Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Green Processing and Synthesis

Editor-in-Chief: Hessel, Volker / Tran, Nam Nghiep

Editorial Board: Akay, Galip / Arends, Isabel W.C.E. / Cann, Michael C. / Cheng, Yi / Cravotto, Giancarlo / Gruber-Wölfler, Heidrun / Kralisch, Dana / D. P. Nigam, Krishna / Saha, Basudeb / Serra, Christophe A. / Zhang, Wei


IMPACT FACTOR 2018: 1.128

CiteScore 2018: 0.97

SCImago Journal Rank (SJR) 2018: 0.263
Source Normalized Impact per Paper (SNIP) 2018: 0.366

Open Access
Online
ISSN
2191-9550
See all formats and pricing
More options …
Volume 1, Issue 4

Issues

Detonation parameters: a basis for the design of microstructured process equipment

Elisabeth Brandes / Markus Gödde / Werner Hirsch
Published Online: 2012-07-28 | DOI: https://doi.org/10.1515/gps-2012-0015

Abstract

Test apparatuses are described which allow to characterize detonations of flammable substance/oxidizer mixtures by the detonation limits, the limiting starting pressure, the detonation velocity, the detonation pressure and the width of the detonation cells at different initial pressures and temperatures. Based on such measurements it is possible to derive a ‘safe capillary diameter’ for microstructured processes for a given composition of the mixture from the correlation of the width of the detonation cells with the initial pressure by the use of the ‘λ/3-rule’. Such safe capillary diameters as well as the detonation limits, the detonation pressures and detonation velocities have been determined for several hydrocarbon + oxygen mixtures in correlation with raising initial pressures and temperatures.

Keywords: detonation parameters; equipment design; microstructured process; safe capillary diameter

1 Introduction

Capillary tubes with very small diameters as used in microstructured process equipment are often thought to be intrinsically safe with respect to the propagation of explosions. Although this may be true with air as oxidizer and at more or less ambient temperature and pressure conditions, it is highly questionable under conditions often used in micro process engineering as oxidizers with enhanced oxidation potential, as well as high pressures and temperatures. Especially the use of oxidizers with enhanced oxidizing potential may enable a detonation (propagation velocity > sound speed) to propagate through capillaries having a diameter below 1 mm. Therefore, the knowledge of the detonation characteristics of the mixture in question is necessary to take respective precaution measures. The propagation of a deflagration (propagation velocity < sound speed) through a capillary was not observed until now.

2 Safety features

To arrange for safety of a microstructured process equipment with respect to detonation transmission, basic information is necessary, e.g., in the case of gas phase oxidations the knowledge of detonation limits [lower detonation limit (LDL), upper detonation limit (UDL)], limiting starting pressure (plim), detonation cell width (λ), detonation velocity (vdet) and detonation pressure (pdet). Detonation limits and detonation cell width including their pressure and temperature dependence as well as the limiting starting pressure including its temperature dependence allow decisions on safe equipment design and/or safe process parameters. If it is not possible to stay at conditions where detonation transmission is excluded, the knowledge of detonation pressure and detonation velocity including their dependence on the process parameters starting pressure, starting temperature and mixture composition allows to judge for the most dangerous conditions.

3 Determination of the necessary parameters

Based on available literature information [19], two experimental setups were established, ‘capillary setup’ and ‘detonation parameter setup’, for the determination of the aforementioned characteristics. Figure 1 shows the ‘detonation parameter setup’. It consists of an ignition vessel with an ignition source, a tube of 6 m length and a diameter of 10 mm, a monitoring unit, devices to meter the components including a mixing unit and a decay part for down-streaming the detonation. The dimensions of the ignition vessel are such to be sure to initiate a detonation in the ignition vessel for mixtures with oxidizers of an enhanced oxidizing potential (O2, N2O). The monitoring unit contains four evenly spaced piezoelectric pressure transducers, followed by a half pipe part having a cylindrical or quadrate profile which is coated with a soot layer on which the detonation cell structure is printed. This detonation cell structure is the result of the interaction of transversal waves with the main detonation wave and the tube wall. The pressure transducers are used for the determination of detonation pressure (Chapman-Joguet pressure) and velocity, their data being recorded at a frequency of 2×106 samples/s. After each run, the cell structure is photographed and, after proper magnification, analyzed manually.

