Experience Curves » economics

Unlimited Power from Continental Drift 2

Don — Fri, 06 Jan 2012 23:55:57 +0000

Scale and reaction Order determine economics

Don — Sun, 31 Jul 2011 01:22:24 +0000

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.

Garnett equation for an Experience Curve

Don — Thu, 07 Apr 2011 05:00:53 +0000

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

Learning from Cumulative Volume?

Don — Sun, 28 Feb 2010 04:39:33 +0000

If the result of repeated activities by mankind always results in learning, what is it that causes mankind to adopt a new learned procedure? Why does it always work no matter what the activity is? And why does it affect cost of manufacture differently for different products?

The post “The Geometry of Experience Curves” in this blog shows that the answer is: “That Men minimize their Time per unit of dimension”. Thus providing the incentive (less time spent by men) and the reason (geometry difference) for each product being different.

You tube

Don — Fri, 19 Feb 2010 22:24:01 +0000

The geometry of experience curves can be seen on youtube.

http://www.youtube.com/watch?v=3EW1DnJg1qY

Q:What Law of Nature Determines Price and Volume etc.

Don — Mon, 09 Nov 2009 17:44:13 +0000

A: For an Economy, like say the U.S. where we have variables Employed Men, Price,Volume,Wages,Investment,Scale of Operation, Production Process Mean Dimensions of Radius R with Number of space dimensions being used = m, Dollars, A Gross National Product, Specific Products and the change in time of these variables then:

For a change in Production of a Product with time the Behavior of Men is to Minimize their time/Per unit of Volume of the product, i.e. that ratio (dMen/dRadius with time)=0.

Using reduced values, or indexed values of these variables based on a given year for GNP, Price, Volume, etc. and the Fact that Dollars=Price*Volume=Wages*Men, and Volume=Radius^m gives a Slope for the Experienc Curve=(1/m-1)*(1-Exp(-k*t)) wherE k=growth rate constant for the product and t=time (usually years) .

Because “All Men involved minimize their time per unit of space dimension, with time”. Thus this Law of Nature is claimed as Garnett’s Minimization Law

(more)

Inherent in the foregoing is also the fact that Investment=Scale^(1/m).

Garnett’s Minimization Law of Human Behavior

Don — Tue, 25 Aug 2009 04:16:19 +0000

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:

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

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,

and the fact that demand is frequently exponential with time.

WCCE8 Presentation: Research as Investment

Don — Sun, 26 Jul 2009 06:05:09 +0000

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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Scale up of Investment with Pressure

Don — Fri, 17 Jul 2009 01:17:20 +0000

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.

Scale-up Investment vs. Scale

Don — Thu, 16 Jul 2009 07:03:10 +0000

Why do scale up rules of thumb work and why is the historic six tenths power six tenths?

The cause and effect relationship is shown in this link (publication)

scale