ChEn 433 Natural Gas

Class 13

Natural gas

Question: what are we looking for in a fuel?

  • Inexpensive
  • Lots of it
  • Easily available
  • Many uses
  • Safe
  • Environmentally friendly
    • Emissions: CO2, NOx, SOx, particulate, other
    • Landscape/footprint

How does natural gas fare?

Natural gas deposits

  • Conventional
    • non-associated
    • assiciated (with oil)
  • Unconventional
    • shale gas
    • tight gas, e.g., sandstone
    • Coalbed methane (~3% 2019, EIA)
  • (Hydrates)
    • Solid: water/methane
    • High pressures (50 atm, 1500 feet), low T
    • Oceans, continental shelves, under arctic permafrost
    • 5-22% of global organic carbon!
    • Energy dense: 1 unit frozen hydrate –> 164 units natural gas

EIA Natural gas explained

US reserves

  • US reserves (2019) = 494,911 billion ft\(^3\)
  • 1000 cf (ft\(^3\)) = 1.037 MMBtu.
  • Problem: convert US reserves to CMO

US production by state

US production by type

interactive plot at bottom of this link

US shale plays

World shale plays

Fracking

Fracking

Fracking

Fracking

Fracking (steering)

See also the drilling minute series, especially this one

Well head

“Christmas Tree”

Composition

Questar Gas Composition, Utah

Composition

(Lakeside M&R 1)

Questar Gas Composition, Utah

Chemical mechanism

  • GRI 3.0
    • 53 chemical species
      • H2 H O O2 OH H2O HO2 H2O2 C CH CH2 CH2(S) CH3 CH4 CO CO2 HCO CH2O CH2OH CH3O CH3OH C2H C2H2 C2H3 C2H4 C2H5 C2H6 HCCO CH2CO HCCOH N NH NH2 NH3 NNH NO NO2 N2O HNO CN HCN H2CN HCNN HCNO HOCN HNCO NCO N2 AR C3H7 C3H8 CH2CHO CH3CHO
    • 325 reactions
  • One step global reaction
    • remember, you get what you pay for!

      \[CH_4 +2(O_2+3.76 N_2) \rightarrow CO_2 + 2H_2O + 7.52N_2\] \[\frac{d[CH_4]}{dt} =-1.3\times 10^8\exp(-24358/T)[CH_4]^{-0.3}[O_2]^{1.3}\] \[(\text{mol/cm}^3\cdot \text{s})\]

Reaction path diagram

High Temperature

Reaction path diagram

Low Temperature

Natural gas power plant

Lakeside Power Station, Vineyard, Utah, 2 units, 657, 728 MW

Plant types

  • Combined cycle
  • Gas turbine
  • Internal combustion (recriprocating)/combined cycle
  • Integrated solar and combined cycle
  • Steam turbine

Size distribution

World Gas Plants

6998 Operating Gas Plants as of September 2021

About 80% are Natural Gas

Combined cycle

Combined cycle

  • A Brayton cycle “tops” a Rankine cycle
  • A steam turbine is driven by the exhaust heat of a gas turbine.
  • The working fluid of the Brayton cycle is at a much higher temperature (combustion) than the working fluid (water/steam) of the Rankine cycle, allowing higher efficiencies.
    • Brayton gets to high T (>1150 \(^oC\), 2100 \(^oF\)), but the exhaust is hot.
      • Peak Rankine T ~ 620 \(^oC\) (1148 \(^oF\))
    • Rankine can get low T exhaust.
    • Combination gives a good Carnot efficiency
    • Higher T in turbine facilitated by turbine blade cooling
  • 55-60% efficiency on a LHV fuel basis

HRSG

Heat Recovery Steam Generator

Gas Production and Delivery

Gas Processing

Radiation

Radiant fraction:

\[\chi_r = \frac{\dot{Q}_r}{\dot{m}\Delta h_c} = \frac{kV\sigma T_f^4}{\rho v_eA\Delta h_c} \propto \frac{kd^3T_f^4}{v_ed^2}\propto\frac{kT_f^4d}{v_e}\propto kT_f^4\tau\]

  • \(k\) is absorption coefficient
  • \(T_f\) is flame temperature
  • \(\tau\) is residence time

Radiant fraction

Radiation intensity: I

  • Geometry:
  • 2D: angle 0-2\(\pi\), 2\(\pi\) radians in a circle
    • \(c = 2\pi r = \int_0^{2\pi}rd\theta\)
  • 3D: solid angle: 0-4\(\pi\); 4\(\pi\) steradians on a sphere
    • \(A = 4\pi r^2 = \int_0^{4\pi}r^2d\Omega = \int_0^{2\pi}\int_0^\pi r^2\sin(\theta)d\theta d\phi\)
  • Intensity \[I (=) \frac{W}{m^2_\perp\cdot\lambda\cdot St}\]

How would the intensity of the sun change if it were twice as far away?

Heat flux

\[q\,\,\, (=)\,\,\, \frac{W}{m^2}\] \[q = \int_{4\pi}I\cos{\theta}d\Omega = \int_0^{2\pi}\int_0^\pi I\cos{\theta}\sin\theta d\theta d\phi\] \[Q = \nabla\cdot q\,\,\, (=)\,\,\, \frac{W}{m^3}\] RTE (nonscattering) \[\frac{dI}{ds} = kI_b - kI\] \[I_b = \frac{\sigma}{\pi}T^4\] Here, \(\sigma = 5.67\times 10^{-8}\,\,\text{W/m}^2\text{K}^4\) is the Stefan Boltzmann constant.

Parallel planes

\[\frac{dI}{ds} = kI_b - kI;\,\,\, I(x=0)=I_0;\,\,\, s = x/\cos\theta\] \[I = I_b - (I_b - I_0)e^{-kx/\cos\theta}\] \[q = \int_{2\pi}\int_0^\pi I\cos\theta\sin\theta d\theta d\phi = 2\pi\int_0^\pi I\cos\theta\sin\theta d\theta\]

\(I_0\) is the intensity at the wall, and \(I_b\) is the black intensity of the gas.

\[\begin{align} q(x) =& 2\pi\int_0^{\pi/2}\cos\theta\sin\theta(I_b-(I_b-I_0)e^{-kx/\cos\theta})d\theta -\\ & 2\pi\int_0^{\pi/2}\cos\theta\sin\theta(I_b-(I_b-I_0)e^{-k(H-x)/\cos\theta})d\theta \end{align}\]

\[Q = -2\pi k(I_b-I_0)\int_0^{\pi/2}\sin\theta(e^{-kx/\cos\theta} + e^{-k(H-x)/\cos\theta})d\theta\]

Gas properties

  • Planck Mean absorption coefficient \[k_{pm} = \frac{\pi}{\sigma T^4}\int_\eta I_{b,\eta}k_\eta d\eta\] \(k_{pm} = k_{pm}(T)\) for a given species \[k_{pm,i} = x_iPa_i(T)\] \[k_{pm} = \sum_ik_{pm,i}\] \[k_{soot} = 1817 f_vT\]