A unified model is presented for describing both single-phase and two-phase flow in complex gas pipeline networks. "The form of the model is such that it can easily admit any energy-loss model that is expressible in a particular non-linear functional form of energy loss-flow rate relationship. Four popular single-phase gas pipeline design equations, namely, Darcy-Weishbach, Panhandle-A. Panhandle-B and Weymouth equations and a two-phase flow equation (Beggs-Brill) are used to test the development. All these tests are successful. A viable algorithm for solving the resulting equations is presented. Four field cases are analyzed using this model. Results show that Weymouth equation underpredicts pressure distribution for single-phase gas flow but predicts comparable pressure distribution to Beggs-Brill's two-phase model for two-phase flow in the network. "The results further demonstrate significant effect of the presence of condensate on network performance.
The increasing role of pipelines as a transportation means for natural gas increases the complexity of designing pipeline network systems. The problem is further compounded by the inevitable introduction of liquid, mainly from condensation, into the pipe system. This network is usually made up of pipes of various sizes, each crossing undulating terrain. Selection of model for designing such system must be carefully done and must account for the presence of the liquid in order to achieve optimal design and operational efficiency. It is this consideration that motivates this work, whose aim is to substantially extend our earlier work [Muchazam and Adewumi, 1990], which laid the necessary framework for the model presented here. presented here. Studies of natural gas transmission have been reported by many researchers. They all agree that the effect of liquid's presence in gas transmission pipeline is rather difficult to predict, even in simple cases of single pipeline system. The main problem is in determining the process of liquid condensation and/or evaporation along the pipeline process of liquid condensation and/or evaporation along the pipeline system where many factors need to be considered such as the hydrodynamic behavior, fluid composition, pressure and temperature of the system. For single-phase fluid system, many models have been proposed for predicting pressure distribution along a single pipeline. Some of the widely used pressure distribution along a single pipeline. Some of the widely used ones in the petroleum industry include Weymouth, Panhandle-A, Panahandle-B and the IGT/AGA equations. These models are derived from the same basic premise, that is the energy balance equation. The basic difference is in premise, that is the energy balance equation. The basic difference is in the method used in determining the friction factor. While the literature on single-pipe two-phase system is voluminous [Adewumi and Bukacek, 1985], reported work on network two-phase systems is scanty. Both laboratory data, field data and models abound for single-pipe two-phase systems.
In this study, a unified approach has been developed using the looped system model to predict the flow performances in complex pipeline network for both single and two phase flow systems. This is achieved by coupling the appropriate flow equation, be it single-phase or two-phase, to the material and energy balance equations or any loop. The Linear Theory Method is used to linearize the flow equations selected such that a pseudo-linear relationship between flow rate and pressure drop is obtained. The resulting system of equations is linear algebraic. This set of equations can be solved by standard procedure. Since the equations for both single-phase and two-phase flows are reformulated in identical form, a unified set of equations and solution technique are adopted. The solution technique developed can be used for any structure of pipeline network with flexible numbering technique. Both the loop and the loopless pipeline network systems can be solved using this model. For the loopless network system, the imaginary lines need to be introduced to create looped network system.
Using these models, analysis of a field system was conducted. The most often-used design equations for single-phase pipe flow were tested and a comparative analysis was conducted. Analysis of the same field was also conducted using a two-phase model. The results of flow prediction from several pipeline networks are compared and analyzed to observe the prediction disparities between these models and the effects of the presence prediction disparities between these models and the effects of the presence of liquid in gas pipeline network system. The analysis suggests guidelines that could aid in the selection of appropriate models for conducting analysis of pipeline network for gas gathering, transmission and distribution, even when liquid exists in the system.