Computer Design of Dense-Phase Pipelines

Abstract

This paper demonstrates the importance of performing simultaneous temperature and pressure profile calculations when designing pipelines for single dense-phase fluids. The sensitivity of the pressure and temperature profiles to design parameters is examined and discussed in detail. profiles to design parameters is examined and discussed in detail. Introduction The pressure and temperature changes for single-phase flow along a pipeline are described by the following differential equations: dp p dv g dZ 2fv2p--- + -- v ---- +p --- ----- + ------- = 0,.......(1)dL gc dL gc dL gcd dh 1 dv g dZ 1 dQ---- +--- v --- + --- ---- + --- --- = 0,......(2)dL gc dL gc dL w dL where the following functional relationships must be specified. p =f(p, T)......................................(3)h =f(p, T)......................................(4)=f(p, T)......................................(5)f =f(N Re, k/d).................................(6) wheredvpN Re = ----.......................................(7) The expressions for p, h, and may be either analytical or graphical, and their complexity depends on the type of fluid being considered. Many different expressions for the friction factor, f, are also available; some are general and some are for specific pipeline and fluid systems. For hand calculations, Eqs. 1 and 2 must be integrated over the length of the pipeline to obtain analytical expressions for pressure and temperature as functions of length, flow rate, fluid properties, and pipe-to-sod interactions. This poses problems for the general case becausethe equations are nonlinear and coupled,the fluid properties depend on pressure and temperature in a complex manner, andthe friction factor is a nonlinear function of viscosity, density, and velocity. Thus, to obtain the analytical expressions, various simplifying assumptions must be made. This procedure has resulted in many design equations that apply to particular systems and are useful when the inherent assumptions are valid. However, in some cases, particularly when dealing with a fluid near the critical region particularly when dealing with a fluid near the critical region (i.e., dense fluid state), variations in the physical and thermodynamic properties are rather complex and no available integrated form of the equations can be used safely. If adequate information is available about the relationships expressed by Eqs. 3 through 6, Eqs. 1 and 2 can be integrated numerically to any desired accuracy without making any simplifying assumptions. Clearly, this approach is only practical when a digital computer is available, but it is completely general and may be followed for any single-phase flow in a pipe (gas, liquid, or dense phase). This procedure is the basis of the computer program used to perform all calculations discussed later. Extension of the approach to multiphase gas-liquid flow in pipes and structure of the program are discussed elsewhere. P. 40