Adjustment of Differential Liberation Data
to Separator Conditions
Muhammad A. Al-Marhoun, SPE, King Fahd U. of Petroleum and Minerals
Summary
Solution gas/oil ratio (GOR) and oil formation volume factor
(FVF) are normally obtained from differential or flash liberation
tests. However, neither the differential liberation process nor the
flash liberation process can represent the fluid flow in petroleum
reservoirs. Therefore, data obtained from any of the two test procedures must be adjusted to approximate the fluid behavior in the
reservoir. At low pressures, the conventional method of adjustment
yields negative values of solution GOR and values of oil FVF of
less than 1. This, of course, is not physically correct.
This paper presents a new method for adjusting the differential
liberation data to separator conditions. The new method overcomes
the limitations of the conventional adjustment method and makes
the low-pressure extension of the curves of solution GOR and oil
FVF more accurate. The method is based on the fact that data
obtained from both the differential and flash liberation tests should
yield the same value of oil relative density at reservoir conditions.
The new method is tested using 425 PVT files, yielding results that
are consistent with the physical behavior of solution GOR and oil FVF.
Introduction
In the differential liberation process, gas is removed as it is released from the oil. In the flash liberation process, however, the
liberated gas is not removed and is allowed to reach equilibrium
with the oil.
Generally, petroleum engineers consider that the gas liberation
process in the reservoir can be represented by the differential liberation process.1,2 The fluid produced from the reservoir to the
surface is considered to undergo a flash process.
The differential solution GOR is not the same as the flash
solution GOR, as shown in Fig. 1. Similarly, the differential and
flash oil FVFs are not the same, as depicted in Fig. 2. Thus,
regardless of the testing procedures—flash or differential—some
correction needs to be made to the obtained data to approximate
the fluid behavior in the oil-production process.
The actual gas liberation process in the reservoir is neither flash
nor differential. In certain localities, the process is flash, but in
others, the process is differential. In some other localities the process does not match either of them. A combination test proposed
by Dodson et al.3 is probably the closest to the reservoir process.
At each step of the differential liberation test, an oil sample is
taken and flashed to obtain Rs, ␥o, Bo, and ␥g. Here it can be seen
that all properties, including the ␥api, are different at different
pressures. Although this combination test is an improvement over
the differential and flash liberation tests, it does not match the
actual reservoir behavior. The appendix to Ref. 4 explains the
differential and flash processes and the combination test. From the
combination test that produces different values for ␥g and ␥o at
different pressures, it is justified to adjust all the properties obtained by the differential liberation test to flash separator conditions, including ␥g and ␥o.
The fluid properties obtained by combining data from the differential and flash liberation tests may be called the “combination
fluid properties.” These data are used to determine the values of
Copyright © 2003 Society of Petroleum Engineers
This paper (SPE 84684) was revised for publication from paper SPE 68234, first presented
at the 2001 SPE Middle East Oil Show, Bahrain, 17–20 March. Original manuscript received
for review 3 May 2001. Revised manuscript received 28 January 2003. Paper peer approved 25 March 2003.
142
solution GOR and oil FVF at pressures below bubblepoint. To
calculate the combination fluid properties from standard data
analysis, several assumptions were stipulated, but these assumptions limit the range of application.
This paper describes a new method to adjust the differential
liberation data to separator conditions. This method overcomes the
disadvantages and limitations of the existing method and comes up
with a correction procedure that results in a consistent physical trend.
Current Correction Procedure
The existing method for adjusting the differential liberation data to
separator conditions was based on several assumptions, the most
important of which (as stipulated by Amyx et al.5) are:
• The standard cubic feet of gas remaining in solution at reservoir conditions that will be liberated upon producing that liquid
to the separator by a flash liberation process is the difference
between the original gas in solution and the differentially liberated
gas corrected for the reservoir shrinkage of the fluid.
• The relationship between the oil FVFs of flash and differentially separated samples remains constant over the entire pressure
range of interest.
In equation form, the corrected differential solution GOR at
pressures below bubblepoint pressure, according to the first assumption mentioned above, is as follows:
RS = Rsbf − 共Rsbd − Rsd兲共Bobf Ⲑ Bobd兲, . . . . . . . . . . . . . . . . . . . . . . . (1)
where R S =solution GOR adjusted to separator conditions;
Rsbf=bubblepoint solution GOR obtained from the separator test;
Rsbd=bubblepoint solution GOR obtained by the differential liberation test; Rsd=differential solution GOR; Bobf=bubblepoint oil
FVF flashed through the separator to stock-tank conditions; and
Bobd=bubblepoint oil FVF differentially liberated to stock-tank
conditions.
Implicitly, the adjusted differential solution GOR at pressures
above the bubblepoint pressure is constant and is equal to the
solution GOR at the bubblepoint obtained from the separator test.
