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\begin_body

\begin_layout Title
Stock Tank Mixing
\end_layout

\begin_layout Abstract
Stock tanks holding homogeneous liquid solutions of coagulant and chlorine
 are key components of AguaClara water treatment plants.
 The plant operators provide the mixing required to produce those homogeneous
 solutions by stirring with a piece of pipe or by rotating a crude mixing
 element inside the tank.
 The stock tank mixing team is working to develop high efficiency human
 powered chemical mixers and measurement methods that allow the operator
 to know when the solution is fully mixed.
 In the future we anticipate that higher concentration stock solutions will
 be used to facilitate use of the linear chemical dose controller for larger
 flow facilities.
 Achieving homogenous solutions at higher concentrations will require more
 mixing and it is important that the operators have methods to ensure that
 mixing is complete.
\end_layout

\begin_layout Labeling
\labelwidthstring 00.00.0000
students 3
\end_layout

\begin_layout Labeling
\labelwidthstring 00.00.0000
skills fabrication, experimentation, fluids
\end_layout

\begin_layout Section*
Introduction
\end_layout

\begin_layout Standard
Stock tanks hold concentrated liquid coagulant or chlorine.
 The liquid chemical stocks are prepared on site from granular chemicals.
 The chemicals must be in liquid form so that the AguaClara chemical dosing
 system can be used to meter the chemicals into the water at a controlled
 dose.
 The granular chemicals must be fully dissolved and then mixed to form a
 homogeneous solution in the stock tanks.
 In conventional mechanized water treatment plants this mixing process is
 accomplished with an 
\begin_inset CommandInset href
LatexCommand href
name "electric motor connected to an impeller"
target "http://www.dynamixinc.com/gmx.html"

\end_inset

 on a long shaft inside the chemical tank.
 In AguaClara plants the mixing is done manually by stirring the tank contents
 with a piece of pipe or by rotating a simple mixing unit assembled from
 pipes.
 In either case the operator mixes for some time and then assumes that the
 solution is homogeneous.
 The operator doesn't have any way of testing the solution to confirm that
 it is homogeneous.
 
\end_layout

\begin_layout Standard
The mixing process requires two steps.
 In the first step the granular material dissolves.
 For alum it takes significant mixing for all of the granules to dissolve.
 Powdered PACl (Poly aluminum chloride) dissolves more quickly than alum.
 Calcium hypochlorite may dissolve relatively quickly, but it leaves behind
 a precipitate of calcium carbonate.
 In all cases the chemical solution is more dense than water and if no mixing
 is provided the dense solution will form a density stratified solution
 in the stock tank with a high concentration at the bottom of the tank and
 a low concentration near the top.
 The challenges are to develop an efficient method to mix the chemicals
 in the stock tanks to produce a homogeneous solution of the desired concentrati
on and to develop a method for the operator to know when a homogeneous solution
 has been created.
\end_layout

\begin_layout Standard
If a low mixing intensity is used (as may easily occur with manual mixing),
 then it is possible for packets of dense fluid to be lifted high in the
 stock tank.
 Because the mixing intensity is low these packets of dense fluid are relatively
 large and molecular diffusion is ineffective at blending the high and low
 concentration liquids.
 After mixing stops the high density packet of fluid can settle back down
 to the bottom of the tank.
 If a higher mixing intensity or energy dissipation rate is used, then the
 turbulent eddies are smaller and the packets of fluid are broken into tinier
 pieces that molecular diffusion can then completely blend to form a homogeneous
 solution.
 Once a homogeneous solution is created it is no longer possible for gravity
 to 
\begin_inset Quotes eld
\end_inset

unmix
\begin_inset Quotes erd
\end_inset

 the solution.
 
