Design of total water networks of multiple properties based on operator potential concepts and an iterative procedure

The design of property-based total water networks by using the concepts of operator potential is investigated with an iterative approach. The precedence order of demands is identified with the operator potential values of demands. The internal sources to be regenerated are selected based on the values of operator potential of sources. A linear programming approach is used to determine the allocation of sources to demands. With the proposed method, the networks which meet both the requirements of demands and environmental regulations can be obtained. Two examples are studied to illustrate the proposed method. It is shown that the results obtained by this work are comparable to that obtained by mathematical programming method in the literature. For Example 1, flowrate of regenerated stream is reduced 28.5% compared to that in the literature results with almost the same freshwater consumption. In addition, the number of interconnections for this work is smaller than that of literature, which means that the design structure of this work is simpler. For Example 2, freshwater consumption is reduced by 4.29% with almost the same regeneration flowrate. However, the number of interconnections for this work is 24, which is higher than 23, that is the value of the literature result. Compared to graphical methods, the method proposed in this paper can handle the networks with more than three properties. Compared to mathematical programming methods, the proposed method has clear engineering meaning.

Resolvent for Non-Self-Adjoint Differential Operator with Block-Triangular Operator Potential

A resolvent for a non-self-adjoint differential operator with a block-triangular operator potential, increasing at infinity, is constructed. Sufficient conditions under which the spectrum is real and discrete are obtained.

A Simple Method for Property Integration

In this paper, a new method is proposed for synthesis of property-based allocation networks. By analogy of concentration potential concepts proposed by Liu et al. (A heuristic design procedure for water-using networks with multiple contaminants,AIChE Journal, 2009; 55: 374-382) for the water-using networks, a new concept: the operator potential of sinks is introduced in this work. The operator potential of a sink is a measurement of the possibility of the sink to reuse the internal source streams. The sink with the lowest operator potential will be satisfied first. A literature example is studied to show the method proposed. The result shows that the method proposed in this work is very simple and the results obtained are consistent with those obtained in the literature.