1. PERMEABILITY Gas Flow in Porous Media
The petroleum industry commonly uses the prefix Mille (one thousand). An Mscf is 103 scf of gas.
An MMscf is 106 scf of gas. A Bscf is 109 scf of gas
Be very careful in the international industry even with common definitions. For example, there is often confusion as to whether a “million” is 106 or 109 in Latin/South America, due to differences in languages

2. Gas Flow vs. Liquid Flow
Gas density is a function of pressure (for isothermal reservoir conditions)
Real Gas Law
We cannot assume gas flow in the reservoir is incompressible
Gas density determined from Real Gas Law
Darcy’s Law describes volumetric flow rate of gas flow at reservoir conditions (in situ)
At any specified temperature and pressure, a specified volume of two different gasses contains the same number of moles, if the Ideal Gas Law is valid. The Ideal Gas Law is valid at standard temperature (e.g. 60 F, Texas) and standard pressure (e.g psia, Texas). This means that zsc=1.
Note that standard conditions of temperature and pressure are legislated values, and may vary between countries, or between states in the U.S.
Gas gravity, g, is the ratio g/ air at standard temperature and pressure. The molecular weight of air, Mair = g/mol (after McCain).
The product, (g Mair) = Mgas.

3. Gas Flow vs. Liquid Flow Gas value is appraised at standard conditions
Standard Temperature and Pressure
qg,sc[scf/day] is mass flow rate (for specified g)
For steady state flow conditions in the reservoir, as flow proceeds along the flow path:
Mass flow rate, qg,sc , is constant
Pressure decreases
Density decreases
Volumetric flow rate, qg , increases
The petroleum industry commonly uses the prefix Mille (one thousand). An Mscf is 103 scf of gas.
An MMscf is 106 scf of gas. A Bscf is 109 scf of gas
Be very careful in the international industry even with common definitions. For example, there is often confusion as to whether a “million” is 106 or 109 in Latin/South America, due to differences in languages

4. Gas Formation Volume Factor
Given a volumetric gas flow rate at reservoir conditions, qg, we need to determine the mass flow rate, qg,sc
Bg has oilfield units of [rcf/scf]
scf is a specified mass of gas (i.e. number of moles)
reservoir cubic feet per standard cubic foot
(ft3)reservoir conditions / (ft3)standard conditions
A good engineer might pre-calculate the value of psc/Tsc in order to work more efficiently.
A poor engineer would use this value in a location where psc and/or Tsc were different.

5. Linear Gas Flow 1-D Linear Flow System
Steady state flow (mass flow rate, qg,sc , is constant)
Gas density is described by real gas law, g=(pgMair)/(zRT)
Horizontal flow path (dZ/ds=0  =p)
A(0s  L) = constant
Darcy flow (Darcy’s Law is valid)
k = constant (non-reactive fluid)
single phase (Sg=1)
Isothermal (T = constant) L qg A 1 2

6. Linear Gas Flow Darcy’s Law: q12 > 0, if p1 > p2 A qg 2 L 1
Pressure, gas viscosity, and z-factor are functions of pressure, and must be kept inside the integral

7. Integral of Pressure Dependent Terms
Two commonly used approaches to the evaluating the integral of the pressure dependent terms:
(zg )=Constant approach, also called “p2 Method”
valid when pressure < 2,500 psia
for Ideal Gas a subset of this approach is valid
z = 1; valid only for low pressures
g depends on temperature only
Pseudopressure approach
“real gas flow potential” - Paul Crawford, 2002 (see notes view).
the integral is evaluated a priori to provide the pseudopressure function, m(p)
specified gas gravity, gg
specified reservoir temperature, T
arbitrary base pressure, p0
valid for any pressure range
Ramey, Crawford and Al-Hussainy first developed the pseudopressure approach using the m(p) function. Dr. Crawford mentioned to me when I was preparing this lecture (Jan. 2002) that if they had it to do over again, he would prefer the name “Real Gas Flow Potential”.
Note that the literature contains other implementations of the pseudopressure approach, specifically, the pp(p) function is also commonly used. However, these other implementations differ only in details.
Note that the literature also sometimes calls the exact m(p) by the name pp(p).
a priori means “ahead of time”
Even though it is not accurate for high pressures, legislated requirements (e.g. Texas) may impose the use of the p2 method for governmental reporting. Engineering decisions should be made using pseudopressure if reservoir pressure is outside the valid range of the p2 method.

8. (zg )=Constant
Assumption that (zg ) is a constant function of pressure is valid for pressures < 2,500 psia, across the range of interest, for reservoir temperature and gas gravity

9. (zg )=Constant At other temperatures in the range of interest
Reservoir Temperature Gradient
dT/dZ  0.01 F/ft

10. (zg )=Constant, Linear Flow
If (zg )=Constant
Gas Flow Rate (at standard conditions)
Recall, flipping integral limits is the same as negation.
The term (p12-p22) is commonly called “delta p-squared”. But when spoken, it sounds like “delta-p squared”. It would probably be more accurate to call it “delta of p-squared” but this is not normally done.

11. Real Gas Pseudopressure
Recall piecewise integration:
the ordering (position along x-axis) of the integral limits a,b
and c is arbitrary
pseudopressure, m(p), is defined as:
Piecewise Integration of the pressure dependent terms:
Dimensions of m(p) [ pressure2 / viscosity]
Oilfield units of m(p) [psia2/cp]
Remember: gas gravity and reservoir temperature are specified for the reservoir under consideration. p0 is an arbitrary base pressure. Choosing p0=0.0 psia (oilfield units) can be a useful choice when implementing this method on a computer, because m(p=0.0) = 0.0 psia2/cp

12. Real Gas Pseudopressure, Linear Flow
Recalling our previous equation for linear gas flow
And substituting for the pressure integral
Recall, flipping integral limits is the same as negation.

13. Radial Gas Flow
The radial equations for gas flow follow from the previous derivation for liquid flow and are left as self study
(zg )=Constant
Pseudopressure