Final_Report_Draft_UPA_Coagulant (3).ipynb

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        "# Unit Processes Analysis: Coagulant, Fall 2019\n",
        "#### Ada Lian, Sarah Paquin\n",
        "#### December 13, 2019\n",
        "\n",
        "## Abstract\n",
        "The Fall 2019 Unit Processes Analysis Coagulant (UPAC) team’s objective is to reduce capital and operating costs and improve particle removal efficiency for the AguaClara water treatment process, specifically by analyzing the response of the system to varying coagulant dosage. To analyze the system response, we will run a series of trials on a treatment plant sedimentation model, varying the coagulant dosage and recording observations regarding the effluent turbidity, floc formation, and floc blanket formation. Through this experiment, the team will be able to establish a minimum coagulant dosage, which could lower operating costs, and to learn valuable information about the interactions between coagulant and the primary particles of the influent water at high coagulant dosages.\n",
        "\n",
        "\n",
        "## Introduction\n",
        "AguaClara’s mission is to develop technologies that enable communities to have access to safe drinking water and sustainable wastewater treatment at a low cost and with minimal maintenance. An important component of AguaClara’s water treatment process is the addition of coagulant to the water. Coagulant is added to influent water to create flocs, which are essentially clumps of primary particles, such as clays and bacteria, which ultimately separate from the water via gravity. Coagulant works by sticking to the particles, and as the particles move around, more and more particles become stuck together via the coagulant. A higher coagulant dosage than necessary can quickly increase operating costs, while not necessarily significantly improving floc formation and the ultimate purity of the water. Additionally, the interaction between coagulant and the primary particles is not completely understood, which could potentially cause problems when trying to modify the water treatment process in the future, thus affecting AguaClara’s ability to develop low cost and high performance technologies.\n",
        "\n",
        "The formation of flocs through coagulation and flocculation is key to the sedimentation process, by which the flocs are actually separated from the water. Flocculation occurs following the addition of coagulant, agitating the water to promote collisions between the particles, increasing the number and size of the flocs. During sedimentation, the water is pushed upward through a floc blanket and sedimentation plates, which promote the settling of flocs. Ultimately, the settling of flocs is the main goal of the coagulation, flocculation, and sedimentation processes. It is this component which affects the turbidity of the effluent water following the entire process, so through our experiment we hope to observe how varying the coagulant dosage affects the settling of flocs during sedimentation.\n",
        "\n",
        "One of the UPAC team’s main goals is to determine a minimum necessary coagulant dosage, which would reduce operating costs and lessen the financial burden of the communities that AguaClara’s water treatment plants serve. The other main goal of the UPC team, to learn more about the interaction between the coagulant and primary particles of the influent water at high coagulant dosages, may be useful for future design projects, as this will provide a more thorough understanding of the factors that influence flocculation and sedimentation processes, and may facilitate the development of high performance, low cost, and minimal maintenance systems. To accomplish these goals, we will run ten trials varying the coagulant by a factor of 2 and observe the effluent turbidity, looking for a target turbidity of 3 NTU, and the formation of flocs and the floc blanket. It is hypothesized that coagulant nanoparticles are more likely to stick to each other than to primary particles. This means that if the coagulant dosage is so high that the primary particles are more than half covered in coagulant, particle collisions are less likely to result in particles sticking together; the nature of the hypothesized coagulant-coagulant interaction could cause coagulant to break off from one particle and stick to another particle’s coagulant during collision, allowing the particles to separate, unattached. If this hypothesis is accurate, we would expect to see minimal floc formation at high dosages of coagulant. We expect that the results and insight gained from our experiment could positively impact AguaClara’s ability to develop high performance, efficient, and low cost water treatment technology and processes.\n",
