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1. University of Baghdad Reservoir Engineering I
Department of Petroleum Engineering 2020
Figure 6 Different water drive mechanisms
The water in these zones will have been reduced to some irreducible minimum. The
forces retaining the water in the oil and gas zones are referred to as capillary forces
because they are important only in pore spaces of capillary size.
Distribution of saturation of fluids in oil and gas reservoirs
In an oil reservoir, initial oil and water saturations add up to unity, or 100% of the
pore space, when no free gas is present:
ܵ௢௜ + ܵ௪௜ = 1
where:
Soi : initial oil saturation, fraction.
Swi : initial water saturation, fraction.
This equation is readily derived from the fact that the oil and water phases must
occupy the entire pore space and add up to 100% of the pore volume. Following
production, oil saturation would decrease, accompanied by the dissolution of gas or
by an increase in water saturation due to the various reservoir drive mechanisms that
may exist. Individual fluid saturations vary with time and location in a producing
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2. reservoir, and they control the relative flow of oil, gas and water towards the
wellbore. As long as any dissolved gas remains in solution, the following is valid
during the life of a reservoir:
ܵ௢ + ܵ௪ = 1
ܵ௢, ܵ௪ = ݂(݈‫݊݋݅ݐܽܿ݋‬ ݅݊ ‫݄݁ݐ‬ ‫ݎ݅݋ݒݎ݁ݏ݁ݎ‬, ‫)݁݉݅ݐ‬
‫ݍ‬௢ = ݂(ܵ௢, ‫ݏݑ݋݅ݎܽݒ‬ ‫ݎ݄݁ݐ݋‬ ‫݇ܿ݋ݎ‬ ܽ݊݀ ݂݈‫݀݅ݑ‬ ‫ݏ݁݅ݐݎ݁݌݋ݎ݌‬ )
where:
qo : average flow rate of oil in porous media.
As shown later in the course, the oil in place can be estimated based on knowledge
of the reservoir's extent, average net thickness, porosity, and initial water saturation.
Initial water saturation is obtained from wireline log studies in a newly discovered
reservoir. It is not expected to vary significantly in a lateral direction in a new
reservoir unless certain geologic discontinuities exist. However, it does vary in a
vertical direction in the transition zones between oil and water as a consequence of
capillary effects. Due to the higher specific gravity of water, the saturation of water
tends to increase with reservoir depth. The trend could be gradual or sharp,
depending on rock and fluid characteristics.
In a dry gas reservoir, where there is no liquid condensate present, initial gas
saturation can be calculated as follow:
ܵ௚௜ + ܵ௪௜ = 1
where:
Sgi : initial gas saturation, fraction.
2

3. Producing oil and gas reservoirs usually exhibit initial hydrocarbon saturations in
excess of 70%. The rest of the pore space is filled with formation water that is not
mobile in most instances. This is often referred to as connate water saturation (Swc),
which fills the pores during deposition of the rock.
When all three phases (oil, gas, and water) are present in a reservoir, such as an oil
reservoir with an initial gas cap, the saturation fractions of all three phases must add
up to unity. At certain depths, however, the saturation of one fluid could be zero.
Descending from the top of the reservoir to the bottom, the saturations of gas, oil,
and formation water can be summarized as follows at any point during production:
Gas cap:
ܵ௚ + ܵ௪௖ + ܵ௢௚ = 1
Gas-oil transition zone:
ܵ௚ + ܵ௢ + ܵ௪௖ = 1; ܵ௢ > ܵ௢௚
Oil zone:
ܵ௢ + ܵ௪௖ = 1; ܵ௚ = 0
Oil-water transition zone:
ܵ௢ + ܵ௪ = 1; ܵ௪ > ܵ௪௖
Bottom water zone:
ܵ௪ = 1; ܵ௢ = 0
where:
Sog : gas-cap interstitial-oil saturation, fraction.
Swc : connate water saturation, fraction.
3

4. When the reservoir produces oil and gas simultaneously below the bubble-point,
knowledge of the saturation of any two phases is necessary in order to calculate the
saturation of the third phase in the reservoir. The basis of calculation is in the
following:
ܵ௚ + ܵ௢ + ܵ௪ = 1
Changes in fluid saturation during the reservoir life cycle
This section describes fluid saturations that are “milestones” in a reservoir during
production, along with their relationship to ultimate oil and gas recovery. These are:
x Irreducible Water Saturation
x Critical Gas Saturation
x Critical Oil Saturation
x Residual Oil Saturation
Furthermore, knowledge of initial and residual oil saturations leads to the estimation
of ultimate recovery.
