Surge and Swab Effects Due to Vessel Heave in Deepwater Wells: Model Development and Benchmarking

Abstract

Abstract During operations in deepwater wells (such as, for instance, running smart completions), there exist periods when the axial movement of the string in the well remains uncompensated. During these periods, vessel heave is imposed on the string at the surface, resulting in transient pressure fluctuations (swab and surge effects) in the fluid downhole. The problem is further complicated by the presence of multiple flow ports in the string, and of choke and kill lines at surface, as well as float valves in the string itself. As the margin between pore and fracture pressure is narrow, these fluctuations can create conditions for an influx or lost circulation, with potentially significant consequences. While existing literature and commercial models address the classical drill pipe induced swab/surge due to tripping, they do not model multiple flow paths and/or continuous forcing functions (such as heave) at the surface of the drill string or completion string. In this paper, we present the development of a semi-analytical approach to model such transient pressure problems. The transient pressure problem is solved using the method of characteristics, and draws from the seminal work of Lubinski et al. and employs the electrical analogy first proposed by Bergeron (Water hammer in Hydraulics and Wave Surges in Electricity", John Wiley, 1961). The method is extended to include Power-Law fluids (as well as Bingham Plastic and Newtonian rheological models). Arbitrary flow ports can be situated anywhere in the string, with either one or two-way flow. Both open- and closed-end pipes are considered, in addition to nozzles at the pipe end. Temperature and pressure effects on the compressibility, as well as the elasticity of the formation, are considered in the calculation of the characteristic impedance. The approach can accept any arbitrary forcing function at surface, either as a periodic wave or as a tabulated time function of displacements. Several limitations of the previous models are also addressed in the theoretical development reported in this work. The method is implemented in a spreadsheet tool that allows the input of a wide variety of situations, incorporates different fluid PVT and rheology models, and calculates transient pressure at any point of interest in the annulus. The model is compared to several benchmark field cases in the literature, and the comparison is shown to be very satisfactory. Finally, a case of a smart completion with one to four flow ports in the lower sections that can be selectively closed or opened, subjected to sinusoidal vessel heave at surface, is examined. Results show that the pressure fluctuations can be substantial in some of the cases, and suggest that with appropriate fluid selection and operational procedure, even large heave can be sustained without initiating either underbalance or lost circulation.