        "\n",
        "\n",
        "\n",
        "## Literature Review and Previous Work\n",
        "\n",
        "Untreated water contains inorganic and organic particles that pose health risks and are difficult to remove. Therefore, coagulation and flocculation are important steps of the water treatment process because they make the removal of these particles easier. AguaClara plants use polyaluminium chloride (PACl), which is a coagulant that precipitates in water to create sticky nanoparticles [(Gebbie, 2006)](http://wioa.org.au/conference_papers/06_qld/documents/PeterGebbie.pdf). The fluid deformation caused by the flocculator allows the particles and coagulant to mix and collide, this creates flocs. Flocs are particle aggregations that are larger and heavier and are therefore easier to settle to at the bottom of the sedimentation tank to create a floc blanket [(Weber-Shirk et al., 2018)](https://aguaclara.github.io/Textbook/Flocculation/Floc_Intro.html). Floc blankets are a fluidized bed of solids that allows for even more collisions between particles in the blanket and the flocs from the flocculator. It is important for the floc blanket to be stable and uniformed in order to efficiently remove as many particles from the water before it flows through the filtration system [(Conneely & Sen, 2018)](https://github.com/AguaClara/HRS-Flow-Recycle/blob/master/HRS-Flow-Recycle-Final-Report.md). \n",
        "\n",
        "Previous teams have researched different variables to optimize the performance of the floc blanket. For example, the High Rate Sedimentation: Flow Recycle team noticed that the floc blanket is denser at the top of the tank due to higher upflow velocities of water. They hypothesized that fabricating a recycle line on the tank would improve the longevity of the floc blanket and make the blanket more stable [(Conneely & Sen, 2018)](https://github.com/AguaClara/HRS-Flow-Recycle/blob/master/HRS-Flow-Recycle-Final-Report.md). Similarly, the High Rate Sedimentation: Bottom Geometry team observed that the regular flat bottom shape of the tank causes floc gelling, where a dense layer of flocs is formed that cannot be broken up. The team therefore designed different inserts that prevent flocs from stacking on top of each other [(Benitez & Lee, 2019)](https://github.com/AguaClara/HRS-Bot-Geo/blob/master/2019%20Spring/Reports/HRSBotGeo2FinalReportDraft.md). \n",
        "\n",
        "William H. Pennock conducted similar research to the UPAC team, which varies the coagulant dosages. Pennock ranged the coagulant dosage from 0.05 to 98 mg/L as Al. Figure 1 reveals that at a certain point of the experiment the performance of the floc blanket decreases, as shown by the increase in effluent turbidity as the coagulant dosage passes a certain point. \n",
        "\n",
        "![Graph](https://raw.githubusercontent.com/AguaClara/Floc_coagulant/master/Images/Coagulant-Turbidity%20Graph%20-%20Pennock.png)\n",
        "Figure 1: Coagulant dose effect on effluent turbidity [(Pennock et al., 2018)](https://www.researchgate.net/publication/326076774_A_Hydrodynamic_and_Surface_Coverage_Model_Capable_of_Predicting_Settled_Effluent_Turbidity_Subsequent_to_Hydraulic_Flocculation). \n",
        "\n",
        "This is because although it might seem like more coagulant will allow bigger and more flocs, it is hypothesized that with too much coagulant nanoparticles, the nanoparticles are more prone to attach to each other rather than to the inorganic and organic particles. The UPAC team will determine the range of coagulant dosages that would minimize the effluent turbidity while preventing floc blanket decay and coagulant wastage. \n",
        "\n",
        "## Methods\n",
        "\n",
        "Before the team is able to run experiments, the team first have to determine the specific parameters of the experimental apparatus in order to vary the coagulant dosage. The team decided to vary the coagulant dosage from 0.14 mg/L to 64 mg/L using a geometric progression with a factor of 2. The team decided on this range based on the other Unit Processes Analysis teams using a constant concentration of 4.5 mg/L of coagulant. Table 1 shows the detailed values of the coagulant pump flow rate and revolutions per second needed to achieve the coagulant values. The code used to calculate these values is found in the Manual. \n",
