The Calculation of Pressure Gradients In High-Rate Flowing Wells
Authors: Baxendell P.B. , Thomas R. 
Published: December 2007

Abstract
Work on the calculation of vertical two-phase flow gradients by Cia. Shell de Venezuela has been based mainly on the "energy-loss" method proposed by Poettmann and Carpenter in 1952. The "energy-loss-factor" correlation proposed by Poettmann and Carpenter was based on relatively low-rate flow data. This correlation proved inapplicable to high-rate flow conditions. In an attempt to establish a satisfactory correlation for high rates, a series of experiments was carried out at rates up to 5,000 B/D in Cia. Shell de Venezuela's La Paz field in Venezuela, using tubing strings fitted with electronic surface-recording pressure elements. As a result of these experiments a correlation between energy-loss factor and mass flow rate was established which is believed to be applicable to a wide range of conduit sizes and crude types at high flow rates (e.g., above 900 B/D for 2 7/8-in. OD tubing). It is anticipated that the resulting gradient calculations will have an accuracy of the order of +/− 5 per cent. At lower flow rates the energy-loss factor cannot be considered as constant for any mass rate of flow, but varies with the free gas in place and the mixture velocity. No satisfactory correlating parameter was obtained. As a practical compromise for low flow rates, a modification of the curve proposed by Poettmann and Carpenter was used. In practice this was found to give gradient accuracies of approximately +/− 10 per cent down to flow rates as low as 300 B/D in 2 7/8-in. tubing.

Introduction
Production operations in Cia. Shell de Venezuela's light- and medium-crude fields are principally concerned with high-rate flowing or gas-lift wells. Under these conditions the analysis of well performance, the selection of production strings and the design of gas-lift installations are vitally dependent on an accurate knowledge of the pressure gradients involved in vertical two-phase flow. Initially, attempts were made to establish the gradients empirically as done by Gilbert, but the results were not reliable due to scarcity of data over a full range of rates and gas-oil ratios. Several methods of calculation based on energy-balance considerations were attempted, but the computations were cumbersome and the results discouraging. In 1952 a paper was published by Poettmann and Carpenter which proposed a new approach. Their method was also based on an energy-balance equation, but it was original in that no attempt was made to evaluate the various components making up the total energy losses. Instead, they proposed a form of analysis which assumed that all the significant energy losses for mutiphase flow could be correlated in a form similar to that of the Fanning equation for frictional losses in single-phase flow. They then derived an empirical relationship linking measurable field data with a factor which, when applied to the standard form of the Fanning equation, would enable the energy losses to be determined. The basic method was applied in Venezuela to the problem of annular flow gradients in the La Paz and Mara fields. This involved establishing a new energy-loss-factor correlation to cover high flow rates and, also, some adaptation of the method to permit mechanized calculation using punch-card machines. The final result was a set of gradient curves for La Paz and Mara conditions which proved to be surprisingly accurate. With the encouraging results of the annular flow calculations, several attempts were made to obtain a corresponding set of curves for tubing flow. Here, unfortunately, little progress could be made. The original correlation of Poettmann and Carpenter was based on rather limited data derived from low-rate observations in 2 3/8- and 2 7/8-in. OD tubing. It did not cover the higher range of production rates, and extrapolation proved unsuccessful. A new correlation covering high flow rates was required, but this proved to be extremely difficult to establish since tubing flow pressure measurements at high rates did not exist-due to the difficulty of running pressure bombs against high-velocity flow. The necessity for reliable tubing flow data increased with the development of the new concessions in Lake Maracaibo, where high-rate tubing flow from depths of 10,500 ft became routine. Thus, it was decided to set up a full-scale test to establish a reliable energy-loss factor for tubing flow conditions. A La Paz field light-oil producer with a potential of approximately 12,000 B/D on annular flow was chosen.