Schematic diagram for the ‘determination parameter setup’.
Figure 1

Schematic diagram for the ‘determination parameter setup’.

This setup is placed in a heating chamber for determinations at elevated temperatures. It can be used for starting pressures up to 20 bar and starting temperatures up to 150°C.

This setup was mainly used to determine the detonation cell width in correlation with the starting pressure and the starting temperature because, based on theoretical consideration, a detonation should be able to pass through a tube of diameter d only if the diameter of the tube is larger than the detonation cell width λ [10]:

The ‘capillary setup’ shown schematically in Figure 2 allows the direct observation of detonations through capillaries by the use of either steel capillaries and pressure transducers or glass capillaries and cameras together with pressure transducers.

Schematic diagram of the ‘capillary setup’.
Figure 2

Schematic diagram of the ‘capillary setup’.

This setup consists of an ignition vessel with an ignition source, a receptacle with a pressure transducer, a bypass, metering devices to meter the components and a mixing unit. The dimensions of the ignition vessel are such to be sure to initiate a detonation in the ignition vessel for mixtures with oxidizers having an enhanced oxidizing potential (O2, N2O). Glass or steel capillaries of different diameters and lengths can be mounted between the ignition vessel and the receptacle. Steel capillaries with a length of up to 5 m and starting pressures up to 5 bar can be used. Owing to handling aspects, glass capillaries, by contrast, can be used only with lengths up to 0.5 m and at starting pressures below 1.5 bar but allowing observations of the propagating detonations with a high-speed camera at 32,000 fps or a video camera. The observations in glass capillaries by use of video cameras in time exposure mode are shown in Figure 3A, B or by high speed cameras in Figure 4A, B.

(A) Transmission of a C2H6/O2 detonation (equivalence ratio = 1) at 1 bar and ambient temperature through a glass capillary (l = 0.4 m, Ø = 0.5 mm; 1/60 s exposure time); : borders of the capillary. (B) Quenching of a C2H6/O2 detonation (equivalence ratio = 1) at 0.16 bar and ambient temperature through a glass capillary (l = 0.5 m, Ø=0.5 mm; 1/60 s exposure time); : borders of the capillary.
Figure 3

(A) Transmission of a C2H6/O2 detonation (equivalence ratio = 1) at 1 bar and ambient temperature through a glass capillary (l = 0.4 m, Ø = 0.5 mm; 1/60 s exposure time); : borders of the capillary. (B) Quenching of a C2H6/O2 detonation (equivalence ratio = 1) at 0.16 bar and ambient temperature through a glass capillary (l = 0.5 m, Ø=0.5 mm; 1/60 s exposure time); : borders of the capillary.

(A) Transmission of a C2H6/O2 detonation (equivalence ratio = 1) at 1 bar and ambient temperature through a glass capillary (l = 0.4 m, Ø = 0.5 mm; shutter frequency = 32,000 fps). (B) Quenching of a C2H6/O2 detonation (equivalence ratio = 1) at 0.16 bar and ambient temperature through a glass capillary (l = 0.5 m, Ø = 0.5 mm; shutter frequency = 32,000 fps).
Figure 4

(A) Transmission of a C2H6/O2 detonation (equivalence ratio = 1) at 1 bar and ambient temperature through a glass capillary (l = 0.4 m, Ø = 0.5 mm; shutter frequency = 32,000 fps).

(B) Quenching of a C2H6/O2 detonation (equivalence ratio = 1) at 0.16 bar and ambient temperature through a glass capillary (l = 0.5 m, Ø = 0.5 mm; shutter frequency = 32,000 fps).

