The current clinical standard of Static Cold Storage (SCS) which involves preservation on ice (ab... more The current clinical standard of Static Cold Storage (SCS) which involves preservation on ice (about +4°C) in a hypoxic state limits storage to a few hours for metabolically active tissues such as the liver and the heart. This period of hypoxia during can generate superoxide and other free radicals from purine metabolism, a well-established component of ischemia/reperfusion injury (IRI). Machine perfusion is at the cutting edge of organ preservation, which provides a functional, oxygenated preservation modality that can avoid/ attenuate IRI. In clinical application, perfusion usually follows a period of SCS. This presentation of oxygen following hypoxia can lead to superoxide and hydrogen peroxide generation, but machine perfusion also allows manipulation of the temperature profiles and supply of antioxidant treatments, which could be used to minimize such issues. However, metabolomic data is difficult to gather, and there are currently no mathematical models present to allow rational design of experiments or guide clinical practice. In this article, the effects of a gradual warming temperature policy and glutathione supplementation to minimize oxidative stress are studied. An optimal gradual warming temperature policy for mid-thermic machine perfusion of a liver metabolic model is determined using a combination of Nash Equilibrium and Monte Carlo optimization. Using this optimal gradual warming temperature policy, minimum GSH requirements to maintain hydrogen peroxide concentrations in the normal region are calculated using a different Monte Carlo optimization methodology. In addition, the dynamic behavior of key metabolites and cofactors are determined. Results show that the minimum GSH requirement increases and that the ratio of GSH/GSSG decreases with increasing hydrogen peroxide concentration. In addition, at high concentrations of hydrogen peroxide it is shown that cytochrome C undergoes dysfunction leading to a decrease in useful oxygen consumption and ATP synthesis from the electron transport chain and an overall reduction in the energy charge for the liver cells.
Recently, Lucia et al. have used a distillation line method to develop the concept of shortest st... more Recently, Lucia et al. have used a distillation line method to develop the concept of shortest stripping line distance approach to minimum energy designs of distillation columns and multiunit processes. It is well known that distillation line methods can be very sensitive to specified product compositions. A two-level distillation design procedure is proposed for finding portfolios of minimum energy designs when specifications are given in terms of key component recoveries. Thus, product compositions are not specified but calculated. It is shown that the proposed two-level design procedure is flexible and can find minimum energy designs for both zeotropic and azeotropic distillations. It is also shown that the two-level design method encompasses Underwood's solution but can find minimum energy designs when Underwood's method fails. Numerical results for several distillation examples involving ternary and quaternary mixtures are presented to support these claims, and geometric illustrations are used to elucidate key points.
The asymptotic behavior of fixed-point methods in the complex domain is studied. Both direct subs... more The asymptotic behavior of fixed-point methods in the complex domain is studied. Both direct substitution and Newton's method exhibit stable periodic and aperiodic behavior from real-or complex-valued starting points. Moreover, multiple stable periodic orbits can exist for direct substitution. Traditional trust region (or dogleg) methods, on the other hand, often terminate at singular points, which correspond to nonzero-valued saddlepoints in the least-squares function that can be arbitrarily far from a solution. Furthermore, the basins of attraction of these singular points are usually dispersed throughout the basin boundaries in the complex domain, clearly illustrating that singular points (via the dogleg strategy) also attract either real-or complex-valued starting points. In light of this, an extension of the dogleg strategy to the complex domain, based on a simple norm-reducing, singular point perturbation, is proposed. This extended trust region method removes all forms of nonconvergent behavior and always terminates at a j'iied point, even from critical point (worst-case) initial values. Many numerical results and geometric illustrations using chemical process simulation examples are presented.
