Dynamic Surge/Swab Pressure Predictions

Abstract

Summary It is generally accepted that the pulling and running of pipe causes pressure surges. The prediction of pressure surges is of economic importance in wells where the pressure must be maintained within narrow limits to prevent lost circulation and formation-fluid influx. For these wells, the drilling engineer needs the best possible method of calculating surge pressures to drill wells with a minimum of trouble. This paper presents a dynamic surge/swab model that extends existing technology with the following features:pipe and annulus pressures are coupled through the pipe elasticity;longitudinal pipe elasticity and fluid viscous forces determine pipe displacement;fluid properties vary as a function of temperature and pressure; andformation elasticity, pipe elasticity, and cement elasticity are all used to determine the composite elastic response of the wellbore. Comparisons between the model and field data demonstrate good agreement. Data matches have been made for both water- and oil-based muds in both shallow and deep wells. Furthermore, the model matches data that had not been previously matched by other models. Introduction Pressure surges have long been known to cause well-control problems. In 1934, Cannon1 identified pressure surges resulting from pipe swabbing as a possible cause of fluid influx, and in extreme cases, blowouts. In 1951, Goins et al.2 measured positive pressure surges and linked surge pressures with lost-circulation problems. In most wells, the magnitude of the pressure surges is not critical because proper casing design and mud programs leave large enough margins between fracture pressures and formation-fluid pressures. A certain fraction of wells, however, cannot be designed with large surge-pressure margins. In these critical wells, pressure surges most be maintained within narrow limits. In other critical wells, pressure margins may be large, but pressure surges may still be a concern. Some operations are particularly prone to large pressure surges---e.g., running of low-clearance line's in deep wells. The need to predict pressure surges in critical wells has produced a number of wellbore fluid-flow models. Burkhardt,3 Fontenot and Clark,4 and Schuh5 represent the most complete examples of "steady-flow" pressure-surge models. In these models, the drilling mud is perfectly displaced by the pipe motion. Fluid pressures are calculated to be consistent with frictional pressure drops caused by fluid motion. These models neglect fluid inertia (Burkhardt includes an approximate inertia effect) and the compressibility of the fluid and wellbore. These models do consider the complexities of the non-Newtonian flow of drilling muds. All these models are sufficiently complex to require the use of a computer program for effective use. The lack of fluid compressibility is considered a conservative assumption because it predicts a higher flow rate, which generates a higher frictional pressure drop. The neglect of fluid inertia is not a conservative assumption. The dynamic surge pressures measured by Rburkhardt3 cannot be predicted by a steady-flow model, particularly the negative pressure surges resulting from fluid backflow when the pipe is brought to rest. The first fully dynamic surge-pressure model, developed by Lubinski et al.,6 emphasized the importance of compressibility in pressure calculations. Lal corrected a number of deficiencies in the Lubinski et al. model and began an investigation of parameters affecting surge pressures.7 Surge field data are much less common than surge-pressure models. Surge data in critical wells are, understandably, even less common. Burkhardt presents surge data in a 2,100-ft [640-m] well, which is specially instrumented to measure pressures in the wellbore and bottom hole. These data are instructive and provide a good test for analytical models, but do not represent a real well situation. Much more useful are the data gathered by Clark and Fontenot,9 who ran surge and circulation tests on two wells. The first was an 18,500-ft [5639-m] well in Mississippi that had been plugged before it was abandoned. This well was completed with a 7-in. [7.8-cm] liner, and the drilling fluid was a 17.5-lbm/gal [2097-kg/m3] oil-based mud. The second well was a 15,270-ft [4654-m] well in Utah. This well was completed with a 5-in. [12.7-cm] liner, and the drilling fluid was a 14.2-lbm/gal [1702-kg/m3] water-based mud. Clark and Fontenot provide very complete information on drilling-fluid properties throughout the tests and full information on pipe motion and resultant surge pressures. Increased use of measurement-while-drilling (MWD) tools may provide additional surge-pressure data in the future. Ramsey et al.10 provide an example of surge pressures recorded by MWD in an 11,954-ft [3644-m] well with 9.45-lbm/gal [1132-kg/m3] mud. Model Formulation Overview The dynamic-surge model consists of two analytical models: the coupled-pipe/annulus model and the pipe-to-bottomhole model (Fig. 1). The coupled-pipe/annulus model has the following features.The full balance of mass and balance of momentum for pipe and annulus flow are solved.Pipe and annulus pressures are coupled through the pipe elasticity. Annulus pressures caused by pipe pressures may be significant.Longitudinal pipe elasticity and fluid viscous forces determine pipe displacement (Fig. 2). The velocity of the pipe end is not necessarily equal to the velocity imposed at the surface.Frictional pressure drop is solved for laminar flow in an annulus with a moving pipe for power-law fluids. Turbulent-flow frictional pressure drop uses the Dodge and Metzner11 friction factor for power-law fluids.Fluid properties vary as a function of pressure and temperature. Plastic viscosity and yield point can vary significantly with temperature.Formation elasticity, pipe elasticity, and cement elasticity are all considered in determining the composite elastic response of the wellbore. For the case of a pipe cemented to the formation, use of only the pipe elasticity will not give conservative surge pressures. The pipe-to-bottomhole model has the following features.Balance of mass and balance of momentum for the pipe-to-bottomhole flow are solved.Frictional pressure drop is solved for laminar flow in the pipe-to-bottomhole region for power-law fluids. Turbulent-flow frictional pressure drop uses the Dodge and Metzner11 friction factor for power-law fluids.Fluid properties vary as a function of pressure and temperature.