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PETE 323-Reservoir Models

PETE 323-Reservoir Models. Spring, 2001. MBE to estimate N and U- Water drive case. Commonly used Most computationally intensive Ideally suited to spreadsheets Usually assumes m known and that c w and c f insignificant. MBE to estimate N and U- Water drive case.

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PETE 323-Reservoir Models

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  1. PETE 323-Reservoir Models Spring, 2001

  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

  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)

  4. MBE to estimate N and U-Water drive case Ignoring cf and cw and letting We = Uf(p,t)

  5. Fractional flow curve fw Slope of fractional flow curve

  6. Frontal Advance Concepts Average Sw from x=0 to x=L Point A Craig Ch 3 -- see interpretation of fractional flow curve after water breakthrough Sw at x=L

  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

  8. Frontal Advance-- atBreakthrough Example: Swave at BT = 56% Sw at x=L at BT = 46% Recovery factor at BT = (Save-Swi)/(1-Swi) = (.56-.2)/(1-.2) = 0.45 (45%) fw =.74

  9. Frontal Advance-- afterBreakthrough 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

  10. Frontal Advance-- afterBreakthrough

  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!

  12. Mobility ratio--Craig Ch 4 Injected water Transition

  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

  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

  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

  16. Stiles Method 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

  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.

  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.

  19. Stiles Method Example: seven layered reservoir

  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 =0.9047619048. That is, over 90% of layer 2 will be flooded out.

  21. Stiles Method Flooded portion Partially flooded portion Total

  22. Stiles Method  Means at time Tj

  23. Stiles Method

  24. Stratified Reservoirs - Stiles Method

  25. Stratified Reservoirs - Stiles Method

  26. Stratified Reservoirs - Stiles Method

  27. Stratified Reservoirs - Johnson Methods

  28. Stratified Reservoirs - Johnson Methods

  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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