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:

In this equation:

- 15.2 is an equation constant
- 144 is a unit conversion constant, in
^{2}/ft^{2} - $+/-$ 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 $\left({E}_{HW}<150\right)$, dimensionless
- ${D}_{ID}$ is the Inner Diameter ($ID$ ) of the tubing, in
- ${g}_{c}$ is the Universal
, 32.174 lb**Gravitational Constant**_{m}-ft/lb_{f}-sec^{2} - $g$ is the
due to gravity, ft/sec**Local Acceleration**^{2}. The local acceleration due to gravity varies from location to location but is approximately 32.174 ft/sec2. The ratio of $\frac{g}{{g}_{c}}$ is approximately 1.0 lb_{f}/lb_{m} - $\rho $ is the density of the fluid, lb
_{m}/ft^{3} - $\Delta l$ 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.

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 |