Economy of (Vertical) Scale

There are lots of proposals emerging seemingly every day, based around the notion that we will mass produce some device, plant or process, and then use those mass-produced devices to produce some commodity product- frequently a product made by devices, plants or processes already operated commercially at much larger scale. A few examples seemingly popular at the moment include:

• small modular nuclear reactors for power generation
• distributed hydrogen generation (particularly for refuelling vehicles)
• small units to generate value from fossil gas that would otherwise be flared, by converting it to fuels or chemicals
• distributed units to process a distributed resource- waste products from agriculture, municipal solid waste, batteries- you name it

The idea is simple enough: we all know that when things are made in large numbers, a couple things happen. One is that we get better at making them, and that learning drives down the cost of each unit produced. The first one costs a lot because it's a prototype. The 2nd, if it is identical, is easier and hence cheaper because we've already proven the concept. And so it goes, with capital cost falling by a certain percentage with each doubling of production- a principle known as Wright's Law.

Another is that when we increase the scale of the manufacturing plant (made possible by increased numbers of units being sold), we can benefit from the savings associated with automation etc. This is actually one of the features which enables Wright's Law for the manufacture of certain types of devices.

The fundamental thesis of the sorts of schemes I'm going to take on in this article series can be stated more or less as follows: building big plants is hard. It takes time and lots of capital. So instead, we'll make a very small plant, do it very well, and then mass produce the very small plant and operate many of them in physical parallel, either on the same site or on a plentitude of sites, the latter to save the costs of distributing the product (or to eliminate the need to build infrastructure to distribute the product). And it's my job in this series, to explain to you why this idea has a rather tall stack of engineering economics- arising from basic physics- in the way of its success.

It's important to provide a little context here, so that people can make sense of where such approaches are necessary, where they make sense, and where they're just somebody playing around with your lack of knowledge of engineering economics and hoping you won't notice.

Economy of Vertical Scale

You've probably noticed that we make many things in large, centralized plants. We distribute feeds of matter and energy and labour to those plants, and we distribute products from those plants to the people/businesses who need them. Why do we do that?

The answer comes from very basic physics, which leads in a very direct way to engineering economics.

Take the simplest example: a piece of pipe to carry a fluid from point A to point B.

Let's say we're moving a commodity with that pipe- doesn't much matter what commodity. Let's compare two pipes: one has a diameter of X, and the next has a diameter of 2X.

The first pipe can carry a given amount of product per unit time at a particular amount of energy input per unit time lost to friction. The correct size of pipe is determined based on what's referred to as an “economic velocity”- the flowrate which gives a linear velocity which is an optimum balance of the cost of pumps/compressors and their energy lost to pressure drop in the pipe (higher for smaller pipes) and the capital cost to build, test and maintain the pipe (higher for larger pipes). A different optimal velocity exists for a chemical plant's piping, for instance, than for a pipeline carrying fluids across a country (with the latter favouring lower velocities).

When we compare pipes with diameter X and 2X, we find right away that we can move four times as much material per unit time in the larger pipe, because the cross sectional area varies as D^2. Indeed it's even more than 4x, because we get a benefit from an improved ratio between wetted perimeter (where wall friction happens), which varies with D, and cross sectional area which varies as D^2.

But the real benefit is this: the pipe capital cost doesn't increase by anything near four times.

We've just discovered the physical basis for the economy of vertical scale, or “economy of scale” for short. It arises because relationships such as the surface area to volume ratio, become more favourable with increasing scale.

Similar physics are active for all things on a project- every pump, valve, tank, heat exchanger, transformer, motor- you name it. The bigger you make it, the cheaper it gets (in capital cost) to produce a unit of value from that device.

Capital Cost Versus Scale

Let's say we have two plants: the first plant produces 1 unit of production (doesn't matter if that's tonnes per day of a chemical, MW of electricity etc.), and the 2nd one produces 10 units per day of the same undifferentiated thing. We say that plant 2 is 10/1 = 10 times the scale of plant 1, ie. we have a scale factor of 10.

To a first approximation, because of relationships like the one for the pipe example, it can be shown that:

C2 =~ C1 S^0.6

Where C2 is the capital cost of the larger plant, C1 is the capital cost of the smaller one, S is the scale factor (the ratio of production throughput of plant 2 to plant 1), and 0.6 is an exponent which is the average for a typical plant. In fact, each thing in the plant has a similar relationship, with an exponential factor which ranges from between 0.3 (for centrifugal pumps) to 1 (for things like reciprocating compressors above a certain minimum size). Normalized over the cost of a typical plant, the exponent of 0.6 gives the best fit.