        "\n",
        "Table 1: The required flow rates and rpm of the coagulant pump to achieve desired coagulant dosage \n",
        "\n",
        "  | Coagulant Dosage (mg/L)| Flow rate (mL/s) | Rpm (rev per min) |\n",
        "  |:----------------------:|:---------------: |:-----------------:|\n",
        "  |   0.140625             | 0.0008383        |   0.33792094      |\n",
        "  |   0.27759326           | 0.00165481       |   0.66705475      |\n",
        "  |   0.54796813           | 0.00326658       |  1.31676376       | \n",
        "  |   1.08168718           | 0.00644822       |  2.59928708       | \n",
        "  |   2.13524672           | 0.01272877       |  5.13098364       |\n",
        "  |   4.21496959           | 0.02512655       |  10.12854384      | \n",
        "  |   8.32033529           | 0.04959972       |   19.99371027     |\n",
        "  |16.42431289             |0.09790967        |39.46751443        |\n",
        "  |32.42153643             |0.19327335        |77.90873603        |\n",
        "  |64                      |0.38152093        |153.79157357       |\n",
        "\n",
        "\n",
        "\n",
        "## Experimental Apparatus\n",
        "Figure 2 shows the current experimental setup the team is using. The setup is similar to the previous subteam's, however the UPAC team does not have an effluent pump due to the limited amount of pumps and the team did not find it necessary. \n",
        "\n",
        "![Experimental Apparatus](https://raw.githubusercontent.com/AguaClara/Floc_coagulant/master/Images/Experimental%20Apparatus%20.png)\n",
        "Figure 2: Current experimental setup \n",
        "\n",
        "Table 2: Equipment and Function \n",
        "\n",
        "|Equipment|Function|\n",
        "|:---|:---|\n",
        "|Water Pump|Control the flow rate of water entering in order to maintain a constant upflow velocity|\n",
        "|Pressure Attenuator| Maintains a constant influent flow|\n",
        "|Clay Stock Tank|Contains known concentration of well-mixed clay|\n",
        "|Clay Pump|Pumps in constant rate of clay to maintain influent turbidity of 100 NTU|\n",
        "|Influent Turbidimeter|Measures turbidity of water and clay|\n",
        "|PaCl Stock Tank|Contains a concentration of 5 mL PaCl/1 L distilled water|\n",
        "|Coagulant Pump|Varies the flow rate of coagulant entering system to maintain known concentration of PaCl|\n",
        "|Flocculator|Coiled tubing to enduce collisions between clay and coagulant|\n",
        "|Tube Settler|Model of sedimentation tank where the floc blanket is formed|\n",
        "|Effluent Turbidimeter|Measures turbidity of water leaving tube settler|\n",
        "|Waste Pump| Pumps waste from top of the tube settler and floc weir|\n",
        "\n",
        "![Schematic Diagram](https://raw.githubusercontent.com/AguaClara/Floc_Blanket/master/Floc%20Blanket%20Blueprint.JPG)\n",
        "Figure 3: Schematic Diagram of the experimental apparatus. \n",
        "\n",
        "### Procedure\n",
        "\n",
        "Before beginning our trials, we followed the procedure outlined on the [HRS Experimental Setup Procedure page](https://github.com/AguaClara/high_rate_sedimentation/wiki/HRS-Experimental-Setup-Procedures). We then ran 10 trials with our sedimentation model, varying the coagulant dosage by a factor of 2 from 0.14 mg/L to 64 mg/L, with the coagulant pump flow rates set as outlined above. We allowed each trial to run until a steady state had been reached, and then collected data on influent and effluent turbidity through ProCoDa. For the tube settler, we used the bottom geometry developed by the HRS Bottom Geometry team in Spring 2019. Additionally, we used an upflow velocity of 1 mm/s, a 100 NTU clay suspension without humic acid, and a flocculator with roughly a Gt of 37000 and a head loss of 50 cm.\n",
        "\n",
        "## Results and Analysis \n",
        "This semester, the team mainly focused on setting up the experimental apparatus so the team was only able to run trials for four different coagulant dosages. \n",
        "\n",
        "![2.14mg/L](https://raw.githubusercontent.com/AguaClara/Floc_coagulant/master/Images/11-30_2.14.png)\n",
        "\n",
        "Figure 4: Effect of 2.14 mg/L coagulant dosage on effluent turbidity\n",
        "\n",
        "![4.2mg/L](https://raw.githubusercontent.com/AguaClara/Floc_coagulant/master/Images/11-28_4.2%20.png)\n",
