The calculation of single phase and two phase flowing pressure gradients in a well annulus is generally based on an extension of empirical correlations developed for Newtonian fluids in circular pipes. Various techniques for extending pipe flow correlations to an annular geometry have been presented in the literature which involve the representation of the annular well geometry with an equivalent circular diameter and the representation of non-Newtonian fluid behavior with an apparent Newtonian viscosity. Unfortunately, little experimental data have been available which would allow a comparison of the relative accuracy of the various proposed techniques. proposed techniques. In this study, experimental pressure gradient data have been taken in two 6000 ft. wells. Frictional pressure losses for single phase flow (mud only) in two pressure losses for single phase flow (mud only) in two annuli were compared to values predicted by the Bingham Plastic and Power law Models. These calculations Plastic and Power law Models. These calculations utilized the equivalent diameters defined by the Crittendon criteria, the hydraulic radius, and the slot approximation. Also, total pressure difference for two-phase flow was measured for one annular geometry. This data was compared to that predicted by the Poettmann and Carpenter, Hagedorn and Brown, Orkiszewski, and Beggs and Brill correlations.
Comparison of experimental data with the various prediction techniques was favorable, each having prediction techniques was favorable, each having advantage in certain situations. For the data investigated, the Crittendon criteria using a Bingham Plastic Model gave the best results. The two phase flow data was best predicted by the Hagedorn and Brown correlation utilizing a hydraulic radius equivalent diameter.
Historically, engineers have had considerable difficulty estimating flowing pressure gradients in a well annulus for drilling or well control operations. Although several calculation procedures have been presented previously in the literature for extending presented previously in the literature for extending empirical pipe flow correlations to annular flow conditions, little experimental annular flow data has been available to establish the reliability of these proposed techniques. In addition, essentially all annular proposed techniques. In addition, essentially all annular flow data presented in the literature have been obtained in laboratory apparatus, which are much smaller lengths and diameters than the well systems of practical interest. practical interest. There are a number of situations in which an accurate description is desired, for either (1) single phase annular flow of a non-Newtonian mud or cement phase annular flow of a non-Newtonian mud or cement slurry or (2) multiphase flow of a mud-gas mixture. The calculation of equivalent circulating density (ECD) during drilling or cementing operations are examples of the need for an accurate single phase, non-Newtonian, annular flow model. Calculation of ECD's can be particularly important in a deep, slim hole geometry, particularly important in a deep, slim hole geometry, or a deepwater drilling location which typically has a greatly reduced formation fracture gradient. The design of a dynamic kill of an uncontrolled flowing well is an example of the need for an accurate multiphase, non-Newtonian, annular flow model. Another example application is the accurate prediction of well behavior during conventional well control operations by means of a well control computer simulator. They are often used for training rig personnel and evaluating alternative pressure control procedures.
In this paper, experimental annular flow data were obtained in two instrumented 6000 ft. wells for both single phase and two phase conditions. These data were then used to test the accuracy of several calculation techniques for predicting single phase and multiphase annular flow pressure gradients. In particular, several schemes for estimating equivalent pipe particular, several schemes for estimating equivalent pipe diameter and apparent viscosity were evaluated using the Bingham Plastic and Power Law Models. Also, several vertical, two phase pipe flow correlations were extended for use in an annulus and evaluated using the experimental data.
Both the Bingham Plastic and the Power Law Rheological Models were used in the study.