Irreducible Water Saturation Swirr is a certain saturation level below which the
fluid will not flow through the microscopic pores and channels in the porous
medium. The reservoir fluid will adhere to the surface of the pores due to the
existence of certain forces. These forces include the surface tension between the
fluid and the rock surface and the interfacial tension between two immiscible fluids
present in the pores, among other factors. Connate Water Saturation, Swc, as
obtained from log and core studies, is the minimum water saturation that would
remain adhered to the pores and not become mobile. During geologic times, rock
pores were originally filled with subsurface water. Initial water saturation of 100%
was later reduced to a considerably low value (typically 20%-30%) due to the
migration of oil into the pore space and expulsion of pore water. This value is known
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5. as connate water saturation and is generally found to vary inversely with formation
permeability in basin-wide studies.
At the time of the discovery of a reservoir, the initial hydrocarbon in place (IHCIP)
is computed based on the value of connate water saturation, as shown in the
following:
Initial hydrocarbon pore volume = Total pore volume - Volume of connate
water
Another particular phase saturation of interest is called the critical saturation and it
is associated with each reservoir fluid. The definition and significance of the critical
saturation for each phase is described below.
Critical Gas Saturation, Sgc, consider an oil reservoir in which no gas evolves out
of solution within the reservoir as long as the reservoir produces above the bubble-
point. When the reservoir pressure declines below the bubble-point, gas evolves out
of solution but is not immediately mobile. Following the buildup of free gas
saturation to a certain threshold value, referred to as critical gas saturation, the vapor
phase begins to flow towards the wellbore. Critical saturation is a term used in
conjunction with increasing fluid saturation.
Critical Oil Saturation, Soc, for the oil phase to flow, the saturation of the oil must
exceed a certain value, which is termed critical oil saturation. At this particular
saturation, the oil remains in the pores and, for all practical purposes, will not flow.
Residual Oil Saturation, Sor, At the end of the productive life of the reservoir, the
oil saturation that is left behind in the reservoir is referred to as residual oil
saturation. Some studies prefer the term remaining oil saturation (ROS) in
quantifying the oil left behind following the primary or a subsequent recovery.
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6. Knowledge of residual oil saturation is of great interest to reservoir engineers as it
points to the ultimate recoverable reserves.
Residual oil saturation, as can be obtained from laboratory displacement studies,
points to a value below which oil is no longer mobile within porous media. The term
residual saturation is used in connection with decreasing fluid saturation.
Oil recovery factor Based on the knowledge of oil saturations, the recovery factor
for an oil reservoir can be estimated as follows:
‫ܧ‬ோ =
ቀ
ܵ௢௜
‫ܤ‬௢௜
െ
ܵ௢௥
‫ܤ‬௢௥
ቁ
ቀ
ܵ௢௜
‫ܤ‬௢௜
ቁ
× 100
where:
ER : recovery factor, %,
Sor : average value of residual oil saturation in reservoir, fraction,
Boi : initial oil formation volume factor (FVF), rbbl/stb, and
Bor : residual oil formation volume factor, rbbl/stb.
Movable Oil Saturation, Som, It is important to recognize that only a fraction of the
oil in place is ultimately produced in most reservoirs. This poses a challenge to attain
better recovery, requiring a thorough understanding of reservoir behavior. This
necessitates the estimation of movable oil saturation, which represents the maximum
volume of oil that can be moved or produced ultimately from a reservoir. Hence,
movable oil saturation is defined as follows:
Movable oil saturation = Initial oil saturation - Residual oil saturation
ܵ௢௠ = ܵ௢௜ െ ܵ௢௥
ܵ௢௠ = 1 െ ܵ௪௖ െ ܵ௢௥
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7. where:
Swc: connate water saturation
Example (1)
Core sample is saturated with oil, gas and water. The initial weight of the saturated
sample is 224.14 gm. After the gas is displaced by water, the weight is increased to
225.9 gm. The sample is then placed in Soxhlet distillation apparatus only a 4.4 cm3
of water is extracted. After drying the core sample, the weight is now 209.75gm. The
sample bulk volume is 95 cm3
, Find the porosity, gas saturation, oil saturation and
water saturation.
