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Conversion Factors for Oilfield Units

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Conversion Factors for Oilfield Units

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  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] · 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. 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 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] · 6894.757[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)])

  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