TRANSMISSION-LINE MODELING OF SIMULATED DRILL STRINGS UNDERGOING WATER-HAMMER

Drill strings and oil production lines are examples of fluid systems f or which time-dependent (dynamic) as well as steady state (static) ana lysis is increasingly needed. These systems are difficult and expensiv e to instrument and test experimentally. Developments of fluidic non-m oving-part controllers to produce water-hammer pulsations stimulated a need to simulate the fluid dynamics of such drill strings to aid the design work. The method of simulation chosen was transmission line mod elling (TLM). It is essentially a time-delay method, borrowing its mai n concepts and the fundamentals of its computational solution scheme f rom early work by others in the field of electrical power lines. In it s elementary form, a fluid network is treated as a set of pipes (or pi pe segments) where waves travel with pure time delay. Connecting the p ipes are junctions of various types at which the waves are scattered ( transmitted, reflected andlor attenuated). The merits and limitations expected with this methodology in comparison with the method of charac teristics (MOC) and other wave-analysis methods are discussed. The fir st adaptations of TLM were for small perturbation analysis. The presen tation here takes such work further forward to model large-scale waves in pipe networks of almost arbitrarily complex topology. The basic th eory behind the method is presented and the solution schemes are formu lated mathematically with comments on the type of data structure and a lgorithms needed to undertake computationally such solutions. With the aid of modules described elsewhere, providing comprehensive steady st ate modelling capability, the software provides a powerful tool for im plementing static and dynamic TLM simulations of networks. One of the novel aspects of considerable benefit is the ease of implementation of time-varying junctions capable of representing the overall action of control elements such as the fluidic controllers mentioned earlier. A large experimental laboratory facility with a simple circuit containin g the essential hydrodynamics of drill strings was used to gather data on water-hammer pulsations. A controlled solenoid valve with a high-r esistance bypass acted as an alternating high and low resistance in th e main pipe loop. A simplified version of the circuit was simulated wi th TLM to compare and discuss the results. The TLM time-domain results took a few seconds of computer processing rime and revealed the basic features of the circuit dynamics quantifying water-hammer to a fair a nd useful accuracy. Such results were encouraging and confirmed the po wer of this computational method as an aid in the design process.