1. Conversion Factors
for
Oilfield Units

2. Need for Unit Conversions
Petroleum Engineers must be able to work with various unit systems
International scope of industry
Unit systems used varies geographically
Team members may not all be located in same geographical location
Joint ventures between companies
Particular units may be required at your location
Legislated units for reporting and regulatory compliance
Company protocol

3. Oilfield Units Oilfield units are non-coherent Newton’s 2nd Law (F=ma)
SI: Force (Newton) is a derived unit to make equation coherent
USCS: Mass (slugs) is a derived unit to make equation coherent
AES, Oilfield Units: A unit conversion constant required (F=ma/gc )
Darcy’s Law
Darcy units: Permeability is a derived unit to make equation coherent
SI: coherent (permeability unit is m2 )
Oilfield Units: A unit conversion constant is required
The constant may include geometry terms (integrated form)
For gas flow, the constant may include standard temperature and pressure, even for Darcy and SI units

4. Learning Objectives Deriving unit conversion constants
Given
A physical relationship expressed as an equation, using coherent units or with a correct conversion constant supplied
and appropriate unit conversion factors between unit systems
Find
The required unit conversion constant (including its units) to express the equation in a different unit system
Correctly apply Darcy Equations for incompressible fluid and real gas, using oilfield units
See handout, “Darcy Equations”
Note definitions of standard temperature and pressure for the Real Gas cases

5. Darcy’s Law - Darcy Units
Linear (1-D) flow of an incompressible fluid
where,
q cm3/s
k darcies
A cm2
p atm
 cp
L cm
The Darcy a derived unit of permeability, defined to make this equation coherent (in Darcy units)

6. Darcy’s Law - Oilfield Units
Linear (1-D) flow of an incompressible fluid
where,
q bbl/D
k millidarcies
A ft2
p psia
 cp
L ft
The approach demonstrated will be to convert each term back to Darcy units, restoring the coherent equation, then collecting the conversion factors to obtain the oilfield unit constant, C

7. Darcy’s Law - Oilfield Units
q [cm3/s] = q [bbl/D] · [ft3/bbl] · (30.48)3 [cm3/ft3] · (1/86400) [D/s]
= [(cm3/s)/(bbl/D)] · q [bbl/D]
k [d] = k [md] · (1/1000) [d/md]
A [cm2] = A [ft2] · (30.48)2 [cm2/ft2]
p [atm] = p [psia] · (1/ ) [atm/psia]
L [cm] = L [ft] · [cm/ft]

8. Darcy’s Law - Oilfield Units
Collecting the constants and canceling
The unit of the constant is defined from the above equation
We were able to cancel leaving the units of C as shown above because,

9. Static Pressure Gradient - SI Units
Static pressure gradient of a fluid
where,
p Pa = N/m2 = (kgm/s2)/(m2) = kg/(ms2)
 kg/m3
g m/s2
h m
Coherent for SI units

10. Static Pressure Gradient - Oilfield Units
Static pressure gradient of a fluid
where,
p psi = lbf/in2
 lbm/ft3
g ft/s2
h ft

11. Static Pressure Gradient - Oilfield Units
p [Pa] = p [psi] · [Pa/psi]
 [kg/m3] =  [lbm/ft3] · [kg/m3)/(lbm/ft3)]
h [m] = h [ft] · [m/ft]
Because the constant D is on the bottom, collect terms on left and cancel using definition of Pascal [Pa]
D= [(lbm /ft3)(ft/s2)(ft)/(psia)]
Alternate derivation from dimensional homogeneity (self study)
D=(144 [in2/ft2]) · (32.174[(lbm·ft)/(lbf·s2)]) OR
D= [(in2/ft2)·(lbm·ft)/(lbf·s2)])

12. Handout - Darcy Equations
Darcy Equations for Real Gas
For pseudopressure, m(p), the unit conversion constant, C, is the same as for p2 equation (Constant (z mg))
A single term of the equation is replaced with the term in brackets having the same units and meaning:
Note that in oilfield units, m(p) has units of [psia2/cp]
Note the constant, C, includes the 1/2 from integration