System Hydraulics and Design A

Fundamentals of liquid Pipeline Hydraulics

proper pipeline design systems must take into account hydraulics : pipeline rout, pipe size, operating temp and pressure and the number of pump stations are determined mechanical design : dictated by relevant codes and standards resulting in pipe material selection & specification as well as burial depth requirements geo-technical design: address surface loads, water crossing, buoyancy control and geo hazard management operations and maintenance design : necessary control system to operate design parameters. pipeline flow equations: dictated by: mass conservation momentum conservation : rate of change of momentum is the sum of applied forces energy conservation : net rate of energy transfer = the rate of energy accumulation Four independent variables that define hydraulic states Pressure temperature flow rate density fourth equation used for the four unknowns is the equation of state

Continuity Equation accounts for mass being conserved in the pipeline. requires knowledge of the density and compressibility of the fluid flow, pressure and temperatures EQUATIONS IN SLIDE (7, LECTURE 3A) Momentum Equation used to calculate the pressure drop due to the friction of fluid flow against the pipe wall. friction pressure drop: linearly proportional to the fluid density and friction factorpipe diameter is the most significant design parameter: flow capacity and frictional pressure drop depend on d Reynolds number--> the ratio of inertial forces to viscous forces it increases as the flow velocity increasesReynolds number classifies flow regimes: Laminar flow Critical flow Turbulent flow: partially turbulent ( smooth pipe law applies) fully turbulent ( rough pipe law applies) EQUATIONS FOR FRICTION IN (LECTURE 3 SLIDE 10) MOODY DIAGRAM (LECTURE 3 SLDIE 11) --> relates friction to reynolds number using relative roughnessJAIN EQUATION (LECTURE 3 SLIDE 12) most liquid hydrocarbon pipelines are operated in partially turbulent flow regimes, with the exception of ethylene and ethan flow with can be fully turbulent and heavy crude which my be laminar flow regime Energy Equation accounts for the total energy of the fluid in and around the pipeline.--> requires information regarding the flow, pressure, and fluid temperature along with conductivity and around temperaturesEQUATION (LECTURE 3 SLIDE 12) Equation of State needed to define the relationship between product density or specific volume, pressure and temperature EQUATION ( LECTURE 3, SLIDE 13)

Solution Methods the four equations discussed above are solved simultaneously for the four primary variables: Q, P, T, density Assumptions for solutions: no chemical reaction takes place in the pipeline system the fluid remains in a single phase initial conditions for time variable to establish initial pipe state boundary conditions to provide boundary values at specific locations SOLUTION METHODS (LECTURE 3, SLIDE16) method of characteristic curves ( changing the coordinates to produce first order differential equations) explicit methods: finite difference in order to use known variables gives you knowledge of the PREVIOUS time step implicit methods: equations are linearized and then expressed by finite difference at the CURRENT time step