A New Mathematical Model For Oil/Water Separation In Pipes And Tanks
Authors: Hafskjold Bjorn , Celius Harald K. , Aamo Ole Morten 
Published: December 2007

Abstract
We consider unstable water-in-oil dispersions occurring in topside processing of reservoir fluids. Two practically important features of such dispersions are (1) water-in-oil dispersions separate better with higher water content, contradictory to what might be intuitively expected, and (2) a few volume percent water remains in the oil, even alter long settling times. These features may be qualitatively understood by considering a combination of coalescence and settling in the separator, but they are not easily quantified and predicted. In this work, we use mathematical and numerical modeling to show that they may also be quantitatively described by coalescence and settling.
A new model was developed, based on information about flow rates, the process unit's (pipe or tank) dimensions, the fluid's physical properties, quality of the fluid, and drop-size distribution of the dispersed phase at the unit's inlet. The model was implemented in a computer code that solved the appropriate material balances, settling equations, and coalescence model to numerically determine observable properties of the outlet streams from each unit.
The model was verified by laboratory experiments, including use of pressurized samples from an operating processing plant, and by data from field tests. The experiments were run for variable water cut, flow rate, pressure drop across a pressure-reduction valve, and oil type. Overall agreement between model and laboratory tests was better than 5% in the water concentration of the oil phase, and 2% in the water concentration in the effluent oil from the field separator.

Introduction
The separation of oil and water can be considered as a combination of emulsification and separation. The former dominates in chokes, valves, and other regions with high shear rates (high energy dissipation). The latter can be further split in two: Drop growth by coalescence, which dominates in pipes, the inlet region of a separator, and other regions of moderate energy dissipation, and settling or creaming of the dispersed phase, which dominates in tanks and other regions of low energy dissipation. In order to fully understand, model, and predict the performance of an oil/water separator, it is therefore necessary to consider not only the separator itself, but also the upstream equipment.
This study was part of a development of a test method for separator performance. The test was focused on oil/water dispersions occurring in reservoir fluid processing, with particular emphasis on coalescence and settling. The test method was implemented in laboratory-scale equipment, field-test equipment, and in operating full-scale separators.
The scope of this paper is limited to the mathematical and numerical modeling of coalescence and settling in oil/water systems. For simplicity, but without loss of generality, we consider water-in-oil dispersions only. Our strategy for relating model results to field separator performance was to distinguish between, and explicitly incorporate (1) the physico-chemical properties, such as interfacial tension between oil and water, viscosity, density, etc., (2) fluid-system variables, in particular the drop-size distribution, (3) equipment design variables, such as tank volume, pipe diameters, and valve design, and (4) field variables, such as flow rates and water cuts.
The physico-chemical properties are essentially the same for a laboratory sample as for a field sample, but due attention must be paid to the aging process, the sample condition, and the sample must be representative. The drop-size distribution is hardly measurable under field conditions, and it is also difficult to ascertain that a laboratory test for such measurements adequately represents field conditions. To properly describe the input drop-size distribution is probably the most difficult step in our modeling approach. Assessment of the equipment design variables is one primary objective of the separator performance analysis (the other is the control of the separator performance during operation). P. 461