Simulation Models of Subsea Umbilicals, Flowlines and Fire Pump Systems
Authors: Bratland Ove 
Published: October 2008

ABSTRACT
This paper discusses mathematical models suited for simulating transient and stationary flow in umbilicals, flowlines and fire pump systems. Most emphasis is put on subsea systems.
Measurements are compared with simulations and good agreement has been achieved. The results show that the dynamics and response time in a hydraulic subsea controlsystem can be influenced by parameters like umbilical elastic properties, umbilical visco-elastic properties, transition between laminar and turbulent flow, and somefrequency-dependant propagation mechanisms. The paper discusses typical problems in different flow systems. It is also shown how the relevant umbilical properties can be determined by simple measurements on a short testsection of the umbilical.
In fire pump systems, cavitation is typically the main transient problem. In long oil and gas pipelines, the friction dominates and an accurate representation of the friction is the best contribution to relevant simulation results.

INTRODUCTION
The dynamic characteristics of transmission lines are important in a number of fields covering engineering, biological and medical applications. The parallel research efforts by workers in these different fields of application and the absence of cross referencing have led to the development of a vast number of apparently differentmodels and solutions of differing complexity, as outlined in reference 1 and 2. This paper concentrates on the model that, to the author's opinion, is the one best suitedfor typical offshore systems.

SUBSEA CONTROL SYSTEMS
Various principles have been used to control the valves in different subsea systems. Direct, piloted and sequenced hydraulic control systems have been used for many years. One of these systems' main disadvantages is the longresponse time due to effects of viscosity and compression. The damping mechanisms have been investigated in previous publications, such as reference 1, 3, 4, 5, 6, 8, 9 and 10.
In electro-hydraulic systems, the time delay in the signal line is overcome and in many cases such systems offer the most cost-effective alternative. Still, understanding the dynamics in the hydraulic lines between the topside and subsea installation is essential for selecting the best compromise between umbilical capacity and costs. Understanding the hydraulic line dynamics includes understanding effects like fluid volumetric elasticity, umbilical expansion, hydraulic friction and the sometimes complicated damping mechanisms in and between the those layers.
Another problem concerning friction in a subsea control umbilical, is that the Reynolds numbers typically may vary between 100 and 10.000. Transition between laminar and turbulent flow can therefore play an important role. As explained in reference 4, such transition is much more complicated in transient than in stationary flow. The criteria for transition used in a simulation program should therefore be offered considerable attention.
Another well-known phenomenon in a highly damped oil filled pipe or hose, is that the velocity of propagation depends on the pressure signal's frequency and average line pressure.
In this paper, a simulation model that accounts for all relevant effects is developed.

EXPERIMENTAL PROCEDURE
A simple single-cord hose was selected for laboratory testing, see Fig. 1. The experimental system is illustrated in Fig. 2.