- Email: [email protected]
Liquid leakage assessment from gas leakage tests
Measurement 151 (2020) 107135
Contents lists available at ScienceDirect
Measurement journal homepage: www.elsevier.com/locate/measurement
Liquid leakage assessment from gas leakage tests V.A.F. Costa TEMA – Centro de Tecnologia Mecânica e Automação, e Departamento de Engenharia Mecânica da Universidade de Aveiro, Campus Universitário de Santiago, 3810-193 Aveiro, Portugal
a r t i c l e
i n f o
Article history: Received 18 April 2019 Received in revised form 14 August 2019 Accepted 6 October 2019 Available online 11 October 2019 Keywords: Pressure difference driven leakage Liquid leakage assessment Gas leakage Pressure decay testing Liquid and gas leakages relationship
a b s t r a c t Liquid leakage assessment is usually difficult, what can be overwhelmed through leakage testing using gases. This happens in many situations of practical interest of pressure-difference driven liquid leakage. Starting from physical principles and laws, analytical expressions relate the liquid and gas leakages occurring through the same leak geometry. Pressure differences driven the liquid and gas leakages can be different. Process of obtaining the analytical expressions highlights the physics behind the process of leakage testing and the involved variables and principles. Obtained analytical expressions relate the governing variables, allowing calculations for results treatment, interpretation, correlation or uncertainty analysis. Developments and results presented in the paper fulfill a gap of the literature concerning the liquid leakage assessment and testing using gases, and of the users’ manuals of the leakage testing equipment. This additional knowledge and information allows equipment use and leak tests conduction with greater confidence, and supported results analyses, criticism and treatment. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Leakage detection, localization, measurement, evaluation and assessment are of major relevance in many activities and economic sectors. If this is true in general, it can be critical in many situations, and among them those characterized by low or even very low flow rate leakages, usually requiring more accurate analyses, methods, sensors and instruments. Leakages are usually unwanted, due to assemblies or sealing defects, the leak geometry through which leakages occur being not well defined, and remaining usually unknown. Liquids leakage tests are usually conducted subjecting the parts or assemblies to the operating conditions. However, liquids leakage tests have a considerable number of disadvantages, some of them being: (i) Liquid leakages correspond to low or even very low liquid flow rates, requiring long time periods for their evaluation or assessment, usually incompatible with fast/high production rates, and requiring highly accurate sensors for the liquid amount evaluation; (ii) It can be pernicious that some liquid belongs with the product after the leakage tests; (iii) Liquid remaining with the product can damage paper packing, and also the writings and/or printed matters over the packing; (iv) Liquid leakages always lead to some liquids waste and/or potential pollution. Leakage tests using gases, and specially those using air, have a lot of advantages, namely: (i) They can be fast, and thus compatible with
E-mail address: [email protected] https://doi.org/10.1016/j.measurement.2019.107135 0263-2241/Ó 2019 Elsevier Ltd. All rights reserved.
fast/high production rates, fastness of the tests being increased as increases the gas pressure; (ii) Parts remain dry and clean during and after the leakage tests; (iii) Leakage tests can be easily automated, and/or included in an automated processes; (iv) Gas leakage tests do not induce any damage of both the product and the packing; (v) If air is used for the gas leakage tests no additional costs and/or pollution exist related with the air losses due to the gas leakage. This work deals with pressure-driven leakage flows. Molecular flows due to Fick or Knudsen diffusion are not considered, as the mean free path of the molecules is significantly lower than the characteristic dimension of the leak geometry. Leakage tests using gases can be made subjecting the gas to a pressure greater than the atmospheric pressure (overpressure tests) or lower than the atmospheric pressure (under-pressure tests). The first option is usually cheaper, as the compressor equipment and operation are usually cheaper than those of a vacuum pump. Additionally, if a pressure greater than the atmospheric pressure is used it is easy to filtrate the gas contacting the part to be tested, while if a pressure lower than the atmospheric pressure is used gas can enter the part from the ambient at unspecified points, and it is not so easy to filtrate it. If gas leakage tests are faster, cheaper, cleaner, and easier than liquid leakage tests, it is tempting to assess the liquid leakages from gas leakage tests, and specially from air leakage tests. Present work shows that this is possible, and how are related the liquid and gas leakages flowing through the same leak geometry, even if the liquid and gas leakages are driven by different pressure differences.
