A systemic approach for optimal cooling tower operation

The thermal performance of a cooling tower and its cooling water system is critical for industrial plants, and small deviations from the design conditions may cause severe instability in the operation and economics of the process. External disturbances such as variation in the thermal demand of the process or oscillations in atmospheric conditions may be suppressed in multiple ways. Nevertheless, such alternatives are hardly ever implemented in the industrial operation due to the poor coordination between the utility and process sectors. The complexity of the operation increases because of the strong interaction among the process variables. In the present work, an integrated model for the minimization of the operating costs of a cooling water system is developed. The system is composed of a cooling tower as well as a network of heat exchangers. After the model is verified, several cases are studied with the objective of determining the optimal operation. It is observed that the most important operational resources to mitigate disturbances in the thermal demand of the process are, in this order: the increase in recycle water flow rate, the increase in air flow rate and finally the forced removal of a portion of the water flow rate that enters the cooling tower with the corresponding make-up flow rate. (C) 2009 Elsevier Ltd. All rights reserved.

Optimal synthesis of anaerobic digester networks

The objective of this paper is to develop a mathematical model for the synthesis of anaerobic digester networks based on the optimization of a superstructure that relies on a non-linear programming formulation. The proposed model contains the kinetic and hydraulic equations developed by Pontes and Pinto [Chemical Engineering journal 122 (2006) 65-80] for two types of digesters, namely UASB (Upflow Anaerobic Sludge Blanket) and EGSB (Expanded Granular Sludge Bed) reactors. The objective function minimizes the overall sum of the reactor volumes. The optimization results show that a recycle stream is only effective in case of a reactor with short-circuit, such as the UASB reactor. Sensitivity analysis was performed in the one and two-digester network superstructures, for the following parameters: UASB reactor short-circuit fraction and the EGSB reactor maximum organic load, and the corresponding results vary considerably in terms of digester volumes. Scenarios for three and four-digester network superstructures were optimized and compared with the results from fewer digesters. (C) 2009 Elsevier B.V. All rights reserved.

Optimal synthesis of Fenton reactor networks for phenol degradation

There is an increasing need to treat effluents contaminated with phenol with advanced oxidation processes (AOPs) to minimize their impact on the environment as well as on bacteriological populations of other wastewater treatment systems. One of the most promising AOPs is the Fenton process that relies on the Fenton reaction. Nevertheless, there are no systematic studies on Fenton reactor networks. The objective of this paper is to develop a strategy for the optimal synthesis of Fenton reactor networks. The strategy is based on a superstructure optimization approach that is represented as a mixed integer non-linear programming (MINLP) model. Network superstructures with multiple Fenton reactors are optimized with the objective of minimizing the sum of capital, operation and depreciation costs of the effluent treatment system. The optimal solutions obtained provide the reactor volumes and network configuration, as well as the quantities of the reactants used in the Fenton process. Examples based on a case study show that multi-reactor networks yield decrease of up to 45% in overall costs for the treatment plant. (C) 2010 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

A Separation Principle for the Continuous-Time LQ-Problem With Markovian Jump Parameters

In this paper, we devise a separation principle for the finite horizon quadratic optimal control problem of continuous-time Markovian jump linear systems driven by a Wiener process and with partial observations. We assume that the output variable and the jump parameters are available to the controller. It is desired to design a dynamic Markovian jump controller such that the closed loop system minimizes the quadratic functional cost of the system over a finite horizon period of time. As in the case with no jumps, we show that an optimal controller can be obtained from two coupled Riccati differential equations, one associated to the optimal control problem when the state variable is available, and the other one associated to the optimal filtering problem. This is a separation principle for the finite horizon quadratic optimal control problem for continuous-time Markovian jump linear systems. For the case in which the matrices are all time-invariant we analyze the asymptotic behavior of the solution of the derived interconnected Riccati differential equations to the solution of the associated set of coupled algebraic Riccati equations as well as the mean square stabilizing property of this limiting solution. When there is only one mode of operation our results coincide with the traditional ones for the LQG control of continuous-time linear systems.

On the Filtering Problem for Continuous-Time Markov Jump Linear Systems with no Observation of the Markov Chain

We consider in this paper the optimal stationary dynamic linear filtering problem for continuous-time linear systems subject to Markovian jumps in the parameters (LSMJP) and additive noise (Wiener process). It is assumed that only an output of the system is available and therefore the values of the jump parameter are not accessible. It is a well known fact that in this setting the optimal nonlinear filter is infinite dimensional, which makes the linear filtering a natural numerically, treatable choice. The goal is to design a dynamic linear filter such that the closed loop system is mean square stable and minimizes the stationary expected value of the mean square estimation error. It is shown that an explicit analytical solution to this optimal filtering problem is obtained from the stationary solution associated to a certain Riccati equation. It is also shown that the problem can be formulated using a linear matrix inequalities (LMI) approach, which can be extended to consider convex polytopic uncertainties on the parameters of the possible modes of operation of the system and on the transition rate matrix of the Markov process. As far as the authors are aware of this is the first time that this stationary filtering problem (exact and robust versions) for LSMJP with no knowledge of the Markov jump parameters is considered in the literature. Finally, we illustrate the results with an example.

