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SOLAR POWERED HYDRO PUMP FULL REPORT
Below is the full report detailing the design process, the applications, and our final results. This report and project was completed by myself, Grace Whitaker, Jacob Whitehouse, and Sam Vander Missen
EXECUTIVE SUMMARY
We coded a model for the system that accepts parameters for the hydropower system as inputs, such as pump efficiency, pump flow volume, reservoir depth, and turbine efficiency, and calculates and outputs the necessary mass, area, and energy input into the system. The code also outputs the final base efficiency of the system and the time taken to fill and empty the water used for energy generation.
Once the code has calculated and printed these basic outputs, the model code then runs through a second process of optimization. The code runs through all of the possible given part configurations based on the parts available to order. There are a total of about 12 million model possibilities. However, the code searches for specific configurations that have a total energy efficiency above 80%. Then, for each of these configurations, the code outputs the required efficiency for each part in the system, such as turbine efficiency and pipe efficiency. Once we are given these optimal possibilities, our team then selects the option with the highest energy efficiency to cost ratio as the best possible option.
Unfortunately, our model does have some limitations. First, the optimization part of our code only outputs configurations that reach an energy efficiency above 80%. If a scenario is presented in which this efficiency level is not possible, then the coded model will not be able to provide an optimal configuration. Similarly, the code also only outputs configurations with an energy efficiency to cost ratio below 0.000005, so if a scenario is presented where that ratio is not achievable, the model code will fail to output any system possibilities.
Overall, when running the code with sample input, we found that a premium pump, glorious pipe, mondo turbine, general pumphouse, and 60 degree pipe bends were the parts that provided the maximum efficiency for the model. We also found that 16 meter high walls and Zone 2 were optimal for energy and cost efficiency, despite Zone 2 having some additional costs pertaining to the land space. With this configuration, we reached an energy efficiency of 0.821 and a cost of $745,545.40. For further improvement of the model, more inputs and outputs could be added to create a more flexible model. A more flexible model could be used to test more factors that could affect the reservoir, such as wall and ground permeability, turbine size, and numbers of parts. This would allow an even more accurate estimation of energy efficiency and final building costs.
COST IMPACT ANALYSIS
The end goal of the model was to evaluate every possible mechanical combination for efficiency and to use this information to calculate a cost and efficiency to cost ratio for further decision data. After initial analysis of trends in the most efficient outcomes the team decided to set constraints on both the efficiency and other physical values of the model to provide more optimal solutions. By creating a model to analyze the cost and efficiency of every mechanical combination, the team intended to choose the build site based on the physical components of the successful combinations, and then revise and implement additional constraints post-build site decision.
The model development process began with the team researching evaluating equations for gain or loss in mass or energy of the system through research and initial calculations. The team utilized the universal accounting equation and systems representation diagrams to depict the mass of the system pumping up, the mass of the system flowing down, and the energy of the system as a whole. The main additional influencing factor considered for the model was the potential for breaks represented by leakage and the potential for reservoir loss represented by seepage. The equation for leakage “LMNO Engineering, Research, and Software. (2017). Leak Rate Calculator. Leak rate calculator.” was referenced from and the equation for seepage was referenced from “Yang, C. (n.d.). A Simplified Calculation Method of Seepage Flux for Slope”.
Final Energy Representation
After coding user-defined functions for each individual physics equation and the different universal accounting equations as a whole, the team tested the course-provided sample validation input values for the pump efficiency, pump flow volume, pipe diameter, pipe length, pipe friction, reservoir depth, reservoir elevation, pipe bend constants, turbine efficiency, and turbine flow. In addition to these user inputs to model, the team utilized worst case scenario values for the unknown variables in leakage and seepage equations. After running the model with worst case scenarios and a version with leakage and seepage not included, the change in outputs was negligible. Because of this outcome with the “worst case scenario” values for leakage and seepage, the team assumed leakage and seepage to be negligible in the model.
