we have produced 24 MMSTB of oil. How much oil do we expect to produce from this reservoir? ( i.e. how much producable oil is left to be produced ?)

Assume that the small sample from this oil yielded the results that have been calculated in example 1.


Solution• In example 1, the oil formation volume was

calculated to be Bo=1.46 bbl/STB• Then, let the amount of oil that we would have at

surface be represented by Np and the total oil volume in the reservoir be VoR

• Note that our sample is the producible reservoir oil (i.e. the reserves now) and hence based on our definition of Bo, and from example 2 , the oil in place is calculated as:

N=VOR/BO=80/1.46=54.79 MMSTB


Solution• Since we can produce only 60% of total oil (oil in

place) Let Npa be the ultimately produced oil

Npa=60% of N=0.6*54.79 =32.87 MMSTBIn ten year the cumulative production is

Np=24 MMSTB

So the remaining reserves Nr are

Nr=Npa-Np=32.87-24 =8.88 MMSTB


Example 4: A well testing has been performed in a black oil reservoir while the reservoir pressure and temperature are above the bubble point curve.

The well is flowed for 72 hours with surface oil flow rate qoSC=300 STBD. Assuming the sample in example 1 is from this reservoir, what is flow in the reservoir during the well testing ?


Solution• In example 1, the oil formation volume was

calculated to be Bo=1.46 bbl/STB• Then, let the surface flow rate be represented by qoSC

and the flow in reservoir be qoR• Note that our sample is the reservoir flow rate and

hence based on our definition of Bo, and from example 2 , the oil in place is calculated as:

BO=qOR/qOSC qOR=qOSCBO

• qOR=300*1.46=438 bbls


Digression: Solution Gas-Oil Ratio

• The quantity of gas dissolved in an oil sample when it istaken to reservoir conditions is called solution gas-oil ratio.In other words;

• Solution gas-oil ratio is the amount of gas that evolves fromthe reservoir oil sample as the oil is transported from thereservoir to surface conditions. This ratio is defined interms of the quantities of gas and oil which appear at thesurface during production.

RS = Volume of gas produced from an oil sample at surface Volume of oil yielded by the same sample at stock tank

• The surface volumes of both gas and liquid are referred tostandard conditions so that the units are standard cubic feet perstock-tank barrel, scf/STB.


Digression: Solution Gas-Oil Ratio

• Note relation between Bo and Rs

RS = Volume of gas yielded by a reservoir oil sample at Tsc and PscVolume of oil yielded by the same sample at Tsc and Psc

B0 = Volume of an oil phase sample in reservoir at reservoir Tand P Volume of oil phase yielded by the same sample at Tsc and Psc

The illustration of Rs equation below is in next slides

oSC

GSCsi V

VR =

Initial solution gas oil ratio


oSC

GSCsi V

VR =


Example 1:

A sample of reservoir liquid occupied a volume of 400 cc in a PVT cell under reservoir conditions. This sample was passed through a mini-separator system and finally allowed to flow into a stock tank at atmospheric pressure 14.7 psia and a temperature of 60 F.

The liquid volume in the stock tank was 274 cc. A total of 1.21 scf of gas was released during the jurneythrough separators.

Calculate the solution gas oil.


Solution

The conversion factor from cc to bbl is 6.2898x10-6 bbl/cc

Using this factor we obtain:

STBSCFSTccSTBxSTcc

SCFRs /702/102898.6*274

21.16 == −


Illustration of Rs and Bo and Bt below bubble point

Solution Gas Oil ratio• Then, from the above figure by definition the

solution gas oil ratio is

• The figure in next slide shows the variation of Rs with pressure. Until Pb, VGSC=VLSG and hence Rs=Rsi. As P drops below Pb, liberation in the reservoir takes place leading to an increase in VGR and hence to a decrease in VLSG as result of which Rs decreases.


oSC

LSGs V

VR =oSC

GSCsi V

VR =


Fig. 6.2 Typical diagram of solution gas-oil ratio of black oil versus reservoir pressure at constant temperature.

Significance of Solution Gas Oil ratio

• In addition to help us identify the reservoir fluid type, the solution gas oil ratio values are useful to employ in the material balance equations and specially useful in employing the concept of two phase or total FVF. Bt will be discussed next.


Two phase or Total FVF• The two phase or total formation volume factor is

defined for the purpose of conveniently carrying out the material balance calculations.

• The two phase FVF namely, Bt, has simplified the material balance equation expressions.

• The total or two phase FVF, Bt, is defined as follows.

• Let’s reconsider that a reservoir sample which is initially at P and T above bubble point values, reduced to low P and T and then expanded to surface conditions



Illustration of Rs and Bo and Bt below bubble point

FVF• Based on the above two step expansion of a

black oil sample, we have

• We know that

• Let’s define

• Since

• We obtainDr. FP-Formation Volume Factor 39

LSGGRSCGSC VVV +=

GRSC

GRg V

VB =oSC

oRo V

VB =

oSC

GRo

oSC

GRoRt V

VBV

VVB +=+

=

GRSCgGR VBV = LSGGSCGRSC VVV −=

oSC

LSGGSCgot V

VVBBB −+=

oSC

oRioi V

VB =

FVF• Also remember the definition the solution gas oil

ratio;

• Thus we obtain

• This is two phase FVF the commonly used in MBE.

• Note also that Bti=Boi


oSC

LSGs V

VR =

)( ssigot RRBBB −+=

oSC

GSCsi V

VR =


Total Formation Volume Factor

• In summary, the total formation volume factor isgiven by:

• Bt = Bo + Bg( Rsi – Rs ) res bbl/STB.

• B0 is the oil FVF at a pressure below bubble pointpressure.

• Rsi is the solution gas oil ratio at and abovebubble point pressure.

• Rs, is the solution gas oil ratio at a pressurebelow bubble point pressure.

• The variation of Bt with pressure is shown next.


Fig 6.4 Total formation volume factor of a black oil as a function of reservoir pressure at constant temperature.


Example:

• Exactly one stock-tank barrel was placed in a laboratory cell. 768 scf of gas was added.

• Cell temperature was raised to 2200F, the cell was agitated to attain equilibrium between gas and liquid, and pressure was raised until thermal bubble of gas disappeared. At that point cell volume was 1.474 barrels and pressure was 2620 psig.

• Pressure in the cell was reduced to 2253 psig by increasing total cell volume to 1.569 barrels. At that point the oil volume in the cell was 1.418 barrels and the gas volume in the cell was 0.151 barrels. Calculate the total formation volume factor at 2253 psig.


Solution

• Vo (P= 2253 psi) = 1.418 bbl• Vg (P= 2253 psi) = 0.151• Bt = Bo + Bg( Rsb – Rs )

• Bt = 1.418 + 0.151= 1.569 res bbl/STB

Modern PVT properties• The previous illustrations shows that there is no

volatilized oil in the gas phase. Thus there is no condensation upon change of P and T to surface values.

• Therefore MBE based on the previous concepts only were applicable only to dry gas and black oil reservoirs.

• The retrograde gases and liberated gas of volatile oil gas contains volatilized oil and hence the illustrations differ.

• Consider the following PVT experiment.


PVT properties for volatile oil and condensates


fluid properties_ comprehensive formation volume factor module

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