Various ways of building quasi-Newton matrix approximations that satisfy the special form of the ... more Various ways of building quasi-Newton matrix approximations that satisfy the special form of the Gibbs-Duhem equation are studied. Partition symmetry, the separability of the functions In y and In 4, and the method of iterated projections are used in order t o develop thermodynamically consistent matrix approximations with good secant information. Many examples are presented which show that exploiting the special form of the Gibbs-Duhem equation results in improved numerical performance. Ways of exploiting the Gibbs-Helmholtz equation in addition to the special form of Gibbs-Duhem equation, and thus the isobaric form of the Gibbs-Duhem equation, are also discussed.
A modified sum-rates method based on insights provided by an analysis given by Sridhar and Lucia ... more A modified sum-rates method based on insights provided by an analysis given by Sridhar and Lucia (Ind. Engng Chem. Res. 28, 793-803, 1989) is presented. Newton's method is used to accelerate the inner loop of combined mass balance and phase equilibrium equations and to solve the outer loop of energy balance equations. All partial derivative information is obtained in analytical form. Several literature examples are used to show that the proposed algorithm is more reliable and more efficient than traditional sum-rates methods and provides the capability of solving problems involving intermediate and narrow boiling mixtures.
A new method for approximating quantities that involve physical properties derivatives in equatio... more A new method for approximating quantities that involve physical properties derivatives in equation-oriented process design is presented. It is a hybrid algorithm that makes combined use of Newton's method and the Schubert update. In doing so, available analytical derivative information is used in an optimal way. This hybrid algorithm is surprisingly close, in terms of the number of iterations required for solution, to an implementation of Newton's method that uses finite difference approximations of any unavailable physical properties derivatives. However, the number of rigorous thermodynamics calculations is usually about 50% fewer for the hybrid method. This can result in a substantial savings for problems in which the physical properties calculations dominate the simulation time. Two examples are presented to support these claims.
Primary oil recovery methods in Saskatchewan’s heavy oil basin extract 5 to 10% of the available ... more Primary oil recovery methods in Saskatchewan’s heavy oil basin extract 5 to 10% of the available resource with the vast majority left in the ground and recoverable only through Enhanced Oil Recovery (EOR) methods. Traditional EOR generates steam in surface facilities and injects it underground to mobilize the oil for production with considerable energy losses inherent in the process. R.I.I. North America’s Solvent Thermal Resource Innovation Process (STRIP) technology moves the steam generator underground, reducing the operating and capital costs of a surface thermal production facility by 30% and 50% respectively, and saving more than 30% of the energy typically required for thermal production. STRIP technology combusts methane to produce in situ CO2 and steam. Because CO2 acts as a co-solvent, STRIP outperforms traditional steam-injection technology. This is demonstrated using a breakthrough modeling technique that couples fully compositional and thermal reservoir flow simulation capabilities. This new approach couples FlashPoint’s equation-of-state solver for the multiphase, multi-component, isothermal, isobaric flash problem, GFLASH, with Stanford’s Automatic Differentiation General Purpose Research Simulator for thermal reservoir flow simulations. This new computational framework exploits advanced techniques for skipping phase-identification computations and only uses exact phase equilibria from GFLASH when needed, reducing computational times by one to two orders of magnitude compared to the full rigorous solution.
Application aux contraintes thermodynamiques dans les problemes de separation multietagee. Develo... more Application aux contraintes thermodynamiques dans les problemes de separation multietagee. Developpement d'une strategie numerique qui exploite simultanement les equations de Gibbs-Duhem et de Gibbs-Helmholtz
We present a novel simulation approach for modeling of reactive flow and transport in multiphase ... more We present a novel simulation approach for modeling of reactive flow and transport in multiphase multi-component mixtures that include light gases, hydrocarbon components, and different ions present in an aqueous electrolyte phase. The phase behavior in these systems involves both thermodynamically-driven phase transitions (e.g. between supercritical vapor and liquid phases) and chemically driven precipitation and dissolution of solid (mineral) phases. All phases are modeled using the multi-scale Gibbs-Helmholtz Constrained Equation of State (GHC EoS), which up-scales molecular length scale information from a priori Monte Carlo simulations to help build accurate estimates of the energy parameter. Our proposed approach is implemented in the combined software system included the Automatic Differentiation General Purpose Research Simulator (ADGPRS) developed at Stanford University and the GFLASH library developed at University of Rhode Island. The extended variable substitution schema for a natural fully implicit formulation is designed to support the potential coexistence of an arbitrary set of phases in the flow. The classical reduction in the number of conservation equations based on element balances is combined with specific local constraints describing simultaneous thermodynamic and chemical equilibrium. Rigorous flash solutions for detecting phase changes in each grid block are computed using phase splitting and phase/chemical equilibrium to ensure equality of component chemical potentials and by monitoring the Gibbs free energy of the system to guarantee a global minimum is found. We present examples that cover a wide range of physical processes related to CO2 sequestration in saline aquifers.
