Studies on resilience of water networks

doi:10.1016/j.cej.2008.06.026

Chemical Engineering Journal

Volume 147, Issues 2–3, 15 April 2009, Pages 117-121

https://doi.org/10.1016/j.cej.2008.06.026 Get rights and content

Abstract

Water system integration is one of the most efficient technologies for saving fresh water and reducing wastewater. However, the compact connection of water units often leads to insufficient resilience of a water system. In order to counteract the fluctuation of a real production process, a water network must be flexible. Two new concepts, maximum tolerance amount of a water unit (MTaWU) and tolerance amount of a water unit (TaWU) are introduced firstly in this paper. Based on these two concepts, the tolerance amount of a water network (TaWN) is proposed to quantify the resilience of a water network. A case study illustrates that these parameters are countable and straightforward.

Introduction

Techniques involving water network synthesis are generally categorized as the water pinch design method [1], [2], [3], [4] and the mathematical programming approach [5], [6], [7]. The water network design is intended to achieve the minimum water targets, however, water network design process assumes that process data are fixed and well-defined, whereas the actual operating conditions such as water flowrate and corresponding mass loads may fluctuate over time. These fluctuations in processing conditions can lead to process disruptions or product quality problem. So we must consider network resilience or flexibility during water network designing. The resilience of a water network can be comprehended as that when some parameters, such as mass load, fluctuate within a certain operating range, the whole water network can also satisfy the operation.

Grossmann and Morari [8] firstly presented the concept of resilience in process industries; and they defined resilience as the ability of a plant to tolerate and to recover from dynamic or transient disturbances. Such as the HEN can response the dynamic disturbance of temperature and flowrate smoothly. There are three kinds of index to evaluate the resilience of a network at present. Saboo et al. [9] proposed the resilience index (RI) to characterize the largest total uncertainty which a HEN can tolerate while remaining feasible. Swany and Grossmann [10] introduced a flexibility index (FI), which defines the maximum parameter range that can be achieved for feasible steady-state operation. Ierapetritou [11] presented a new method, which is called as feasible convex hull ratio (FCHR) to evaluate the resilience, which is based on the interconnected feasible region and its size.

The resilience studies of networks mainly concentrate on the HEN. Colberg and Morari [12] incorporated the resilience concept within a synthesis approach for flexible HEN, proposing a “flexibility index target”. Cerda et al. [13] proposed a different synthesis methodology for obtaining flexible HEN, introducing the concept of “transient” and “permanent” streams in order to describe variations in inlet temperatures and flow rates. Floudas and Grossmann [14], [15] proposed a sequential HEN synthesis method that combines the multiperiod mixed-integer linear programming (MILP) transshipment model with the active set strategy to guarantee the desired HEN flexibility. Li [16] presented a method using multiple linear equations to design the resilience of HEN.

There is little about the resilience or flexibility analysis and design of water networks available. Wang [17] proposed a method of water network design under uncertain parameters. It involves two methods: fixed resilience design and optimal flexibility design. The author also presented the principle of selecting prime modulation design parameters according to sensitivity analysis theory. Du [18] analyzed the resilience of water network and the design of water network involving resilience by calculating the resilience index and the FCHR. Tan et al. [19] use the Monte Carlo simulation to assess the sensitivity of water networks to noisy mass loads. The method can select the most robust network configuration from three alternation designs. Lama et al. [20] introduced a preliminary controllability and resiliency analysis for a whitewater network. The proposed approach is available to analyze the real dynamics of the process.

However, resilience or flexibility studies on resilience of water network analysis and design are still at theoretical phrase presently. The main reasons that prevent the practical application of resilience research are as follows. First, the presented approaches or models are too complicated, which are hard to apply in complex system. Second, nearly all of related issues are highly nonlinear, there are not effective resolving techniques.

Hence, this paper presents another more simple approach to quantify the resilience of a water network (WN). This method is straightforward and easily calculated.

Section snippets

The tolerance amount of a water unit

For an existing water network, if the inlet and outlet concentrations are less than their limiting concentrations, water using processes will meet the operation requirements. Therefore, to estimate the flexibility of an existing water network, we only need to consider the relative size between limiting inlet and outlet concentrations and the actual concentrations.

If the outlet concentration of a water unit is less than the limiting outlet concentration, then the operation is quite normal when

The tolerance amount of a water network

A water network consists of a number of water units. The outlet concentrations of a unit, which is decided by the outlet concentrations of the upstream units and water using condition of itself, must be less than the limiting outlet concentrations.

If the outlet concentrations of each unit reach the limiting outlet concentration, which means that there is no Ta in this water network at such operating conditions, the mass load in the water network is the limiting mass load. The network has Ta

Example 1

A water network of a chemical plant is shown in Fig. 3, which has three units. The data for this system are shown in Table 1. Using the data in Table 1, the actual outlet concentration of each unit can be calculated. Then based on Eq. (1), the MTaWU can be determined, which is $M_{i}^{\max}$ shown in Table 2. The detailed calculation is as follows: $\begin{array}{l} M_{1}^{\max} = F_{1} \times (C_{1, out}^{\max} - C_{1, out}) = 60 \times (120 - 105) \times 10^{- 3} = 0.9 \\ M_{2}^{\max} = F_{2} \times (C_{2, out}^{\max} - C_{2, out}) = (48 + 12) \times (130 - 113) \times 10^{- 3} = 1.02 \\ M_{3}^{\max} = F_{3} \times (C_{3, out}^{\max} - C_{3, out}) = (12 + 4 + 24) \times (140 - 114) \times 10^{- 3} = \end{array}$

Conclusions

Through defining Ta, the problem of evaluating the resilience of a water network is transformed into that of calculating the TaWN. This methodology is simple and straightforward. Example in the paper shows the feasibility and practicability of the method when evaluating the resilience of water networks.

Although the approach is used in single contaminant systems, it can be applied to multiple contaminants systems, if a key contaminant is chosen. Meanwhile, this method can only be used to

Acknowledgement

Financial support provided by the National Natural Science Foundation of China under Grant no. 20436040 is gratefully acknowledged.

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Studies on resilience of water networks

Abstract

Introduction

Section snippets

The tolerance amount of a water unit

The tolerance amount of a water network

Example 1

Conclusions

Acknowledgement

Chem. Eng. Sci.

J. Clean. Prod.

Comput. Chem. Eng.

Trans. Inst. Chem. Eng. A

Comput. Chem. Eng.

Comput. Chem. Eng.

Comput. Chem. Eng.

Comput. Chem. Eng.

Comput. Chem. Eng.

Resour. Conserv. Recycl.