Wednesday, May 11, 2011

Theory for Design

The CFD-ACE+ flow modeling software served as the backbone for the group’s system design. The theory behind this software involves the conservation of mass, conservation of momentum and conservation of energy equations. Together these equations form a set of coupled, nonlinear differential equations. Because these cannot feasibly be determined analytically, this program finds computer-based solutions governing these equations for fluid flow. Also, because the group did not have success in the laboratory, this software became an invaluable resource and guided the process of design selection.

In order to get the software functioning properly, a 3-Dimensional model of the microreactor used in the lab was created. Next, various properties such as density, viscosity, molar mass and chemical formulas of the fluids (soy oil, methanol and biodiesel) were defined. Then, the chemical reaction of transesterification spurred by the NiO catalyst was added to the program. That is, a reaction was added at all surfaces of the microreactor channel in which a molar ratio of 3:1 for methanol to soy oil produced 3 moles of biodiesel. As research from the University of Tennessee indicates, the kinetics of biodiesel formation (soy oil reaction) catalyzed by NiO is first order with a rate constant of k = 0.0002 per second. This value is part of the following relationship:

[soy oil at t] = [soy oil initial] exp(-kt)

where [] means concentration of, and t is time. This rate constant was determined at 80˚C, which is precisely the temperature that the Green Machine operates at. Therefore, this constant was incorporated into the software to determine the rate at which biodiesel was formed in the channel. One other key parameter used in the software is diffusivity. While it is known that soy oil and methanol are very immiscible, meaning they do not readily mix, there is no concrete number for their diffusivity. However, for liquid-liquid diffusivity at elevated temperatures such as 80˚C, a diffusivity of 10-9 N s/m2 is a reasonable assumption. Therefore, this is the value that was used in the CFD-ACE+ software.

Another key tool that aided the software was the use of spreadsheet analysis in Excel. By setting up one spreadsheet, the group was able to manipulate variables and run different simulations in order to optimize results. Clearly, optimization is key to the Green Machine’s design. Essentially what is being optimized is the number of microreactors needed in the system. The goal here is to use as few microreactors as possible to produce 1 gallon of biodiesel in 24 hours, while keeping the pressure drop in each reactor under 1,300 Pa. Consequently, there is an optimal microreactor channel length, residence time, velocity and flow rate that must be found first in order to get the optimal number of microreactors needed. Therefore, the two most important variables to manipulate in the Excel spreadsheet were the length of the microreactor channel and the residence time of the reactants in the channel. By changing these two variables, the group was able to alter the flow rates and velocity of the reactants, and ultimately, the number of microreactors. As a first cut, the group chose a 5 minute residence time to provide ample time for mixing, and a microreactor channel length of 3.5 cm because it was the length of the reactor being used in the lab. Starting with these assumed values, a spreadsheet was set up to calculate flow rates and velocity according to the following two equations:

V = L/t

Q = VA

where t is the residence time, L is the length of the microreactor channel, Q is the flow rate, V is the velocity of the reactants, and A is the cross-sectional area of the channel. As shown, the flow rate is directly related the velocity, and it was essential to know the velocity because the software required a velocity input in order to run simulations. It should be noted that the Q in the above equation represents the total flow rate which is simply the sum of the flow rate of methanol and that of soy oil. In order to get each individual flow rate, it was essential to make use of the chemistry and molar ratios of the two fluids.

The optimization of the Green Machine design was an iterative process. Therefore, the group calculated initial values to fill in an Excel spreadsheet, ran a simulation, analyzed the results, altered the parameters and then repeated the process many times. With the initial values that were chosen of a 5 minute residence time and 3.5 cm microreactor channel, the number of microreactors needed was 15,000. This number was far above the performance specification of 1,000 microreactors or less, and hence, many iterations were performed until the group finally arrived at its final value of 750 microreactors.

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