Sizing pressure relief valves in flashing and two-phase service: an alternative procedure

In view of the greater accuracy of the ω HEM correlation and the resulting conservative PR valve sizing (relative to the traditional PR valve sizing methods), the ω HEM-based flow calculations are recommended for all situations where flashing or two-phase flow occurs within the PR valve. However, as with any correlation, the accuracy of the ω HEM correlation results drops as the system to which it is applied diverges from the data used to develop it. Analysis of 15 different systems representative of actual refinery streams indicate that for fluids with a wide boiling range and for very non-ideal systems such as those containing hydrogen, the HEM correlation underpredicts the mass flux significantly (i.e. overpredicts the PR valve size). Since the large deviations are on the conservative side, the procedure will result in excessively large PR valves that may cause problems because of chattering of the PR valves, but would not present potential for vessel failure. The majority of the deviations are a result of the fact that the simplifying assumptions built into the correlation for single component do not truly characterize the actual flashing behaviour of many multicomponent fluids. The alternative approach presented, in which the correlation parameter ω is based on the actual flashing behaviour, eliminates nearly all the deviations and significantly improves the results of the correlation regardless of the system analysed. For trouble systems (those containing more than 0.1 wt% hydrogen and for some multicomponent fluids with a nominal boiling range greater than 80°C (150°F), the alternative approach should be used to define the correlation parameter ω. Use of this alternative approach is valid for any system (and will improve the accuracy of the correlation) but does require an additional flash calculation. However, for other systems the original formulation of ω is adequate and can be used.     

REGIONAL WATER SUPPLY PLANNING BY INTERACTIVE SYSTEMS ANALYSIS1

Abstract: This paper describes an interactive data and model generator that is intended to bridge the gap between the water resource enginner and planner and the mathematical progrmming systems approach to regional water supply planning. The optimization objective is to minimize total annual cost with respect to capital investment and operation and maintenance costs. The matrix generator formulates the necessary hydrologic, demographic and programming problem for system optimization. The interactive program guides the user through the input and optimization segments, totally eliminates the chore of manually structuring the model matrix aides in eliminating errors, and allows use by planners without skill in mathematical programming.     

WATER RESOURCES MODELING AND OPTIMIZATION BASED ON CONSERVATION AND FLOODING POOLS1

ABSTRACT: A new and practical concept in water resources modeling and optimization is introduced. Instead of unrealistically assuming a multipurpose reservoir to be composed of a single lumped pool of water, it is treated as two different pools namely conservation and flood pools. Based on this treatment, the optimization problem is stated using the concepts of Lagrange multipliers and parameter optimization. The optimization problem consists of the material balance equation, the constraints on control and state variables and the objective function.     

A Model for Managing Irrigated Agriculture1

ABSTRACT: Irrigation in arid and semiarid regions has led to accumulation of salts, destruction of soil texture, decline in fertility and yield, and eventual abandoning of the land. The problems of irrigated agriculture may be attributed to the fact that managers seldom consider irrigated land as a system consisting of a number of components and that the individual health of each component is vital to the overall health of the entire system. A management model is described here which considers all the important components of an irrigated system and may help maintain a permanent irrigated agriculture. The model optimizes net farm income, maintains favorable hydrologic and salt balance in the irrigated system, meets the concentration requirements of the drainage water for the individual crops, and simulates the impact of the irrigation on the unsaturated and the saturated zone.     

A novel radiant floor system: Detailed characterization and comparison with traditional radiant systems

ABSTRACT

Radiant floor systems have the potential to reduce energy consumption and the carbon footprint of buildings. This study analyzed a novel radiant panel configuration comprising a metal plate with small spikes that can be pressed into cement board or wood. The behavior of this configuration was simulated for different materials for the metal plate, spike dimensions, and varying spacing between spikes. An annual energy simulation model compared the radiant panel configuration with the traditional concrete-based system. Simulations were run under heating dominant, cooling dominant, and neutral conditions; significant cost savings and greenhouse gas emission reduction were seen across all scenarios.     