Long-time exposures reveal the transmission of the detonation as a bright streak reaching from one end of the capillary to the other. In case the conditions are not suited for transmission of a detonation, a pulsating light emission is recorded just after the detonation wave entered the capillary before fading out completely (Figure 3B, Figure 4B). Whereas a detonation pressure signal is registered by the pressure transducer in case the detonation passes through, no pressure signal is observed in these cases, indicating that also no deflagration passes. To also take into account the possible influence of the length of the capillary, ‘no detonation transmission possible’ was assigned when there was just no light emission registered by the camera.

This setup is used to check the trustability of the λ/3-rule by direct observation and also allows the determination of the detonation limits and limiting starting pressure in correlation with the starting pressure, the starting temperature and the capillary diameter.

4 Detonation characteristics for a safe design

4.1 Detonation limits

Knowledge of the detonation limits (LDL and UDL) including their dependence on starting pressure, starting temperature and capillary diameter allows to chose mixture compositions which are not able to detonate under the conditions used.

Figure 5 shows with ethane/O2 mixtures, as an example, the influence of the capillary diameter. Narrowing of the capillary diameter leads to a narrowing of the detonation range until a minimum diameter where a detonation transmission is no longer possible.

Dependence of detonation limits of ethane/O2 mixtures on the diameter of the tube/capillary at 20°C and ambient pressure.
Figure 5

Dependence of detonation limits of ethane/O2 mixtures on the diameter of the tube/capillary at 20°C and ambient pressure.

The detonation limits as well as this minimum diameter where a detonation transmission is no longer possible are, however, dependent on the starting pressure. The limits widen with increasing starting pressure (Figure 6) and the minimum diameter decreases. The limits are substance-specific (Figure 6).

Dependence of detonation limits of hydrocarbon/O2 mixtures on initial pressure at ambient temperature measured in a 10-mm tube.  Ethane LDL,  Ethane UDL,  Propane LDL,  Propane UDL,  n-Butane LDL,  n-Butane UDL.
Figure 6

Dependence of detonation limits of hydrocarbon/O2 mixtures on initial pressure at ambient temperature measured in a 10-mm tube.

Ethane LDL, Ethane UDL, Propane LDL, Propane UDL, n-Butane LDL, n-Butane UDL.

4.2 Limiting starting pressure

The aforementioned correlations allow in reverse to derive a limiting starting pressure (the minimum pressure necessary to enable a detonation just passing through a capillary) in conjunction with a desired capillary diameter (Table 1).

Table 1

Dependence of the ‘limiting starting pressure’ from capillary diameter for stoichiometric (equivalence ratio = 1) ethane/oxygen mixtures.

4.3 Detonation cell width

A well-known method to evaluate the ability of a detonation to pass through a tube is the determination of the width λ of the detonation cells that are printed on the soot-coated walls of the tube. Their ideal shape is shown schematically in Figure 7 as well as the reality. In practice, detonation cell structures are not as regular as outlined.

(A) Photograph of a detonation cell pattern (ethane/O2, equivalence ratio = 1, p0 = 0.6 bar) λ = detonation cell width; ↑ = detonation direction. (B) Sketch of an ideal detonation cell structure. λ = detonation cell width; ↑ = detonation direction.
Figure 7

(A) Photograph of a detonation cell pattern (ethane/O2, equivalence ratio = 1, p0 = 0.6 bar) λ = detonation cell width; ↑ = detonation direction. (B) Sketch of an ideal detonation cell structure. λ = detonation cell width; ↑ = detonation direction.

For this reason, a large number of detonation cells is necessary to obtain good statistics of cell width distributions. Because of these irregularities in the cell structure, the standard deviation of the detonation cell is typically 15–20%.

Detonation cell widths vary with the composition of the mixture and are smallest at or near an equivalence ratio of 1. Figure 8 shows this for measurements with ethane/O2 mixtures in a 10-mm tube. The correlation of the detonation cell width with the composition of the mixture between the LDL and the UDL is, however, asymmetric. Near the LDL the detonation cell width rises very steeply [(Eq. (1)]. Near the UDL no such remarkable increase of the detonation cell width could be found for the investigated substances ethane, propane and n-butane. It becomes only somewhat larger for rich mixtures (Figure 8). Assuming the ‘λ/3-rule’ would be valid without restrictions over the whole detonation range, cell widths of up to 30 mm should be possible in the present case (tube diameter: 10 mm). Because of the steep increase of the cell width near the LDL, it is not excluded that at the LDL the ‘λ/3-rule’ is still valid (Figure 8). The UDL, however, does not comply with a detonation cell width of approximately 30 mm.

