ChE Models Earth’s Temperature Response to Fuel Combustion
Written by Pierre R Latour, PhD Chemical Engineer
Internationally renowned Chemical Engineer, Pierre R Latour, details why government academics have failed to successfully model the planet’s climate. Showing precisely where climate scientists have ignored specialists from industry, Latour herein expertly signposts the way to a better understanding of that complex atmospheric thermostat.
Situation. Climatologists, astrophysicists and UN IPCC scientists have taken a piecemeal approach1, 2, 3 to forecasting sensitivity of temperatures to CO2, emphasizing data correlations (that cannot prove causality), radiation absent radiant energy transfer laws, ad hoc atmospheric feedbacks, and the simplifying black body radiator assumption, emissivity = 1. So far they estimate global warming, 0.5C < CS < 2.2C, where CS is temperature change for a doubling of CO2 from current 400 to 800 ppmv. The consensus is CS < 0 is impossible, without proof.
Engineering approach. Here is how chemical process control systems engineers model a chemical process to determine the effect of CO2 on Earth’s temperatures. This is needed to design a temperature controller, thermostat, for any system.
Simplify complex three-dimensional system of Navier-Stokes partial differential equations which is known to be difficult to solve4, with a uniform, well-mixed (lumped-parameter) system.
Start with instantaneous mass and energy conservation laws for atmosphere and surface; four equations.
Rate of accumulation in system + output rate = input rate
These four coupled ordinary differential equations give the relationship and response of T and [CO2] for atmosphere and surface to any change in specified inputs or forcing functions: solar, volcanoes, combustion, de-forestation, clouds. S(t), V(t), C(t), DF(t). Inputs may be any functions of time, like step, ramp, sine, exponential, impulse or actual.
MCp dT/dt + sum energy outputs = sum energy inputs, watts
V d[CO2]/dt + sum CO2 outputs = sum CO2 inputs, moles/sec
Include energy, mass and chemical transport rate laws: radiation, convection, fluid flow, diffusion, reaction kinetics, electricity, gravity. Most of these are known. The system is nonlinear. Chemical process control system engineers developed commercial methods for controlling dynamic multivariable systems like this in 1980’s.
Rate Laws. Rate laws for flow of matter and energy take the form of a driving force = potential difference: pressure for fluid flow, temperature for thermal heat by conduction and convection, composition for chemical species, voltage for electric current, intensity for radiant energy transfer.
Rate of radiant energy transfer from point 2 to 1 is I2 – I1 > 0, where intensity of radiation is given by S-B Law I2 = 5.67 ε (T2/100)4, T is radiator temperature, K, e is emissivity, 0 < ε < 1 and I2 is intensity, w/m2.
Photosynthesis reaction in presence of plant chlorophyll is CO2 + H2O = O2 + starch, cellulose and sugars.
Rate of photosynthesis reaction consumption of atmospheric CO2 by plants with chlorophyll, moles CO2 consumed/day, is K A [CO2] [H2O] I exp(-E/RT)
[CO2] is concentration of CO2 in air, mol CO2/mol air, 0.000400
[H2O] is concentration of H2O in air, humidity, moles H2O/mol air, 0.02
I is solar radiation intensity, avg 160 w/m2
T = leaf temperature, deg K, 273 + 25
E is Arrhenius activation energy, cal/g mol, known since 1928
R is ideal gas constant, 1.987 cal/g mol – K
A is leaf area, m2, hard to estimate for jungles and oceanic phytoplankton
K is specific reaction rate constant, moles/joule * 60*60*24 sec/day, known since 1928
This says the rate is linearly proportional to molar concentrations of CO2, H2O, sunlight intensity and increases nonlinearly with T. This equation links the atmosphere’s energy and CO2 mass balances with the surface, they interact nonlinearly.
So as either of these four factors increases, the rate of their consumption increases, tending to reduce each of them until consumption equals production and new steady state is reached. This is a natural negative feedback stabilizing mechanism on the atmosphere’s CO2, moisture content and temperature. It indirectly reduces the radiation emissivity and radiation rate from Earth’s surface while increasing its absorptivity. The amount of cooling by photosynthesis increases with global warming T and [CO2]. Of course rate does increase A, which increases rate, another, slower, positive feedback mechanism that is limited by other factors, like flora density, land area and deforestation.