2
V.A.F. Costa / Measurement 151 (2020) 107135
Nomenclature L m _ m P Q_ R R t T V x
Length of the leakage channel [m] mass [kg] Mass flow rate [kg/s] Pressure [Pa] Volumetric flow rate [m3/s] Radius of the leak channel [m] Particular gas constant [J/(kg.K)] Time [s] Temperature (absolute) [K] Volume [m3] Length coordinate, along the leakage [m]
Dt
l q s
Testing time period [s] Dynamic viscosity [kg/(m.s)] Density [kg/m3] Time constant [s]
Subscripts atm Atmospheric value g Gas i Initial l Liquid max Maximum value min Minimum value
Greek letters a Dimensionless auxiliary pressure [] b Dimensionless auxiliary variable []
This is not a new issue and equipment exist to do that, examples being those referred in [1] and [2]. Concerning available equipment for leakage measurements/assessment, some information is available on how to use the equipment on the respective users’ manual. However, few reliable information is available concerning the involved physical principles and laws, the involved variables, the relationships between the involved variables, the pressures’ scales, the variables’ units, etc. It is also unclear how to relate the liquid and gas leakage flow rates, and how to relate them for different operating and test conditions. This work aims to fulfill this leak of analysis and information, joining in a concise and grounded way the issues concerning the physics of the involved processes, and the relationships between the involved variables, including the additional complexity associated with the gas compressible character. If the equipment’s manuals are not of great help concerning the aspects referred above, the scientific literature on the leak measurement/assessment is also not very rich. Amesz [3] reports the development of rules for conversion of gas and liquid leakages, as in many cases leakage is tested by means of a gaseous medium for systems that operate with a liquid medium. Some correlations, instead of analytical closed relationships, are proposed to relate liquid and gas leakage flows. This is the work whose main objectives are closer to those of the present work, but the approach, results and readability are considerably different. Lorenz and Persson [4] present a medium theory of the leak rate of rubber seals, based on a contact mechanics theory, emphasis being given to the particular nature of the rubber seals. Emphasis of the work by Murvaya and Silea [5] is on the state-of-the-art in leak detection and localization methods, based on the principle that gas leakage detection can avoid the major incidents resulting from gas leakages. However, no emphasis is given to the relationship between the liquid and gas leakage flow rates through the same leak geometry Work by Grine and Bouzid [6] develops an analytical leak rate prediction methodology applying for the particular case of gasketed joints, including the estimation of the leak porous structure through a pseudo analytical-experimental approach. The analytical model is validated by comparison with experimental results. Work by Martinsanz [7] is devoted to the technological developments and methods of sensors based on physical, chemical or biological principles aiming fluid leak detection, starting from the point that leakage is a problem that can cause important economic losses and environmental pollution, putting human, animal or plant lives at risk. Work by Felix and Franchi [8] deals with a sealing system designed to perform simulations of air leaks. Air leakage is measured using a mass flow sensor, directly indicating the volumetric
leakage. The automation of the process has been developed and implemented on an open-source platform using low-cost controller. Adedeji et al. [9] deal with the leakage detection and localization in pipelines of large-scale potable water distribution networks, relying mainly on wireless sensor networks for leakage detection purposes. Even if few, no any of the works found in the literature follows the approach, answers the questions, and leads to the results as proposed by the present work. 2. Fluid flow through a leak 2.1. Base formulation for the laminar fluid flow through a leak The basis for the evaluation of the laminar fluid flow driven by a pressure difference against a given resistance dependent on the leak geometry and on the fluid viscosity, is the Hagen-Poiseille Law. In the differential form, for a leakage through a circular duct, it sets that locally [10].
p 1 dP Q_ x ¼ R4 8 l dx
ð1Þ
Geometries other than the circular duct for the leak can be considered, but this particular geometry is not relevant for the present purposes, once it is the same for the liquid and gas leakages, by the reasons explained below. 2.2. Liquid flow leakage Liquid is considered to be incompressible, its volumetric flow rate being independent of the local pressure, no liquid storage/ accumulation occurs in leak system, and the surface tension effects are neglected when compared with the pressure difference forces. It is also assumed that no liquid-vapor phase change occurs as the liquid pressure decreases along the leak. Under the above referred conditions, for the situation illustrated in Fig. 1, Eq. (1) set for the liquid can be integrated along the whole length of the leak to give
p R4 1 ðP l Patm Þ Q_ l ¼ 8 L ll
ð2Þ
where on the right-hand side are observed, from left to right, the influence of the geometry of the leak system, the liquid viscosity, and the pressure difference forcing the liquid leakage (Fig. 1).