Correlation between the mean detonation cell width and the composition of ethane/O2. Mixtures measured using the 10-mm tube;  ambient pressure, ambient temperature; pini = 2 bar, ambient temperature; pini = 3 bar, ambient temperature; pini = 3 bar, T = 100°C.
Figure 8

Correlation between the mean detonation cell width and the composition of ethane/O2.

Mixtures measured using the 10-mm tube; ambient pressure, ambient temperature; pini = 2 bar, ambient temperature; pini = 3 bar, ambient temperature; pini = 3 bar, T = 100°C.

The detonation cell width is remarkably pressure-dependent. Plotting the detonation cell width against initial pressure on a double-logarithmic scale, a straight line is obtained for stoichiometric (equivalence ratio = 1) (Figure 9) as well as for non-stoichiometric (equivalence ratio ≠ 1) (Figure 10) mixtures.

Correlation between initial pressure and mean detonation cell width for stoichiometric mixtures (equivalence ratio = 1) at ambient temperatures.
Figure 9

Correlation between initial pressure and mean detonation cell width for stoichiometric mixtures (equivalence ratio = 1) at ambient temperatures.

The pressure exponent for stoichiometric (equivalence ratio = 1) as well as for non-stoichiometric (equivalence ratio≠1) mixtures is remarkably larger than -1 as assumed by [3]. The correlation is substance-specific. The following dependencies (confidence interval 95%) were found to hold for stoichiometric mixtures with oxygen (equivalence ratio = 1):

For different mixture compositions of the same system the pressure exponent varies and differs more from that of the stoichiometric composition (equivalence ratio = 1) the more the composition gets nearer to the detonation limits (Figure 10).

Correlation between initial pressure and mean detonation cell width for stoichiometric and non-stoichiometric ethane/O2 mixtures at ambient temperatures.  φ = 1.0;  φ = 0.7;  φ = 2.0;  φ = 2.4;  φ = 0.5.
Figure 10

Correlation between initial pressure and mean detonation cell width for stoichiometric and non-stoichiometric ethane/O2 mixtures at ambient temperatures.

φ = 1.0; φ = 0.7; φ = 2.0; φ = 2.4; φ = 0.5.

The temperature influence on cell width was found to be fairly small (Figure 8). A similar result has been obtained by Tieszen et al. [11] for ethane/air.

4.4 Detonation velocity and detonation pressure

The results for propane/oxygen mixtures of an equivalence ratio of 1 measured in a tube of 10 mm diameter as an example are given in Figure 11, together with theoretical values calculated by GASEQ software [12]. In general, both the measured values and the calculated (theoretical) values fit well (for examples, see Table 2). Although the detonation velocity at starting pressures of more than 1 bar is only marginally dependent on initial pressure, it decreases with decreasing starting pressure. A similar behavior was reported by Fischer et al. [13] for ethene/oxygen mixtures of an equivalence ratio of 1. However, as can be seen from Figure 11, for very low pressures the detonation velocity decreases more rapidly than predicted by theory, probably due to the higher ratio of the surface to the number of active species in the oxidation reaction. The detonation (Chapman-Joguet) pressure is proportional to the starting pressure. Similar results have been obtained for ethane/oxygen and n-butane/oxygen mixtures.

Table 2

Comparison of measured and calculated detonation velocities and pressures for stoichiometric (equivalence ratio = 1) hydrocarbon/oxygen mixtures at ambient conditions (T = 21°C, p = ambient).

Dependence of detonation velocity and detonation pressure on initial pressure compared with theoretical values for stoichiometric (equivalence ratio = 1) propane/O2 mixtures.  detonation velocity, experimental;  detonation velocity, calculated;  detonation pressure, experimental;  detonation pressure, calculated.
Figure 11

Dependence of detonation velocity and detonation pressure on initial pressure compared with theoretical values for stoichiometric (equivalence ratio = 1) propane/O2 mixtures.

detonation velocity, experimental; detonation velocity, calculated; detonation pressure, experimental; detonation pressure, calculated.

