Patricia M. Hoch

Optimisation of azeotropic distillation columns combined with pervaporation membranes

The main objective of this work is the analysis and optimisation of azeotropic distillation columns, when a liquid side stream with the distributing non-key component is treated in a pervaporation membrane and the retentate is recycled to the column. The objective is to separate the pure distributing non-key component using a pervaporation membrane, thus helping to improve the purity in the top and/or bottom products. The operating conditions of the column such as reflux ratio, product and side draw flowrates and pressure are selected optimally to minimise the operating cost of the hybrid system. The simulation of the pervaporation membrane units is implemented solving the differential–algebraic equation system of mass transport and energy balances. The optimisation of the operating conditions of the azeotropic distillation column in the hybrid distillation/pervaporation system for Methyl tert-butyl ether production is presented. Numerical results with a significant reduction in the operating cost are reported.

Flexibility analysis of an ethylene plant

It is desirable to know the variations around the normal feed conditions that a real plant can handle ensuring feasible operation and to detect the plant bottlenecks for these perturbations. This information is provided by a flexibility analysis of the real plant. Perturbations on total flow rate and ethane composition are expected in the feed of an ethylene plant. Due to the fact that only two uncertain parameters are contemplated, the maximum feasible displacement from the nominal point in different directions of the uncertain space can be evaluated. The maximum displacement is determined solving a nonlinear programming problem where the main operating conditions of the plant are the optimization variables. An active capacity constraint indicates a plant bottleneck. Therefore the flexibility analysis of a real plant allows the quantification of the perturbations that the plant can accommodate for different directions of interest, associating bottlenecks with scenarios in which they will take place.

Optimal operation of an ethylene plant at variable feed conditions

Abstract Ethylene is produced from an ethane rich feed. Variations in the feed flowrate and ethane composition are expected. It is important to know whether the existing plant can operate in the feasible region for the expected deviations. In particular, the questions raised in this work are how much feed can be processed in the plant and how can plant bottlenecks be detected in order to increment plant capacity. For a given feed, the operating conditions of the ethylene plant are evaluated solving a non lmear programming problem. The objective function is the profit maximization and the feasible region is limited by the design specifications and equipment capacities. Active constraints related to equipment capacities indicate plant bottlenecks. A numerical example is presented for a real ethylene plant where the feed flowrate and ethane composition vary within expected ranges. Bottlenecks are detected in two sectors of the plant: in the furnaces and in the ethylene-ethane splitter. Possible solutions to overcome the bottlenecks are also studied.

Evaluation of design flexibility in distillation columns using rigorous models

Abstract A methodology is presented for the evaluation of the flexibility and bottlenecks detection of a given distillation column design, using rigorous simulation models. The flexibility index is calculated as proposed by Swaney and Grossmam (1985), solving a nonlinear programming (NLP) problem in the direction of each vertex in the uncertain space, in which the objective is the maximization of the displacements. The control variables, reflux and product flow rates, are the optimization variables of the NLP. The purity specifications, recovery and maximum equipment capacities are posed as the constraints for feasibility of the NLP. Numerical results will be presented for the case of a debutanizer column. Uncertainties are considered in components feed flow rate, maximum allowed vapor velocity, heat transfer coefficients of condenser and reboiler, and cooling water inlet temperature. Great physical insight can be gained from the NLP solutions in the directions of the vertices, detecting bottlenecks and the worst combinations of uncertain parameters.

Biological Wastewater Treatment: Dynamic Global Sensitivity Analysis and Parameter Estimation in a System of Waste Stabilization Ponds

Abstract In this work, we propose a dynamic mathematical model describing main biochemical processes that take place within wastewater stabilization ponds. Mass balances for main microorganisms, nutrients, dissolved oxygen and biochemical demand of oxygen have been formulated. The wastewater biological treatment system under study is composed of two stages of oxygenated ponds in series. The first stage is aerobic oxygenated and the last one is facultative oxygenated. Global sensitivity analysis has been performed prior to the formulation of a parameter estimation problem, subject to the differential algebraic system describing the biological wastewater treatment system. Experimental data from a fruit juice plant have been collected throughout one year. Numerical results provide a deep insight on the complex relations among microorganisms, nutrients and organic matter concentration in wastewater treatment ponds.