Multi-criteria PSO-based optimal design of grid-connected hybrid renewable energy systems

ABSTRACT

Human-induced climate change through the over liberation of greenhouse gases, resulting in devastating consequences to the environment, is a concern of considerable global significance which has fuelled the diversification to alternative renewable energy sources. The unpredictable nature of renewable resources is an impediment to developing renewable projects. More reliable, effective, and economically feasible renewable energy systems can be established by consolidating various renewable energy sources such as wind and solar into a hybrid system using batteries or back-up units like conventional energy generators or grids. The precise design of these systems is a critical step toward their effective deployment. An optimal sizing strategy was developed based on a heuristic particle swarm optimization (PSO) technique to determine the optimum number and configuration of PV panels, wind turbines, and battery units by minimizing the total system life-cycle cost while maximizing the reliability of the hybrid renewable energy system (HRES) in matching the electricity supply and demand. In addition, by constraining the amount of conventional electricity purchased from the grid, environmental concerns were also considered in the presented method. Various systems with different reliabilities and potential of reducing consumer’s CO₂ emissions were designed and the behavior of the proposed method was comprehensively investigated. An HRES may reduce the annualized cost of energy and carbon footprint significantly.     

OPTIMIZATION OF WATER ALLOCATION DECISIONS AFFECTING ESTUARINE ECOLOGY1

ABSTRACT .The problem analyzed in this paper is how to allocate optimally the available surface water in a river system among those who compete for its use, while acknowledging explicitly that for coastal states the ecology of bays and estuaries must be numbered among the competitors. The objective is to maximize the benefit resulting from water use while satisfying a set of constraints on flow. Benefit is assumed to be a function of the amount of water used and the time period in which the water is used. A mathematical model of this problem is shown to fit the format of the minimum cost circulation network flow problem. The Out-of-Kilter algorithm of D. R. Fulkerson is proposed as a solution technique. Sensitivity analysis on the input data is described as a means of determining the minimum economic benefit required to justify the allocation of a given volume of water needed to sustain the ecology of an estuary.     

A MULTI-BASIN PLANNING STRATEGY1

ABSTRACT. The purpose of this paper is to present and discuss a procedure for finding an optimal staging plan for implementing a multi-basin water resource system-a system that must meet, with tolerable shortages, pre-specified but highly variable demands for water that increase over time-a system such as the proposed Texas Water System. The paper stresses that, in the past, planners have paid little attention to quantifying explicitly the impact that uncertainty has on the decision process, and in that context, presents a means for explicitly evaluating the impact that uncertainty has on finding and evaluating the performance of the optimal and several alternate staging plans. The procedure presented evaluates the impact that uncertainty, in both the hydrologic and the economic variables, has on the decisions that need to be made. The decisions requiring resolution are (1) which of an over-specified set of facilities should be constructed, (2) how large each of the facilities should be at various points in time, and (3) how should the system be operated so as to minimize the capital plus operational costs over the planning period.     

DESIGN OF SEWER SYSTEMS1

In order to cope with the ever increasing problems of the urban environment, new approaches are being sought to their solution. The objective of this paper is to review and evaluate the merits of certain new methods aimed at finding optimal solutions in sewer design. Based on principles similar to the ones advanced by Deininger [1966] and Holland [1968] the authors propose an integer programming algorithm for optimizing pipe sizes and slopes. The new algorithm is applied to an actual situation and compared with a solution arrived at by a traditional design approach.     

ON THE CAPACITY-EXPANSION OF DESALINATION PLANTS AND STORAGE TANKS1

ABSTRACT A mathematical programming model is structured to find the optimal time and capacity expansion path of desalination plants and storage tanks for a hypothetical community which depends on desalination as its sole, or major, water supply source. The objective is to determine the least costly combination of sues and times of installation (of both desalting plants and storage tanks) which can meet a rising water demand over a finite planning horizon. The optimality criterion used in the model is based on two major economic elements: the economies of scale inherent in such facilities and the time-value of money represented by the interest rate, the former favoring large capacities and the latter small capacities. The model is applied using three population growth patterns and two interest rates. The water demand components for every year in the planning period are computed using empirical formulas which are based on population and other basic data. The model is solved for each of the above cases with the aid of a computer program based on the method of feasible conjugate directions. The results clearly reflect the balance between the economies of scale and the time-value of money under every demand growth function.