A Dynamic Simulation of a Subsea Separation and Boosting System for Offshore Petroleum Production
Authors: Carvalho P.M. , Minami K. , Rosa E.S. 
Published: December 2007

A Dynamic Simulation of a Subsea Separation and Boosting System for Offshore Petroleum Production.

Summary
The objective of this work is to develop a numerical model to simulate the operation of a Subsea Separation and Boosting System. In short, the system is composed of two separation vessels, two gas pipelines, one oil pipeline and a set of remotely controlled hydraulic valves. The numerical model simulates the transient behavior of the fluids in the whole system for typical initial and boundary conditions. The modeling of the flow of fluids in the pipelines was based on the simultaneous solution of the mass and momentum conservation equations that forms a pair of quasi-linear hyperbolic equations in terms of two dependent variables (velocity and hydraulic head) and two independent variables (distance along the pipe and time). The method of characteristics was applied to solve the system of two partial differential equations transforming it into four ordinary differential equations.. This method leads to an exact solution of the systems. Newton's method was used to solve the nonlinear system of equations resulting from the coupling of the pipelines conditions with the vessels conditions.

Introduction
Subsea separation processes applied to offshore petroleum production have been studied as one of the most promising ways to produce deep water hydrocarbon reserves. The main objectives of these devices are to increase the reservoir recovery factor and the wells' flowrates, by reducing the back pressure on the well head. This is achieved by splitting the incoming multiphase stream in two single phase streams and piping them to the platform.
The objective of this work is to develop a numerical model describing the separation system as presented in fig. 1.
Shortly it can be described as a system composed by two vessels, two gas pipelines one operating at high pressure (HP) and the other at low pressure (LP), one oil pipeline and a set of hydraulic control valves. The incoming multiphase stream, from a single well or a cluster of wells, feeds one of the vessels which is connected to the low pressure gas pipeline. In this low pressure vessel, during the feeding step, separation occurs between the two phases. The gas phase exits the system through the low pressure gas pipeline and the oil accumulates in the vessel. Simultaneously, the high pressure vessel, is transferring oil by action of high pressure gas injected from one platform which provides sufficient pressure difference that promotes liquid flow. Once the feeding and transferring steps occurring in the low and high pressure vessels, respectively, are completed, the set of valves changes the alignment of the pipelines between the vessels and another cycle starts.
The numerical model simulates the transient behavior of the fluids during the cycles. It consists of simultaneous solution of the mass and momentum balance equations by the method of characteristics applied to the high and low pressure gas pipelines as well as to the oil pipeline. In the transferring step the system, comprising high pressure gas pipeline, oil pipeline and high pressure vessel is coupled and solved together. Simultaneously the feeding step is solved to low pressure gas pipeline, low pressure vessel and petroleum source. The whole system boundary conditions are given by the outlet compressor pressure for the upstream high pressure gas pipeline, by the gas scrubber pressure for downstream low pressure gas pipeline and by the surge tank pressure for the downstream oil pipeline.

Gas Pipeline Modeling
The one dimensional mass and momentum Eqs. for the gas flow in a pipeline are, respectively, written as [Wylie and Streeter, 1982].
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