Page 387 - Petrophysics 2E

PROBLEMS 355

PROBLEMS

1. Explain why the meniscus in a capillary inserted in mercury is
depressed below the surface of the mercury. (See Figure 5.5c, where
the meniscus is depressed below the water surface of a water-oil
system.)
2. Explain how the equation for capillary pressure in straight capillaries
is derived from the Plateau equation.
3. Assume that the following data were obtained by injection of mercury
[o = 465 x N/m] into a core having a total pore volume of 2.8 cm3
at 20°C:

pc (psi) sw
3 1 .oo
4 0.88
7 0.70
11 0.58
19 0.40
36 0.25
56 0.19
78 0.19

(a) What is the value of the threshold pressure, the maximum pore
size, and the minimum pore size that can conduct a fluid?
(b) Determine the pore size distribution and show all graphs used.

4. If the capillary pressure data given in Problem 3 was obtained from oil
displacing water in a centrifuge, where P, is the core inlet pressure
and Sw is the average water saturation, calculate the following:

(a) The core inlet saturation vs. the inlet capillary pressure, using
Equation 5.43.
(b) Plot P,i vs. Si and determine the threshold pressure.
(c) Compute the vertical saturation profile if the water-oil contact
occurred at 2,000 feet (pw - po = 0.180 &em3).
(d) What is the meaning of cavitation when used with respect to
centrifuge determination of capillary pressure?

5. If the porosity = 0.16 and permeability = 0.120 darcy for the core in
Problem 4, calculate the J-function vs. saturation for the system, and
show the graph.