Discrete-time mean variance optimal control of linear systems with Markovian jumps and multiplicative noise

In this article, we consider the stochastic optimal control problem of discrete-time linear systems subject to Markov jumps and multiplicative noise under three kinds of performance criterions related to the final value of the expectation and variance of the output. In the first problem it is desired to minimise the final variance of the output subject to a restriction on its final expectation, in the second one it is desired to maximise the final expectation of the output subject to a restriction on its final variance, and in the third one it is considered a performance criterion composed by a linear combination of the final variance and expectation of the output of the system. We present explicit sufficient conditions for the existence of an optimal control strategy for these problems, generalising previous results in the literature. We conclude this article presenting a numerical example of an asset liabilities management model for pension funds with regime switching.

Generalized Coupled Algebraic Riccati Equations for Discrete-time Markov Jump with Multiplicative Noise Systems

In this paper we consider the existence of the maximal and mean square stabilizing solutions for a set of generalized coupled algebraic Riccati equations (GCARE for short) associated to the infinite-horizon stochastic optimal control problem of discrete-time Markov jump with multiplicative noise linear systems. The weighting matrices of the state and control for the quadratic part are allowed to be indefinite. We present a sufficient condition, based only on some positive semi-definite and kernel restrictions on some matrices, under which there exists the maximal solution and a necessary and sufficient condition under which there exists the mean square stabilizing solution fir the GCARE. We also present a solution for the discounted and long run average cost problems when the performance criterion is assumed be composed by a linear combination of an indefinite quadratic part and a linear part in the state and control variables. The paper is concluded with a numerical example for pension fund with regime switching.

New Analytic Solution Related to the Richards, Philip, and Green-Ampt Equations for Infiltration

Based on physical laws of similarity, an analytic solution of the soil water potential form of the Richards equation was derived for water infiltration into a homogeneous sand. The derivation assumes a similarity between the soil water retention function and that of the soil water content profiles taken at fixed times. The new solution successfully described soil water content profiles experimentally measured for water infiltrating downward, upward, and horizontally into a homogeneous sand and agrees with that presented by Philip in 1957. The utility of this analysis is still to be verified, but it is expected to hold for soils that have a narrow pore-size distribution before wetting and that manifest a sharp increase of water content at the wetting front during infiltration. The effect of van Genuchten`s parameters alpha and n on the application of the solution to other porous media was investigated. The solution also improves and provides a more realistic description of the infiltration process than that pioneered by Green and Ampt in 1911.

New Analytic Solution of Boltzmann Transform for Horizontal Water Infiltration into Sand

The use of the Boltzmann transform function, lambda(theta), to solve the Richards equation when the diffusivity, D, is a function of only soil water content,., is now commonplace in the literature. Nevertheless, a new analytic solution of the Boltzmann transform lambda(h) as a function of matric potential for horizontal water infiltration into a sand was derived without invoking the concept or use of D(theta). The derivation assumes that a similarity exists between the soil water retention function and the Boltzmann transform lambda(theta). The solution successfully described soil water content profiles experimentally measured for different infiltration times into a homogeneous sand and agrees with those presented by Philip in 1955 and 1957. The applicability of this solution for all soils remains open, but it is anticipated to hold for soils whose air-filled pore-size distribution before wetting is sufficiently narrow to yield a sharp increase of water content at the wetting front during infiltration. It also improves and provides a versatile alternative to the well-known analysis pioneered by Green and Ampt in 1911.

Distribution and storage characterization of soil solution for drip irrigation

The increased use of marginal quality water with drip irrigation requires sound fertigation practices that reconcile environmental concerns with viable crop production objectives. We conducted experiments to characterize dynamics and patterns of soil solution within wet bulb formed by drip irrigation. Time-domain reflectometry probes were used to monitor the distribution of potassium nitrate (KNO(3)) and water distribution from drippers discharging at constant flow rates of 2, 4 and 8 L h(-1) in soil-filled containers. Considering results from different profiles, we observed greater solute storage near the dripper decreasing gradually towards the wetting front. About half of the applied KNO(3) solution (48%) was stored in the first layer (0-0.10 m) for all experiments, 29% was stored in the next layer (0.10-0.20 m). Comparing different dripper flow rates, we observed higher solution storage for 4 L h(-1), with 45, 53 and 47% of applied KNO(3) solution accumulating in the first layer (0-0.10 m) for dripper flow rates of 2, 4 and 8 L h(-1), respectively. The results suggest that based on the volume and frequency used in this experiment, it would be advantageous to apply small amounts of solution at more frequent intervals to reduce deep percolation losses of applied water and solutes.

Optimal irrigation depth for bean crops considering water constraints and farmer`s risk aversion level

Nowadays, the rising competition for the use of water and environmental resources with consequent restrictions for farmers should change the paradigm in terms of irrigation concepts, or rather, in order to attain economical efficiency other than to supply water requirement for the crop. Therefore, taking into account the social and economical role of bean activity in Brazil, as well as the risk inherent to crop due to its high sensibility to both deficit and excessive water, the optimization methods regarding to irrigation management have become more interesting and essential. This study intends to present a way to determine the optimal water supply, considering different combinations between desired bean yield and level of risk, bringing as a result a graph with the former associated with the latter, depending on different water depths.

