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Physical Hydronomics

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The application of the Exergoecological approach to the natural resource “water” is named as “Physical Hydronomics” (PH).


The thermodynamic value of a natural resource characterized by its specific properties like structure or concentration is defined as “the minimum work (exergy) needed to produce it from common materials in the reference environment”. The best suitable environment taken as reference for calculating the exergy of water bodies is seawater.

The specific exergy of a water body is defined by its mass flow and six measurable parameters characterizing the thermodynamic status of water: temperature, pressure, composition, concentration, velocity and altitude . The exergy method associates each parameter with its exergy component: thermal, mechanical, chemical, kinetic and potential. The model assumes the approximation to an incompressible liquid where the exergy is defined through the mentioned components.

Once the specific exergy (b) is properly calculated, studying individually each component (physical parameters, salts, organic matter, nitrogen and phosphor), the absolute exergy of a water flow can be obtained.  The absolute exergy in power units (kW) can be easily calculated with through the water flow, the density of the solution and the mass flow:

Exergy profile of a river

The exergy profile of a river along its course has a characteristic curve which is quite similar for all of them. This fact can be explained analysing the typical profiles of specific exergy and water flow of rivers.

The ideal and simplified specific exergy profile of a river is illustrated in Fig. 1a. At the river source, water is found at the highest elevation and at the most pure state, therefore its physical and chemical exergies are the highest at that point. As it flows into the mouth, the water body loses height and purity and therefore its specific exergy decreases until it reaches the point of minimum exergy (maximum degradation) which is the sea (reference environment). The water flow usually follows exactly the opposite path (Fig. 1a): minimum at the source and maximum at the mouth. Both effects together give an ideal total exergy pattern of the bell-shaped curve given in Fig. 1b.

This ideal pattern of Fig. 1b is modified in present rivers, since the specific exergy and water flow lines do not follow a perfect straight line. The existence of tributary rivers, filtrations to aquifers, catchments to diverse consumptive uses, solar evaporation, spill outs, etc. create positive or negative deviations in Figs 1a and 1b, i.e. in the quality and quantity of rivers.

Physical costs

The sum of the obtained values for each exergy component is the total exergy that can be understood as the minimum energy required for restoring the resource from the sea. However, real man-made processes are far from the ideal conditions because of inefficiencies of our technology resulting in irreversibilities. Energy requirements to obtain a resource are always greater than those dictated by the Second Law. In order to overcome that problem, we must include the real physical unit costs known as Exergy Replacement Costs (ERC) in the thermodynamic evaluation of resources. These are defined as the relationship between the energy invested in the real process for obtaining the resource and the minimum energy required if the process were reversible. It has a dimensionless value and measures the number of exergy units needed to obtain one unit of exergy of the product. Generally, the exergy replacement cost is tens or even hundreds of times greater than its exergy content. The non-reversible physical value of a resource (total exergy cost) B* is determined then by the sum of each specific exergy component (bi) multiplied by the unit exergy replacement cost (ERCi) of the process to restore that physical feature of the resource as in the following equation:

The knowledge of suitable technologies, with their range of application and specific consumptions (SC) is mandatory to calculate ERCs. Once SC have been reviewed (including energy consumption for producing plant consumables) for all of them, the relation between the real energy cost and the energy required in an ideal reversible process (exergy) gives us the unit ERC.

Exergy costs oriented to WFD objectives

The total exergy costs B* give an indication of the actual effort we should make to restore the river because of its departure in quality and quantity from the sea. It measures the cost for producing water (through desalination) and pumping and transporting it to the point under consideration, with the given available technology. This measure is useful for establishing an objective guide for water management, as it offers a map of maximum costs in a certain territory.

However, if the objective is to calculate the degradation costs of a certain water body or flow due to the anthropogenic presence, those previous costs are not representative because it is not necessary to extract, desalt and pump seawater to bring existing waters to a better status. In other words, the interest resides in comparing the exergy difference obtained with the total exergy profiles of water courses under present (Bp) and any other objective conditions (Bo).

One possibility is to compare existing waters with a desirable state labelled as the “good ecological status” (GES) of water bodies, as promoted by the WFD. The latter would be the state at whose achievement all the efforts should be aimed: in this way, with the exergy difference between present and objective qualities, it could be evaluated in a physical manner the Action Plan that EU Member States will have to apply in order to reach the GES objectives for water bodies in 2015, a WFD mandatory.  Anyway the definition of this profile (Bo) will remain open to technical/legal agreements.

GES is quite ambitious because it includes both the quality and quantity of the water body and its ecological status as a life support system. Physical Hydronomics will only deal with the physical status of the water flow, without accounting for living organic forms. Jorgensen through its “ecoexergy” has studied the exergy of organic systems. Ecoexergy could also be considered as an additional component in our approach for establishing biological costs. However, given the still existing distance between both methodologies this part needs still to be refined.

Once both states are established, the idea is to calculate the exergy cost of the exergy drop DB that was generated between the present and objective situations provoked by human activities. This gap has to be restored by means of the available technology (in energy terms) and obviously will have a cost. Furthermore, it could be divided into the quantitative and qualitative terms, as the following equation:

The exergy replacement costs (ERCl and ERCt) derived respectively from both exergy gaps are defined as follows:

  • In order to restore the exergy gap Bl due to the loss of quality of the water course, diverse purification technologies have to be applied up to the desired limits. Different tertiary treatments will be the most adequate in this case since it is assumed that in the EU all waters are previously treated in seawage plants.
  • For eliminating the exergy gap Bt due to the loss of quantity of the water course because of human consumptions, we have to desalt seawater in a desalination plant located in the river mouth, and then pump out this water flow to its corresponding point in the water course.

Assessing costs to end users

The conversion of physical into monetary costs is very simple because they are obtained by multiplying the energy demand (kWh) by the current energy price ($ or €/kWh). If investment and O&M costs are also added to each technology, the resulting monetary recovery costs (MRCt and MRCl) could serve as an objective reference for assessing the environmental costs.

Drawbacks of PH

The main drawback of the PH methodology is the huge amount of information needed (specially the quality parameters). The model can be locally applied to rivers, flows and lakes or reservoirs with sampling stations (a discrete representation is obtained instead of continuous curves), but it is very difficult to obtain all the information needed for an accurate application of the model on a global scale. The minimum required data would be temperature, altitude, conductivity, organic matter, nitrogen and phosphor (both for the studied point and for the reference). In order to define more accurately the chemical exergy component, it is more desirable to calculate the exergy of each ionic component instead of obtaining it from conductivity measurements (what means assuming no specific ion identification)

Nevertheless, if enough data is available, PH could become a fundamental tool for assessing the real physical cost of water.

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Created by aliciavd
Last modified 2015-09-11 02:39 PM
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Thanatia: The Destiny of the Earth's Mineral Resources

A Thermodynamic Cradle-to-Cradle Assessment by (author): Antonio Valero Capilla (CIRCE — Universidad de Zaragoza, Spain), Alicia Valero Delgado (CIRCE — Universidad de Zaragoza, Spain)

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