RS = Rsbf at p ⱖ pb. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (2)
According to the second assumption, the adjusted differential
oil FVF at pressures below the bubblepoint pressure is evaluated
from a combination of differential liberation data and separator test
data; that is,
Bo = Bod 共Bobf Ⲑ Bobd兲 at p ⱕ pb, . . . . . . . . . . . . . . . . . . . . . . . . . . (3)
where Bod⳱oil FVF obtained by differential liberation tests, and
Bo⳱oil FVF adjusted to separator conditions.
Implicitly, the adjusted differential oil FVF at bubblepoint pressure is equal to the oil FVF at bubblepoint pressure obtained from
the separator test; that is,
Bo = Bobf at p = pb. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (4)
Disadvantages of the Current
Correction Procedure
The adjustment method used in the industry as outlined above has
the following disadvantages:
• At lower pressures, the solution GOR became negative. This
does not conform to the physical trend, as Rs should be equal to or
greater than zero. This is undoubtedly the result of not taking into
account the required adjustment in gas and oil relative densities.
The gas liberated in the differential liberation test has a relative
density, which increases with the decreasing pressure. The oil
June 2003 SPE Reservoir Evaluation & Engineering
Fig. 1—Typical solution GOR curves.
Fig. 2—Typical oil FVF curves.
relative densities for the flash and differential liberation tests are
different.
• For the correction of oil FVF, the value obtained at lower
pressure leads to a value of less than 1, which does not conform to
the physical behavior. Because of these problems, the range of
application of the calculation procedure is limited to pressures
above 500 psi. Actually, the following observation should be true:
Bo ⱖ 1.
• When the values of corrected properties were used to calculate the live-oil relative density at bubblepoint pressure, it did not
agree with the flash live-oil relative density at bubblepoint pressure. These data should yield the same value of oil relative density
at bubblepoint pressure. This problem is encountered because oil
and gas relative densities at standard conditions are not corrected
to separator conditions, as can be seen from the following equation:
and where ␥gdn–1 is the gas relative density at the lowest pressure,
with an RS value that is not equal to zero.
The adjusted differential oil relative density and API oil gravity
at pressures below the bubblepoint pressure are evaluated from the
following equations:
␥ob = 共␥o + 2.18 × 10−4 Rsb␥g兲 Ⲑ Bob. . . . . . . . . . . . . . . . . . . . . . . . (5)
The New Method
The new method of adjustment of the differential liberation data to
the separator conditions is based on the following assumptions:
• The properties obtained from the differential liberation test at
bubblepoint are corrected to bubble point properties obtained by
the flash liberation test. The corrected properties include GOR, oil
FVF, and oil and gas relative densities.
• The properties obtained from the last differential liberation
stage to the atmospheric pressure do not need any correction. This
is considered a flash liberation.
• The properties at pressures between bubblepoint pressure and
atmospheric pressure are adjusted proportionally. The properties
that need to be adjusted from the differential liberation test to the
separator test are GOR, oil FVF, oil relative density, and gas
relative density.
The adjusted differential solution GORs at pressures below
bubblepoint are evaluated from the following equation:
␥oi = ␥of + ci 共␥od − ␥of兲. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (11)
␥apii = 141.5 Ⲑ ␥oi − 131.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (12)
Recently, McCain6 discovered that the equation commonly
used to calculate the solution GOR is incorrect. He suggested an
equation similar to Eq. 6 in this paper. This supports the present
method, which was originally presented in Ref. 7. McCain,6 however, considered the equation used to calculate oil FVF from blackoil PVT reports (Eq. 3) to be correct. As mentioned earlier, the
value of the oil FVF obtained at a lower pressure leads to a value
of less than 1, which does not conform to the physical behavior.
Results and Discussion
The new method of adjusting the differential liberation data to the
separator condition has been tested on 425 PVT files with 3,181
data points from all over the world, and the result is consistent with
physical behavior. Table 1 depicts the statistical analysis of the
validation data. The detailed results of an example for one experimental data set taken from a PVT file (given in Table 2) are
presented in Tables 3 through 7.
