(486q) Optimizing An Intensive Energetically Integrated Dynamic Process with Advanced Mathematical Programming Techniques

In this work, we address dynamic optimization of an energetically integrated large-scale natural gas processing plant. In a typical turboexpansion process, the feed gas is cooled both in countercurrent cryogenic heat exchangers with residue gas coming out of the demethanizing column and in demethanizer side and bottom reboilers. The partially condensed gas feed is sent to a high-pressure separator. The vapor is expanded through a turboexpander to obtain the low temperatures required for high ethane recovery and is fed to a demethanizer column. The liquid from the high-pressure separator enters the demethanizer at its lowest feed point. Methane and nitrogen constitute top product and ethane and heavier hydrocarbons are obtained as bottom product. The high integration between process streams and the small driving forces required for increased process efficiency, make this process a challenging case study. Much effort has been devoted to natural gas plants steady state optimization. However, studying the process dynamic optimization has received less attention, mainly due to the lack of adequate mathematical tools for addressing this large-scale, energy integrated process.

We have developed a rigorous dynamic optimization model for the cryogenic sector of a natural gas processing plant within a simultaneous dynamic optimization framework. Detailed models of separation tanks, turboexpanders, distillation columns and countercurrent shell and tube heat exchangers with partial phase change have been formulated, with thermodynamic predictions of a cubic equation of state (SRK, Soave, 1972). In particular, dynamic heat and mass balances in shell and tube heat exchangers give rise to a partial differential algebraic equation (PDAE) system, which has been transformed into an ordinary differential algebraic (DAE) system by applying the Method of Lines to spatially discretize the PDAE (Rodriguez and Diaz, 2007). The DAE optimization problem is then transformed into a large nonlinear programming (NLP) problem applying orthogonal collocation over finite elements in time. The resulting NLP problem is solved with an Interior Point method with reduced Successive Quadratic Programming (SQP) techniques within program IPOPT (Biegler, 2007), which takes advantage of the special structure of the problem. The inclusion of rigorous thermodynamic models provide a realistic representation of the process, but adds high nonlinearity to the model, which has been efficiently handled within the simultaneous approach. Furthermore, the inclusion of path constraints on carbon dioxide solubility in the upper stages of the demethanizing column has also been possible within this approach. Model resolution provides optimal temporal and spatial profiles and information describing the two-phase flow and fluid separation in a highly integrated large scale plant. Several scenarios have been analyzed, regarding changes in feed flowrate and composition. Numerical results have shown good agreement with plant data.

References

Biegler, L.T. (2007). An overview of simultaneous strategies for dynamic optimization, Chemical Engineering and Processing

Rodriguez, M., M.S. Diaz (2007) Dynamic modelling and optimisation of cryogenic systems, Applied Thermal Engineering, 27, 1182-1190.

Soave G. (1972) Equilibrium Constants for a Modified Redlich-Kwong Equation of State. Chem. Eng. Sci. 27: 1197-1203.