A rock sample of 12 cm long and 2.5 cm^2 in cross section flows 0.01 cm^3/sec of

Question

A rock sample of 12 cm long and 2.5 cm^2 in cross section flows 0.01 cm^3/sec of a 3 cp oil under a 2 atm pressure drop. If the core sample is fully saturated by oil (S_p = 1), what is the absolute permeability? What will be the rate of a 0.9 cp brine in the same core under a 3 atm pressure drop if the core is fully saturated by brine (S_w = 1)? Is the rock more permeable to the oil at 100% oil saturation or to the brine at 100% brine saturation? The same core is maintained at 40 water saturation and 60% oil saturation. Under a 2.5 atm pressure drop the oil flow is 0.004 cm^3/sec and the water flow is 0.005 cm^3/sec. What are the effective and relative permeabilities to water and to oil at these saturations? What is the relative permeability ratio k_ro/k_rw at 40% water saturation? Explain why the sum of the two effective permeabilitis to oil and water is less than the absolute permeability

Explanation / Answer

Data given:

L=12 cm

A=2.5 cm2

q=0.01 cm3/sec

µ =3 cP

P=2 atm

Using Darcay's law:

Permeability k=q*µ *L/A*P =0.01*3*12/2.5*2=0.072 d =72 md

If µ=0.9 cP and P= 3 atm

q=kAP/µ *L=0.072*2.5*3/0.9*12=0.05 cm3/sec

A=r2=D2/4

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