An-Najah Staff

Prosperity of any society is predicted by the availability of inexpensive, abundant and sustainable sources of energy that are capable of providing energy needs for current and future generations. Conventionally, hydrocarbons have been exploited as the major sources of energy in recent history (although sun, wind and tidal powers have, to a lesser extent, been used as suppliers of some of the needed energy).

Due to the finite nature of existing hydrocarbons, accompanied by the ever-increasing costs associated with their recovery, societies will eventually face an inevitable energy crisis, unless of course other feasible, inexpensive sources of energy are utilized. Typically, in a sustainable energy setting, the “other” forms of energy must be either infinite in their existence or otherwise renewable. Although, in one sense, the renewable energy concept points towards utilization of the abundant sun, wind and tidal energies, (and hence a complete exploitation of such natural phenomena would represent a sustainable approach to energy), it is felt that existing technologies are incapable of efficiently utilizing these energy sources in such a way that satisfies society's total energy needs.

However, provision of even a small percentage of society's energy needs from renewable resources would result in sustaining other (non-renewable) sources a little longer, and hence would slow down the “arrival” of the energy crisis. Furthermore, due to the close connection between resources and some energy sources, attention must be given to the generation of energy from other unconventional sources (such as the recovery of heat energy from methane gas liberated from animal waste; the use of carbon dioxide in enhanced and tertiary oil recovery, which saves energy and reduces environmental pollution by CO₂). In addition, energy reusing/recycling from waste-energy represents a viable means of energy conservation that is necessary in any sustainable energy setting (for example, heat energy absorbed by coolants in an industrial plant can be used as a source of energy in a nearby office building).

In the absence of a single infinite supply of energy that can efficiently be used to satisfy society's energy needs, the above discussion reiterates the vital need for management strategies that must be implemented to provide a sufficient supply of energy from various sources (non-renewable, renewable, potentially renewable and energy recycling/recovery) in a manner that is sustainable. With the current availability of non-renewable, renewable, recyclable and potentially recoverable energies, society must strike an optimal balance in the rates of use and reuse of these energies to achieve energy sustainability in addition to society's welfare and its optimal utility.

From the point of view of resource conservation, an abundance of research work has been carried out on resource recovery and recycling as an approach to sustainability (cf. [1] and the references therein). In addition, optimal recycling rates and recyclable ratios have been determined for general and specific purpose recycling. In this work, we provide the mathematical analysis and develop a mathematical model that is necessary for an optimal distribution of energy sources, in an n-sector society, that will maximize society's utility from energy. The model is expected to shed some light on the policies that need to be implemented in order to achieve this optimal distribution.