Extended abstract aiche12d

Half Order reactions and Scale determine economics:
1. The order of a reaction, like the hydroformylation of a double bond with a Rhodium triphenyl phosphine catalyst is half order, meaning that reaction rate is proportional to the square root of the catalyst concentration.
2. The investment in the reactor containing the catalyst/reaction is proportional to the cube root of the volume of the reactor. Annual costs for that reactor are proportional to it’s investment.
3. The price of Rh is relatively high ($2000/oz. in July, 2011) and if the proposed concentration in the reactor is 400 ppm, then for each carbonyl group added (H2=C=O or 30 lbs) the cost per pound of added product weight for once through use of Rh would be 2000*400*10^-6*14/30= 37.3 cents per lb.
4. An acceptable cost per pound of added product weight might be 5.0 cents per lb for catalyst cost, or nearly 10 fold lower than proposed. Rh recovery for recycle would normally be proposed.
5. Because of the reaction order and scale effect on reactor cost a preferred alternative would be to drop the Rh concentration by 100 fold while increasing the reactor volume by 10 fold.
6. Assuming a reactor investment of $1,000,000 for the 400 ppm case for 30*10^6 lbs of carbonyl with annual costs for maintainence, depreciation, taxes , insurance and other of $200,000/yr. the annual reactor cost would be 200,000*100/30,000,000=0.667 cents/lb of carbonyl. The larger reactor case would be 1.44 cents/lb of carbonyl cost.
Summary:
Case 400ppm 4ppm
Catalyst cost $/lb carbonyl 0.37 0.037
Reactor cost $/lb carbonyl 0.0067 0.0014
Sub total 0.377 0.0384

Conclusion:
The effect of scale and order combine to make an otherwise uneconomic proposal economic.

Agriculture, is primarily limited by area from the capture of the suns energy falling on earth.

While the industrial and agriculture revolutions have increased the number of dimensions being used, agriculture to date has remained limited to two dimensions and is therefore areal (n=2) not volumetric (n=3).

This limitation can be overcome by providing agro-lighting of the fields. They could/can become volumetric vice area limited. What is needed is a source for that electricity that is essentially unlimited.

One essentially unlimited source of electricity is to use continental drift as that source. As the continents move apart at a given fault line a cable across that fault can be loaded with weights and when the continents move apart the lifted weights can have their energy recovered. An accumulation of the energy of continental drift of the continents over millions of years exists in the mountains that it has built and some have been ground to dust (sand) by the winds powered by the sun and blown out to sea (e.g. off shore of the west Sahara desert of Africa). At such a place the gradient (of about 3%) down to the subduction trench can supply a head of >10,000 ft hydraulic head for a dredge supplied, reasonable length, pipeline driving a power station. All continents have such subduction trenches and gradients to them, arising from wind or water born deposits of ground up mountains, ergo the world power needs can be supplied by such.

Copyright, Donald I. Garnett, 7/11/2011, Corpus Christi, Texas.
Copyright, Donald I. Garnett, 12/6/2011, Corpus Christi, Texas.

t=time
kg=exponential growth rate constant for product or activity
n= number of dimensions of production activity, (1,2 or 3)

the-geometry-of-experience-curves-aiche5-cut

Defines what an experience curve really is and why.

In the world of Supply and Demand the money that one group of people are willing to spend for something is equal to the amount of Money another group of  people are willing to provide (sell) that something.  The something can be anything, either goods (a product) or services.  Money is identical to the time of Employed men times their Wage rate as that is exactly what one can buy with money.  The production of that something in a physical facility has dimensons, like the Radius of a spherical tank brewing beer, and the quantity of beer or its Volume is proportional to the Radius raised to the power of the number of dimensions.  In this case V=R^(N)=R^(3), since the number of dimensions is 3.  In general, the economy is evolving, that is, it is a function of Time.  The rate of change with time for the variable, say Employed is dE/dT, and Radius  is dR/dT.  The behavior of people when it comes time to change supply and demand is defined as Garnett’s Minimization Law:

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“People minimize their time per unit of dimension, namely d((dE/dt) / (dR/dT))/dT  = zero = 0 .

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The result is that the Log(Money)=(1/N)*Log(Volume).  Also,

Log(Price)=(1/N-1)*Log(Volume)

and other relationships that can be worked out from Money=Price*Volume=Wages*Employed=Wealth+Costs,

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and the fact that demand is frequently exponential with time.

The price of the flu is death of a fraction (shown below) of those infected.  The volume is those that have been infected.  The experience curve of the h1n1 flu follows:

recent-us-deaths

Which has slope of 2.

The number of dimensions m, normally being used is: Slope=1/m-1, hence in this case 1/m=2+1=3.

However, we are not infecting the virus it is the other way around.  Hence from the viruses point of view the number of dimensions is 1/m not m, and therefore=3.  It is a volumetric production rate.  Presumably the graph of deaths vs. invections will continue until the number of uninfected people is beginning to diminish, somewhere over half of the population.

The death rate per thousand infected people (the “fraction”) has been rising but recently has been diminishingas shown in:

recent-us-deaths1

Presentation made on August 24, 2009, in Montreal, Canada.

dig-presentation-v3

Power Point presentation “with recorded voice”.  Research as Investment

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Once you accept that the investment for a tank or reactor or container scales up with the 1/3rd power of volume then the scale up with pressure naturally follows.

If the rate of reaction of a chemical reaction is proportional to pressure (P) then raising pressure will lower the volume required at the same time that it will raise the thickness of the walls to contain that higher pressure.  It follows that Investment will be:

Investment=k*(1/P)^(1/3)*P

Investment =k*P^(2/3)

If the reaction is proportional to the pressure squared (2 species->one species)

Investment=k*(P)^(1-2/3)=k*(P)^(1/3)

For a 3rd order pressure dependency on the reaction rate the Investment is independent of pressure, i.e.

Investment=k*P^(1-3/3)=k

For orders higher than 3 other things like heat transfer to/from the reactants (i.e. area or order 2),  or limiting conversion to limit temperature rise, or use of diluents to control temperature rise,  may become dominant, limiting the pressure effect between P^0 to P^(1/3).

By my memory the investment for polyethylene plants scale as the 1/4th power of Pressure.

The foregoing is applicable for a fixed production rate.  However if one is in the position of building a plant where the justification of the capital is a key element then one likes to consider investment per annual pound.  Larger plants tend to give lower investments/annual lb.  Since production rate is proportional to P raised to the power of 1,2, or 3 preceding the investment per annual lb will be proportional to Pressure raised to the power of -1/3, -5/6, -6/3=-2.  That being the case plants tend to be at the highest pressure and largest scale.

Is the Learning Curve the cause for the Experience Curve?

Bruce Henderson in his “Perspective on Experience” alluded to learning being responsible for the experience Curve being the way that it is. However, he never did quantify the relationship between price and cumulative volume much less their relationship to learning. Henderson’s lack of understanding of the cause and effect relationships is exemplified by the many assertions of not knowing why the curves were as they were. Michael Rothschild in his Bionomics: Economy as Ecosystem asserts Henderson as writing:

“The experience curve phenomenon is as real as gravity. . . . [Its] effect can be observed and measured in any business, any industry, any cost element, anywhere. . . . The reason for the experience curve effect are not particularly important. The important fact is that the experience curve is a universally observable phenomenon.”

Clearly Henderson did not know and did not want to know the reasons behind experience curves as long as his experience curve phenomenon continued to be acknowledged.

See link for more:

rats_motivation