The Havlena and Odeh Method of Applying the Material Balance Equation

As early as 1953, van Everdingen, Timmerman, and McMahon recognized a method of applying the material balance equation as a straight line.⁹ But it wasn’t until Havlena and Odeh published their work that the method became fully exploited.^3,4 Normally, when using the material balance equation, an engineer considers each pressure and the corresponding production data as being separate points from other pressure values. From each separate point, a calculation for a dependent variable is made. The results of the calculations are sometimes averaged. The Havlena-Odeh method uses all the data points, with the further requirement that these points must yield solutions to the material balance equation that behave linearly to obtain values of the independent variable.

The straight-line method begins with the material balance equation written as

The terms W_I (cumulative water injection), G_I (cumulative gas injection), and B_Ig (formation volume factor of the injected gas) have been added to Eq. (3.7). In Havlena and Odeh’s original development, they chose to neglect the effect of the compressibilities of the formation and connate water in the gas cap portion of the reservoir—that is, in their development, the compressibility term is multiplied by N and not by N(1 + m). In Eq. (3.12), the compressibility term is multiplied by N(1 + m) for completeness. You may choose to ignore the (1 + m) multiplier in particular applications. Havlena and Odeh defined the following terms and rewrote Eq. (3.12) as

In Eq. (3.13), F represents the net production from the reservoir. E_o, E_f,w, and E_g represent the expansion of oil, formation and water, and gas, respectively. Havlena and Odeh examined several cases of varying reservoir types with this equation and found that the equation can be rearranged into the form of a straight line. For instance, consider the case of no original gas cap, no water influx, and negligible formation and water compressibilities. With these assumptions, Eq. (3.13) reduces to

This would suggest that a plot of F as the y coordinate and E_o as the x coordinate would yield a straight line with slope N and intercept equal to zero. Additional cases can be derived

Once a linear relationship has been obtained, the plot can be used as a predictive tool for estimating future production. Examples are shown in subsequent to illustrate the application of the Havlena-Odeh method.