Calculation of Pressure And Temperature Profiles In Multiphase Pipelines And Simpne Pipeline Networks
Authors: Gregory Ga , Aziz K. 
Published: March 2010

Abstract
The structure and related theory for a computer program to perform detailed design calculations for pipelines and simple pipeline networks are presented and discussed.
The sensitivity to calculated pressures, temperatures and total liquid holdups of parameters such as pipe-to-ground heat transfer coefficient, ground temperatures, pipeline orientation (horizontal, uphill and downhill) and total flow rate are examined and discussed in detail for a typical natural gas - condensate system.
Some characteristics of several different design calculation procedures are noted.

Introduction
Multiphase flow in wells and gathering systems is of considerable interest to petroleum engineers as well as many working in other branches of engineering. Petroleum engineers arc particularly interested in the prediction of flow pattern, holdup and pressure drop in well tubings and gathering lines or networks. These calculations areusually rather involved and the problem is further complicated because:no single design method is "best" under all conditions:several design methods must be tried to get some appreciation for the possible range of answer andwhere reliable fluid property or other data are not available, sensitivity of results to variations of these data must be investigated.
This makes hand calculations impractical. The calculations are, however, particularly amenable to computer programs and one such program is discussed in this paper. Applications of a previous version of the program are discussed elsewhere.(1,2)

Program Structure
For calculation purposes, the actual pipeline elevation profile is approximated by choosing a series of modal points on the profile for which x and z coordinates are available. The pipeline is assumed to have a constant slope, mass flow rate and diameter between nodal points; however, any or all of these parameters may change at the nodes. In the program, the distance between nodes is divided into a specified number of segments and, starting with the end where the pressure and temperature are known calculations are performed in a sequential fashion for one segment at a time until calculations are completed for the entire system. The segment size is selected so that the variation of fluid properties over its length is small and differential forms of the flow and energy equations can be used. The flow equation may be written as follows:
There are many methods available in the literature for calculating the various terms in Equation (1). These are discussed in detail by Govier and Aziz(3) and compared with experimental data in a series of papers by the authors and Mandhane(4,3,6). In most cases of practical interest, ~PKE is negligible with respect to ΔPHH + ΔPr and can be neglected without significant error. The program contains fouf flow pattern prediction method(4), ten different holdup calculation methods(5) and fourteen different pressure- drop calculation methods(6). The energy equation is discussed in different forms in several references(7,8,9). In the energy equation the heat transfer term q may be estimated from
(Equation Available In Full Paper)
Estimation of the over-all heat transfer coefficient, U, is possible by a number of available method (10,11,12).