Help is appreciated.

The purpose of this experiment is to measure the air permeability of a core plug

at four different mean pressures using a gas permeameter. The Klinkenberg$-$

corrected gas permeability will then be determined.

$4\mathrm{.}1\mathrm{.}1$ Calculations

When turbulence effects are included in the flow equations, the gas permeability

$k$ can be determined from the mean pressure by plotting the data according to

the following formula:

$\frac{A}{l{p}_0}*\frac{\frac{p}{b}ar(p{)}_{\frac{?}{abs}}}{q_o}=\frac{1}{k}+\frac{p_0}{A}\frac{q_o}{\frac{?}{\text{b}\text{a}\text{r}}(p{)}_{\frac{?}{abs}}}$

where $k$ is the gas permeability, $$ is the gas viscosity from Figure $4\mathrm{.}1,l$ is the

plug length, $A$ is the cross$-$sectional area of the plug, $p_0$ is the atmospheric pres$-$

sure $($barometric pressure$),$ is a turbulence constant, and $q_o$ is the gas rate at

atmospheric pressure. The absolute mean pressure is given by

$\frac{?}{\text{b}\text{a}\text{r}}(p{)}_{abs}=\frac{1}{2}(p_1+p_2)+p_0$

and the pressure drop across the plug is given by

$p=p_1-p_2$

Let

$y=\frac{A}{l{p}_0}*\frac{\frac{p}{b}ar(p{)}_{\frac{?}{abs}}}{q_o}$

and

$x=\frac{q_o}{\frac{?}{\text{b}\text{a}\text{r}}(p{)}_{abs}}$

Equation $4\mathrm{.}1$ can thus be written as:

$y=\frac{1}{k}+ax$

where

$a=\frac{p_0}{A}$

By plotting $y$ as a function of $x$ as shown in Equation $4\mathrm{.}6,$ the gas permeability

$k(p)$ can be found by drawing a straight line through the data points and letting

$\frac{1}{k}$ be the point where the line intersects the $y-$axis.

The Klinkenberg$-$corrected gas permeability of the plug can be found by plotting

the permeability $k(p)$ as a function of $\frac{1}{\frac{?}{?}}$bar $(p{)}_{abs}$ and then letting $\frac{?}{\text{b}\text{a}\text{r}}(p{)}_{abs}.$ The air

will then behave like a liquid, and this permeability will be approximately equal

to the liquid permeability.

A $=4,95$ cm$^2$

L $=10,0$ cm

T $=20\mathrm{.}8$ c