Transcript Conversion Factors for Oilfield Units

Conversion Factors
for
Oilfield Units
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
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
vs 
q
A

 C k dΦ
μ
ds
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
Darcy’s Law - Darcy Units
• Linear (1-D) flow of an incompressible fluid
q 
kA
μL
Δp 
– where,
•
•
•
•
•
•
q
k
A
p

L
cm3/s
darcies
cm2
atm
cp
cm
– The Darcy a derived unit of permeability, defined to make this equation
coherent (in Darcy units)
Darcy’s Law - Oilfield Units
• Linear (1-D) flow of an incompressible fluid
q 
CkA
μL
Δp 
– where,
•
•
•
•
•
•
q
k
A
p

L
bbl/D
millidarcies
ft2
psia
cp
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
Darcy’s Law - Oilfield Units
q [cm3/s] = q [bbl/D] · 5.61458 [ft3/bbl] · (30.48)3 [cm3/ft3] · (1/86400) [D/s]
= 1.84013 [(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] · (1/14.6959) [atm/psia]
L [cm] = L [ft] · 30.48 [cm/ft]
q[bbl/D]  1.84013[(c m /s)/(bbl/D )]
3

k[md]  0.001[d/md
] A[ft
2
]  929.03[cm
μ[cp] L[ft]  30.48[cm/f t]
 Δp[psia]  0.068046[a tm/psia]

2
2
/ft ]
Darcy’s Law - Oilfield Units
– Collecting the constants and canceling
q[bbl/D]

0.001127
k[md] A[ft
2
]
μ[cp] L[ft]
Δp[psia] 
• The unit of the constant is defined from the above equation
[bbl/D]  [cp]  [ft]
C  0.0011271
[md][ft
2
][psia]
• We were able to cancel leaving the units of C as shown above because,
[cm /s]  [cp]  [cm]
3
1[d]  1
2
[cm ][atm]
Static Pressure Gradient - SI Units
• Static pressure gradient of a fluid
dp  ρ g dh
– where,
•
•
•
•
p

g
h
Pa = N/m2 = (kgm/s2)/(m2) = kg/(ms2)
kg/m3
9.80665 m/s2
m
– Coherent for SI units
Static Pressure Gradient - Oilfield Units
• Static pressure gradient of a fluid
dp 
ρg
dh
D
– where,
•
•
•
•
p

g
h
psi = lbf/in2
lbm/ft3
32.174 ft/s2
ft
Static Pressure Gradient - Oilfield Units
p [Pa] = p [psi] · 6894.757[Pa/psi]
 [kg/m3] =  [lbm/ft3] · 16.01846 [kg/m3)/(lbm/ft3)]
h [m] = h [ft] · 0.3048 [m/ft]
dp[psi]  6894.757[P a/psi] 
ρ[lb
/ft ]  16.01846[( kg/m )/(lb
3
m
3
 g[ft/s2]  0.3048[m/f
 dh[ft]  0.3048[m/f
3
m
/ft )]
t]
t]
• Because the constant D is on the bottom, collect terms on left and cancel using
definition of Pascal [Pa]
D=4633.06 [(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=4633.06 [(in2/ft2)·(lbm·ft)/(lbf·s2)])
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 g))
 (p 2  p 2 ) 
1
2


z
μ


g
Replaced
by
m(p 1 )  m(p 2 ) 
– A single term of the equation is replaced with the term in brackets having the
same units and meaning:
p1
p
p2
zμg
Term   2 
dp
• Note that in oilfield units, m(p) has units of [psia2/cp]
• Note the constant, C, includes the 1/2 from integration