PETE 323-Reservoir Models Spring, 2001 10/13/2018

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 10/13/2018

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) 10/13/2018

MBE to estimate N and U- Water drive case Ignoring cf and cw and letting We = Uf(p,t) 10/13/2018

Fractional flow curve fw Slope of fractional flow curve 10/13/2018

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 10/13/2018

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 10/13/2018

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) = 0.45 (45%) fw =.74 10/13/2018

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 10/13/2018

Frontal Advance-- after Breakthrough 10/13/2018

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! 10/13/2018

Mobility ratio--Craig Ch 4 Injected water Transition 10/13/2018

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 10/13/2018

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 10/13/2018

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 10/13/2018

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 10/13/2018

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. 10/13/2018

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. 10/13/2018

Stiles Method Example: seven layered reservoir 10/13/2018

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. 10/13/2018

Stiles Method Flooded portion Partially flooded portion Total 10/13/2018

Stiles Method  Means at time Tj 10/13/2018

Stiles Method 10/13/2018

Stratified Reservoirs - Stiles Method 10/13/2018

Stratified Reservoirs - Stiles Method 10/13/2018

Stratified Reservoirs - Stiles Method 10/13/2018

Stratified Reservoirs - Johnson Methods 10/13/2018

Stratified Reservoirs - Johnson Methods 10/13/2018

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 10/13/2018