\end_layout

\begin_layout Standard
The mixing process may seem trivial for small stock tank volumes.
 However as AguaClara plants are built to serve larger cities it is imperative
 that we understand how much mixing is required and that we design efficient
 mixing systems.
 An 
\begin_inset CommandInset href
LatexCommand href
name "AguaClara philosophy"
target "https://confluence.cornell.edu/display/AGUACLARA/Design+Philosophy"

\end_inset

 is that the operator should receive feedback for each step of the treatment
 process.
 Thus the operator needs to know when mixing is complete.
 The alternative is to specify a certain amount of mixing that would be
 different for each chemical, concentration, tank volume, and mixer design.
 The operator could confirm that mixing is complete by comparing the density
 of the fluid in the top of the stock tank with the expected value (based
 on the chemical concentration).
\end_layout

\begin_layout Standard
The mixing process can be idealized as beginning with two distinct concentration
s with their respective densities.
 The theoretical minimum amount of energy required to mix two fluids with
 different densities can be calculated based on the difference between the
 potential energy of the two fluids and the potential energy of the mixed
 solution.
 Unfortunately the mixing process is highly inefficient and most of the
 mixing energy is dissipated as heat without effectively blending the two
 solutions.
 Thus it isn't possible to use the potential energy difference as a guide
 for how much mixing energy or shaft energy is required to create a homogeneous
 solution.
 
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\begin_inset Graphics
	filename cuatrocommunidadesstocktanks.png
	width 7cm
	BoundingBox 0cm 0bp 912bp 608bp

\end_inset


\begin_inset Graphics
	filename Marcalastock.png
	width 6cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Coagulant stock tanks (blue drums in middle of the photo on the left) provide
 more than 24 hours supply of liquid coagulant.
 The chlorine tanks (photo on the right) contain a concentrated bleach solution
 made from calcium hypochlorite.
 The pipe mixing device used to stir the chlorine solution is visible on
 the right.
\end_layout

\end_inset


\end_layout

\begin_layout Plain Layout

\end_layout

\end_inset


\end_layout

\begin_layout Section
Density and Concentration
\end_layout

\begin_layout Standard
Density and concentration information is required to understand the nature
 of the mixing problem and to develop strategies to conduct laboratory experimen
ts using substitute chemicals that will have similar mixing problems.
 Given that a significant goal of mixing is to blend two solutions of different
 densities it will be possible to use a glucose solution with red dye as
 a surrogate for the chemicals used in AguaClara facilities.
\end_layout

\begin_layout Standard
The density of many solutions can be modeled as
\end_layout

\begin_layout Standard
\begin_inset Formula 
\begin{equation}
\rho_{Solution}=\rho_{H_{2}O}+m_{Solute}C_{Solute}
\end{equation}

\end_inset


\end_layout

\begin_layout Standard
where the dimensions of density, 
\begin_inset Formula $\rho$
\end_inset

, and concentration, 
\begin_inset Formula $C_{Solute}$
\end_inset

, are the same and the coefficient 
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\begin_inset Formula $m_{Solute}$
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 is different for each solute.
 
\end_layout

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status open

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\begin_inset Caption

\begin_layout Plain Layout
Properties of chemicals used in water treatment and surrogates for testing
 mixing requirements
\end_layout

\end_inset


\end_layout

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Solute
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Molecular Weight 
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Maximum recommended stock concentration 
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Max dose
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Flow ratio 
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Alum
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600
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800
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0.0125
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500 
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 as alum
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1225
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80 
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 as alum
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6250
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PACl (liquid)
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69.3 
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 as aluminum (commercial standard)
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7 
\begin_inset Formula $\frac{mg}{L}$
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 as Al?
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10000
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436 
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 as powder (69.3 
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 as aluminum)
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4.4 
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 as powder?
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\begin_inset Formula $Ca\left(ClO\right)_{2}$
\end_inset


\end_layout

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142.98
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210 (
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80
\begin_inset Formula $\frac{kg}{m^{3}}$
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 (based on 5% estimate as equivalent 
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3 
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 as 
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180.16
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0.378
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58.44
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The maximum alum concentration is set by a dramatic increase in viscosity
 above 550
\begin_inset space \thinspace{}
\end_inset


\begin_inset Formula $\frac{kg}{m^{3}}$
\end_inset

 
\begin_inset CommandInset citation
LatexCommand citet
key "key-3"

\end_inset

.
\end_layout

\begin_layout Standard
Commercial PACl is often shipped in liquid form in the United States and
 has a concentration of 69.3
\begin_inset space \thinspace{}
\end_inset


\begin_inset Formula $\frac{kg}{m^{3}}$
\end_inset

 as aluminum and a liquid density of 1240
\begin_inset space \thinspace{}
\end_inset


