464244 A Simplified Dynamic Model of a Continuous Subsea Oil-Water Gravity Separator for Estimation of Unmeasurable Oil and Water Purities
A common gravity separator design is a horizontally oriented cylindrical vessel, in which mixed fluids enter from one end and the separated fluids are removed from the other. Inside the separator, the fluids separate into layers. The layers from bottom to top are water layer, emulsion layer and oil layer. The emulsion layer consists of two sections: sedimentation layer and dense-packed layer. At the end of the separator, a weir prevents the emulsion layer and the water layer from flowing over the weir. The liquid levels inside the separator are controlled in such a way that only oil flows over the weir to the oil outlet section, while the water is removed continuously from the bottom of the separator.
In previous years, the modeling of gravity separation has focused on studying mechanisms that govern batch separation of two liquids, such as oil and water. The models for gravity separation presented in the literature have been summarized by Frising . The models can be classified as sedimentation-based models and coalescence-based models. Sedimentation based models [2-6] consider sedimentation of droplets and interfacial coalescence between droplets and interface. These models are typically tuned to match the results from the batch experiments that demonstrate four layers: clear oil, sedimentation zone, dense-packed zone and clean water. On the other hand, coalescence based models [7,8] focus on the dense-packed zone considering binary as well as interfacial coalescence of the droplets of dispersed phase. They predict mean droplet size based on lifetime of a single film and assume that the presence of surfactant only scales the coalescence time. A model by Henschke , which is a coalescence-based model, is, perhaps, the most relevant for modeling continuous gravity separation because it predicts drop size in the dense-packed zone using a single coalescence parameter, which is independent of experimental equipment, mixing intensity and volume fraction of dispersed phase.
Some of these mechanisms of oil-water separation have been used for modeling continuous gravity separation. Sayda et al. developed a simplified dynamic model for a continuously operating gravity separator based on material balances, and phase equilibrium equations. Their model takes into consideration simplified hydrodynamics, thermodynamics and spatial evolution of separation profiles. They used a standard form of Stoke's law for vertical settling velocity of droplets based on a constant average droplet diameter of oil droplets in water. Hence, their model does not consider coalescence effects that are typically very important in oil-water separation. Another attempt to model a continuous oil-water separation was conducted in , in which they model a horizontal pipe separator. They combine some of the principles from sedimentation based models  and Henschke’s model . Their approach is quite useful for modeling a gravity separator because horizontal pipe separator is quite similar to the conventional gravity separator. However, they model a pipe separator that is completely filled with fluids and does not have a weir. On the other hand, gravity separators often include a weir and are operated with the separator only partially filled with liquids.
In this work, we present a dynamic model for a continuous cylindrical gravity separator for oil-water separation to predict the purity of outlet streams based on operating conditions by assuming that there exists three layers of liquids: oil, emulsion and water inside the separator. It is based on lumped total mass balances and partial mass balances for each layer, in which the inter-layer mass transfer equations are derived using principles from the previous work in sedimentation based models and Henschke’s model.
The model is solved in MATLAB using solver ode15s. It captures the effect of total inlet flow rate, inlet oil cut and inlet droplet size on purities of outlet streams and thickness of each layer of liquid. We use the model in a Kalman-based non-linear estimator for estimating unmeasurable variables, such as oil and water purities using level and density measurements and other measurements of inlet conditions, such as inlet flow rate, oil cut, droplet size and water outflow rate. Further, we study the effects of the variations to water level set point on the performance of the separator.
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