The GHGT is based incorrectly on radiation energy transfer rates alone4, ignoring cooling effects like photosynthesis.
Physical properties. Assign appropriate physical properties, rate constants and any empirical constant coefficients. Emissivity of gas mixtures is difficult because it depends on composition, pressure, density and temperature and atmosphere is not homogenous with altitude, due to gravity gradient.
Solutions. These equations can be easily solved by numerical integration, giving responses Ta(t), Ts(t), [CO2]a(t) and [CO2]s(t) for specified inputs. But system engineers can learn much about the responses and how the interacting system works without numerical solutions by examining the rates.
First normalize the equations to standard mathematical form
τa1 dTa/dt + Ta + f1(Ta) = sum F1 in, F’s are independent of Ta.
Four τ parameters are time constants, residence times or approximately linear first order lag times (to reach 1 – 1/e = 0.632 of final value).
Physically they are inventory/throughput rate or residence time. They depend on size of system and reciprocal rates out. (Big systems with small rates have large τ.) Energy time constant for atmosphere circulation is about 5 years1 (Salby) and for surface, mostly ocean circulation, about 800 – 1000 years. For CO2 they are about the same. The coupled system lag of CO2 to T from 420,000 year data set5 is measured to be about 800 years. (Long term CO2 depends on ocean T, T does not depend on CO2.)
Analysis. Consider increasing anthropogenic CO2 from fossil fuel combustion. It is actually ramping up since 1900 about 21 ppmv/decade1 with sine wave amplitude 6 ppmv superimposed by annual variations in flora consumption of CO2 by photosynthesis. Salby1 recently showed about 30% of the rise is anthropogenic; the rest is natural, naturally.
To study how this system works, assume a sudden step change in combustion and CO2 input and follow the transient and final steady-state response. The steady-state solution can be computed directly by setting derivatives to zero and solving the four coupled algebraic equations.
Studying the coupled system, we can discern a simplified description of how it works. As CO2 increases, atmosphere and hence global emissivity immediately increases, decreasing atmosphere’s radiating Ta by S-B Law and surface Ts because some solar is absorbed by CO2 at 2-3 and 4-5 microns and re-radiated to space. Photosynthesis consumes CO2, sunlight and water, cooling surface that emits less intensely. CO2 diffuses to ocean at slow rate because its partial pressure increased and mass transfer coefficient across vapor liquid interfaces is small. CO2 remains in liquid phase because solubility of CO2 in water decreases with T.
The system is stable and reaches a new equilibrium steady-state point after the increased CO2 input, with only slightly more CO2 in atmosphere and ocean, and slightly lower T’s.
The dominate mechanisms as CO2 input increases follow.
- Atmospheric [CO2] steps up, say 100 ppm, from 400 to 500.
- Short term (5 years) atmosphere absorptivity and emissivity increases, atmospheric radiating T drops by S-B Law.
- Ocean surface CO2 partial pressure increases, mass transfer driving force = partial pressure P[CO2] – Henry Law vapor pressure, vp (or fugacity) increases, CO2 diffuses into solution, [CO2] and emissivity drops a bit, T increases a bit by S-B Law. This is a significant stabilizing feedback mechanism counteracting the postulated [CO2] increase.
- Photosynthesis rate increases with [CO2] & T, so [CO2] drops another bit, T increases another bit. Another stabilizing feedback mechanism.
- New steady state [CO2] < +100 input, T decrease very small.
- Longer term (800 years) ocean T drop is small. Solubility increases and vp decreases, driving force to solution increases again, ocean CO2 content increases, CO2 is withdrawn from atmosphere, [CO2] drops a bit further at very slow rate, almost to starting point. T increases another bit by S-B Law, almost to starting point.
- Steady-state gain or sensitivity ΔT/Δ[CO2] is the final net of these – and + rates. Likely ΔT/Δ[CO2] < 0 is vanishingly small. This value depends on the parameters of numerous rate laws, important ones were mentioned.
- Step [CO2] down, say -100 ppm and the same mechanism works to give a similar small result; it will not be exactly the same as +100 ppm because the rate laws are nonlinear.
