A new model is proposed for predicting the pressure drop in liquid-cut gas well tubing. The liquid holdup is modeled as a function of dimensionless gas and liquid velocity numbers, as well as liquid viscosity number. It involves five parameters that are related to flow regimes and can be optimized using the field data. The friction loss is based on Mukherjee and Brill correlation. In this model, the pressure gradient equation is treated as an initial value problem for an ordinary differential equation, and is directly solved by Runge-Kutta method.
Based on the field measured data from 159 gas wells covering a wide range of production conditions, the model was found to be able to predict the pressure drops with an improved overall accuracy compared to the modified single-phase model and five commonly used empirical correlations.
Sensitivity of the models to liquid/gas ratio is also presented.
Accurate prediction of pressure drop is the basis for gas well design and performance analysis. For gas wells with low liquid/gas ratio, modified single-phase flow models can be used. These models are based on the Cullender and Smith equation. To use these, one needs to modify the gas density according to the liquid/gas ratio and liquid density and adjust the friction factor by using an apparent roughness instead of an absolute one. Because of the complexity of two-phase flow, many empirical correlations have been developed for prediction of pressure drop. Each of these correlations was developed and/or tested for a specific range of flowing conditions. Therefore, no correlation should be used in any field before testing and evaluating its accuracy under the specific field conditions.
Determination of liquid holdup is essential for the calculation of the pressure drop caused by gravity and friction. In this paper, the liquid holdup is described by three dimensionless numbers and five independent parameters related to practical flow regimes. The approach is similar to MONA model by Asheim. In MONA model, the liquid holdup is a functional relationship of gas and liquid superficial velocity only and the effects of fluid properties are however not considered.
The fourth order Runge-Kutta method is applied in this paper to integrate the pressure gradient equation. This method does not require an estimation of average pressure. As a result, more accurate and faster computation can be achieved, compared with the popular trial-and-error method.
A computer program was developed to evaluate the overall performance of several calculation methods for pressure gradients. It can also be used to generate and plot pressure gradient curves.
Data from 159 wells were used to evaluate this model. These include data from 95 wells from Govier and Fogarasi, 50 wells from the Texas Railroad Commission and 14 wells from the gas fields of Southwest Sichuan, China. These field data cover a wide range of production conditions. It is found that the new model, on the whole, is more accurate than the modified single-phase model and five commonly used empirical correlations. Using the practical field data for optimizing liquid holdup parameters, the calculated results are close to the actual. The new model has been used, with good results, in the gas fields located in Southwest Sichuan, China. Pressure gradient equation and its numerical solution
The gas and liquid flow in well tubing can reasonably be considered as one dimensional.