2πhc λ(e –1) hc/λkT
R (λ,T) = = dI dλ
Φ ε x σ x T = object (Stefan-Boltzmann equation)
T1 = 5500˚K (sun) T2 = 4500˚K T3 = 3000˚K (light bulb) The rainbow area represents the sensitivity of the human eye Total power P radiated from a black object with surface area S heated to temperature T is:
T1
1.2E14 1.4E14 1.6E14 1.8E14
Target object
Atmosphere
P = S∫R(λ,T)dλ = σST ∞ 0
2πk 15hc
1.0E14
σ =
= 5.67 x 10 [W/m K]
ε
(Stefan-Boltzmann law)
8.0E13
T2
At any temperature T the wavelength λ corresponding to the peak is: max
Camera
6.0E13
hc 5kT
2.898 x 10 T
λ
= = max
[m]
4.0E13
Background
(Wien’s displacement law)
2.0E13
T3
Φ ε x τ x Φ(T) = total
+(1–ε) x τ x Φ(T)
+(1–τ) x Φ(T)
0.0E0
object
background
atmosphere
0 10
10
10
2 3 4 5
2 3 4 5
2 3
Wavelength λ [m]
Figure 2 Planck’s Radiant Function and Stefan-Boltzmann equations
‘Online’ monitoring techniques Infrared (IR) technology has been used as an ‘online’ temper- ature monitoring approach within steam reformers for many decades. IR is a non-destructive, non-intrusive, non-contact method for mapping thermal patterns on the surface of tubes and refractory within the reformer during operation. Understanding the tube metal temperature defines the per - formance capability and inherent reliability of the reformer and, ultimately, the risk of a tube rupture failure. IR is accomplished with two primary instrument types, such as thermal imaging cameras and pyrometers. The thermal imaging camera forms a two-dimensional ther- mal image of the target surface, while the pyrometer provides only a single target point temperature. Each instrument has advantages and disadvantages, and effec- tive programs will apply both to leverage the strengths. The imaging camera provides meaningful images and measurements for a historical record, which can be used to assess tube creep damage rates and long-term perfor- mance changes. The pyrometer should be used for accu- rate field measurements to compare specific tubes and
troubleshoot real-time performance issues. Pyrometers also require adherence to well-written procedures to maintain the accuracy and consistency of the temperature measurements. An effective IR program is an absolute necessity to mon- itor the steam reformer tubes, as well as provide a wealth of diagnostic information that may be used to evaluate the performance and reliability of other reformer components (tubes, tube supports, burners, and refractory). Radiation signals are strong functions formed from many sources within an operating reformer. Planck’s Radiant Function and the Stefan-Boltzmann equations set the the- oretical foundation for these temperature measurements (see Figure 2 ). The complexity of the measurement envi- ronment, coupled with differing materials that change over time, makes accurate temperature measurements difficult but possible with technical know-how and properly applied measurement techniques. To confirm temperature measurements in a reformer, a contact pyrometer, aka ‘Goldcup’ (see Figure 3 ), can be used. This water-cooled tool allows temperature meas-
urements to +/-2°C of mid-wall temperature when properly applied. To maintain data accu- racy, one must be very cautious about properly calculating the cooling effect via shielding and contact by the Goldcup when in use. After a field survey of a reformer with a Goldcup, these in-situ temperature calibration locations can be used to improve the measurement accuracy of easier-to-field tools (IR cameras and pyrometers). With proper procedures and training, the basic optical pyrometers can approach the Goldcup accu- racy after correction factors are
Figure 3 Goldcup tool for mid-wall temperature measurements
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