\begin_inset Formula $\frac{kg}{m^{3}}$
\end_inset

.
 It appears that the maximum stock concentration for PACl and alum have
 very similar aluminum concentrations.
 PACl is also available as a dried powder and it is this dried powder that
 is used at AguaClara plants in Honduras.
 The powder form of PACl should be used to create a 5 to 10% solution according
 to 
\begin_inset CommandInset href
LatexCommand href
name "Asia Chemical Engineering Co."
target "http://www.yatai.cn/poly-aluminium_chloride_(PAC).htm"

\end_inset

 More dilute solutions may begin hydrolysis and slowly lose their effectiveness.
 Dilute solutions should be used within 24 hours.
 The powdered PACl is 30% 
\begin_inset Formula $Al_{2}O_{3}$
\end_inset

 equivalent or 16% Al (
\begin_inset CommandInset href
LatexCommand href
name "*"
target "http://www.yuqing.cc/product/PAC_SprayDriedProcess/"

\end_inset

).
 An estimate of 
\begin_inset Formula $m_{PACl_{powder}}$
\end_inset

can be obtained from published density and concentration information for
 liquid PACl
\begin_inset CommandInset href
LatexCommand href
name "*"
target "http://www.gujaratalkalies.com/new/polyaluminum_chloride.htm"

\end_inset

.
 
\end_layout

\begin_layout Standard
Calcium hypochlorite is unstable at high liquid concentrations.
 Further literature review is required to determine the maximum acceptable
 stock tank concentration of calcium hypochlorite.
\end_layout

\begin_layout Standard
The maximum flow for a linear dose controller with a single dosing tube
 is approximately 2
\begin_inset space \thinspace{}
\end_inset


\begin_inset Formula $\frac{mL}{s}$
\end_inset

.
 The flow ratio for the chemical feeds suggests that a 20
\begin_inset space \thinspace{}
\end_inset


\begin_inset Formula $\frac{L}{s}$
\end_inset

 plant would only need a single dosing tube for PACl and that a plant flow
 of 50
\begin_inset space \thinspace{}
\end_inset


\begin_inset Formula $\frac{L}{s}$
\end_inset

 would only need a single dosing tube for calcium hypochlorite.
\end_layout

\begin_layout Standard
The minimum stock tank volume that AguaClara facilities have used is a 220
\begin_inset space \space{}
\end_inset

L plastic drum.
 At the maximum flow rate of 2
\begin_inset space \thinspace{}
\end_inset


\begin_inset Formula $\frac{mL}{s}$
\end_inset

 the 220
\begin_inset space \space{}
\end_inset

L would last about 24
\begin_inset space \space{}
\end_inset

hr.
 This suggests that the 220
\begin_inset space \space{}
\end_inset

L drums will be adequate for the coagulant for plants up to 20
\begin_inset space \thinspace{}
\end_inset


\begin_inset Formula $\frac{L}{s}$
\end_inset

.
 Smaller flow rate plants would simple use more dilute stocks.
 Thus the volumes and corresponding chemical concentrations and densities
 can easily be computed for the coagulants.
\end_layout

\begin_layout Section
Evaluate mixer designs
\end_layout

\begin_layout Standard
Evaluate the three mixer designs based on required energy input to move
 fluid from the bottom of the tank to the top of the tank, the resulting
 energy dissipation rate, and the total flow that is generated.
 Use sugar water to create a dense solution and add red dye #40 to make
 it visible.
 Use a transparent tank to make it easy to see the depth of the more dense
 sugar water and to see the effect of the mixing unit on the two fluids.
 A hydrometer that can measure up to 1220
\begin_inset space \thinspace{}
\end_inset


\begin_inset Formula $\frac{kg}{m^{3}}$
\end_inset

 is available to determine if mixing is complete.
 
