An Emergency Operation Model in Upstream Pools of the Accident Pool of the Middle Route of South-to-North Water Diversion Project

Considering the potential emergency accident in the Middle Route of South-to-North Water Diversion Project (MRP), previous studies required upstream pools of accident pool where accident occurs to maintain constant downstream level in the final state of emergency operation, which could cause large amount of abandoned water. In order to save water resources, an emergency operation model in upstream pools of the accident pool of the MRP was built, which allows downstream levels to rise by a certain amount in the final state, and can minimize the total abandoned water through allocating volumes in the upstream pools. This model could play an important role to determine reasonable emergency operation measures in the upstream pools.


Introduction
Water shortage has become a problem of global concern that poses a substantial threat to food security, economic development and ecological health [1]. A promising way to solve the problem of uneven spatial and temporal distribution of water resources is the construction of water diversion projects [2]. Up to now, over 350 longdistance water diversion projects have been constructed in 39 countries worldwide [3]. In China, the most wellknown water diversion project is the Middle Route of South-to-North Water Diversion Project (MRP), which aims to divert water from Danjiangkou Reservoir in southern China to the arid northern China, including Henan, Hebei, Tianjin and Beijing [4].
The MRP passes through a lot of roads, bridges and is along with many chemical factories, making emergency accidents potential to occur, such as sudden water pollution accidents, which may endanger water supply safety and cause economic losses [5]. If serious emergency accident occurs, the main canal can be divided into the accident pool where the accident occurs, and pools upstream and downstream of the accident pool. The two check gates at both ends of the accident pool should be closed rapidly, the discharge of the diversion gates of upstream pools should remain unchanged, and the water supply of downstream pools should be maintained for a period of time using their own water volume [6]. Emergency operation of upstream pools is very difficult, and previous studies [7,8] required that the upstream pools should be operated according to constant downstream level [9], which could make surplus volume abandoned and cause huge economic losses.
Our team briefly introduced an emergency operation model of upstream pools in a published paper [10], which allows downstream levels to rise by a certain amount in the final state to minimize the total abandoned water by allocating volumes in the upstream pools. The objective of this paper was to present this model in detail, which could help readers understand more clearly.

Study area
The MRP ( Figure 1) is one of the largest inter-basin water diversion projects ever constructed in the world, and it plays a strategic role in solving the problem of uneven spatial and temporal distribution of water resources in China. The main canal is 1432 km long, the total amount of water to be diverted is 9.5 billion m 3 per year, and the design discharge at the canal head is 350 m³/s. There are more than 1800 hydraulic structures along the canal, including 64 check gates that divide the canal into 63 cascade pools, 97 diversion gates that transfer water to cities along the canal, and 54 drainage gates that abandon water in the case of an emergency.

Emergency operation model
If serious emergency accident (e.g., sudden water pollution accidents) occurs, the two check gates (K and K+1) of the accident pool need to be closed quickly ( Figure 2). After check gate K is closed, the diversion gates in the upstream pools still need to maintain the initial outflows, while upstream check gates need to be closed to the final discharge. When emergency operation is taken, the discharge of upstream pools would decrease, if maintaining constant downstream water levels in upstream pools in the final state, the volume in the upstream pools should be reduced and surplus volume can only be abandoned. This model allows downstream levels to rise by a certain amount in the final state of emergency operation, and can minimize the total abandoned water through allocating volumes in the upstream pools.

Objective
The objective is to minimize the total abandoned water during emergency operation process: Where W is the total abandoned water; W i is the i th pool's abandoned water.

Constraint conditions
The constraint conditions are as follows: 1) Rises of upstream water levels of check gates in the final state are not over the maximum values:

Solution
In the initial state, the discharges and upstream water levels of check gates, and discharges of diversion gates are known. In the final state, discharges of diversion gates in the upstream pools are unchanged, and discharges of check gates can easily be determined. Besides, the maximum rise of upstream water levels of check gates in the final state are pre-defined. Model solution steps are as follows: Step 1: the initial volume 0,i V and final maximum volume max,i V (i=1, 2… K-1) in the upstream pools were calculated using the hydraulic model we developed [10]; Step 2: the differential between the initial volume and final maximum volume in each pool was calculated: If 0 i V Δ > , which indicates that the i th pool needs to abandon water out of itself or drain water into the downstream pool; If 0 i V Δ = , which indicates that the i th pool doesn't need to abandon water nor need to receive drainage from the upstream pool; 2 If 0 i V Δ < , which indicates that the i th pool can receive drainage from the upstream pool.
Step 3: the spatial relation about weather each pool need to abandon water or receive drainage is analyzed: If each pool satisfies  [12] would be used to optimize volumes allocation in upstream pools.
The decomposition-coordination model can be divided into three layers: The first layer: dividing the upstream pools into subsections: If the first pool satisfies 0

Allocation rules
Water can only be drained out of itself or flow into the downstream pool, therefore the following rules are determined: 1) Rules of abandoning water out of the pool: if there is any drainage gate in the pool, water will be drained out through the drainage gate; otherwise water will be drained into the downstream pool and then abandoned out through the drainage gate in the downstream pool.
2) Rules of draining water into the downstream pool: if a pool needs to drain water into the downstream pool, then water can be drained according to the initial discharge of the downstream check gate, then the discharge of the check gate should be adjusted to the final value according to emergency operation requirement.
3) Rules of allocating water between the pools: if the surplus water of upstream pools needs to allocate, in order to simplify gate operation process, the downstream pool should receive the maximum amount according to the spatial orders.

Gate operation
Volume allocation between upstream pools can be determined by the above solution process, and the emergency operation measure of check gate K is predetermined, therefore, starting from the K-1 th pool to the first pool, the emergency operation measures of check gate and drainage gate in each pool can be determined step by step.

Conclusions
In order to save water resources, the emergency operation model in upstream pools of the accident pool of the MRP was built, which allows downstream levels to rise by a certain amount in the final state of emergency operation, and can minimize the total abandoned water through allocating volumes in the upstream pools.
Once emergency accident occurs in the MRP, this model would play an important role to determine reasonable emergency operation measures in upstream pools of the accident pool. In the future, the applications of this model and how to recover normal water supply after emergency operation will be deeply researched.