Optimization of water network integrated with process models

Abstract

In this paper, a novel approach for the synthesis of water network incorporated with process models is introduced. The process models are utilized to relate the variables (i.e., flow rate and concentration) of process output (typically defined as internal water source) with those of process input (i.e., water sink). A generalized water network superstructure is developed to embed all possible process units and all the connections among resources, interceptors, process units, and wastes. The problem is formulated as four optimization problems (minimum freshwater flow rate, intercepted flow rate, intercepted mass load, and number of connections), and the four models are solved in sequence to locate the targets. A literature case is used to validate the proposed approach. Moreover, a sour water network of a practical refinery plant is presented to illustrate the applicability and effectiveness of the proposed approach.

Appendix

As mentioned in the proposed NLP/MINLP optimization model, the appropriate determination of lower and upper bounds for those variables is necessity for process operation. Besides, the given appropriate bounds would narrow the solving space and are helpful for the solving procedure.

For each process unit, the inlet flow rate cannot exceed its maximum input capacity. Hence, the upper bounds (FSU ^UB _s,u and FUU ^UB _u′,u ) would be set to equal to the maximum input capacity (FU ^max_input _u ).

$${\text{FSU}}_{s,u}^{\text{UB}} = {\text{FU}}_{u}^{{{\text{max\_input}}}} \;\;\;\;\forall s \in {\text{NFS}},u \in {\text{NPU}} $$

(34)

$${\text{FUU}}_{u',u}^{\text{UB}} = {\text{FU}}_{u}^{{{\text{max\_input}}}} \;\;\;\;\forall u',u \in {\text{NPU}} $$

(35)

Besides, the outlet flow rate for each process unit cannot exceed its maximum output capacity. Thus, the upper bounds (FUU ^UB _u,u′ and FUE ^UB _u ) would be set to equal to the maximum output capacity (FU ^max_output _u ).

$${\text{FUU}}_{u,u'}^{\text{UB}} = {\text{FU}}_{u}^{{{\text{max\_output}}}} \;\;\;\;\forall u',u \in {\text{NPU}} $$

(36)

$${\text{FUE}}_{u}^{\text{UB}} = {\text{FU}}_{u}^{{{\text{max\_output}}}} \;\;\;\;\forall u \in {\text{NPU}} $$

(37)

Similarly, the inlet/outlet flow rate for each interceptor unit cannot exceed its maximum input/output capacity. Thus, the upper bounds (FSI ^UB _s,i , FII ^UB _i′,i , FII ^UB _i,i′ and FIE ^UB _i ) could be set to equal to the maximum input/output capacity.

$${\text{FSI}}_{s,i}^{\text{UB}} = {\text{FI}}_{i}^{{\hbox{max} \_{\text{input}}}} \;\;\;\;\forall s \in {\text{NFS}},i \in {\text{NIU}} $$

(38)

$${\text{FII}}_{i',i}^{\text{UB}} = {\text{FI}}_{i}^{{\hbox{max} \_{\text{input}}}} \;\;\;\;\forall i,i' \in {\text{NIU}} $$

(39)

$${\text{FII}}_{i,i'}^{\text{UB}} = {\text{FI}}_{i}^{{\hbox{max} \_{\text{output}}}} \;\;\;\;\forall i,i' \in {\text{NIU}} $$

(40)

$${\text{FIE}}_{i}^{\text{UB}} {\text{ = FI}}_{i}^{{\hbox{max} \_{\text{output}}}} \;\;\;\;\forall i \in {\text{NIU}} $$

(41)

In addition, the upper bounds (FUI ^UB _u,i and FIU ^UB _i,u ) would be restricted by the minimum input/output capacities for both process unit and interceptor unit. Thus, the upper bounds (FUI ^UB _u,i and FIU ^UB _i,u ) could be determined by the following equations:

$${\text{FUI}}_{u,i}^{\text{UB}} {\text{ = min(FU}}_{u}^{{{\text{max\_output}}}} ,{\text{FI}}_{i}^{{\hbox{max} \_{\text{input}}}} ) { }\;\;\;\;\forall u \in {\text{NPU}}\;\;\;\;\forall i \in {\text{NIU}} $$

(42)

$${\text{FIU}}_{i,u}^{\text{UB}} {\text{ = min(FI}}_{i}^{{\hbox{max} \_{\text{output}}}} ,{\text{FU}}_{u}^{{{\text{max\_input}}}} ) { }\;\;\;\;\forall u \in {\text{NPU}}\;\;\;\;\forall i \in {\text{NIU}} $$

(43)