Dependence of detonation velocity and pressure on the composition of ethane/O2 mixtures.  detonation velocity, experimental: ambient pressure, ambient temperature,  calculated;  detonation velocity, experimental ambient: pressure, 100°C,  calculated;  detonation pressure, experimental: ambient pressure, ambient temperature,  calculated;  detonation pressure, experimental: ambient pressure, 100°C,  calculated.
Figure 12

Dependence of detonation velocity and pressure on the composition of ethane/O2 mixtures.

detonation velocity, experimental: ambient pressure, ambient temperature, calculated; detonation velocity, experimental ambient: pressure, 100°C, calculated; detonation pressure, experimental: ambient pressure, ambient temperature, calculated; detonation pressure, experimental: ambient pressure, 100°C, calculated.

The variation of detonation velocity and pressure with mixture composition is shown in Figure 12. The maximum is at an equivalence ratio of approximately 2. This behavior is again predicted by theory [12]. For propane and n-butane similar results were obtained.

Reactions in microstructured devices usually take place at elevated temperatures. As Figure 12 shows, an increase in temperature has little influence on the detonation velocity but causes the maximum detonation pressure to decrease substantially. Chapman-Joguet theory predicts for the ratio of the maximum detonation pressure to the starting pressure pCJ/pini:

Eq. (6) is roughly confirmed by experiment.

5 Discussion

The present results show that capillaries, as often used in microstructured devices, cannot be seen as intrinsically safe with respect to the transmission of a detonation and, therefore, do not necessarily constitute an ‘intrinsic flame arrester’. On the contrary, a detonation hazard exists for the mixtures with oxidizers with enhanced oxidizing potential and high pressures even for small diameters. Knowing the detonation limits for the respective process parameters or the limiting starting pressure for the respective system would allow staying beyond these limits.

A ‘safe capillary diameter’ can be derived directly from capillary experiments by changing the diameter of the capillary for a given composition of the mixture in connection with the initial pressure and temperature until quenching is achieved. Another possibility exists if the width of the detonation cells for the conditions in question are known or can be calculated using the respective pressure: detonation cell width correlations. Then the ‘safe capillary diameter’ can be calculated by use of the so-called ‘λ/3-rule’ [Eq. (1)].

Table 3 shows for stoichiometric mixtures (equivalence ratio = 1) that this method works well for simple tube geometries, if a suitable safety margin is applied to take into account the scatter and uncertainty of the measurements.

Table 3

Comparison of safe capillary diameters for stoichiometric (equivalence ratio = 1) ethane/oxygen mixtures calculated by Eqs. (1) and (2) with direct observations.

The determination of the ‘safe diameter’ should be based on the data for stoichiometric compositions (equivalence ratio = 1) because mixtures with an equivalence ratio of 1 have been found to be the most critical ones with respect to detonation cell dimensions and therefore to detonation transmission. Although the starting pressure has a large influence, elevated temperatures, by contrast, seem to have less influence.

Because of the large influence of the starting pressure on the detonation cell width, it is important to take into account possible precompression effects when choosing the respective starting pressure on which the detonation cell width will be based on. Such precompression effects that may be generated by deflagrations occurring in upstream parts of the equipment or failing of the intended chemical reaction should be considered, as well as a possible influence by multiple rectangular bent design of capillary tubes.

As usual in explosion safety an additional safety margin has to be applied before transferring the results to practice and all conformity assessment procedures where required need to be applied.

