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

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 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)

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

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]

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,

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

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

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] 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 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