EOR - 7 - PETE 471 EOR EOR 8 Fractional Flow Equation PETE...

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PETE 471 - EOR J.TRIVEDI 1 EOR – 8 : Fractional Flow Equation PETE 471 1 Immiscible Displacement Let’s derive the fractional flow equation for a one-dimensional oil-water system, and calculate the recovery, production rates etc. Assumptions Incompressible flow The fractional flow of water is a function only of the water saturation No mass transfer between phases A flood front exists, with only oil moving ahead of the front. Oil and water move behind the front Reservoir is a single homogeneous layer. Cross-sectional area to flow is constant. Linear steady-state flow occurs and Darcy’s law applies (q inj = q pro) There is no residual gas saturation behind the front Fractional flow of the displacing and displaced fluids after break through is assumed to be a function of mobility ratio of the two fluids (capillary and gravity effects are neglected) 2
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PETE 471 - EOR J.TRIVEDI 2 Derivation of fractional flow equation We start with Darcy’s equations: And replace the water pressure by P w = P o - P cow ) 2 ......... ( sin ) 1 ......... ( sin g x p A kk q g x p A kk q w w w rw w o o o ro o ) 5 ......... ( sin ) 4 ......... ( sin : as written be may equations the g, rearrangin After ) 3 ......... ( sin g x p x p A kk q g x p A kk q g x p p A kk q w cow o rw w w w o ro o o w cow o w rw w 3 ) 7 ......... ( 1 sin 1 1 o w rw ro cow t o ro o w rw ro w k k g x p q A kk k k f : flowing water of fraction for expression following obtain the we flowing, water of fraction for the solving and , for ng Substituti ) 6 ......... ( sin 1 get we one, second the from equation first the ng Substracti t w w o w t cow ro o o rw w w q q f q q q g x p k q k q kA o w w t w w o w o t o o q q q q q f q q q q q f 1 w
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