Flexibility analysis leads to a sizing strategy in distillation columns

A sizing strategy for distillation columns is presented to ensure a feasible operation for any possible realization of the uncertain parameters. The flexibility analysis of a given design identifies the worst set of uncertain parameters for each equipment size of the column. A systematic way of associating sizes with critical subspaces and the corresponding active constraints leads to the sizing strategy presented. The evaluation of sizes for a given flexibility requires the solution of a set of algebraic equations derived from the flexibility analysis.

MINLP Wastewater Stabilisation Ponds Synthesis using Rigorous Models under Different Scenarios

Abstract In this work, we formulate a network embedding rigorous models for three different types of stabilisation ponds (aerobic, anaerobic and facultative). The model is formulated as a mixed integer non-linear programming (MINLP) problem implemented in GAMS. The ponds are modelled taking into account mass balances for the main groups of bacteria, different types of organic load, algae biomass and nutrients. The objective is to synthesise and design the wastewater treatment networks (WWTN) that minimises the total annual costs, including operating and capital costs, subject to maximum allowable concentration of contaminant on the effluent in order to fulfil environmental regulations. The optimisation is performed under different scenarios of inlet concentration of organic load to take into account process uncertainty. For the base scenario studied, optimal configuration consists of a sequence of two aerobic ponds followed by a facultative one (aer-aer-fac), with recycle only in the first pond. System efficiency on COD removal is more than 65% with a total cost of USD 52,749. Scenarios’ analysis shows that results strongly depend on inlet organic load concentration.

Global sensitivity analysis in bioreactor networks

Abstract A global sensitivity analysis applying variance-based techniques is implemented for a bioreactors network used in the production of ethanol from molasses sugar and vinases distillates. Two types of bioreactors are considered, an aerobic for biomass production and an anaerobic for ethanol production. Probability distributions are assigned to each uncertain parameter, thus temporal profiles for the sensitivity indices are obtained for the main differential and algebraic variables. Sobols method (1990) is used, performing stochastic simulations within gPROMS environment ( PSEnterprise, 2009 ). Numerical results show the time-variant influence of the parameter during the fermenters operating time.

Unconstrained optimisation for the design of distillation columns

Abstract In the traditional constrained formulation the separation objectives are posed as inequality constraints. The optimisation variables are the number of stages on each section of the column, the reflux ratio and the product flow rates. The main objective of this work is to reformulate the original constrained problem into an unconstrained problem. The reflux ratio and product flow rate are calculated to satisfy the two active constraints at each stage of the optimisation problem, adding two equations to the modelling system of the distillation column. The design problem of a distillation column is formulated as an unconstrained optimisation problem where the number of stages in each section of the column is treated as continuous optimisation variable. Therefore an unconstrained non-linear programming problem is solved. The objective function used corresponds to the minimisation of the total cost, thus leading to a convex problem. A numerical example corresponding to a real column is included. The total cost versus the number of stages in each section of the column is graphically shown.

Optimal Control Strategies for Wastewater Stabilization Ponds

Abstract In this work, we address the control problem of wastewater stabilization ponds by formulating an optimal control problem considering electrical motor power for mixers and nutrient addition rate as control variables (degrees of freedom of the problem). Nitrogen and phosphorus are the added nutrients. Constraints are embedded in the DAE model and boundaries on the control variables. As the specification on biochemical oxygen demand (BOD) in the outlet stream is far from the target one, the objective is to minimize the offset between the desired value and the current one, along a time horizon of a year. As a result of the dynamic optimization problem the optimal time profiles of motor power and nutrient addition rates (phosphorus and nitrogen) are obtained for the time horizon of a year, while the BOD is kept below the required level.