        "\n",
        "Figure 5: Effect of 4.2 mg/L coagulant dosage on effluent turbidity\n",
        "\n",
        "![4.5mg/L](https://raw.githubusercontent.com/AguaClara/Floc_coagulant/master/Images/11-26_4.5.png)\n",
        "\n",
        "Figure 6: Effect of 4.5 mg/L coagulant dosage on effluent turbidity\n",
        "\n",
        "![8.2mg/L](https://raw.githubusercontent.com/AguaClara/Floc_coagulant/master/Images/11-29_8.2.png)\n",
        "\n",
        "Figure 7: Effect of 8.2 mg/L coagulant dosage on effluent turbidity\n",
        "\n",
        "As shown in the graphs, there is a lot of fluctuations in the data and there are a lot of instances throughout the trials that the effluent turbidity reads 1100 NTU, which means that the effluent turbidity is too high for the turbidimeter to read. \n",
        "\n",
        "A source of the high turbidity may be the high influent NTU during the beginning of each trial. As shown in Figure 7, there is gelling in the tube settler, which means that the floc blanket is really dense and not uniformed. The team noticed that the influent turbidity was around 700 NTU for about 30 to 40 minutes in the beginning of trials, even though the desired influent turbidity is 100 NTU. The team resolved this issue by modifying the experimental appartus and adding more bypasses so the influent would flow directly to the waste line rather than through the whole system in the beginning of the trials. The bypass to the whole system will be opened when the influent turbidity stablizes to 100 NTU. \n",
        "\n",
        "![Gelling](https://raw.githubusercontent.com/AguaClara/Floc_coagulant/master/Images/11-27-2019%20zoom.png)\n",
        "\n",
        "Figure 8: Tube Settler during 4.2 mg/L coagulant dosage \n",
        "\n",
        "Another issue the team encountered was that the flocs would move pass the floc weir and up the plate settler, this causes the floc blanket to not be at a constant height and be not uniformed. The source of this issue has to be further investigated and solved. \n",
        "\n",
        "![Tube Settler](https://raw.githubusercontent.com/AguaClara/Floc_coagulant/master/Images/11-28-2019.png)\n",
        "\n",
        "Figure 9: Tube Settler during 4.2 mg/L coagulant dosage with modified experimental apparatus \n",
        "\n",
        "Despite the issues caused by the floc gelling, the ranges over which the effluent turbidities were steady were wide enough to determine steady state values for each coagulant dosage, summarized in the following table and graph.\n",
        "\n",
        "Table 3: Steady State Turbidities by Coagulant Dosage\n",
        "\n",
        "|Coagulant Dosage (mg/L)|Effluent Steady State Turbidity (NTU)|\n",
        "|:---|:---|\n",
        "|2.13524672|0.4223231383999997|\n",
        "|4.21496959|0.28004829577142876|\n",
        "|4.5|0.2869809781600001|\n",
        "|8.32033529|0.25635503970666657|\n",
        "\n",
        "![Results Summary](https://raw.githubusercontent.com/AguaClara/Floc_coagulant/master/Images/summary%20graph.png)\n",
        "\n",
        "Figure 10: A summary of the steady state effluent turbidities for each coagulant dosage.\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "# Manual\n",
        "\n",
        "## Fabricating a Tubesettler \n",
        "This semester the team had to fabricate a tube settler and the team used the dimensions shown in Figure 9 to cut the sizes of the tube settler and floc wier. \n",
        "\n",
        "![Tube Settler](https://raw.githubusercontent.com/AguaClara/high_rate_sedimentation/master/Images/Setup/Sedimentation%20Tank%20A.png)\n",
        "\n",
        "Figure 11: Diagram of the specific dimensions of a tube settler\n",
        "###### Bending the tube settler\n",
        "1. Use a marker to mark where the bend of the tube settler should be. \n",
        "2. Using a heat torch, slowly start heating up the marked area. Making sure to keep moving the torch around almost the whole circumference of the tube so the PVC would not burn and would be easier to bend. \n",
        "3. Slowly start to bend the tube little by little as the tube is being heated.\n",
        "\n",
        "###### Making cuts on the PVC tubes where the tube settler and floc weir connects\n",
        "1. Tilt the drill machine in about 50-60 degree angle, depending on how much the tube settler was bent. (The team is using a 48 degree angle). \n",
