6.3.2.4: 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:

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 $\left(E_{HW}<150\right)$, dimensionless
• $D_{ID}$ is the Inner Diameter ($ID$ ) of the tubing, in
• $g_c$ is the Universal Gravitational Constant, 32.174 lb_m-ft/lb_f-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 $\frac{g}{g_c}$ is approximately 1.0 lb_f/lb_m
• $\rho$ is the density of the fluid, lb_m/ft³
• $\Delta l$ 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.