Transmission line modelling of simulated drill strings undergoing water-hammer

Drill strings and oil production lines are examples of fluid systems for which time-dependent (dynamic) as well as steady state (static) analysis is increasingly needed. These systems are difficult and expensive to instrument and test experimentally. Developments of fluidic non-moving-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 modelling (TLM). It is essentially a time-delay method, borrowing its main concepts and the fundamentals of its computational solution scheme from early work by others in the field of electrical power lines. In its elementary form, a fluid network is treated as a set of pipes (or pipe segments) where waves travel with pure time delay. Connecting the pipes are junctions of various types at which the waves are scattered (transmitted, reflected and/or attenuated). The merits and limitations expected with this methodology in comparison with the method of characteristics (MOC) and other wave-analysis methods are discussed. The first adaptations of TLM were for small perturbation analysis. The presentation here takes such work further forward to model large-scale waves in pipe networks of almost arbitrarily complex topology. The basic theory behind the method is presented and the solution schemes are formulated mathematically with comments on the type of data structure and algorithms needed to undertake computationally such solutions. With the aid of modules described elsewhere, providing comprehensive steady state modelling capability, the software provides a powerful tool for implementing 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 containing the essential hydrodynamics of drill strings was used to gather data on water-hammer pulsations. A controlled solenoid valve with a high-resistance bypass acted as an alternating high and low resistance in the main pipe loop. A simplified version of the circuit was simulated with TLM to compare and discuss the results. The TLM time-domain results took a few seconds of computer processing time and revealed the basic features of the circuit dynamics quantifying water-hammer to a fair and useful accuracy. Such results were encouraging and confirmed the power of this computational method as an aid in the design process.