Energy-Water Nexus: An Input-Output Dynamical MODEL

Geraldo Andrade de Oliveira   and  Fernando Menezes Campello de Souza

Energy and water are of utmost importance for any country’s economy and way of life. Understanding the intricate relationship between energy and water and developing technologies to keep that relationship appropriate is an important key to a sustainable and secure future for any country.

There are trade-offs between energy and water. Large scale power plants — nuclear, coal, biomass and of course, hydroelectric — use lots of water. Conversely, making drinkable, potable water, and piping it into big cities, involving typically large distances, certainly requires plenty of energy.

Water and energy are strongly tied and certainly dependent on each other, with each affecting the other’s availability. Water is necessary for energy development and generation, and energy is needed to supply, use, and treat drinking water and waste water. Both, energy and water, are essential to our health, quality of life, and economic growth, and demand for both these resources continues to rise.

Water and energy are the two most fundamental resources of modern civilization. People die, and one cannot grow food, if water is not available. Without energy, one cannot run computers, or power homes, schools, offices, farms, and industrial plants. As the world’s population grows in number and affluence, the demands for both resources are increasing faster than ever.

The earth holds about eight million cubic miles of freshwater — tens of thousands of times more than humans’ annual consumption. Only about 2.5% of the world’s water is freshwater. Unfortunately, less than 1% is accessible via surface sources and aquifers, and the rest is imprisoned in underground reservoirs and in permanent ice and snow cover. Also, the available water is often not clean or not located close to population centers.

The reality that each of these precious resources, energy and water, might soon cripple the use of the other has been under-appreciated. To generate energy, massive quantities of water are consumed, and to deliver clean water, massive quantities of energy are consumed. Desalination, a process that removes salt from water, is the most energy-intensive and expensive option for treating water and is used where alternatives are very limited. Other energy needs associated with water occur at the point of end-use, often in households, primarily for water heating, water cooling, clothes washing, and pumping water. Many people are concerned about the perils of peak oil — running out of cheap oil. A few are voicing concerns about peak water. But almost no one is addressing the conflict between the two: water restrictions are hampering solutions for generating more energy, and energy problems, particularly rising prices, are curtailing efforts to supply more clean water.

Physical constraints on the availability of water for energy sector use encompasses both quantity and quality issues: there may not be enough of it or that which is available may be of insufficient quality. These restrictions may be natural or may arise from regulation of water use. One cannot build more power plants without taking into account that they impinge on the freshwater supplies. And one cannot build more water delivery and cleaning facilities without increasing energy demand. Solving the dilemma requires new global policies that integrate energy and water solutions and innovative technologies that help to boost one resource without draining the other. One need an analytical tool, a mathematical tool, to treat this problem. One mathematical dynamical model is proposed here.

Water and energy are fundamentally linked. Policy reforms in both industries, however, do not appear to acknowledge the links nor consider their wider implications. This is clearly unhelpful, particularly as policy makers attempt to develop effective responses to water and energy issues, underpinned by prevailing drought conditions and impending climate change, and an ever increasing demand for both resources.

Energy production requires a reliable, abundant, and predictable source of water, a resource that is already in short supply throughout much of the world.

The time has come to consider both issues as one. Instead of water planners assuming they will have all the energy they need and energy planners assuming they will have all the water they need, one must get them in the same room to make decisions. A restructuring of the institutional arrangements is in order. And one will need an analytical tool. This is the underlying idea of this proposed analytical model.

One analyzes here the links between water and electricity — termed water-energy nexus, or energy-water nexus — in the general context. For that matter a dynamic input-output Leontief model is proposed.

The Supply Chain Model

The supply chain management is a central tool in business administration.

The input-output matrix summarizes the matching of supply and demand amongst the various sectors of the economy; the gross purchase or sales of physical products among the various sectors of economy. It also describes the technology of production.

Two important economic variables are supply, s, and demand, d. It is assumed that if demand grows, then supply will grow, or should grow, to match it. And vice-versa. In other words, supply keeps tracking demand. There exists thus a feedback phenomenon.

Since demand is always varying, there will be always a dynamic equilibrium. The system is, in general, always moving. It is the dynamics of this movement that one wants to study and control. It is the essence of a supply chain management. In the case of the energy-water interplay this is crucial, since these two variables are closely intertwined.

The variable which provokes the increasing or decreasing of production is the difference between demand and supply. As the population grows, the demand for water (which has no substitute) and energy will grow, and not always in a balanced fashion. There will be a “demand surplus” or a “supply surplus”.

Earth and the communities that live upon it are part of a system. By approaching these massive problems from an integrated standpoint, one begins to solve problems in a more systematic way.

The energy-water nexus is attracting the attention of diverse stakeholders around the world and it is becoming more and more clear that one cannot plan for the planet’s future if one does not consider energy and water as a whole.

Water and energy policy, planning and management must be integrated to encourage conservation, motivate innovation and ensure sustainable use of water and energy. It takes a significant amount of water to create energy, and a significant amount of energy to move and treat water.

One may not realize it, but when one uses energy, one is also using water indirectly — lots of it!

The model proposed here includes the dynamical aspects of the interplay between water and energy, due to the necessity of having stocks, and allows a thoroughly comprehension and control of this interaction. It was implemented in a spread sheet. Several possibilities concerning the links between these two resources, as well as the control of the system (policies) are analyzed.