The biochemical oxygen demand has been carefully discussed in this report and how it may increase the rate of pollution when a sewage leak occurs in a river system. With the aid of Microsoft Excel, a simulation of varying states was conducted resulting in achieving data of the modelling of a river system. In this report, individual element was to be simulated as either a plug flow reactor (PFR) or a continuous flow stirred reactor (CFSR). Both systems are thoroughly studied as they are essential elements of the report. There are three changes in the level of BOD which are discussed in detail. Inconclusion, the outfall storage was effective in decreasing the level of BOD to a safe quantity and sustaining the EU limits and the modelling method gave very accurate results with a few limitations that could be further enhanced by studying the required setting (Coursework, 2020).

## INTRODUCTION

The Microsoft Excel software was used to collect data in a spreadsheet which show the variation of changes in the system that may distress the end results. We insert a series of values into the spreadsheet that forecast the end results for a sewage leakage in the river, allowing it to be immensely helpful in reflecting the possibilities of preventing damage. This procedure also allows to supervise the quality of the flow of water in the river allowing us to consider how the flow may be disturbed by sewage. A layout of the system has been provided which is to be used to build on this report;\n

Figure 1, represents a schematic diagram of the River and Lake system (WormLeaton, 2020)\nThis scheme shows that sewage outfall takes place in the river between Reach 1 and Reach 2 which then leads to polluting the river starting at Lake A and flowing through to Reach 3 and 4, reaching Lake B, joining Reach 5 and finally entering Wormville.

## AIMS AND OBJECTIVE

The main aim of this report is to investigate the significance of sewage outfall from any chemicals entering the river system in figure 1. The biochemical level of oxygen is considered carefully with BOD in the river system and an analysis is put in place to take prevent further serious damages caused to Wormville. The following objectives are closely considered, such as study the two types of reactor models, the plug flow reactor (PFR) and continuous flow stirred reactor (CFSR) and investigate the effect on the environment due to BOD. Be able to use Microsoft excel to do calculations of the level of BOD in Wormville and examine the effects of the sewage outfall.

BIOCHEMICAL OXYGEN DENAMD (BOD)

This measures the amount of oxygen (in mg/L) that tends to oxidise or decompose organic material by the bacteria from water, BOD is an efficient way of testing any water system to ensure safety from any contamination. Pollution is then produced via the proteins, carbohydrates, and other organic materials that are then transferred and dissolved into water due to the breakdown of materials by bacteria to gain energy. Anaerobic oxidisation occurs when there is no oxygen available in the water, this leads to forming toxic chemicals that affect the aquatic life and the ecosystem. The Biochemical oxygen demand, BOD number is used to measure the quantity of the wellbeing of the aquatic system. A lower BOD value suggests a lower amount of oxygen required to oxidise organic material, therefore leading to less anaerobic oxidation and a healthier system (Clifford C. Hach, 1997).

## CALCULATION OF BOD

There are two general form of calculating the BOD method, the manometric method and the dilution method. The dilution method consists of taking a sample into tubes and filling it with diluted water but adding the sample into the tube in a known and constant increments. The diluted water involves a certain amount of oxygen, nutrients and a pH buffer which is dissolved, being vacuum-packed for a standard of 5 days at 20^°. After this time period, the amount of remaining oxygen is obtained, BOD is calculated using the relationship between the amount of oxygen consumed and the volume of the sample used. A nitrification inhibiter is added to only carbonaceous BOD is measured. To calculate the Bod at the end of day 5 the following equation may be used:

BOD end of day 5=(Initial Dissolved O_2-Final Dissolved O_2)/( Dilution Factor)

Equation 1 represents a formula used to calculate the difference between initial dissolved oxygen and end of day 5, final dissolved oxygen using a diluted factor.

During the manometric process, the oxygen intake is directly measured as the test is conducted in the samples regular state. The state or performance of the sample will be very similar to that of the actual river consisting of the sewage. The difference in the pressure due to air is measured using the manometer hence resulting in a relationship between the amount of oxygen intake at any desired time. The diluted method is more likely used as it is approved by the U.S Environmental Protection Agency (Clifford C. Hach, 1997).

## EFFECT OF BOD

The level of BOD is usually constant unless an unusual increase in the number of bacteria present in the water which may generate an increase in the biochemical oxygen demand. This could be caused by new industries with new chemicals also infecting the river system with their sewage, creating more pollutants due to new fertilisers being used. Global warming can also increase the level of BOD as the temperature increases leads to warmer water, hence affecting rate of oxygen being dissolved. Thus, affecting the aquatic life enormously but increasing the rate of death of the life under water and distressing the level of BOD. In this report, temperature and the pH value of the water have not been considered and therefore are not calculated for. The importance of a balanced oxygen level is necessary, especially for living organisms.

## REACTOR MODEL

Surface water river systems can be examined using the modelling of simple finite volume reactor tank, where an estimated procedure will take place and as a result, we can achieve a few substantial characteristics of water. As part of this report, Continuous Flow Stirred Reactors (CFSR) and Plug Flow reactors (PFR) are discussed.