Table 3 presents the adjustment of the solution GOR curve to
the separator conditions. Columns 1 and 2 in Table 3 are from
Table 2. Column 3 is calculated from Eq. 1, and Column 4 is
calculated from Eq. 6. Fig. 3 shows the three curves: differential
data, the existing correction method (Eq. 1), and the new method
(Eq. 6). At the bubblepoint pressure, the values obtained at both
new and existing methods are equal to the bubblepoint value obtained from flash liberation. At atmospheric pressure, both the
differential liberation value and the value obtained from the new
method are the same and are equal to zero. This is the expected
Rsi = Rsdi 共Rsbf Ⲑ Rsbd兲. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (6)
The adjusted differential oil FVF at pressures below the
bubblepoint pressure are evaluated from the following equation:
Boi = Bobf + ci 共Bodn − Bobf兲, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (7)
where ci = 共Bobd − Bodi兲 Ⲑ 共Bobd − Bodn兲. . . . . . . . . . . . . . . . . . . . . . . . (8)
The adjusted differential gas relative density at pressures below
bubblepoint is evaluated from the following equation:
␥gi = ␥g f + di 共␥gdn−1 − ␥g f兲, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (9)
where di = 共␥gd1 − ␥gdi兲 Ⲑ 共␥gd1 − ␥gdn−1兲 . . . . . . . . . . . . . . . . . . . . . . (10)
June 2003 SPE Reservoir Evaluation & Engineering
143
value, while the existing correction procedure results in a negative
value, which cannot be physically correct. The new method adjusts
the data between bubblepoint pressure and atmospheric pressure
proportionally, according to Eq. 6.
Table 4 presents the adjustment of oil FVF to the separator
conditions. Columns 1 and 2 in Table 4 are from Table 2; Column
3 is calculated from Eq. 3, and Column 4 is calculated from Eq. 7.
Fig. 4 compares the three curves: differential data, the existing
correction method (Eq. 3), and the new approach (Eq. 7). The
figure shows that at the bubblepoint, both the new method and the
existing correction method are giving the same value of oil FVF,
and it equals the bubblepoint value obtained from the flash liberation. At atmospheric pressure, the oil FVF values obtained from
both the differential liberation and the new method are the same.
This is because the last differential step is similar to a flash liberation. The data between the two endpoints are corrected proportionally, according to Eq. 7. The existing correction method gives
values for oil FVF lower than the values obtained from the differential liberation at atmospheric pressure, which cannot be explained rationally.
Table 5 presents the adjustment of the gas relative density
curve to the separator conditions. Columns 1 and 2 in Table 5 are
from Table 2. Column 3 is the same as the differential values; the
144
current practice does not adjust the gas relative density, but it takes
the differential value for gas relative density. Column 4 is calculated from Eq. 9. Fig. 5 shows two curves; one of the curves shows
the differential data, and the other curve represents the new correction method for gas relative density, according to Eq. 9. The
value of the gas relative density at the bubblepoint for the new
method is the same as that of the bubblepoint value obtained from
the flash liberation. At the lowest pressure at which RS > 0, the gas
relative density is the same as that obtained from the differential
liberation test. This is because of the assumption that at the last
step in pressure reduction down to atmospheric pressure, the differential liberation is a flash liberation. Eq. 9 calculates the values
of gas relative density between the bubblepoint and the lowest
pressure proportionally.
Table 6 presents the adjustment of the oil relative density curve
to the separator conditions. Columns 1 and 2 in Table 6 are from
Table 2. Column 3 is the same as Column 2 because the current
practice takes the differential values without correction. Column 4
is calculated from Eq. 11. Fig. 6 shows the two curves of the
differential data and the new correction method for oil relative
density based on Eq. 11. It is noticeable that, at bubblepoint pressure, the new method assumes the flash value as the adjusted
value. At atmospheric pressure, the new method takes the differ-
June 2003 SPE Reservoir Evaluation & Engineering
ential value as the adjusted value. The atmospheric pressuredifferential step is considered to be a flash liberation. Eq. 11 calculates the values of oil relative density between bubblepoint and
atmospheric pressure proportionally. The correction of oil relative
density at different pressures is valid because if oil samples at
different pressures were flashed to atmospheric pressure, different
API gravity would result.
Table 7 presents the calculated live-oil relative density at different reservoir pressures. Columns 1 and 2 in Table 7 are from
Table 2. Column 3 is calculated using Eq. 5 with an existing
method of adjustment. Column 4 presents the new approach values
using Eq. 5 with corrected properties. Fig. 7 shows that the values
obtained from the new approach are the same as those obtained
from the flash liberation test for the live-oil relative density at the
bubblepoint pressure and reservoir temperature. At atmospheric
pressure, the live-oil relative density based on the new approach is
the same as the calculated value from differential liberation. The
existing method of correction, however, failed to match the
bubblepoint and the atmospheric values.
Conclusions
1. A new method to adjust differential liberation data to separator
conditions is outlined and tested on numerous experimental data
sets, and the method is found to give the correct physical trend.
Fig. 3—Adjustment of solution GOR to separator conditions.
June 2003 SPE Reservoir Evaluation & Engineering
2. The new method gives the correct oil relative density at reservoir conditions when the adjusted data are used. In contrast, the
existing method of correction fails to give the right oil relative
density at reservoir conditions.
