To simulate a tilted water contact it is necessary to properly define the grid array “Water Cap Pres Shift/Offset” which corresponds to the IMEX keyword PCOW_SHIFT.
“Water Cap Pres Shift/Offset” can be used to add an offset to each block’s oil or water-gas capillary pressure. This is used to set up a stable offset to each block’s water-oil contact.
The PCOW_SHIFT option can only be used only if the *DEPTH_AVE initialization method is in effect.
In order to use this technique to model a tilted contact (1) each PVT region’s WOC_PC must either be defaulted (to zero) or explicitly set to zero and (2) the water-oil /water-gas capillary pressure curves must extend to a water saturation of 1.00.
This tutorial assumes that PVT region averaged estimates of reservoir pressure and bubble point pressure can be used to calculate average PVT properties in a region. The average PVT properties are used to convert between contact heights and capillary pressure offsets.
This tutorial also assumes that that the effect of water and oil compressibility on the initial water and oil density can be ignored or accounted for by slightly altering the average value of Bw or Bo.
A digitized WOC map should opened in BUILDER. This map is then used to calculate the input array “Water Cap Pres Shift/Offset”. The single map should be used to calculate the
“Water Cap PresShift/Offset” for all layers.
An estimate of each PVT region’s average pressure P(est) must also be made in order to approximate an average water formation volume factor Bw(est). The water formation volume factor should also approximately account for water compressibility (i.e. Bw(est) = Bwi *(1-Cw*(P(est)-Prw)). Normally the input reference pressure REFPRES in a PVT region is a good estimate of P(est).
If the model being initialized is a Black Oil Model, an estimate of each PVT region’s average bubble point pressure Pb(est) must be made in order to estimate oil properties. Normally the input bubble Pressure table PBT in a PVT region can provide a starting point in determining Pb(est).
If the model being initialized is a Gas Water model, P(est) is also used to estimate the gas formation volume factor Bg(est).
Note: In a Gas Water model the input array is still “Water Cap Pres Shift/Offset” and the IMEX input keyword is stilled PCOW_SHIFT.
Procedure for Black Oil Models:
1. Open the WOC map you wish to use in BUILDER.
2. Define the model’s PVT regions. Normally a single PVT region would be used.
The input requires the user to define a WOC depth (DWOC) which is the PVT region’s water-oil contact. This water-oil contact will be used as a reference value for the shifted water-oil contact calculation (the WOC when PCOW_SHIFT=0.0).
The value of the reference WOC must lie between the highest and lowest WOC in the input WOC map to minimize the offset from the reference.
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3. Use Pb(est) in each PVT region to determine a value of Rs(est) and Bo(est). Bo(est) may need to approximately account for oil compressibility if the reservoir is significantly above its bubble point. Bo(est) = Bo(Pb(est))*(1-Co(p(P(est)-Pb(est)).
4. Use P(est) in each PVT region to determine Bw(est). Bw(est) may need to be altered to approximately account for water compressibility if the reservoir pressure is significantly different from Prw. Bw(est) = Bwi*(1-Cw*(P(est)-Prw)).
5. Calculate the approximate reservoir density difference between water and oil phases in each PVT region.
Den_diff = Denw(STC)/Bw(est)-(Denw(STC)+Rs(est)*Deng(STC))/Bo(est) This enables the user to relate a WOC height difference in each block to a pressure difference in each block. If Den_diff changes significantly between PVT regions separate calculations must be done for each PVT region.
6. In BUILDER, specify that the temporary grid array “CMGTemp Prop 1” for a single layer is to be calculated from the WOC map. Copy the input specification to all layers in the model. Calculate the array.
7. In BUILDER, define a formula to subtract the calculated WOC array from the reference WOC for each PVT region from the calculated WOC array and then multiply the result by Den_diff.
(Reference WOC - CMGTemp Prop1)*Den_diff
8. Use the formula above to define “Water Cap Pres Shift/Offset”. This will change the WOC map into a capillary pressure offset map. If the reference DWOC or Den_diff is significantly different in different PVT regions, the formula must account for individual PVT region’s unique reference WOC and/or Den_diff.
