## 1 Introduction  
Power plants intake massive amounts of water for their cooling systems. Typically, nuclear and coal-combustion power plants use cooling water at rates of 100-220 m\({}^{3}\) hr\({}^{-1}\) to generate 1 MW of electricity [1; 2; 3]. Since nuclear power plants typically produce 1000 MW of electricity [4], such plants are frequently built on coasts, where 28-60 m\({}^{3}\) sec\({}^{-1}\) of water can be easily supplied for their cooling systems. The raw seawater drawn into the cooling systems also contains a variety of organisms. These sea organisms often grow within the inner surface of cooling pipe, potentially leading to issues such as increased pumping-load, corrosion, and reduced heat-exchange efficiency [5; 6]. For example, more than 5% of condenser efficiency could be lost owing to bio-growth (or biofouling) within a cooling pipe [7]. The economic impact of biofouling on a 550 MW power plant is estimated to be $0.93 million annually [8]. Over other biocidal options, the effectiveness and low cost of chlorination make it the preferred method to prevent sea-organism growth and biofouling. Chlorination is generally conducted by directly injecting chlorine into pipes or by electrochemically producing chlorine using seawater in water-intake pipes. The latter is called in-situ electro-chlorination, and a few of its advantages include the reduced production of harmful byproducts and the elimination of chlorine storage needs [9]. Furthermore, if electrodes are prepared with an optimized shape and installed at appropriate intervals near the inner surface of water-intake pipes, in-situ electro-chlorination can be controlled to maintain a relatively high concentration of chlorine specifically near the pipe wall, where biofouling occurs. However, due to the difficulty in optimizing its operational conditions, few attempts have been made to apply in-situ electro-chlorination in practice [10]. The chlorine concentration is a main factor to be controlled in chlorination systems. Chlorine levels should be controlled considering the following: First, a minimum residual chlorine concentration should be determined and maintained to ensure effective anti- biofouling. It is known that chlorine concentration should be maintained above 0.05 mg L\({}^{-1}\) in cooling water before it is drawn into the system; otherwise, biofouling can occur [11]. This in turn increases the minimum effective chlorine dosage [12]. However, the residual chlorine concentrations of used cooling water discharged to the sea should remain under a certain level to protect the costal environment. According to the European Integrated Pollution Prevention and Control [13], European countries require the total residual oxidants in used cooling water not to exceed 0.2 mg L\({}^{-1}\) (daily average). Typically, the chlorine concentrations of cooling water employed by a power plant and the residual chlorine concentration of used water are maintained at 0.5-1.5 mg L\({}^{-1}\) and 0.05-0.2 mg L\({}^{-1}\), respectively [6; 11; 12; 14]. However, it can be challenging to maintain chlorine concentration at these levels due to variations in water quality and flow rate of cooling water [11; 12]. Therefore, models have been applied for predicting chlorine concentrations and determining the levels needed to prevent biofouling in pipes. Several models to predict chlorine decay in bulk water have been suggested and evaluated. First-order kinetics is often applied for modeling chlorine decay in water. Since actual chlorine decay in real water is impacted by many reactants, first-order equations have been accurate enough to properly describe this process [15; 16; 17; 18]. Some researchers deal with chlorine decay in two phases: a rapid-decaying phase and a slow-decaying phase. This approach has been successfully applied to predict decay in real water with acceptable levels of error and complexity [17; 19; 20; 21; 22]. Computational fluid dynamics (CFD) has developed remarkably over the past five decades.