        "2. Attach a small drill bit to the machine to create a pilot hole in the tube settler. (The purpose of the pilot hole is to help guide the larger drill bits because the larger drill has more torque and is difficult to control the angle). \n",
        "3. Using a hole saw close to the outer diameter of the floc weir, slowly start to drill a hole into the tube settler making sure to use the pilot hole as a guide. \n",
        "4. Using a drill bit that is close to exactly the size of the outer diameter of the floc weir, drill a hole again onto the exact location of where the hole saw drilled. \n",
        "5. Using a small drill bit, make a pilot hole in the floc weir. \n",
        "6. Using a hole saw with the small diameter as the inner diameter of the tube settler, drill a hole into the floc weir using the pilot hole as a guide.\n",
        "\n",
        "###### Attaching the tube settler and floc weir \n",
        "1. Prime the two PVC tubes. \n",
        "2. Use the heavy duty PVC cement either under the fume hood or outdoors to glue the two pieces together. \n",
        "3. Allow at least 12 hours for the cement to dry under the fume hood. \n",
        " \n",
        "##Conclusions\n",
        "As expected, and following the trend observed in the Pennock graph for this dosage range, the steady state effluent turbidity decreased as the coagulant dosage increased. However, the turbidities were much lower than expected for the coagulant dosages, nowhere near the 3 NTU target. It is unclear why this occurred, and more investigation is required.\n",
        "\n",
        "Unfortunately, because of the limited number of coagulant dosages that were tested, the team could neither establish a minimum coagulant dosage nor observe the effects of high coagulant dosage on effluent turbidity and floc formation.\n",
        "\n",
        "This semester, the team made many modifications to simplify the research process for future subteams such as creating a code to calculate the PID values for ProCoDa (refer to the UPA [Floc Blanket](https://github.com/AguaClara/Floc_Blanket) report) and removing one of the effluent pumps. \n",
        "\n",
        "\n",
        "##Future Work\n",
        "\n",
        "## Python Code\n",
        "\n",
        "### Code for Experimental Design\n",
        "\n",
        "```python\n",
        "from aguaclara.core.units import unit_registry as u\n",
        "import aguaclara as ac\n",
        "import numpy as np\n",
        "D = 1 * u.inch\n",
        "A = ac.area_circle(D)\n",
        "v_up = 2 * u.mm/u.s\n",
        "Q_water = (A * v_up).to(u.mL/u.s)\n",
        "print('The water flow rate is',Q_water)\n",
        "\n",
        "# Use an easy-load pump head with tubing codes 14, 16, 17, or 18.\n",
        "# Tubing 14 won't work because the 50 rpm pump can't deliver the required flow\n",
        "# The choice of which tubing to use is somewhat arbitrary. High rpm wears out the tubing faster\n",
        "#. Low rpm likely has bigger pulsations. Your choice! Here I compromise...\n",
        "Water_tubingcode = 17\n",
        "# find the volume per rev for Masterflex L/S pump heads\n",
        "Pump_water_per_rev = ac.vol_per_rev_LS(id_number = Water_tubingcode)\n",
        "print('The volume of water per revolution is',Pump_water_per_rev)\n",
        "Pump_water_rpm = (Q_water/Pump_water_per_rev).to(u.rpm)\n",
        "print('The water pump rpm is',Pump_water_rpm, 'for tubing size', Water_tubingcode)\n",
        "\n",
        "# The coagulant dose range is 0.5 to 8 mg/L of aluminum.\n",
        "# We need the peristaltic pump pulses to be very fast compared with the residence time of the flocculator\n",
        "# Let's assume flocculator residence time 5 minutes (300 seconds)\n",
        "# Set max pulse time to be 10% of flocculator residence time (3 seconds)\n",
        "# Ismatec pump heads have 6 rollers, thus 6 pulses per rev\n",
        "# minimum time for a pump revolution is 18 s\n",
        "Pump_dosing_min_rpm = (1/(5*u.min * 0.1 * 6/u.turn)).to(u.rpm)\n",
        "print('The minimum dosing pump rpm is',Pump_dosing_min_rpm)\n",
        "# The coagulant stock has 70 grams/L of aluminum\n",
        "C_PACl_super_stock = 70 * u.g/u.L\n",
        "# Define a set of coagulant dosages over the target range with a logarithmic scaling\n",
        "# the number of coagulant dosages to test. This doesn't include an extra \"free\" starting value of 0 to create a control that ProCoDA adds automatically\n",
        "Max_x = 10\n",
        "dose_min = 0.140625 * u.mg/u.L\n",
        "dose_max = 64 * u.mg/u.L\n",
