exercise 3-waterflood w shock
TRANSCRIPT
Short Course " Fractional Flow Methods for Modeling Enhanced Oil Recovery" Exercise 3
Consider a one-dimensional incompressible waterflood with the following relative permeabilities for both oil and water: krw = 0.465 [(Sw-Swr)/(1-Swr-Sor)]
2.98 for Sw ≥ 0 kro = 0.662 [(1-Sw-Sor)/ (1-Swr-Sor)]
3.44 for Sw ≤ (1-Sor) Residual phase saturations are Swr = 0.2 and Sor = 0.17. The relative-permeability curve are illustrated below. Water viscosity is 1 cp (0.001 Pa s) and oil viscosity 5 cp (0.005 Pa s). On the next page are two copies of the fractional-flow plot; below is a plot of total relative mobility as a function of water saturation. The reservoir is initially at irreducible water saturation (Sw = Swr). Starting at time zero a waterflood is initiated (fw = 1). Plot the initial condition I and injection condition J on the fractional-flow plot. Find a path from J to I with monotonically increasing slopes, using shock(s) if necessary. Two copies of the fractional-flow plot are given on the next page to allow for false starts toward the solution. Using this solution, plot the time-distance diagram for this displacement on the blank page following, for times up to 4 pore volumes injected. Use dimensionless position (x/L) and time (pore volumes injected). Indicate regions of constant state, any shocks, and several characteristics in any "spreading wave" regions. "Eyeball accuracy" for slopes and velocities (estimated from the graphs using a ruler) is sufficient for this exercise. Using the time-distance diagram, make a rough plot of oil fraction in the fluid produced at the outlet (xD = 1) over time and also of the saturation in the medium at a dimensionless time of 0.3 pore volume injected. If you have time, mark in the total relative mobility of fluids at various positions in the plot of water saturation at 1 PV injected.
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Relative Perm
eab
ility
Water Saturation
water relativepermeability
oil relativepermeability
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0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Total relative
mobility, 1/(Pa s)
water saturation
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water fractional flow
water saturation
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water fractional flow
water saturation
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dimensionless position
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ensionless tim
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water saturation
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ensionless position
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water frectional flow
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ensionless tim
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