Chemical engineering research & design, Nov 1, 2019
Many compounds of interest do not have critical properties, mostly because they decompose before ... more Many compounds of interest do not have critical properties, mostly because they decompose before reaching a critical state. Examples include polymers, ionic liquids, and asphaltenes. In this work, a novel numerical methodology for determining the glass transition temperature and boundary condition for the energy parameter in the Gibbs-Helmholtz Constrained (GHC) equation of state framework for compounds without critical properties is proposed. The glass temperature and boundary condition are then used in the multi-scale GHC equation to predict thermo-mechanical properties of a model asphaltene fluid proposed by Mullins (2010). Computational results for the GHC equation for the model asphaltene over the temperature range [263.15, 593.15 K] give mass densities that range from 1190.66 to 1064.37 kg/m 3 and coefficients of thermal expansion in the range [9.04 × 10 −5 , 8.97 × 10 −4 K −1 ] at 1 bar pressure. Multi-scale GHC-predicted isothermal compressibilities for the model asphaltene for pressures from 1 to 600 bar and temperatures of 380 and 480 K range from 7.43 to 1.56 × 10 −5 bar −1. These results compare favorably with available experimental data for asphaltenes reported in the open literature and show that the GHC equation can accurately and reliably predict mass and molar densities, molar volumes, isothermal compressibilities, and coefficients of expansion over wide ranges of temperature and pressure. Advantages and disadvantages of the proposed approach are also given.
Global optimization problems with so-called 'rough' or rugged objective function landscapes are s... more Global optimization problems with so-called 'rough' or rugged objective function landscapes are studied. These problems often have many, many stationary points and show considerable differences between small and large-scale geometry. A novel multiscale global optimization algorithm for solving 'rough' objective functions, based on the alternate use of terrain methods and new funneling algorithms, is presented. Small-scale information is gathered using a terrain optimization methodology while funneling algorithms are used to guide the overall optimization calculations and to make 'large' moves within the feasible region. A molecular modeling example is used to clearly illustrate that the proposed methodology is capable of finding a global minimum without calculating all stationary points and can lead to significant reductions in computational work.
Analytical support for recent numerical work in process simulation in the complex domain is discu... more Analytical support for recent numerical work in process simulation in the complex domain is discussed. In particular, the observation that nondegenerate singular points are saddle points of the two‐norm on the complex domain is proved rigorously and its numerical implications are discussed. The isothermal isobaric flash problem admits only real‐valued two‐phase solutions, provided that the feed conditions are real. Both single‐ and multivariable chemical process examples illustrate the theoretical results.
An aerofoil body, for example a "delta" wing aircraft, in which strip-form devices proj... more An aerofoil body, for example a "delta" wing aircraft, in which strip-form devices project rearwards from the trailing edge of the wing and serve to improve the lift-to-drag ratio of the body, in some conditions of flight at least, by modifying the formation of the trailing edge vortex to allow the axes of the primary vortex sheets to lie closer to the fore-and-aft centerline of the body than would otherwise be the case. When the strips are basically flat in shape, the strips may project straight backwards from the trailing edge or may be angled in various ways. The use of twisted strips is also described.