## THE CONTINUOUS FLOW STIRRED REACTORS (CFSR)

All content in a CFSR is mixed in a uniform manner throughout the while mixture, a concentration gradient will not exist. The reactor will have inlet and outlet with different concentrations but to ensure uniform concentration an external step is required using the following equation 2: \nQC_i-QC=V dC/dt

Mass inflow rate-Mass outflow rate-Reactive product mass rate=Rate of change of the mass stored

Equation 2, Mass Balance Equation\n Q is the volumetric flow of water (m^3/s)

C_iis the concentration of water at the inlet (mg/l)

V is the volume if water in tank 〖(m〗^3)

dC/dt Is the rate of change of concentration in the tank with time (mg/ls)\nWhen using equation 2, temperature and density of fluid is to be presumed to be unchanging due to the uniform mixing in the tank. The following equation 3 is used to calculate the concentration in the tank:

C=C_0 exp(-t/∅)+C_i [1-exp(-t/∅)]

Equation 3, Concentration equation

∅ is the detention time (delayed time) (sec)\n\nThe following equation 4 represents an alternative equation 2 considering the first order decay:

QC_i-QC+kV=V dC/dt

Equation 4, mass balance equation considering first order decay

K is the rate constant of first order of decay \nUsing equations 2 to 4 we then create a simple equation to find the concentration of the outflow of fluid shown below:\nC=C_0 exp(-((1+k∅))/∅ t)+C_i/((1+k∅))[1-exp(-((1+k∅))/∅ t)]

Equation 5, concentration equation for the outflow\nThe Continuous Flow Stirred Reactor method is to be most reliable to model the lake as it is more or less very similar to the actual rivers input and output. \n

Figure 2 represents a CFSR design used in lecture notes (QmPlus, 2020)\nA Continuous Flow Stirred Reactor can also be found in series, the main difference between the two is the number of tanks which are of equal size. Being able to distribute CFSR into many tanks allows us to gain more detailed examinations and how pollution may affect level of BOD.

C_o=C_i/((1+τk)^n )

Equation 6 represents the concentration of the outflow of CFRS in series

τ is the rate of volume of tank against the volume flow rate\n THE PLUG FLOW REACTOR

The plug flow reactor is also known as the tubular reactor that consists of a hollow vertical thin tube where one end has inflow and the other end has outflow. The fluid is not completely mixed throughout the tube as due to the properties of the tube being thin and long, hence there is a vertical gradient present. The fluid is therefore not dependable and steady throughout the reactor. The constant properties in a CFSR are no longer constant in the PRF rather vary within the concentration gradient in the horizontal direction. The following equation is used to calculate the mass balance of a PFR: \nQC_x-Q(C_x+δC/δx ∆x)+r∆V=δC/δx ∆V

Equation 7, Mass Balance equation for a PFR\n C_x is the concentration of water at a distance of x (mg/l)

x is a specified distance from the tank (m)

r is the rate of change of concentration in the tank (mg/l)\nIn this case as first order decay is considered the following equation is formed:\nδC/δt+Q/A δC/δx=-kC

Equation 8, Considers first order of decay in the mass balance equation\nIn a PFR we also have to consider the concentration as we have mentioned that the concentration at inflow is different to the outflow therefore equation 9 is formed:\nC_out=C_i exp(-k∅)

Equation 9, represents the concentration of the outflow\nThe PFR is a very simple assumption of a model, this reduces the precision of the model. It is less realistic and therefore probably cannot be used to assume what the actual river geometry will be like. There will be a time delay in this process (detention) which is not being considered in this case where the volume of pollutant decomposed with the time consumed in the reactor is considered. This can be calculated by diving the volume of the reactor by the volume of the flow rate.

Figure 3 represents a PFR design used in the lecture notes (QmPlus, 2020)

## PROCEDURE

Figure 4 represents a modified version of the schematic diagram used in this report (WormLeaton, 2020).\nA developed schematic diagram is presented in figure 4 which is used in this analysis. In figures 1 and 4 there are two main junctions one from reach 1 to the sewage outfall and second from reach 3 to Tributary. The reaches represent the rivers as models in a 1st Order Plug Flow Reactors. The detention time (delay) in the reaches can be calculated using the following equation:

φ=AL/60Q

Equation 9 represents equation used to calculate the detention time between the reach.

L is the length (m)

A is the Cross-Sectional Area of the reactor (〖(m〗^2)

φ is the detention time (sec)

The detention time calculated using equation 9 is then substituted into equation 8 to calculate the overall concentration of the outflow.

At the junctions we can use a simplified equation to calculate the mass balance:\nQ_1 C_1+Q_2 C_2= C_o (Q_1+Q_2)

Equation 10 represents a combined mass balance

SCENARIO 1

This scenario is presented in figure 1, consists of a river system which uses the reactor modelling stated in this report. It involves of four reaches, one sewage plant connected to each individual reach. Lake A is situated after reach 2, Tributary situated after reach 3 and lastly the Town Wormville after the end of reach 4. There has been an accidental contamination at the lake. This leads to an increased level of BOD in the water, the maximum concentration of BOD is about 25g〖/m〗^3. The simulation carried out is used to test the effect of the level of BOD downstream and the lake which was the means of a continuous flow stirred reactor, while keeping close focus on the inflow into Wormville. Plug flow reactors were then made of the sewage outfall, tributary and the reaches 1-4.

