PE 212E Rock Properties Mustafa Onur Given Date: April 13, 2007 Due Date: April 20, 2007 Subject: Permeability Based on Hagen-Poiseuille’s Law Homework No:8 Problem 1: Consider linear flow through a cylindrical core with cross sectional area equal to 39.458 cm 2 and a length equal to L. Assume that we can model the flow as through a bundle of capillary tubes of two different sizes. Specifically, assume that there are ten million capillary tubes of radius 5 micrometers and 200,000 capillary tubes of radius 10 micrometers. (a) Estimate the permeability in Darcies of the core using this model. (b) Estimate the porosity of the core using this model. (Note: 1 micrometer = 10 -6 meters) Problem 2: Consider linear flow through a core length L with cross sectional area equal to A. Assume that flow through the core can be modeled as flow through n capillary tubes of radius r and length L. Show that 2 6 10 04 . 4 r k × φ × × = where φ denotes porosity, and k denotes permeability in Darcies. Explain why Eq. 1 does not necessarily mean that porosity and permeability are correlated. (Hint: To derive the equation, use the equation that we have derived for permeability, then derive an equation for porosity and combine the resulting two equations.)
Given Date: April 13, 2007 Due Date: April 20, 2007 Subject:
Permeability Based on Hagen-Poiseuilles Law
Homework No:8 Problem 1: Consider linear flow through a
cylindrical core with cross sectional area equal to 39.458 cm2 and
a length equal to L. Assume that we can model the flow as through a
bundle of capillary tubes of two different sizes. Specifically,
assume that there are ten million capillary tubes of radius 5
micrometers and 200,000 capillary tubes of radius 10
micrometers.
(a) Estimate the permeability in Darcies of the core using this
model. (b) Estimate the porosity of the core using this model.
(Note: 1 micrometer = 10-6 meters) Problem 2: Consider linear
flow through a core length L with cross sectional area equal to A.
Assume that flow through the core can be modeled as flow through n
capillary tubes of radius r and length L. Show that
261004.4 rk = where denotes porosity, and k denotes permeability
in Darcies. Explain why Eq. 1 does not necessarily mean that
porosity and permeability are correlated. (Hint: To derive the
equation, use the equation that we have derived for permeability,
then derive an equation for porosity and combine the resulting two
equations.)
