Flow Equation and what to do with the savings
I’ll take the opportunity to give some background on relevant equations and then answer your question on what to do with the benefits.
If we look at a pipeline, the key driver is friction loss along the pipe
For oil flowing in a pipe at a certain velocity, there is an emprical equation that predicts how the liquid will behave, and how much friction loss will occur along the pipe. You can use this equation to model a range of scenarios.
The inputs to the equation, called the Darcy Weisbach equation include
• Pipe length
• Pipe diameter
• Oil Velocity
• Reynolds number - An indicator of when flow transitions from laminar to turbulent flow. The Reynolds number depends on viscosity, pipe diameter, velocity and density. Higher numbers mean turbulence (>2320) low numbers mean laminar (<2320)
• Friction Factor depends on Reynolds number, Pipe inner surface roughness and pipe diameter but the equation for friction factor is very different for laminar vs turbulent flow with the influence of viscosity.
Equation result
• Frictional head loss is the outcome of the equation
The friction loss per mile is important because it determines the power required to pump oil at a given velocity in a given pipeline
• Power use - This is directly proportional to friction head loss
There is a 1:1 relation between head loss and power consumption. Reduce the former and the latter goes down in proportion.
Relating AOT to the equation
AOT has two impacts that affect the equation outcome
1 Viscosity reduction
• As viscosity goes down the friction factor goes down, 1:1 for laminar , much less so for turbulent.
• As the friction factor goes down head loss reduces in direct proportion.
• As head loss goes down power use goes down.
2 Suppressing the transition from Laminar to Turbulent flow
• Friction losses are modest under laminar flow but skyrocket when a pipeline becomes turbulent.
• When that happens pressure loss per mile of pipeline skyrockets and so does power use.
• If turbulent flow can be induced to revert to laminar flow the friction factor goes down some 80%. I have run this through my spreadsheet model to get this.
• The scale of this benefit is much greater than the friction reduction benefit from viscosity reduction.
Your point on how much viscosity reduction would be required to hit 75% power savings.
On this question, I tried it in my spreadsheet model and even at 90% viscosity reduction with turbulent flow, the power use only goes down 40%. This means 75% power savings are literally impossible under turbulent flow. The only possible explanation then is that the flow must have reverted to laminar flow. We still need to hear more detail of course but that’s what the equation clearly indicates.
I haven’t yet posted all the parts of the equation but can do if need be. Initially I wanted to focus on principles.
Your question - What are the implications of that 75% drop in energy for the pump—does that mean with the pressure constant? No it reduces too.
• As shown above a reduction in power use arises directly and in proportion to a reduction in friction head loss.
• So a 75% reduction in head loss is the cause and a 75% reduction in power use is the outcome.
To answer your question - what to do with the power savings:-
The equation focuses on predicting head loss given a defined flow rate and other conditions.
If you reduce friction head loss then the power required to maintain the existing flow rate decreases in proportion.
You then have these choices
1. Fully Reduce pump power so as to maintain the existing flow rate –Pumping the same amount of oil with much less power. Power saving directly proportional to the reduction in head loss.
This option is direct clean and simple you just need less power to achieve the exact same result.
2. Maintan pump power :- keep the pumps working at the existing power level and pump more oil. The exact increase would need to be recalculated because velocity would increase and the head loss then changes. There is a possibility of reintroducing turbulence if greatly increase velocity. If that occurs there is another option.
3. Partly reduce power and still pump more Bring pump power back down to the maximum power savings (1 above) then increase it but only while the flow remains laminar and no further. With this option you get a combination of lower power use and increased flow. Keep in mind this “optimal” pressure will always be less than they use now so we aren’t hitting any pressure limits, rather we are reducing pressure in the pipeline.
Gives pipeline operators choice in what they want to do
Each pipeline owner may have different drivers and priorities and the appeal of the above option will vary by pipeline circumstances.
1. Providing clients with these three choices is of itself a fantastic offering. It gives the client choice in how to maximise the benefits for them
2. I suspect that the third one would be pretty attractive to most. “Save money, reduce pipeline operating emissions and get more throughput – avoiding the next to build more pipelines – saving the company capital.”. This is effectively the exact sweet spot you referred to in your post.
Overall using strictly turbulent flow in my spreadsheet model and using a set of parameters as close as i can obtain for Keystone, the model predicts savings much less than 75%. (40% at best)
This implies that the flow has reverted to laminar because that equation indeed predicts savings of around 80%, very much in line with Professor Tao’s results of 75%. Of course this is no substitute for a real experiment but it does give us an alternative reference point that supports Professor Taos' contention that turbulent flow is being suppressed.
The 75% savings is extraordinary and highly valuable for STWA. This is the key driver of the economics and shareholder value. Viscosity reduction and suppression of turbulence provide the reasons why it occurs.
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