Nickel adsorption in two Oxisols and an Alfisol as affected by pH, nature of the electrolyte, and ionic strength of soil solution

Background, aim, and scope The retention of potentially toxic metals in highly weathered soils can follow different pathways that variably affect their mobility and availability in the soil-water-plant system. This study aimed to evaluate the effects of pH, nature of electrolyte, and ionic strength of the solution on nickel (Ni) adsorption by two acric Oxisols and a less weathered Alfisol. Materials and methods The effect of pH on Ni adsorption was evaluated in surface and subsurface samples from a clayey textured Anionic `Rhodic` Acrudox ( RA), a sandy-clayey textured Anionic `Xantic` Acrudox (XA), and a heavy clayey textured Rhodic Kandiudalf (RK). All soil samples were equilibrated with the same concentration of Ni solution (5.0 mg L(-1)) and two electrolyte solutions (CaCl(2) or NaCl) with different ionic strengths (IS) (1.0, 0.1 and 0.01 mol L(-1)). The pH of each sample set varied from 3 to 10 in order to obtain sorption envelopes. Results and discussion Ni adsorption increased as the pH increased, reaching its maximum of nearly pH 6. The adsorption was highest in Alfisol, followed by RA and XA. Competition between Ni(2+) and Ca(2+) was higher than that between Ni(2+) and Na(+) in all soil samples, as shown by the higher percentage of Ni adsorption at pH 5. At pH values below the intersection point of the three ionic strength curves (zero point of salt effect), Ni adsorption was generally higher in the more concentrated solution (highest IS), probably due to the neutralization of positive charges of soil colloids by Cl(-) ions and consequent adsorption of Ni(2+). Above this point, Ni adsorption was higher in the more diluted solution (lowest ionic strength), due to the higher negative potential at the colloid surfaces and the lower ionic competition for exchange sites in soil colloids. Conclusions The effect of ionic strength was lower in the Oxisols than in the Alfisol. The main mechanism that controlled Ni adsorption in the soils was the ionic exchange, since the adsorption of ionic species varied according to the variation of pH values. The ionic competition revealed the importance of electrolyte composition and ionic strength on Ni adsorption in soils from the humid tropics. Recommendations and perspectives The presence of NaCl or CaCl(2) in different ionic strengths affects the availability of heavy metals in contaminated soils. Therefore, the study of heavy metal dynamics in highly weathered soils must consider this behavior, especially in soils with large amounts of acric components.

Novel and facile solution-phase synthesis of 2,5-diketopiperazines and O-glycosylated analogs

This work describes the synthesis in Solution of a series of related diketopiperazines with potential biological activities: cyclo(L-Pro-L-Ser), cyclo(L-Phe-L-Ser), cyclo(D-Phe-L-Ser) and the corresponding glycosylated analogs of the latter, cyclo[D-Phe-L-Ser(alpha GlcNAc)] and cyclo[D-Phe-L-Ser(beta GlcNAc)]. The synthetic approach involved coupling reactions of -OH or O-glycosylated serine benzyl esters with NFmoc-protected amino acids (Pro or Phe), followed by one-pot deprotection-cyclization reaction in the presence of 20% piperidine in DMF. (C) 2009 Elsevier Ltd. All rights reserved.

Stability property of matchings is a natural solution concept in coalitional market games

Stability of matchings was proved to be a new cooperative equilibrium concept in Sotomayor (Dynamics and equilibrium: essays in honor to D. Gale, 1992). That paper introduces the innovation of treating as multi-dimensional the payoff of a player with a quota greater than one. This is done for the many-to-many matching model with additively separable utilities, for which the stability concept is defined. It is then proved, via linear programming, that the set of stable outcomes is nonempty and it may be strictly bigger than the set of dual solutions and strictly smaller than the core. The present paper defines a general concept of stability and shows that this concept is a natural solution concept, stronger than the core concept, for a much more general coalitional game than a matching game. Instead of mutual agreements inside partnerships, the players are allowed to make collective agreements inside coalitions of any size and to distribute his labor among them. A collective agreement determines the level of labor at which the coalition operates and the division, among its members, of the income generated by the coalition. An allocation specifies a set of collective agreements for each player.

Debt Maturity: Is Long-Term Debt Optimal?

We model and calibrate the arguments in favor and against short-term and long-term debt. These arguments broadly include: maturity premium, sustainability, and service smoothing. We use a dynamic-equilibrium model with tax distortions and government outlays uncertainty, and model maturity as the fraction of debt that needs to be rolled over every period. In the model, the benefits of defaulting are tempered by higher future interest rates. We then calibrate our artificial economy and solve for the optimal debt maturity for Brazil as an example of a developing country and the US as an example of a mature economy. We obtain that the calibrated costs from defaulting on long-term debt more than offset costs associated with short-term debt. Therefore, short-term debt implies higher welfare levels.