PNG 301
Introduction to Petroleum and Natural Gas Engineering The Hazen-Williams Equation for Liquid Production/Injection Wells


In addition to the Darcy-Weisbach Equation for liquid production/injection wells, the Hazen-Williams Equation also has applications in the oil and gas industry (most commonly for injection wells, but also valid for light hydrocarbon liquids). The Hazen-Williams Equation is an Empirical Method (based on observations, not theory) which pre-dates the Darcy-Weisbach Equation. It was used in times prior to the widespread use of computers due to its simplicity, as it does not include a friction factor. The Hazen-Williams formula replaces the general friction factor with a material specific constant, C HW , and modifies the equation constant and exponents. The Hazen-Williams Equation in oilfield units is:

q=15.2  C HW D ID 2.63 { g c ρ Δl [ ( p 1 p 2 )/+ gρ 144 g c ( z 1 z 2 ) ] } 0.54
Equation 6.14

In this equation:

  • 15.2 is an equation constant
  • 144 is a unit conversion constant, in2/ft2
  • +/ is the sign convention used in the equation with “ ” for production or “ + ” for injection
  • q is the flow rate through the tubing, bbl/day
  • C HW is the Hazen-Williams (tuning) Factor for the tubing section ( E HW <150 ) , dimensionless
  • D ID is the Inner Diameter ( ID ) of the tubing, in
  • g c is the Universal Gravitational Constant, 32.174 lbm-ft/lbf-sec2
  • g is the Local Acceleration due to gravity, ft/sec2. The local acceleration due to gravity varies from location to location but is approximately 32.174 ft/sec2. The ratio of g g c is approximately 1.0 lbf/lbm
  • ρ is the density of the fluid, lbm/ft3
  • Δl is the length of the section of tubing along its axis, ft
  • p 1 and p 2 are the pressures at two points in a section of tubing, psi
  • z 1 and z 2 are the elevations at two points in a section of tubing, psi

Note in the Hazen-Williams Equation, that we have replaced the efficiency factor, E eff , with the Hazen-Williams Factor, C HW , and removed the friction factor, f DW (in addition to modifying the constant and exponents). Typical values of C HW for different materials are listed in Table 6.04. While the Hazen-Williams Factor is not an efficiency factor; in practice, it is used in much the same way as E eff in the Darcy-Weisbach Equation: to tune the equation to match field measured data.

The computational simplicity of the Hazen-Williams Equation now becomes apparent – there is no need for the Reynolds Number and friction factor calculations. These calculations are included implicitly in the empirical Hazen-Williams Factor and the modified exponents. As mentioned earlier, the Hazen-Williams Equation is valid for water and light hydrocarbons, such as, gasoline and possibly condensates.

Table 6.04: Typical Values of the Hagen-Williams Constant, C HW [8]
Material Minimum Value Maximum Value
Polyvinyl chloride (PVC) 150 150
Fiber reinforced plastic (FRP) 150 150
Polyethylene 140 140
Cement, Mortar Lined Ductile Iron Pipe 140 140
Asbestos, cement 140 140
Copper 130 140
Cast iron – new 130 130
Galvanized iron 120 120
Cast iron – 10 years 107 113
Concrete 100 140
Steel 90 110
Cast iron – 20 years 89 100
Cast iron – 30 years 75 90
Cast iron – 40 years 64 83