A method is presented for calculating flowing bottomhole pressures in gas wells producing liquids. This method, a refinement of the Average Temperature and Pressure Method, includes an adjustment to the gas gravity to account for the presence of well stream liquids and the use of an optimum absolute roughness in the calculation of the friction factor. The effect of dividing the wellbore into multiple segments was also investigated.
The proposed method was tested against 144 wells obtained from a paper by Peffer et. al. Of the wells tested, 94 were originally from a paper by Govier and Fogarasi. The other 50 wells were taken from the files of the Texas Railroad Commission.
The purpose of this investigation was to develop a simple and accurate method for calculating bottomhole pressures in gas wells that produce liquids. This investigation closely followed the work of Peffer et. al. using the Cullender and Smith Method.
Many methods exist for calculating bottomhole pressures in gas wells. These include both single-phase and multi-phase procedures. Two common single-phase methods currently in use are the Cullender and Smith Method and the Average Temperature and Pressure Method. Because of the simplicity of the Average Temperature and Pressure Method, it was chosen for this study. While this method is not generally considered to be the more accurate of the two, the results of this investigation prove that it does produce very acceptable results with a minimum amount of calculation.
The above methods are based on a single-phase occupying the wellbore. While this assumption is acceptable in gas wells producing at high gas-liquid ratios (GLR's), it underestimates the bottomhole pressure in wells that produce a significant percentage of liquids. In order to develop a simple method that minimizes the required calculations, only single-phase methods were considered in this study. Thus, a procedure to correct the above stated deficiency was required.
To improve the accuracy of the proposed method, three areas were investigated. First, the gas gravity was adjusted to account for the presence of wellbore liquids. Second, the optimum absolute roughness was determined. Third, the consequences of dividing the wellbore into multiple segments were studied.
This method is based on solving the general mechanical energy balance for a gas well by considering that the variation in the Z-factor can be accounted for by assuming the well to be at an average pressure and temperature throughout the entire wellbore. For a steady-state system in which the kinetic energy effects are neglected, the resulting equation, as presented by Beggs, is:
Pwf = flowing bottomhole pressure, psia Ptf = flowing tubing pressure, psia S = 0.0375 gamma g (H) / (T Z) gamma g = gas gravity, air=1