The current clinical standard of Static Cold Storage (SCS) which involves preservation on ice (ab... more The current clinical standard of Static Cold Storage (SCS) which involves preservation on ice (about +4°C) in a hypoxic state limits storage to a few hours for metabolically active tissues such as the liver and the heart. This period of hypoxia during can generate superoxide and other free radicals from purine metabolism, a well-established component of ischemia/reperfusion injury (IRI). Machine perfusion is at the cutting edge of organ preservation, which provides a functional, oxygenated preservation modality that can avoid/ attenuate IRI. In clinical application, perfusion usually follows a period of SCS. This presentation of oxygen following hypoxia can lead to superoxide and hydrogen peroxide generation, but machine perfusion also allows manipulation of the temperature profiles and supply of antioxidant treatments, which could be used to minimize such issues. However, metabolomic data is difficult to gather, and there are currently no mathematical models present to allow rational design of experiments or guide clinical practice. In this article, the effects of a gradual warming temperature policy and glutathione supplementation to minimize oxidative stress are studied. An optimal gradual warming temperature policy for mid-thermic machine perfusion of a liver metabolic model is determined using a combination of Nash Equilibrium and Monte Carlo optimization. Using this optimal gradual warming temperature policy, minimum GSH requirements to maintain hydrogen peroxide concentrations in the normal region are calculated using a different Monte Carlo optimization methodology. In addition, the dynamic behavior of key metabolites and cofactors are determined. Results show that the minimum GSH requirement increases and that the ratio of GSH/GSSG decreases with increasing hydrogen peroxide concentration. In addition, at high concentrations of hydrogen peroxide it is shown that cytochrome C undergoes dysfunction leading to a decrease in useful oxygen consumption and ATP synthesis from the electron transport chain and an overall reduction in the energy charge for the liver cells.
Recently, Lucia et al. have used a distillation line method to develop the concept of shortest st... more Recently, Lucia et al. have used a distillation line method to develop the concept of shortest stripping line distance approach to minimum energy designs of distillation columns and multiunit processes. It is well known that distillation line methods can be very sensitive to specified product compositions. A two-level distillation design procedure is proposed for finding portfolios of minimum energy designs when specifications are given in terms of key component recoveries. Thus, product compositions are not specified but calculated. It is shown that the proposed two-level design procedure is flexible and can find minimum energy designs for both zeotropic and azeotropic distillations. It is also shown that the two-level design method encompasses Underwood's solution but can find minimum energy designs when Underwood's method fails. Numerical results for several distillation examples involving ternary and quaternary mixtures are presented to support these claims, and geometric illustrations are used to elucidate key points.
The asymptotic behavior of fixed-point methods in the complex domain is studied. Both direct subs... more The asymptotic behavior of fixed-point methods in the complex domain is studied. Both direct substitution and Newton's method exhibit stable periodic and aperiodic behavior from real-or complex-valued starting points. Moreover, multiple stable periodic orbits can exist for direct substitution. Traditional trust region (or dogleg) methods, on the other hand, often terminate at singular points, which correspond to nonzero-valued saddlepoints in the least-squares function that can be arbitrarily far from a solution. Furthermore, the basins of attraction of these singular points are usually dispersed throughout the basin boundaries in the complex domain, clearly illustrating that singular points (via the dogleg strategy) also attract either real-or complex-valued starting points. In light of this, an extension of the dogleg strategy to the complex domain, based on a simple norm-reducing, singular point perturbation, is proposed. This extended trust region method removes all forms of nonconvergent behavior and always terminates at a j'iied point, even from critical point (worst-case) initial values. Many numerical results and geometric illustrations using chemical process simulation examples are presented.
