1. PETE 323-Reservoir Models
Spring, 2001
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2. MBE to estimate N and U- Water drive case
Commonly used
Most computationally intensive
Ideally suited to spreadsheets
Usually assumes m known and that cw and cf insignificant
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3. MBE to estimate N and U- Water drive case
General Form of Schilthuis equation
We changes with time and pressure.
N is constant.
We can be approximated by Uf(p,t)
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4. MBE to estimate N and U- Water drive case
Ignoring cf and cw
and letting We = Uf(p,t)
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5. Fractional flow curve fw
Slope of fractional flow curve
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6. Frontal Advance Concepts
Average Sw from x=0 to x=L
Point A
Craig Ch see interpretation of fractional flow curve
after water breakthrough
Sw at x=L
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7. Frontal Advance Calculations
Draw fw curve from rel. perm.
Construct straight line from Swi to point A
This determines breakthrough Sw and average Sw.
Slope of fw curve at point A gives Wi in pore volumes
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8. Frontal Advance-- at Breakthrough
Example:
Swave at BT = 56%
Sw at x=L at BT = 46%
Recovery factor at BT =
(Save-Swi)/(1-Swi) =
(.56-.2)/(1-.2) = (45%)
fw =.74
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9. Frontal Advance-- after Breakthrough
Point A= BT
Point B slope =1.0, Swave=0.58, RF =47.5%
Wi = 1 PV,fw=0.83
Point C slope = .90
Swave=0.62, RF = 52.5%
Wi = 1/.9= 1.11 PV,fw=.94
Point D slope = 0.24
Swave=0.68, RF = 60%
Wi = 1/.24 = 4.16 PV,fw=.99 D C B A
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10. Frontal Advance-- after Breakthrough
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11. Buckley Leverett comments
Theory useful to understand details of immiscible displacement
Transition zone is actually very small in real reservoir situations
Actual waterflood performance often depends more on reservoir heterogenieties and well configuration than on relative permeabilities and viscosities!
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12. Mobility ratio--Craig Ch 4
Injected water
Transition
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13. Predicting Waterflood Performance
Large number of methods
Each has severe limitations
Use idealized reservoirs and operating conditions
Will look at three traditional methods:
Stiles Dykstra-Parsons
Craig-Geffen-Morse
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14. Stiles Method
Assumes that the reservoir is linear and layered with no cross-flow.
All layers have the same porosity, relative permeability, initial and residual oil saturations.
Transition zone length is zero (piston-like)
Layers may have different thicknesses and absolute permeabilities
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15. Stiles Method
Probably the most limiting assumption is that the distance of the advance of the flood front is proportional to the absolute permeability of the layer.
This is assumption is only true if the mobility ratio is =1.
Nevertheless, the Stiles method is useful in the fairly common case where M ~ 1
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16. Stiles Method ith layer hi = thickness of ith layer
Lowest k
Water in
Water and oil out
hi = thickness of ith layer
ki= absolute permeability of ith layer
Vertical slice of reservoir
Highest k
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17. Stiles Method Re-order layers:
Highest permeability layer on top,lowest on bottom.
Number layers from highest permeability to lowest.
Natural layering
Highest permeability layer breaks thorough first, then second highest, etc.
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18. Stiles Method
n layers, with permeabilities k1 (highest), k2,…..kn (lowest)
The thicknesses of the n layers are
Dh1, Dh2,….. Dhn
Total physically recoverable oil (STB) = W*DSo*f*H*L/(5.614*Bo)
W=reservoir width-ft
Dso = change in oil saturation
f-porosity, pore vol./bulk vol.
H=total reservoir thickness, ft
L=reservoir length,ft
Bo-oil formation volume factor, res vol/sur.vol.
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19. Stiles Method
Example: seven layered reservoir
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20. Stiles Method Mathematical development:
At the time, Tj, that the jth layer has broken through, all of the physically recoverable oil will have been recovered for that layer and from all layers having higher permeability.
Since the velocities of the flood fronts in each layer are proportional to the absolute permeabilities in the layers, the fractional recovery at Tj in the j+1th layer will be
In the above example, the fractional recovery in layer 2 at the time layer 1 has broken through (Tj) will be
190/210 = That is, over 90% of layer 2 will be flooded out.
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21. Stiles Method Flooded portion Partially flooded portion Total
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22. Stiles Method
 Means at time Tj
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23. Stiles Method
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24. Stratified Reservoirs - Stiles Method
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25. Stratified Reservoirs - Stiles Method
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26. Stratified Reservoirs - Stiles Method
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27. Stratified Reservoirs - Johnson Methods
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28. Stratified Reservoirs - Johnson Methods
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29. Stiles Method
Stiles method as presented above does not allow for fill-up due to the presence of gas.
Since it is linear, it does not account for complex flooding geometry.
Stiles is often used together with other methods to correct for geometry and areal sweep. These combination methods also take time into account by considering water injection rate. qo
Time
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