\end_layout

\begin_layout Subsection
Centrifugal Pump
\end_layout

\begin_layout Standard
Build a completely transparent model of the centrifugal pump and stock tank.
 See Figure 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:red dye pump"

\end_inset

 for an example.
 A 
\begin_inset CommandInset href
LatexCommand href
name "transparent container"
target "http://www.usplastic.com/catalog/item.aspx?itemid=24373&catid=758"

\end_inset

 is available for your use.
 A new design for the pumping system is needed.
 An analysis of the pumping system is available in a 
\begin_inset CommandInset href
LatexCommand href
name "Mathcad worksheet"
target "https://confluence.cornell.edu/download/attachments/137953883/Stock+Tank+Mixing+Spring+2011.xmcd?version=1&modificationDate=1307715534000"

\end_inset

 on the 
\begin_inset CommandInset href
LatexCommand href
name "stock tank mixing wiki page"
target "https://confluence.cornell.edu/display/AGUACLARA/Stock+Tank+Mixing"

\end_inset

.
 Design a better system to hold the bottom of the pump centered in the tank
 and to allow the high density solution to enter the vertical pipe.
 Devise a pumping system that can easily be installed in a 55 gallon drum.
 The pumping system must be stable and held in place both at the bottom
 of the tank and near the top of the tank.
 Verify using the experimental model that the analysis in the analytical
 model is correct.
 If the analytical model is incorrect, determine the source of the error
 and correct it.
 Use the analytical model to determine the best pipe sizes for the centrifugal
 pump and calculate the time required to mix the contents of a 55 gallon
 drum.
 
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\begin_inset Graphics
	filename PumpedRedDye.jpg
	width 10cm

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "fig:red dye pump"

\end_inset

 The centrifugal pump is able to lift the dense red sugar solution and discharge
 it near the surface of the tank.
 A 
\begin_inset CommandInset href
LatexCommand href
name "movie"
target "http://www.youtube.com/watch?v=np0-6kBLpFs"

\end_inset

 of this is posted online.
 
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Subsection
Axial Flow Impeller
\end_layout

\begin_layout Standard
Axial flow impellers (think airplane propeller or window fans) cause flow
 primarily along the axis of rotation of the impeller.
 There is plenty of literature on impeller mixers.
 See the 
\begin_inset CommandInset href
LatexCommand href
name "literature review"
target "https://confluence.cornell.edu/download/attachments/137953883/Final+Report+Stock+Tank+Mixing+Team+Spring+2011.docx?version=1&modificationDate=1307716238935 from Spring 2011"

\end_inset

from spring 2011.
 The impeller will need to provide sufficient velocity to the fluid to cause
 high density fluid to flow into the low density fluid or vice versa.
 Impellers may be needed at multiple elevations to provide enough mixing
 energy to blend the two fluids.
\end_layout

\begin_layout Subsection
Radial Flow Impeller
\end_layout

\begin_layout Standard
Radial flow impellers cause flow in the radial direction.
 The goal could be to cause flow towards the outside of the bottom of the
 tank and then up along the inside of the tank walls.
 It isn't clear yet whether radial flow or axial flow impellers will create
 the highest vertical velocities.
\end_layout

\begin_layout Section
Baffles to minimize solid body rotation of fluid
\end_layout

\begin_layout Standard
The three design options all require rotation of a mixer and that rotation
 will tend to set up solid body rotation of the fluid in the tank.
 This fluid rotation will reduce the effectiveness of the mixing because
 it will reduce the velocity of the impeller relative to the fluid.
 The solid body rotation of the fluid can be reduced by adding vertical
 baffles attached to the tank walls.
 
\end_layout

\begin_layout Section*
Experimental methods
\end_layout

\begin_layout Standard
Use a hydrometer to measure density and use visual observation and a rule
 to measure height of the red dye solution in the vertical shaft of the
 centrifugal pump and in the transparent stock tank.
 Use the rate at which the interface drops initially to measure the flow
 rate from the centrifugal pump.
 Determine whether the hydrometer is well suited for the plant operators
 to use in Honduras.
 Evaluate whether it would be better to fabricate our own hydrometers or
 to purchase them.
\end_layout

\begin_layout Bibliography
\labelwidthstring References
\begin_inset CommandInset bibitem
LatexCommand bibitem
key "key-3"

\end_inset

GUREVICH R.
 A., BALMAEV B.
 G., LAINER Yu.
 A., and YAMPUROV M.
 L.: A study of density and viscosity of aluminum sulfate solution.
 2003
\end_layout

\end_body
\end_document