List of abbreviations

d:

tube diameter

LDL:

lower detonation limit

pini:

initial pressure

pdet:

detonation pressure

pmax, det:

maximum detonation pressure

plim:

limiting starting pressure

r:

tube radius

UDL:

upper detonation limit

vdet:

detonation velocity

vmax,det:

maximum detonation velocity

T:

temperature

λ:

detonation cell width

References

  • [1]

    Wagner HG. In Handbook of Explosion Prevention and Protection, Hattwig M, Steen H, Eds., Wiley-VCH-Verlag GmbH&Co.: Weinheim, 2004, p. 25 Google Scholar

  • [2]

    Nettleton MA. Gaseous Detonation: Their Nature, Effects and Control, Chapman and Hall Ltd.: New York, 1987Google Scholar

  • [3]

    Fickett W, Davis WC. Detonation: Theory and Experiment, 2nd ed., Dover Pubn. Inc.: Mineola, 2001 Google Scholar

  • [4]

    Manson N, Guenoche H. Rev. Inst. Fr. Petrole Ann. Comb. liq. 1954, 9, 214Google Scholar

  • [5]

    Bull DC, Elsworth JE, Shuff PJ, Metcalfe E. Comb. Flame 1982, 45, 7Google Scholar

  • [6]

    Lee JH, Guirao CM, Knystautas R. Combust. Flame 1982, 48, 63–83Google Scholar

  • [7]

    Weber M. Detonationswellen in Engen Spalten. 1. Süsterfeldstr. 83, 52072. Verlagshaus Mainz GmbH: Aachen, 2007Google Scholar

  • [8]

    Manzhalei VI. Combust. Explos. Shock Waves 1992, 28, 296–302Google Scholar

  • [9]

    Gödde M, Liebner Ch, Hieronymus H. Chem. Ingen. Techn. 2009, 81, 73–78 Google Scholar

  • [10]

    Knystautas R, Guirao CM, Lee JH, Sulmistras A. Prog. Astronaut. Aeronaut. 1984, 94, 23–37 Google Scholar

  • [11]

    Tieszen SR, Stamps DW, Westbrook CW, Pitz WJ. Comb. Flame 1991, 84, 376 Google Scholar

  • [12]

    Morley C. GasEQ 0.79 (http://www.arcl02.dsl.pipex.com 2008) 

  • [13]

    Fischer J, Liebner C, Hieronymus H, Klemm E. Chem. Eng. Sci. 2009, 64, 2951–2956 Google Scholar

About the article

Elisabeth Brandes

Elisabeth Brandes received a diploma in chemistry in 1978 and a Dr. rer. nat. in 1982 at TU Braunschweig. She worked as a scientist at Physikalisch-Techniche Bundesanstalt Braunschweig since 1982 with the explosion safety department. Since 1994, she is heading the PTB working group ‘Safety Characteristics’.

Markus Gödde

Markus Gödde received a diploma in chemistry in 1994 and a Dr. rer. nat. in 1999 at TU Braunschweig. He worked as a research engineer at BASF SE Safety Engineering Group in the field of explosions of gases, vapors and dusts, electrostatics, ignition processes in Ludwigshafen from 1999 to 2003. During 2003–2004, he worked in the process safety department of BASF. Since 2004, he is responsible for the safety assessment of chemical reactions and for the classification tests in the BASF SE Safety Engineering Group.

Werner Hirsch

Werner Hirsch received a diploma in chemistry in 1980 and a Dr. rer. nat. in 1987 at FU Berlin. From 1989 to 1991 he worked as a researcher at the Hahn-Meitner-Institut at Berlin. Since 1992 he works as a scientist at Physikalisch-Technische Bundesanstalt, Braunschweig with the Explosion Safety Department.


Corresponding author: Elisabeth Brandes, Physikalisch-Technische Bundesanstalt, AG 3.41, Bundesallee 100, 38116 Braunschweig, Germany


Received: 2012-03-05

Accepted: 2012-04-17

Published Online: 2012-07-28

Published in Print: 2012-08-01


Citation Information: Green Processing and Synthesis, Volume 1, Issue 4, Pages 345–352, ISSN (Online) 2191-9550, ISSN (Print) 2191-9542, DOI: https://doi.org/10.1515/gps-2012-0015.

Export Citation

©2012 Walter de Gruyter GmbH & Co. KG, Berlin/Boston.Get Permission

Comments (0)

Please log in or register to comment.
Log in