9. Calculate “Water Cap Pres Shift/Offset”. The array now contains the capillary pressure offset required to maintain the desired tilted WOC.
In Field Units, the conversion constants in the Den_diff equation results in the following equation.
Den_diff (psi/ft) = (Denw(STC)/Bw(est) –
(Deno(STC)+Rs(est)/5.615*Deng(STC))/Bo(est))/144 In SI Units,
Den_diff (kpa/m) = (Denw(STC)/Bw(est) –
(Deno(STC)+Rs(est)*Deng(STC))/Bo(est))*0.009806 Procedure for Gas Water Models
1. Open the WGC map you wish to use in BUILDER.
2. Define the model’s PVT regions. Normally a single PVT region would be used. The input requires the user to define a WGC depth (DWGC) which is the PVT region’s water-gas contact. This water-gas contact will be used as a reference value for the shifted water-gas contact calculation (The WGC when PCOW_SHIFT=0.0). The value of the reference WGC must lie between the highest and lowest WGC in the input WGC map to minimize the offset from the reference
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3. Use P(est) in each PVT region to determine Bg(est).
4. Use P(est) in each PVT region to determine Bw(est). Bw(est) may need to be altered to approximately account for water compressibility if the reservoir pressure is significantly different from Prw. Bw(est) = Bwi*(1-Cw*(P(est)-Prw)).
5. Calculate the approximate reservoir density difference between water and gas phases in each PVT region.
Den_diff = Denw(STC)/Bw(est)-Deng(STC)/Bg(est)
This enables the user to relate a WGC height difference in each block to a pressure difference in each block. If Den_diff changes significantly between PVT regions separate calculations must be done for each PVT region.
6. In BUILDER, specify that the temporary grid array “CMGTemp Prop 1” for a single layer is to be calculated from the WGC map. Copy the input specification to all layers in the model. Calculate the array.
7. In BUILDER, define a formula to subtract the calculated WGC array from the reference WGC for each PVT region from the calculated WGC array and then multiply the result by Den_diff.
(Reference WGC - CMGTemp Prop1)*Den_diff
8. Use the formula above to define “Water Cap Pres Shift/Offset”. This will change the WGC map into a capillary pressure offset map. If the reference DWGC or Den_diff is significantly different in different PVT regions, the formula must account for individual PVT region’s unique reference WGC and/or Den_diff.
9. Calculate “Water Cap Pres Shift/Offset”. The array now contains the capillary pressure offset required to maintain the desired tilted WGC.
In Field Units, the conversion constants in the Den_diff equation results in the following equation.
Den_diff (psi/ft) = (Denw(STC)/Bw(est)– Deng(STC)/Bg(est)/5.615)/144 In SI Units,
Den_diff (kpa/m) = (Denw(STC)/Bw(est)– Deng(STC)/Bg(est))*0.009806
Denw(STC) Standard Condition water density (DENSITY WATER keyword) Deno(STC) Standard Condition oil density (DENSITY OIL keyword)
Deng(STC) Standard Condition gas density (DENSITY GAS keyword) Bw(est) Water formation volume factor at P=P(est)
Bwi Water formation volume factor at P=Prw (BWI keyword) Bo(est) Oil formation volume factor at Pb=Pb (est) in a PVT region Bg(est) Gas formation volume factor at P=P(est) in a PVT region Rs(est) Solution gas ratio at Pb=Pb (est) in a PVT region
Prw Water reference pressure (PRW keyword)
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P(est) Estimated average reservoir pressure in a PVT region (estimated from REFPRES Keyword)
Pb(est) Estimated average bubble point pressure in a PVT region (estimated from PBT table or PB array)
Co Oil compressibility above the bubble point (CO keyword) Cw Water compressibility (CW keyword)
The simulator array PCOW_SHIFT corresponding to the BUILDER property “Water Cap Pres Shift/Offset” will now be written when the data set is saved.
Finish defining the model and when complete run the simulator for one timestep. Open the resulting SR2 file in RESULTS and examine the WOC/WGC distribution (viewing Water Saturation) and compare this with the desired distribution. Normally differences are very small.
Some Geological packages output Capillary Pressure Entry Pressure values for each gridblock. PCOW_SHIFT may be used to accept Entry Pressure input.
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