        "C_PACl_dose = np.logspace(np.log10(1),np.log10(dose_max/dose_min),Max_x)* dose_min\n",
        "print('The coagulant dosages in the geometric series are',C_PACl_dose.magnitude, C_PACl_dose.units)\n",
        "# Find the multiplication factor (the base) between each dose\n",
        "base = (dose_max/dose_min)**(1/(Max_x-1))\n",
        "print('The base of the geometric series is',base)\n",
        "# The coefficient for our increment function is the minimum dose.\n",
        "\n",
        "# Use the smallest tubing possible so we can use as high a concentration of PACl as possible.\n",
        "# The smallest diameter tubing that we like to work with is 1.52 mm yellow-blue.\n",
        "Pump_coag_per_rev = ac.vol_per_rev_3_stop('yellow-blue')\n",
        "print('The coagulant tubing volume per turn is',Pump_coag_per_rev)\n",
        "Coag_min_Q = (Pump_coag_per_rev*Pump_dosing_min_rpm).to(u.mL/u.s)\n",
        "print('The minimum coagulant flow is',Coag_min_Q)\n",
        "\n",
        "# now we can find the maximum coagulant stock concentration using the min dose and min flow rate\n",
        "C_PACl_stock = ac.floor_step(dose_min*Q_water/Coag_min_Q,10*u.mg/u.L)\n",
        "\n",
        "print('The PACl stock concentration is',C_PACl_stock)\n",
        "\n",
        "# Now find the flow of the PACl stock for these target dosages\n",
        "Q_PACl_stock = Q_water*C_PACl_dose/C_PACl_stock\n",
        "\n",
        "print('The coagulant flow rate is',Q_PACl_stock.magnitude, 'mL/s')\n",
        "\n",
        "Pump_coag_rpm = (Q_PACl_stock/Pump_coag_per_rev).to(u.rpm)\n",
        "print('The pump rpm for the different flow rates are',Pump_coag_rpm.magnitude, Pump_coag_rpm.units)\n",
        "```\n",
        "Output: \n",
        "The water flow rate is 1.013 milliliter / second\n",
        "The volume of water per revolution is 2.8 milliliter / turn\n",
        "The water pump rpm is 21.72 revolutions_per_minute for tubing size 17\n",
        "The minimum dosing pump rpm is 0.3333 revolutions_per_minute\n",
        "The coagulant dosages in the geometric series are [ 0.140625    0.27759326  0.54796813  1.08168718  2.13524672  4.21496959\n",
        "  8.32033529 16.42431289 32.42153643 64.        ] milligram / liter\n",
        "The base of the geometric series is 1.974 dimensionless\n",
        "The coagulant tubing volume per turn is 0.1488 milliliter / rev\n",
        "The minimum coagulant flow is 0.0008269 milliliter / second\n",
        "The PACl stock concentration is 170 milligram / liter\n",
        "The coagulant flow rate is [0.0008383  0.00165481 0.00326658 0.00644822 0.01272877 0.02512655\n",
        " 0.04959972 0.09790967 0.19327335 0.38152093] mL/s\n",
        "The pump rpm for the different flow rates are [  0.33792094   0.66705475   1.31676376   2.59928708   5.13098364\n",
        "  10.12854384  19.99371027  39.46751443  77.90873603 153.79157357] revolutions_per_minute\n",
        "\n",
        "  ### Code for Data Analysis\n",
        "  ```python\n",
        "#importing the data for one coagulant dosage\n",
        "import pandas as pd\n",
        "df= pd.read_csv('https://raw.githubusercontent.com/AguaClara/Floc_coagulant/master/Data/datalog%2011-29-2019.tsv', sep='\\t')\n",
        "\n",
        "#plotting the graph for one coagulant dosage of effluent turbidity against time\n",
        "import matplotlib.pyplot as plt\n",
        "day_frac_new=df.iloc[9200:14000, 0]   #the range determined by the relevant data range\n",
        "timenew=[(i - 0.54110337)*24 for i in day_frac_new]   #correcting for the RUN start time, to create time elapsed\n",
        "eff_turb_new=df.iloc[9200:14000, 3]\n",
        "plt.plot(timenew, eff_turb_new)\n",
        "plt.xlabel(\"Time Elapsed (hours)\")\n",
        "plt.ylabel(\"Effluent Turbidity (NTU)\")\n",
        "\n",
        "#after determining the steady state turbidities for each dosage by taking the average effluent turbidity reading for each over the range after time 0 where the turbidity is fairly steady\n",
        "#plotting the steady state effluent turbidities for each coagulant dosage\n",
        "doses=[2.13524672, 4.21496959, 4.5, 8.32033529]\n",
        "effturbs=[0.4223231383999997, 0.28004829577142876,  0.2869809781600001, 0.25635503970666657]\n",
        "plt.semilogx(doses, effturbs, 'x', markersize=12, color=\"blue\")\n",
        "plt.xlabel(\"Coagulant Dosages (mg/L)\")\n",
        "plt.ylabel(\"Steady State Effluent Turbidity (NTU)\")\n",
        "```\n",
        "\n"
      ]
    }
  ]
}