Conversion Factors

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
• Newtons 2nd Law (Fma)
• 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 (Fma/gc )
• Darcys 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
Darcys 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
Darcys 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
Darcys 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

8
Darcys 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 9.80665 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 32.174 ft/s2
• h ft

11
Static Pressure Gradient - Oilfield Units

• p Pa p psi 6894.757Pa/psi
• ? kg/m3 ? lbm/ft3 16.01846
  kg/m3)/(lbm/ft3)
• h m h ft 0.3048 m/ft
• Because the constant D is on the bottom, collect
  terms on left and cancel using definition of
  Pascal Pa
• D4633.06 (lbm /ft3)(ft/s2)(ft)/(psia)
• Alternate derivation from dimensional homogeneity
  (self study)
• D(144 in2/ft2) (32.174(lbmft)/(lbfs2))
• OR
• D4633.06 (in2/ft2)(lbmft)/(lbfs2))

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