Abstract

Gas pipeline design is greatly affected by the amount of a pressure drop anticipated during different phases of natural gas transportation. The outlet pressure can be computed by a common gas pipeline equation such as Weymouth or Panhandle formulas at the desired flow rate and pipe size. In addition to selecting the proper size of a pipeline, the compressor capacity and the related cost are determined based on the discharge pressure. The flow rate, in these equations, is defined in terms of a turbulent friction factor. The friction factor relationship approximates the turbulent behavior as a function of surface roughness in the pipe. An efficiency factor is employed in the equations for adjusting deviations in the pressure drop calculations. Existence of a sublayer, due to the pipe surface condition and accumulations of condensate, can generate cases that cannot be defined properly by the use a single friction factor. The proper sizing of a pipeline can be improved by defining the ranges of errors introduced with the use of different friction factors.

Different correlations exist for the calculation of the friction factor, t, as a function of Reynold's number and the relative roughness of the pipe. The formulas for f either require an iterative procedure or may be solved explicitly. Also, each friction factor correlation exists with its own valid limits regarding Reynold's number and relative roughness. Thus, some equations are simple to use but not accurate and some are accurate but not easy to incorporate into the final equation.

In this study, the effect of the friction factor on the pressure drop calculations for gas flow is presented. Various correlations for friction factors are utilized to demonstrate their impact on the design of natural gas pipelines. Also, a summary and a comparison of results are presented for different flow rates, pipe sizes, and for field data.

Introduction

Pressure is the driving force for the flow of natural gas in gathering systems and transmission pipelines. The pressure drop between two points allows the engineer to optimize the pipeline diameter as well as the compressor using basic flow equations such as Weymouth or Panhandle equations.

The basic flow equations consist of three components called elevation, velocity, and friction. The elevation component is dependent upon the gas gravity and, when computed over the length of a horizontal or inclined pipeline or gathering system, will become negligible due to its small effect upon the result.

In pipe flow, the velocity of gas is much higher than that of the oil and it plays a significant role within both the velocity component and the friction component. When the size of a pipeline is selected, the velocity component is fixed at the desired field gas production rate.

On the other hand the calculation of frictional pressure drop component requires the knowledge of pipe condition in terms of roughness. The pipe roughness plays a major role in the determination of pressure loss since the smoothness of the internal surface is changing over time. The general approach in the determination of frictional pressure losses is to use an empirical friction factor. Different friction factors are presented by various investigators.

The most commonly used friction factors were presented by Colebrook-White. The Colebrook-White equation has been applicable over a very wide range of Reynolds numbers and relative roughness values within an acceptable standard of accuracy. In Colebrook-White's formulation, the friction factor is determined using an iterative technique. That is, the friction factor appears on both sides of the equation and must be solved with a trial and error approach.

Over time, many authors created approximations to the Colebrook-White equation. These approximations could be grouped into two types of equations - iterative and direct. The iterative equations allowed for a trial and error approach to determine the friction factor and were often not as precise as the Colebrook-White formulation.

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