Claire S. Adjiman

Chapter 7 - The derivation of size parameters for the SAFT–VR equation of state from quantum mechanical calculations

This chapter describes the derivation of size parameters for the SAFT-VRequation of state from quantum mechanical calculations. The chain length parameter, m , and the segment diameter, σ , for SAFT-VR are derived by mapping molecular dimensions calculated via the Restricted Hartree-Fock (HF) formalism onto a spherocylinder. The dimensions used are the molecular volume, calculated by integrating the electronic density, and the smallest and largest dimensions of a box containing the molecule. The molecular volume and the molecular aspect ratio as obtained from the HF calculation are then used to determine the SAFT parametes m and σ. Once m and σ have been computed, the remaining SAFT-VR parameters are estimated using experimental VLB data. The proposed approach is useful in several ways. Firstly, it allows a physical value for the chain length parameter m to be established. Secondly, the proposed approach leads to a reduction in the number of parameters which must be estimated by numerical optimisation, and therefore an increase in the statistical significance of those parameter values, especially when experimental data are scarce. Finally, by combining the proposed method with ab initio techniques to derive the other SAFT parameters, this work provides a stepping stone towards data-free methods to model the phase behaviour of new compounds.

Proof of Convergence for a Global Optimization Algorithm for Problems with Ordinary Differential Equations

A deterministic spatial branch and bound global optimization algorithm for problems with ordinary differential equations in the constraints has been developed by Papamichail and Adjiman [A rigorous global optimization algorithm for problems with ordinary differential equations. J. Glob. Optim. 24, 1–33]. In this work, it is shown that the algorithm is guaranteed to converge to the global solution. The proof is based on showing that the selection operation is bound improving and that the bounding operation is consistent. In particular, it is shown that the convex relaxation techniques used in the algorithm for the treatment of the dynamic information ensure bound improvement and consistency are achieved.

Global optimization and modeling techniques for planar multilayered dielectric structures.

We present a multilevel global optimization strategy for synthesizing planar multilayered dielectric structures. A low discrepancy sequence of sample points with uniform variable space coverage allows a global-level search while systematic refinement using gradient-based techniques identifies optima at the local level. Since efficient local optimization is important for this method, a fast calculation approach based on mode matching is presented; this also facilitates the compact derivation of analytical gradients. The approach is compared with genetic and simulated annealing algorithms through an antireflection coating design. The method proves to be competitive in terms of its performance, nonadaptive algorithm, and ability to track local solutions.

Enhancement of optical extraction from OLEDs using scattering layers

We present an enhancement scheme for optical extraction from Organic based LEDs (OLEDs). Enhancement layers, developed by Mitsubishi Chemical Corporation, facilitate the engineering of scattering near an OLEDs emitter. An approximate scattering model based on rigorous optical field calculations of the OLED structure is described and optimised. Experimental and numerical results indicate that up to 2-fold efficiency enhancements are achievable across a broad spectral range.

Integrating advanced thermodynamics and process and solvent design for gas separation

The integrated design of a solvent and process for high-pressure gas separations requires thermodynamic models which can reliably predict high-pressure phase equilibrium as a function of the solvents molecular structure. A methodology to tackle such a design problem is developed using the SAFT-VR equation of state to obtain the thermodynamic properties of the materials involved. It is applied to the problem of CO 2 capture from methane, given a high-pressure feed of high-CO 2 content. Optimal operating conditions and an optimal alkane solvent (C 20 H 42 ) are identified and found to maximise the recovery of both CO 2 and CH 4 , thus offering a promising alternative to current processes.

Risk analysis and robust design under technological uncertainty

Technological innovation in process design often leads to increased technological risk arising from incomplete knowledge. We propose a systematic approach to manage this risk using mathematical models that are sufficiently detailed to quantify risk. Global sensitivity analysis is used to determine the complete probability distributions for the key performance indicators of the process, thereby allowing informed decisions to be taken regarding the acceptability of the risk inherent in a given design. It also produces global sensitivity indices which allow the identification of the critical uncertain parameters on which additional R&D needs to be foused if the risk is deemed to be unacceptably high. If the risk is acceptable, then scenario-based approximation is used to handle the residual uncertainty in the critical parameters. Issues regarding the robust and efficient solution of problems involving large numbers of scenarios based on nonlinear models with thousands of variables are considered. The methodology is demonstrated via a case study concerning the design of a catalytic tubular reactor.

A computer-aided methodology for optimal solvent design for reactions with experimental verification

An extension of a hybrid experimental/computer-aided methodology for the design of solvents for reactions is presented. Previous work (Folic et al., 2004a,b) was based on the use of reaction rate measurements to build a reaction model, followed by the formulation and solution of an optimal computer-aided molecular design problem (CAMD). In this work, feedback is introduced in the methodology to verify the suitability of the solvent candidates identified in the CAMD step via experimentation and to assess the reliability of the model used in the CAMD step. When the reliability of the model is found to be insufficient, experimental data for the candidate solvents are added to the original data set to create an updated reaction model which can be used to find new candidate solvents. This methodology is illustrated through application to a solvolysis reaction and to a Menschutkin reaction.

A computer-aided methodology with robust design criteria for selection of solvents for reactions

Abstract Our previous work [1,2] was based on the use of a few reaction rate measurements to build a reaction model, followed by the formulation and solution of an optimal computer-aided molecular design problem (CAMD). Because of the small number of experimental data used, we investigate the impact of uncertainty in the reaction model parameters and formulate and solve a stochastic optimisation problem to arrive at the solvent that gives the best expected performance. These results are compared against the solvents obtained by deterministic optimisation. This methodology is illustrated through application to a solvolysis reaction.

State estimation for dynamic prediction of hydrate formation in oil and gas production systems

Abstract Since oil and gas production is moving to deeper waters, subsen pipelines are being subjected to higher pressures and lower temperatures. Under such conditions, the formation of hydrates is promoted. Hydrates are solid, non-flowing compounds of gas and water whose formation can cause line blockages, with the consequent economical losses and safety risks. The increasing hydrate formation propensity suggests the necessity to predict the possibility of hydrate formation in on-line operation so as to take preventive control actions and thereby provide flow assurance. Although a detailed dynamic model will enable the prediction of the possibility of hydrate formation, model inaccuracies and process disturbances will make this prediction less accurate. The usage of key available measurements will enable to address these disadvantages. The aim of this paper is to develop a combined state and parameter estimator for this process, by combining a dynamic model with available measurements.

Chapter 3 – A method for the systematic estimation of parameters for a stochastic reptation model

Abstract A parameter estimation algorithm for the thermodynamically consistent reptation model ( Ottinger, 1999 ; Fang et al., 2000) , which is based on stochastic differential equations, is proposed. The problem is formulated using the maximum likelihood (MLE) objective function, and a modified Levenberg-Marquardt algorithm is developed for its solution. Stochastic sensitivity equations are derived and used in order to obtain reliable parameter estimates. The issue of computational efficiency is addressed by varying the number of ensembles used in the integration of model based on the proximity of the current iterate to the optimal solution, as quantified by the magnitude of the trust region radius. The algorithm is applied to data for a sample of LDPE, to estimate mesoscale polymer properties from measurements of shear viscosity.