Various ways of building quasi-Newton matrix approximations that satisfy the special form of the ... more Various ways of building quasi-Newton matrix approximations that satisfy the special form of the Gibbs-Duhem equation are studied. Partition symmetry, the separability of the functions In y and In 4, and the method of iterated projections are used in order t o develop thermodynamically consistent matrix approximations with good secant information. Many examples are presented which show that exploiting the special form of the Gibbs-Duhem equation results in improved numerical performance. Ways of exploiting the Gibbs-Helmholtz equation in addition to the special form of Gibbs-Duhem equation, and thus the isobaric form of the Gibbs-Duhem equation, are also discussed.
A modified sum-rates method based on insights provided by an analysis given by Sridhar and Lucia ... more A modified sum-rates method based on insights provided by an analysis given by Sridhar and Lucia (Ind. Engng Chem. Res. 28, 793-803, 1989) is presented. Newton's method is used to accelerate the inner loop of combined mass balance and phase equilibrium equations and to solve the outer loop of energy balance equations. All partial derivative information is obtained in analytical form. Several literature examples are used to show that the proposed algorithm is more reliable and more efficient than traditional sum-rates methods and provides the capability of solving problems involving intermediate and narrow boiling mixtures.
A new method for approximating quantities that involve physical properties derivatives in equatio... more A new method for approximating quantities that involve physical properties derivatives in equation-oriented process design is presented. It is a hybrid algorithm that makes combined use of Newton's method and the Schubert update. In doing so, available analytical derivative information is used in an optimal way. This hybrid algorithm is surprisingly close, in terms of the number of iterations required for solution, to an implementation of Newton's method that uses finite difference approximations of any unavailable physical properties derivatives. However, the number of rigorous thermodynamics calculations is usually about 50% fewer for the hybrid method. This can result in a substantial savings for problems in which the physical properties calculations dominate the simulation time. Two examples are presented to support these claims.
Primary oil recovery methods in Saskatchewan’s heavy oil basin extract 5 to 10% of the available ... more Primary oil recovery methods in Saskatchewan’s heavy oil basin extract 5 to 10% of the available resource with the vast majority left in the ground and recoverable only through Enhanced Oil Recovery (EOR) methods. Traditional EOR generates steam in surface facilities and injects it underground to mobilize the oil for production with considerable energy losses inherent in the process. R.I.I. North America’s Solvent Thermal Resource Innovation Process (STRIP) technology moves the steam generator underground, reducing the operating and capital costs of a surface thermal production facility by 30% and 50% respectively, and saving more than 30% of the energy typically required for thermal production. STRIP technology combusts methane to produce in situ CO2 and steam. Because CO2 acts as a co-solvent, STRIP outperforms traditional steam-injection technology. This is demonstrated using a breakthrough modeling technique that couples fully compositional and thermal reservoir flow simulation capabilities. This new approach couples FlashPoint’s equation-of-state solver for the multiphase, multi-component, isothermal, isobaric flash problem, GFLASH, with Stanford’s Automatic Differentiation General Purpose Research Simulator for thermal reservoir flow simulations. This new computational framework exploits advanced techniques for skipping phase-identification computations and only uses exact phase equilibria from GFLASH when needed, reducing computational times by one to two orders of magnitude compared to the full rigorous solution.
Application aux contraintes thermodynamiques dans les problemes de separation multietagee. Develo... more Application aux contraintes thermodynamiques dans les problemes de separation multietagee. Developpement d'une strategie numerique qui exploite simultanement les equations de Gibbs-Duhem et de Gibbs-Helmholtz
We present a novel simulation approach for modeling of reactive flow and transport in multiphase ... more We present a novel simulation approach for modeling of reactive flow and transport in multiphase multi-component mixtures that include light gases, hydrocarbon components, and different ions present in an aqueous electrolyte phase. The phase behavior in these systems involves both thermodynamically-driven phase transitions (e.g. between supercritical vapor and liquid phases) and chemically driven precipitation and dissolution of solid (mineral) phases. All phases are modeled using the multi-scale Gibbs-Helmholtz Constrained Equation of State (GHC EoS), which up-scales molecular length scale information from a priori Monte Carlo simulations to help build accurate estimates of the energy parameter. Our proposed approach is implemented in the combined software system included the Automatic Differentiation General Purpose Research Simulator (ADGPRS) developed at Stanford University and the GFLASH library developed at University of Rhode Island. The extended variable substitution schema for a natural fully implicit formulation is designed to support the potential coexistence of an arbitrary set of phases in the flow. The classical reduction in the number of conservation equations based on element balances is combined with specific local constraints describing simultaneous thermodynamic and chemical equilibrium. Rigorous flash solutions for detecting phase changes in each grid block are computed using phase splitting and phase/chemical equilibrium to ensure equality of component chemical potentials and by monitoring the Gibbs free energy of the system to guarantee a global minimum is found. We present examples that cover a wide range of physical processes related to CO2 sequestration in saline aquifers.