Figure 5 represents a graph of the time variation of Sewage Outfall Spillage in the town with time increments of 15 minutes used in the model (WormLeaton, 2020).

SCENARIO 2

Figure 4 is used to present scenario 2, the only difference between scenario 1 and 2 is the addition of an outfall storage situated after reach 1 and connecting to reach 2. The first scenario was effective in being able to demonstrate that there is a significant increase in the concentration of BOD, however, an additional component of sewage outfall could reduce the amount of pollutants entering the river system. This lessened the undesirable impact from chemicals due to the delayed entrance of the sewage into the system.

## RESULTS

In this report the Plug Flow Reactor was used to achieve results for this specific modelling, this was due to irregular quality of water in the river. On the other hand, if it was lake water which had little more stability then the continuous flow stirred reactor would have been a better choice. To carry out further calculations, it was assumed that uniform mixing takes place throughout the mixture and therefore equation 10 was rearranged to form:\nQ_1 C_1+Q_2 C_2= C_in (Q_1+Q_2 ) Rearrange,\nC_in=(Q_1 C_1+Q_2 C_2)/(Q_1+Q_2 )

As the model is using PFR, equation 9 is used to calculate the concentration for all four rivers. \nAfter the formation of the spreadsheet using the Microsoft Excel software which can be found in the appendix of this report, a graph was created with time increasing in increments of 15 minutes against the concentration of Biochemical Oxygen Demand. The following graph represents the concentration with increasing time at the Town Wormville with respect to the three given periods without the outfall storage:\n

Graph 1 represents a graph created using table 1 to 3 from the appendix, relating the BOD concentration at the inflow against time for a model without the outfall storage.

The following graph shows the concentration with increasing time at the Town Wormville with respect to the three given periods including the outfall storage:

Graph 2 represents a graph created using table 4 to 7 from the appendix, relating the BOD concentration at the inflow against time for a model with the outfall storage. The following graph shows the percentage differemce of the level of BOD of Wormville with respect to the percentage change in decay:

Graph 3 represents a graph created using table 7 from the appendix, relating the percentage difference of BOD level against percentage change in decay.

## DISCUSSION

Finite volume reactors were established to be successful in generating approximate characterisation of water. However, there were limitations to overcome when attaining results due to restrictions of the tanks, this could affect the accuracy of the solutions. One of the greatest limitations were that the average values were used hence, forfeiting the precision of the results. A greater constraint causing low efficiency of the experiment was due to relating CFRS norms to the PFR, this is a major issue. PFR does not have the ability to have a fully mixed uniform mixture whereas, the CFSR does, and in this case this assumption was put in place. PFR has a concentration gradient throughout the water which in this case was not considered, although this would be most likely true and exact to compare with the real reactor.

Graph 1 shows that the maximum concentration of the biochemical oxygen demand was achieved just after the first hour and then starts to slowly decease. The maximum concentration of BOD was reached around 6.64mg/L at about 532 minutes. This result is obtained without the use of an external outfall storage. The maximum concentration found in this investigation was slightly above 6mg/L which is the acceptable limit set by EU. On the other hand, this led to carrying out an investigation if the use of a outfall storage will reduce this maximum concentration value. In graph 2, it can be seen the maximum concentration of the biochemical oxygen demand is about 5.98mg/L which obeys the limit set by EU, however, it took about 693 minutes to reach this point which is more than that if the storage was not used.

To enable further accuracy of the experiment, the first order decay should have been considered as this is a complex process which examinants pollutant elimination. It acts on the surface of the water rather than just the outlet. \nThis particular experiment was conducted on the 13th of December at 9:00am, the weather also affects the results and as it is also early morning the time will also have an effect. The concentration of BOD is to be higher in warmer temperatures but in December it is cold hence lower concentration of BOD. At a cooler temperature, the particles present in the water would have less energy therefore less reaction, consequently for organic materials there will be less oxidisation by the bacteria present in the water. Like any member of the unicellular micro-organism, bacterium work best at its optimal temperature where they reproduce and grow rapidly.

CONCLUSION

In conclusion, the demonstration of a reactor of a river system is a brilliant method used to comprehend the concept for a simulation of an outsized platform. From this investigation it can be seen, as the contamination of the water rises the level of biochemical oxygen demand also rises as the concentration of the pollutant increases. Microsoft Excel was used to create a scheme to resolve this concern, to make the process time efficient. An investigation was carried out using a sewage outfall storage and one without. It can be almost guaranteed that with the aid of an outfall storage the level of BOD can be controlled and by increase the time period of the sewage as it travels through the process, it would have a greater chance of decaying. To ensure a higher accuracy of results, in the future a smaller time increment could be used rather than 15 minutes.