After this, the team was able to simplify the code and only operate based on an energy systems representation diagram and its corresponding universal accounting equation could be manipulated to solve for mass rather than needing an intermediate mass to be predefined. With the new simplified universal accounting equation for systems energy, the team developed an equation to calculate the mass necessary in the system, M = 120 * 3600000000 / (gH - (f * L * vdown2) / 2D - gH * (1 - nt) - E * (vdown2 / 2)). Utilizing the iteratively improved model, the team retested the sample validation inputs. The final validation values were within an acceptable range, +/- 3%, of the expected validation outcomes.
Running the Optimization Model
After validating the initial physics model, the team began developing the optimization model. This code utilized the same basic model from above, but implemented eight nested loops to account for the variable parts and physical options with the model. The eight variable options that replaced user inputs for the model were friction factor of the pipe, efficiency of the pump, pipe loss coefficient of the bend, efficiency of the turbine, effective performance height of the system, internal diameter of the pipe, flow volume of the pump, and flow volume of the turbine. By creating lists of each part and its variable options and looping through these lists, the model tested 12,870,000 combinations. This model was chosen as the most complete evaluation of system options. In order to eliminate sub-optimal system options, the model would only output data that passed specified constraints.
An initial run of the optimization model utilized an efficiency constraint requiring systems to be greater than 80%efficient, a efficiency to cost ratio greater than5.0 *10-6 efficiency/dollar spent, and a time to fill and empty constraint being less than 12 hours. Another major assumption in the team’s model was that the availability of sunlight and therefore convertible solar energy would be a limiting constraint because average daylight hours could be estimated as 12 hours/day. After this trial, the team looked at trends in the physical factors of the passing solutions such as the pipe bend coefficients, effective performance height, and volume to influence the site choice.
Between these trending physical factors and an initial review of each sites costs site #2 most closely matched the optimized model solution. The team established further physical constraints on the system based on the required effective performance height, pipe length, and pipe bends of the selected site, Site #2. The new physical constraints added to the model included pipe bends of 60 degrees corresponding to 0.22 on the parts catalog, and an effective performance height of 110 meters because of elevation of site #2. The final outputs of the optimization equation provided data points including: the solution number, the loop combination number, the friction factor, pump efficiency, pipe loss coefficient, turbine efficiency, effective performance height, internal diameter, pump flow volume, turbine flow volume, efficiency, cost, efficiency to cost ratio, and volume. In addition to the outputs which define a “winning combination” of physical choices and part choices, a scatter plot is created comparing each passing solution and their efficiency to cost ratios. The model accessed the dictionaries to attain the corresponding part cost. The keywords of each part catalog dictionary were created by the row-column combination of each part variation in the catalog. The cost of the system was then calculated utilizing the equationSystem Cost = [(efficiency of turbine cost * turbine flow volume) + (2 * pipe loss coefficient cost) + (friction factor cost * pipe length) + (efficiency of pump cost * pump flow volume)], and inputting the corresponding variables from each solution combination. In addition to this final cost estimation calculated within the code, the team utilized an excel spreadsheet to display and calculate the total cost of the project which would include both system costs and build site costs.
DISCUSSION OF OTHER FACTORS
One social and environmental impact the team decided to research was the potential greenhouse gas emissions that comes from reservoirs. In a study published by BioScience, 10 authors from U.S., Canadian, Chinese, Brazilian, and Dutch universities concluded that reservoirs may be emitting just shy of a gigaton, or billion tons, of annual carbon dioxide equivalents. That would mean they contributed 1.3 percent of the global total. The emissions being talked about are mostly in the form of methane. Methane has a very strong short-term warming effect. Methane emissions along with other GHG emissions from reservoirs mostly occur when the pooling water of the reservoir creates a stagnant lake, interrupting natural flow, often killing a lot of the existing ecosystem. Excess water is also pushed onto the banks, and plants are exposed to it. They can become smothered and die. Bacteria in the water then decompose these dead plants, in turn creating carbon dioxide and methane. This gas can bubble up to the surface of the reservoir and be released into the atmosphere. Hydropower in itself may not be as carbon-neutral as we once thought, however it is still better than alternatives such as burning coal. Our team decided to monitor the emissions of our reservoir using a floating chamber with an NDIR instrument attached to keep track of GHG emissions so we can respond to the issue as we collect data in real time on the area. This will cost an additional $3000 for the floating device and instrumentation, but it was decided that it’s an important thing to take into consideration when constructing our reservoir. The team ended up including it in the final cost, as we felt it was a social responsibility of this massive construction project, to take into account the potential environmental impacts of our reservoir.