Let's say that 1 unit of production generates 1 unit of revenue per day. Ten units would generate 10 units per day. But let's say that 1 unit of production rate costs us $1 million in capital. Ten units of production would therefore cost us 10^0.6 x $1 million = ~ $4 million in capital. The cost of capital per unit produced is therefore $1 million/unit/day for the first plant, and $4/10 = $0.4 million/unit/day for the 2nd plant. The marginal capital cost per unit of production is dramatically lower for the larger plant- assuming:

• there's a market big enough to consume all the production of the larger plant
• there's feedstock sufficient to feed the larger plant
• the product and its feedstocks are both legal and possible to transport by practical means
• we're within the limits of the scaling equation, meaning that each thing we're using in the plant, simply gets bigger
• we're making a commodity which is fungible, meaning that it's interchangeable with the same product made elsewhere

We've just discovered the reason we do stuff at large scale! It doesn't matter what undifferentiated fungible commodity product we're making, as long as it meets our assumptions above (or only bends them a little), every unit of production (every tonne of product, or kWh of electricity etc.) becomes cheaper if we make it in a plant of larger scale.

Limits of Vertical Scaling

Of course there ultimately will be an optimization here too. We rarely think it's a good idea to make all the world's supply of any one thing of value in a single plant at one location on earth. That's putting too many eggs in one basket. Distribution isn't free of charge, much less free of risk, and logistics limits how far you can move a particular product before the cost of distributing it overwhelms the capital savings. Similarly, the feedstocks are often distributed and their logistics matters too.

Some products- and some starting materials – are too voluminous or unstable or dangerous to make the trip. Doesn't matter how badly we want to make ozone, for instance, in one centralized plant to make it cheaper, because in 90 minutes, even under ideal conditions, it's gone- it falls back apart to oxygen again. If you want ozone, you must make it on site and use it as it's made.

With hydrogen as a feed, unless we're using a tiny amount, it is generally better (in economic terms) to either set up production near an existing hydrogen plant, or to transport something else to make hydrogen from and then build a small to medium sized plant of our own- because the infrastructure to economically move more than very small quantities of a bulky gas like hydrogen doesn't exist beyond a few “chemical valley” type situations where large number of plants are co-located in the same geography. Bespoke new infrastructure suitable for moving pure hydrogen is very costly and slow to build.

The same with hazardous wastes: we may find it very efficient to process them in one giant plant, but there are often rules about transporting wastes across borders etc that make it impossible to do so.

Vertical scale, within those limits, is king. It's the reason we have centralized power plants, oil refineries, chemical plants, car manufacturing plants etc., rather than having one in every town, or every home. The resulting economy of scale can pay for considerable distribution infrastructure too- within limits.

Additional Advantages to Vertical Scale

Many other factors tend to generate lower costs of capital for larger projects rather than smaller ones. The proportion of a project spent on factors like engineering, permitting, controls and instrumentation, accessory facilities, civil/structural work, utilities etc. all tend to be lower per unit of production rate for larger rather than smaller plants, with exceptions of course.

When capital cost intensity decreases, so does the incremental cost of improvements to save energy such as heat integration. Whereas small projects often heat using fuel and cool using a cooling utility, heat integration becomes economically possible as projects become larger. And when plants are integrated into even larger facilities, energy integration from one plant to another becomes possible. Plants can share utilities such as steam, such that surplus steam from one plant is used for motive power or heating by another.

Is There Such A Thing As "Too Big"?

Absolutely. At a certain point, things are just too big to build in practical terms. With some pieces of equipment, you get to the point where there's only one company in the world who would even try, and they get to name their price and delivery schedule. Sometimes, the issue is shipping the finished article to the site. Sometimes it's a matter of not being able to afford to build the thing in place, because doing so requires basically building a factory with specialized equipment only for the purpose of building the one unit, squandering much of the benefit of greater scale.

All of these factors lead to the conclusion that there is a maximum practical scale for most things. And beyond that maximum practical scale, you're pioneering- you're going one larger, and taking onboard all the learnings of doing so on just your project. Future projects might look at your ruins and laugh, or they may benefit from your suffering, but you're going to suffer either way.

A certain amount of “heroics” in terms of specialized logistics, heavy cranes, special crawler trailers, or site construction, is necessary in any big project. But when a project goes too far, the result can be a higher cost than if you'd simply built two or even four smaller units which didn't require heroics to the same extent. You bet that major projects teams suffer over these details, in an effort not to become a signpost on the road of project development which says, “go no further”.

In the next article in this series, we'll discuss what you do when you reach the limits of vertical scaling.

Recommended Reading: "Capital Costs Quickly Calculated" - Chemical Engineering magazine, April, 2009