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

dig-presentation-v3

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

spare1a1-research-as-investment-power-point1

spare1a2-research-as-investment-power-point1

spare1a3-research-as-investment-power-point1

spare1a4-research-as-investment-power-point1

spare2a-research-as-investment-power-point1

spare2b1-research-as-investment-power-point1

spare2b2-research-as-investment-power-point1

spare2c-research-as-investment-power-point1

spare2d1research-as-investment-power-point

spare2d2research-as-investment-power-point

spare2e-research-as-investment-power-point

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

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