fluid properties_ comprehensive formation volume factor module
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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..
Dr. FP-Formation Volume Factor 2
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.
Dr. FP-Formation Volume Factor 3
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.
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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
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• 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
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Derivation of Bg for dry gases
• From real gas low we have
• Rearranging
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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
Dr. FP-Formation Volume Factor 9
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
Dr. FP-Formation Volume Factor 10
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
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Dr. FP-Formation Volume Factor 12
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
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• 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
Dr. FP-Formation Volume Factor 14
Dr. FP-Formation Volume Factor 15
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
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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.
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Dr. FP-Formation Volume Factor 19
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.
Dr. FP-Formation Volume Factor 20
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
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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.
Dr. FP-Formation Volume Factor 22
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.
Dr. FP-Formation Volume Factor 23
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.
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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
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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
Dr. FP-Formation Volume Factor 26
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 ?
Dr. FP-Formation Volume Factor 27
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
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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.
Dr. FP-Formation Volume Factor 29
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
Dr. FP-Formation Volume Factor 30
oSC
GSCsi V
VR =
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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.
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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 == −
Dr. FP-Formation Volume Factor 33
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.
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oSC
LSGs V
VR =oSC
GSCsi V
VR =
Dr. FP-Formation Volume Factor 35
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.
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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
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Dr. FP-Formation Volume Factor 38
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
Dr. FP-Formation Volume Factor 40
oSC
LSGs V
VR =
)( ssigot RRBBB −+=
oSC
GSCsi V
VR =
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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.
Dr. FP-Formation Volume Factor 42
Fig 6.4 Total formation volume factor of a black oil as a function of reservoir pressure at constant temperature.
Dr. FP-Formation Volume Factor 43
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.
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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.
Dr. FP-Formation Volume Factor 45
PVT properties for volatile oil and condensates
Dr. FP-Formation Volume Factor 46
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