Chemical engineering research & design, Nov 1, 2019
Many compounds of interest do not have critical properties, mostly because they decompose before ... more Many compounds of interest do not have critical properties, mostly because they decompose before reaching a critical state. Examples include polymers, ionic liquids, and asphaltenes. In this work, a novel numerical methodology for determining the glass transition temperature and boundary condition for the energy parameter in the Gibbs-Helmholtz Constrained (GHC) equation of state framework for compounds without critical properties is proposed. The glass temperature and boundary condition are then used in the multi-scale GHC equation to predict thermo-mechanical properties of a model asphaltene fluid proposed by Mullins (2010). Computational results for the GHC equation for the model asphaltene over the temperature range [263.15, 593.15 K] give mass densities that range from 1190.66 to 1064.37 kg/m 3 and coefficients of thermal expansion in the range [9.04 × 10 −5 , 8.97 × 10 −4 K −1 ] at 1 bar pressure. Multi-scale GHC-predicted isothermal compressibilities for the model asphaltene for pressures from 1 to 600 bar and temperatures of 380 and 480 K range from 7.43 to 1.56 × 10 −5 bar −1. These results compare favorably with available experimental data for asphaltenes reported in the open literature and show that the GHC equation can accurately and reliably predict mass and molar densities, molar volumes, isothermal compressibilities, and coefficients of expansion over wide ranges of temperature and pressure. Advantages and disadvantages of the proposed approach are also given.
Global optimization problems with so-called 'rough' or rugged objective function landscapes are s... more Global optimization problems with so-called 'rough' or rugged objective function landscapes are studied. These problems often have many, many stationary points and show considerable differences between small and large-scale geometry. A novel multiscale global optimization algorithm for solving 'rough' objective functions, based on the alternate use of terrain methods and new funneling algorithms, is presented. Small-scale information is gathered using a terrain optimization methodology while funneling algorithms are used to guide the overall optimization calculations and to make 'large' moves within the feasible region. A molecular modeling example is used to clearly illustrate that the proposed methodology is capable of finding a global minimum without calculating all stationary points and can lead to significant reductions in computational work.
Analytical support for recent numerical work in process simulation in the complex domain is discu... more Analytical support for recent numerical work in process simulation in the complex domain is discussed. In particular, the observation that nondegenerate singular points are saddle points of the two‐norm on the complex domain is proved rigorously and its numerical implications are discussed. The isothermal isobaric flash problem admits only real‐valued two‐phase solutions, provided that the feed conditions are real. Both single‐ and multivariable chemical process examples illustrate the theoretical results.
An aerofoil body, for example a "delta" wing aircraft, in which strip-form devices proj... more An aerofoil body, for example a "delta" wing aircraft, in which strip-form devices project rearwards from the trailing edge of the wing and serve to improve the lift-to-drag ratio of the body, in some conditions of flight at least, by modifying the formation of the trailing edge vortex to allow the axes of the primary vortex sheets to lie closer to the fore-and-aft centerline of the body than would otherwise be the case. When the strips are basically flat in shape, the strips may project straight backwards from the trailing edge or may be angled in various ways. The use of twisted strips is also described.
Uploads
Papers by Angelo Lucia