Assume that ȡo=0.85 gm/cm3
, and ȡw=1 gm/cm3
Solution
Wt= 224.14 gm Wt= 225.9 gm 4.4 cc of water Wt= 209.75 gm
Vb= 95 cm3
Weight of water that displaces gas = 225.9-224.14= 1.76 gm
Volume of water = 1.76/1 = 1.76 cm3
Since water displaces gas,
ᄱ Volume of gas = 1.76 cm3
Volume of extracted water = Volume of water initially saturated the core + volume of water displaced the gas
Volume of water initially saturated the core = 4.4 – 1.76 = 2.64 cm3
ᄱ Weight of water initially saturated the core = 2.64/1= 2.64 gm
Weight of oil + water = Weight of core saturated with oil and water – Weight of dry core
Gas
+
Oil
+
Water
Gas
displaced
by water
Oil
+
Water
Extraction
Dry Core
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8. ᄱ Weight of oil + water = 225.9-209.75 = 16.15 gm
Volume of extracted water = 4.4 cm3
Weight of extracted water = 4.4 gm
Then,
Weight of oil = 16.15-4.4=11.75 gm
Volume of oil= 11.75/0.85 = 13.82 cm3
Pore volume = Volume of gas + Volume of oil + Volume of water
Vp = 1.76 + 13.82 + 2.64
Vp = 18.22 cm3
‫׎‬ =
ܸ
௣
ܸ௕
=
18.22
95
‫כ‬ 100 = 19.2 %
ܵ௚ =
ܸ
௚
ܸ
௣
=
1.76
18.22
‫כ‬ 100 = 9.66%
ܵ௢ =
ܸ
௢
ܸ
௣
=
13.82
18.22
‫כ‬ 100 = 75.85%
ܵ௪ =
ܸ
௪
ܸ
௣
=
2.64
18.22
‫כ‬ 100 = 14.49%
Average Saturation
Proper averaging of saturation data requires that the saturation values be weighted
by both the interval thickness hi and interval porosity Ø. The average saturation of
each reservoir fluid is calculated from the following equations:
ܵ௚
തതത =
σ ‫׎‬௜ ݄௜ ܵ௚௜
௡
௜ୀଵ
σ ‫׎‬௜ ݄௜
௡
௜ୀଵ
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9. ܵ௢
തതത =
σ ‫׎‬௜ ݄௜ ܵ௢௜
௡
௜ୀଵ
σ ‫׎‬௜ ݄௜
௡
௜ୀଵ
ܵ௪
തതതത =
σ ‫׎‬௜ ݄௜ ܵ௪௜
௡
௜ୀଵ
σ ‫׎‬௜ ݄௜
௡
௜ୀଵ
where the subscript i refers to any individual measurement and hi represents the
depth interval to which Øi, Soi, Sgi, and Swi apply.
Example (2)
Calculate average oil and connate water saturation from the following
measurements:
Sample hi, ft Øi, % Soi, % Swci, %
1 1 10 75 25
2 1.5 12 77 23
3 1 11 79 21
4 2 13 74 26
5 2.1 14 78 22
6 1.1 10 75 25
Solution
Construct the following table and calculate the average saturation for the oil and
water phase:
Sample hi, ft Øi Soi, % Swci, % Øi hi Øi hi Soi Øi hi Swci
1 1 0.1 0.75 0.25 0.1 0.075 0.025
2 1.5 0.12 0.77 0.23 0.18 0.1386 0.0414
3 1 0.11 0.79 0.21 0.11 0.0869 0.0231
4 2 0.13 0.74 0.26 0.26 0.1924 0.0676
5 2.1 0.14 0.78 0.22 0.294 0.2293 0.0647
6 1.1 0.1 0.75 0.25 0.11 0.0825 0.0275
Sum 1.054 0.8047 0.2493
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10. Calculate average oil saturation by applying the following equation:
ܵ௢
തതത =
σ ‫׎‬௜ ݄௜ ܵ௢௜
௡
௜ୀଵ
σ ‫׎‬௜ ݄௜
௡
௜ୀଵ
=
0.8047
1.054
= 0.7635 = 76.35%
Calculate average water saturation by applying the following equation:
ܵ௪
തതതത =
σ ‫׎‬௜ ݄௜ ܵ௪௜
௡
௜ୀଵ
σ ‫׎‬௜ ݄௜
௡
௜ୀଵ
=
0.2493
1.054
= 0.2365 = 23.65%
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