3. The new method successfully gives the expected values for all
the PVT properties at both bubblepoint and atmospheric pressures, while the existing method succeeds in some cases and
fails in others.
Nomenclature
Bo ⳱ oil FVF, bbl/STB [res m3/stock-tank m3]
Bob ⳱ bubblepoint oil FVF
Bobd ⳱ bubblepoint oil FVF differentially liberated to
stock-tank conditions
Bobf ⳱ bubblepoint oil FVF flashed through the separator to
stock-tank conditions
Bod ⳱ oil FVF obtained by the differential liberation test
ci ⳱ variable defined by Eq. 8
di ⳱ variable defined by Eq. 10
p ⳱ pressure, psi (kPa)
pb ⳱ bubblepoint pressure, psi (kPa)
RS ⳱ solution GOR, scf/STB [std m3/stock-tank m3]
Rsb ⳱ solution GOR at bubblepoint pressure
Fig. 4—Adjustment of oil FVF to separator conditions.
145
Fig. 5—Adjustment of gas relative density to separator conditions.
Fig. 6—Adjustment of oil relative density to separator conditions.
Rsbd ⳱ bubblepoint solution GOR obtained by the differential
liberation test
Rsbf ⳱ bubblepoint solution GOR obtained from the separator
test
Rsd ⳱ solution GOR obtained by the differential liberation
test
␥api ⳱ stock-tank oil gravity, °API
␥g ⳱ gas relative density (air⳱1)
␥gd ⳱ gas relative density obtained by the differential
liberation test (air⳱1)
␥gf ⳱ gas relative density obtained from the separator test
(air⳱1)
␥o ⳱ oil relative density (water⳱1)
␥ob ⳱ bubblepoint oil relative density (water⳱1)
␥od ⳱ oil relative density obtained by the differential
liberation test (water⳱1)
␥of ⳱ oil relative density obtained from the separator test
(water⳱1)
␥op ⳱ oil relative density at pressure p and reservoir
temperature (water⳱1)
Acknowledgments
The author is grateful to the Dept. of Petroleum Engineering
at King Fahd U. of Petroleum and Minerals, Dhahran, Saudi
Arabia, for the facilities used to perform the present work and for
their support.
Subscripts
d ⳱ differential liberation test
f ⳱ flash liberation test
i ⳱ ith differential stage
n ⳱ number of stages in the differential liberation test
References
1. Standing, M.B.: Volumetric and Phase Behavior of Oil Field Hydrocarbon Systems, Millet Print Inc., Dallas (1977) 81.
2. McCain, W.D. Jr.: The Properties of Petroleum Fluids, second edition,
PennWell, Tulsa (1990) 283.
3. Dodson, C.R., Goodwill, D., and Mayer, E.H.: “Application of Laboratory PVT Data to Reservoir Engineering Problems,” Trans., AIME
(1953) 198, 287.
4. Moses, P.L.: “Engineering Applications of Phase Behavior of Crude
Oil and Condensate Systems,” JPT (July 1986) 715.
5. Amyx, J.W., Bass, D.M. Jr., and Whitting, R.L.: Petroleum Reservoir
Engineering, McGraw-Hill Book Co. Inc., New York City (1960)
392–399.
6. McCain, W.D. Jr.: “Analysis of Black Oil PVT Reports Revisited,”
paper SPE 77386 presented at the 2002 SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 29 September–2 October.
7. Al-Marhoun, M.A.: “Adjustment of Differential Liberation Data to
Separator Conditions,” paper SPE 68234 presented at the 2001 SPE
Middle East Oil Show, Bahrain, 17–20 March.
SI Metric Conversion Factors
°API 141.5/(131.5+ oAPI)
bbl × 1.589 873
ft3 × 2.831 685
°F (°F + 40)/1.8 – 40
psi × 6.894 757
°R / 1.8*
scf / bbl × 1.801 175
⳱ g/cm3
E–01 ⳱ m3
E–02 ⳱ m3
⳱ °C
E+00 ⳱ kPa
E+00 ⳱ K
E–01 ⳱ std m3/ m3
*Conversion factor is exact.
Fig. 7—Calculated live-oil relative density at reservoir temperature.
146
Muhammad Ali Al-Marhoun is a professor and former chairman of the Petroleum Engineering Dept. at King Fahd U. of
Petroleum and Minerals, Dhahran, Saudi Arabia. e-mail:
marhounm@kfupm.edu.sa. His research interests include fluid
properties and reservoir engineering, and he has published
several research and technical papers. Al-Marhoun holds a BS
degree in general engineering and an MS degree in mathematics from King Fahd U. of Petroleum and Minerals and a
PhD degree in petroleum engineering from the U. of Oklahoma. He served as a 2001–02 SPE Distinguished Lecturer.
June 2003 SPE Reservoir Evaluation & Engineering