CONCLUSION AND RECOMMENDATIONS
After thoroughly researching, evaluating possible solutions, and coding an effective model, we found that a reservoir should be built at a height of 16 meters along the perimeter of site 2, which would produce an efficiency of 0.821. From this optimal solution, we ran the numbers and came up with a final cost of implementation of $754,545.40. This price was fairly similar to other examined solutions, so we believe this to be a reasonable number. Our design, however, was not similar to the rest. We picked site 2, while most other teams seemed to favor site 1. The reason behind this decision was that site 2 favored some of the geometry for the most optimal parts, so we felt that the tradeoff in cost was well worth the site. Along with this, many other teams seemed to form a cylindrical reservoir. Ours, however, reached around the entire perimeter of site 2 and was therefore a triangular prism. This made some difference in the cost for the walls, but again led to only slight cost differences.
As is evident, there are clear differences between our group’s chosen decision and other possible solutions to this problem. This could be due to the assumptions that were made. In coming up with a solution, we assumed that this would have to run at the longest during a 12-hour work day, that the effective performance rating of the pipes were due to the vertical elevation of the reservoir, and that the pipe bend was the outside angle between the pipe and the ground. These assumptions did end up impacting the part choices that we made and the bounds set on our model.
Our model had some limits. For one, when validating the code, while it was within an acceptable margin of error, it was not perfect. There could be influencing factors that were not accounted for or assumed negligible in the team’s model. Also, the model does not include the difference in the sites. Therefore, it will not find the most optimal combination with regard to site costs. This is something we would look to improve on in the future to make our model more accurate. If we were able to code in something that would take the site into consideration when determining the most optimal parts, this would eliminate any need for human-based decisions aside from ethical concerns. Our model would be entirely code-based and would be justified through the logic of the code. We would look into what caused the marginal error in our validation with the code, but this is minimal and would not change our model much in the big picture of things.
REFERENCES
Greenhouse Gas Emissions from Reservoir Water Surfaces: A New Global Synthesis. (2016, October 5). Retrieved December 06, 2020, from https://academic.oup.com/bioscience/article/66/11/949/2754271
Hydropower. (n.d.). Retrieved December 06, 2020, from https://www.engineeringtoolbox.com/hydropower-d_1359.html
LMNO Engineering, Research, and Software. (2017). Leak Rate Calculator. Leak rate calculator. https://www.lmnoeng.com/Flow/LeakRate.php.
Lu, B., Stocks, M., Blakers, A., & Anderson, K. (2018, April 10). Geographic information system algorithms to locate prospective sites for pumped hydro energy storage. Retrieved December 06, 2020, from https://www.sciencedirect.com/science/article/pii/S0306261918305270
Mooney, C. (2019, April 29). Reservoirs are a major source of global greenhouse gases, scientists say. Retrieved December 06, 2020, from https://www.washingtonpost.com/news/energy-environment/wp/2016/09/28/scientists-just-found-yet-another-way-that-humans-are-creating-greenhouse-gases/
Total Head Loss in Pipe or Duct Systems. (n.d.). Retrieved December 06, 2020, from https://www.engineeringtoolbox.com/total-pressure-loss-ducts-pipes-d_625.html
Yang, C. (n.d.). A Simplified Calculation Method of Seepage Flux for Slope ... Retrieved December 6, 2020, from https://www.researchgate.net/publication/341808237_A_Simplified_Calculation_Method_of_Seepage_Flux_for_Slope-Wall_Rock-Fill_Dams_with_a_Horizontal_Blanket