Such a vanishingly small process gain or sensitivity, whether >0 or <0, calls for a powerful manipulated input variable with wide range to counteract unwanted deviations from any desired controller setpoint target for Earth’s T (which human institutions lack the knowhow to set properly even if they could) in the face of uncontrollable and unmeasurable input disturbances. Since fossil fuel combustion accounts for only 30% of [CO2] increase, no such human adjustable manipulated variable exists. Should the gain switch from – to + unknowingly, the negative feedback controller becomes positive and unstable until its sign is switched to negative feedback again.
This is the basis of my 1997 proof this system in unmeasurable, unobservable and uncontrollable, hence a human managed thermostat for Earth will never work, thank God. Yet government scientist and UN IPCC continue to waste $1 billion/day of humanity’s treasure trying to do the impossible since 1990, building that thermostat, with a greenhouse gas theory that constituted a perpetual motion, energy creating, global warming machine. Pure nonsense. Greatest fraud of all time.
Thermodynamics. Some GHGT promoters claim radiation is not subject to the second law of thermodynamics. They are wrong.
“The energy of the radiation which is at equilibrium within an enclosure depends only on the volume and the wall temperature T. It is known also that the pressure of the radiation is equal to one-third of the energy per unit volume. The energy u and entropy s per unit volume of the radiation are given by u = α T4 and s = (4/3) α T3, where α is a constant.” 6
Second Law says entropy S = dQrev/T of an adiabatic/closed system cannot decrease. Second law applies to radiation, mass transfer by diffusion of chemical species6. It applies to GHGT as well7. I proved7 GHGT back-radiation heat transfer from cold CO2 to warmer surface violates Second Law of Thermodynamics and leads to energy creation, a violation of First Law of Thermodynamics and an impossible perpetual motion machine to drive global warming in perpetuity. Which is why I am a GHGT skeptic, denier and cynic. GHGT promoters threaten me and call me terrible names.
Chemical engineers apply the laws of thermodynamics, chemistry, physics and biology to commercialize chemical products and build process plants to manufacture them. It borders on the bizarre that they are barred from offering their services to academic meteorologists and politicians struggling since 1990 to model Earth’s atmosphere for the purpose of building a thermostat, which engineers have proven to be impossible and hence uneconomic.
Conclusion. The chemical process control engineering modeling approach is given, revealing the mechanism involved for CO2’s effect on T. While the system is complex, many qualitative characteristics can be discerned. The net long term effect is vanishingly small, in the neighborhood of zero. If anything, it is probably on the cooling side. The system has strong natural feedback mechanisms; it is very stable.
Studying pieces of the system alone, like radiation, energy flows, photosynthesis, ocean capture cannot give the complete model or valid results. Statistical fitting of historic data to empirical computer models are provably known to have no predictive capability. Even using data to validate or invalidate hunches or assumptions is not possible unless all inputs are considered. That effort for this system is worthless.
Prof Tim Ball provided valuable insights and comments. Lord Christopher Monckton provided a critical peer-review of reference 3.
- Salby, Murry, “Physics of Atmosphere & Climate”, 2012 and talk, “Control of Atmospheric CO2”, London, 17Mar2015, published 24Jun2015. https://www.youtube.com/watch?v=rCya4LilBZ8#t=56
- Monckton, Christopher, “I Only Ask Because I Want to Know”, WUWT, 27Jun2015. http://wattsupwiththat.com/2015/06/27/i-only-ask-because-i-want-to-know/ (Latour blog at 1152, 27Jun2015)
- Latour, Pierre R, “Professor Singer Finds CO2 Has Little Effect on Global Temperature V2”, PSI, 21May2015. http://www.principia-scientific.org/professor-singer-finds-co2-has-little-affect-global-temperature-v2.html
- Gerhard Gerlich & Ralf Tscheuschner, “Falsification Of The Atmospheric CO2 Greenhouse Effects Within The Frame Of Physics V4”, Int.J.Mod.Phys.B23:275-364, 6Jan2009. http://arxiv.org/PS_cache/arxiv/pdf/0707/0707.1161v4.pdf
- Gore, Al, “Inconvenient Truth”, Apr2007.
- Denbigh, Kenneth, “The Principles of Chemical Equilibrium”, Cambridge U Press, 1961, pg 105.
Latour, Pierre R, “No Virginia, Cooler Objects Cannot Make Warmer Objects Even Warmer Still”, PSI, 20Nov2013. http://www.principia-scientific.org/no-virginia-cooler-objects-cannot-make-warmer-objects-even-warmer-still.html