Notes:
1. The original oil wet option initialization in IMEX is still available with the BLOCK_CENTER reservoir initialization method. This version of the oil wet option initialization assumes the reservoir began its existence as an oil wet reservoir.
The new oil wet option initialization option assumes that the reservoir is initially water wet and has undergone a wettability alteration to become an oil wet reservoir.
These assumptions have a significant impact on how fluids are placed during reservoir initialization. The user should understand completely the difference in order to obtain the initial conditions which most reflect his reservoir model.
2. Within a PVT region, all rock types should either be oil wet or water wet. If both oil wet and water wet rock types are found, unphysical results may occur. The DEPTH_AVE initialization option will warn the user if this occurs and stop the simulation.
Oil Wet Initialization (BLOCK_CENTER initialization):
The initialization of a BLOCK_CENTER oil wet reservoir assumes that the reservoir is initially oil wet. We assume that initially we have a 100% oil filled reservoir into which water migrates. As water is heavier than oil it fills the region of the reservoir below the present water oil contact.
As the migrating water cannot replace the connate oil:
The water zone below the water oil contact is made up of water and connate oil.
The oil zone does not contain any water at all.
The gas zone is made up of gas and connate oil.
The Pcwo (non-wetting minus wetting pressure) controls the transition zone of oil into the water zone.
It is possible to adjust the oil in the oil zone to be less than 100% by using the *WOC_SW keyword. When using water wet initialization this allows the user to adjust the amount of water in the water zone. When using the oil wet option with BLOCK_CENTER
initialization, this now refers to the oil saturation (wetting phase saturation) in the oil zone.
Hence it is possible to alter the oil phase saturation for each PVT region. Setting a WOC_SW equal to 0.80 limits the oil saturation in the oil zone to a maximum of 80%.
It is also possible to adjust the amount of oil above the gas oil contact by using the
*GOC_SW keyword. When using the oil wet option with BLOCK_CENTER initialization,
*GOC_SW now controls the wetting phase (oil) saturation in the gas zone. Setting GOC_SW equal to 0.05 can change the maximum oil saturation in the gas cap to 5%.
This initialization option although entirely consistent does not represent the type of oil wet reservoirs normally encountered. More commonly oil wet reservoirs initially begin life as water wet and change wettability at a later time. This type or reservoir should be initialized using the DEPTH_AVE initialization option.
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Oil Wet Initialization (DEPTH_AVE initialization):
This type of initialization (when used with the oil wet option) assumes that the reservoir is initially water wet and has had its wettability altered (to oil wet). The capillary pressure between non wetting and wetting phases still govern the transition zones, but the gas zone contains gas and water, the oil zone contains oil and water (both mobile and immobile) and the water zone contains water (not water and oil).
Unless specified explicitly, the WOC_PC (the capillary pressure at the water oil contact) is internally set equal to the maximum Pcwo (see Pcwo definition below), which occurs at the lowest oil (wetting phase) saturation. Therefore the transition zone occurs within the oil zone and not below the water oil contact.
If a WOC_PC equal to the minimum Pcwo, which occurs at the largest oil (wetting phase) saturation, is input in an oil wet model, the WOC would represent the free water level in the reservoir. The oil water transition zone would occur below the free water level.
A different WOC_PC can be entered for each PVT region.
This type of initialization produces results which are very similar to a water wet reservoir initialization which at a later date undergoes a wettability change to oil wet, and is then allowed to re-equilibrate.
Flow in an Oil Wet Model
In an oil wet model (regardless of initialization option), three phase flow is modelled
assuming water is the intermediate phase. Therefore Kro is a function of oil saturation, Krg is a function of gas saturation, while Krw is a function of both oil and gas saturation (through Krwo and Krwg).
The normal three phase flow models (e.g. Stone 1, Stone 2, segregated, etc) are used to determine water relative permeability not oil permeability.
( )
g ro( )
o rw(
o g)
rg f S K f S K f S ,S
K = = =
When modelling 3 phase flow for example using Stone’s 2nd model we would obtain Krw
from:
Where Krwco is the water relative permeability at connate oil, Krwo is the water relative permeability obtained from the water-oil table (So+Sw = 1) and Krwg is the water relative permeability obtained from the liquid-gas table (Sl+Sg = 1, So = connate oil). This approach for oil wet rock is a direct extension of Stone’s model which originally developed for water wet systems.
Relative Permeability/Capillary Pressure Curves in an Oil Wet Model
When the oil wet option is used the meanings of the columns in the relative permeability tables are altered. Normally water is the wetting phase and oil is the nonwetting liquid phase.
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SWT Table
When the oil wet option is active the column which normally contains water saturation (the first) should now contain the saturation of the wetting phase (oil). The Krw column (2nd column) should contain the wetting phase relative permeability (oil relative permeability).
The Krow column (3rd column) contains the nonwetting phase relative permeability (water relative permeability).
The fourth and fifth columns which normally (for water wet models) contain the Pcow and Pcowi now contain Pcwo and Pcwoi. These represent the positive capillary pressure between the non wetting water phase and the wetting oil phase. Since the tables still tabulate non wetting phase pressure minus wetting phase pressure versus wetting phase saturation (So), the shape of the Pcwo curves resembles that of the Pcow curves versus water saturation in a water wet system.
( )
o w o cow( )
w o wcwo f S p p and p f S p p
p = = − = = −
SLT Table
The meanings of the columns of the gas-liquid tables are not altered. However the liquid saturation in the table is made up of water and connate oil. In the DEPTH_AVE initialization option the Pc curve entered in the liquid gas table must be the Pcog curve (even though oil is not the intermediate phase. When using the BLOCK_CENTER initialization option the capillary pressure curve in the liquid gas table must be the Pcwg curve.
If the capillary pressure received is from a water-gas system, pcgw = pg – pw, to accommodate IMEX table input for DEPTH_AVE initialization, the user needs to convert pcgw to pcgo using pcgo = pcgw + pcwo.
Endpoint Arrays in an Oil Wet Model
The use of the oil wet option also changes the meaning of the user specified grid block specific end point arrays. Unless these changes in definition are accounted for, the unscaled relative permeability curves will be incorrect.
The normal definitions of the affected arrays are.
Swcon = Connate water saturation Swcrit = Critical water saturation Soirw = Irreducible oil saturation Sorw = Residual oil saturation
Sorg = Residual oil saturation (gas liquid table)
Slcon = Connate liquid saturation which is equal to connate water
(Swcon) plus irreducible oil saturation (Soirg) if the *NOSWC option is not used, and equal to irreducible oil saturation (Soirg) alone, if the *NOSWC option is used
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When using the oil wet option they are modified to be.
Swcon = Connate wetting phase (oil) saturation Swcrit = Critical wetting phase (oil) saturation
Soirw = Irreducible nonwetting phase (water) saturation Sorw = Residual nonwetting phase (water) saturation
Sorg = Residual nonwetting phase (water) saturation (gas liquid table) Slcon = Connate liquid saturation which is equal to connate oil
(Swcon) plus irreducible water saturation (Soirg) if the *NOSWC option is not used, and equal to irreducible water saturation (Soirg) alone, if the *NOSWC option is used
The scaling ARRAYS *KRWIRO, *KROCW, *KROGCG, *PCWMAX, *PCGMAX,
*JFWMAX and *JFGMAX must also be used with altered definitions if the oil wet option are used.
The normal definitions of these arrays are:
Krwiro = Water rel. perm. at irreducible oil (oil-water table) Krocw = Oil rel. perm at connate water (oil-water table) Krogcg = Oil rel. perm at connate gas (liq.-gas table) Pcwmax = Oil water capillary pressure at connate water Pcgmax = Gas oil capillary pressure at connate liquid Jfwmax = Oil water J function at connate water Jfgmax = Gas oil J function at connate liquid When using the oil wet option they are modified to mean.
Krwiro = Wetting Phase (Oil) rel. perm. at irreducible water (oil-water table) Krocw = Non Wetting Phase (water) rel. perm at connate oil (oil-water table) Krogcg = Non wetting phase (water) rel. perm at connate gas (liq.-gas table) Pcwmax = Water-oil capillary pressure at connate oil
Pcgmax = Gas oil capillary pressure at connate liquid (DEPTH_AVE)
Gas water capillary pressure at connate liquid (BLOCK_CENTER) Jfwmax = Water oil J function at connate oil
Jfgmax = Gas oil J function at connate liquid (DEPTH_AVE)
Gas water J function at connate liquid (BLOCK_CENTER)
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Example Oil Wet Rock Type Curves (Relative Permeability)
Figure 1
Water and Oil Wet Curves vs Water Saturation
0
Oil Wet Curves vs. Oil Saturation
0
Oil wet curves are extracted from figure 1 and plotted against Oil saturation which for an oil wet case is the wetting saturation (figure 2). It is the curves in figure 2 which must be entered as relative permeabilities in an oil wet rock type. In column 1, oil (wetting phase) saturation is entered instead of water saturation. In column 2 relative permeability to oil (wetting phase) is entered instead of relative permeability to water and in column 3, relative permeability to water (non wetting phase) is entered instead of relative permeability to oil.
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It is interesting to note that the relative permeability curves for the water wet and oil wet curves in Figure 1 are in good agreement if they are plotted vs. wetting phase (water for water wet and oil for oil wet). The figure below presents this.
Figure 3
Water Wet Curves vs. Water Saturation
0
Oil Wet Curves vs. Oil Saturation
0
Example Oil Wet Rock Type Curves (Capillary Pressure)
If the capillary pressure received are in terms of Pcow (water phase pressure minus oil phase pressure) in an oil wet system versus water saturation (the non wetting phase) the expected capillary pressure curve would resemble Figure 4 below.
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Figure 4
Pcow (OW) vs. Water Saturation
-90 -80 -70 -60 -50 -40 -30 -20 -10 0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Sw
Pcow (psi)
Pcow (OW)
To use this data in IMEX, it is necessary to translate the Pcow capillary pressure into the Pcwo curve (non wetting phase pressure minus wetting phase pressure) that the oil wet model requires as a function of wetting (oil) phase saturation.
For example pcwo =−pcow andSo =1−Sw
The resulting curve is shown below. This curve is similar in shape to pcow versus water saturation in a water wet system.
Pcwo (OW) vs. Oil Saturation
0 10 20 30 40 50 60 70 80 90
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Oil Saturation
Pcwo (psi)
Pcwo (OW)
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The relative permeability and capillary pressure examples are from Anderson, W.G. (JPT Oct. and Nov. 1987).
Oil Wet Option and Hysteresis
Due to the fact that the oil wet option rock type tables are tabulated against wetting phase saturation, all of the hysteresis options in IMEX function. Pcwo hysteresis and nonwetting phase relative permeability hysteresis are modelled. It must be remembered that in the oilwet model the nonwetting liquid saturation referred to is water so HYSKRO ‘somax’ refers to a water residual saturation and not an oil residual saturation.
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