3
V.A.F. Costa / Measurement 151 (2020) 107135
In general, the geometry of the leak system is not well known nor well defined. It can be a straight circular channel, a straight rectangular cross section channel, a straight circular or rectangular annular cross section channel, tortuous circular or rectangular cross section channels, tortuous channels with variable cross sections, a series association of tortuous channels with variable cross sections, a parallel association of tortuous channels with variable cross sections, etc. Conceptually, any particular geometry can be condensed in a geometry factor G, with units of m3, and Eq. (2) reads, for a generic leak system
1 Q_ l ¼ G ðPl P atm Þ
ð3Þ
ll
In practical situations of liquid leakage evaluation and assessment, some kind of criterion sets the limit Q_ of the admissible
Pg
dPg 8 1 _ l PQ ¼ dx p R4 g g g x
ð6Þ
Using Eq. (5) to take P g Q_ g ¼ constant, Eq. (6) can be intex
grated along the leak and the result arranged as
1 Pg þ P atm p R4 1 Q_ g ¼ Pg Patm x 2 8 L lg Pg x
ð7Þ
which is the Hagen-Poiseille Law for an isothermal (Ideal Gas) compressible flow, noting that pressures in Eq. (7) are absolute pressures. 3. Pressure decay associated with the gas leakage from a test chamber
l;max
volume flow rate for the liquid leakage, as
Q_ l 6 Q_ l;max
ð4Þ
In some situations the admissible liquid leakage is specified through the number of liquid drops that escape during a given time period. In these situations attention needs to be given to the liquid volume corresponding to some drops that holds attached to the solid parts due to the surface tension effects, the number of drops that escaped through the leakage differing from the number of drops that fall from the part being tested during the specified time period. 2.3. Gas flow leakage Contrarily to the liquid, the gas is compressible and locally its volumetric flow rate depends on the local pressure. If the gas can be assumed to behave as an Ideal Gas, it is [11]
P Q_ _ g ¼ qg Q_ g ¼ g g m Rg T
ð5Þ
If no gas storage/accumulation occurs in the leak system and assuming the temperature of the gas is constant along the leak, it _ ¼ constant at any point of the leak [11], and from Eq. (5) it is m g ¼ Pg ¼ constant at any point of the leak. is P g Q_ Q_ g
x
x
g
x
Starting with Eq. (1), in this case for the gas as presented in Fig. 2, rearranging and multiplying both sides by P g results in
Gas flow leakage is usually measured through a pressure decay method, as illustrated in Fig. 3: a chamber of volume V g (constant, corresponding to the whole volume filled with the gas that experiences the pressure decay due to the gas leakage) filled with gas initially at pressure P g;i . During a given test period Dt g , after a pressure stabilization period, gas pressure decreases in volume V g , and it is from this gas pressure decay with time that the gas flow leakage is evaluated. It is assumed that the geometry through which the gas leakage occurs is the same as that through which the liquid leakage occurs, in order to allow the evaluation/assessment of the liquid leakage from the measurement of the gas leakage through a pressure decay test. It is assumed that the gas behave as an Ideal Gas, and that the expansion process experienced by the gas filing volume V g is sufficiently slow to be considered isothermal, at absolute temperature T. From the Ideal Gas Law it is [11]
Pg V g ¼ mg Rg T )
dmg V g dPg _g ¼ ¼m dt Rg T dt
ð8Þ
Introducing Eqs. (8) into (7) leads to an equation that can be integrated for the pressure of the gas filling volume V g changing from Pg;i to P g ðtÞ, during the time t, from which results
2
3
P g ðt ÞP atm P ðt ÞþP atm 5 ln4 Pg Patm g;i Patm P g;i þP atm
1
¼
p R4 1 1 t 8 L lg V g
ð9Þ
On the left-hand side of this equation is present, in a nonlinear form, the pressure variation experienced by the gas filling volume V g . On the right-hand are observed, from left to right, the influence of the geometry of the leak, the gas viscosity, the volume of the chamber from which the gas escapes, and the time period t during which pressure in the chamber changes from P g;i to P g ðtÞ. It is to be retained that pressures in this equation are absolute pressures. Defining the auxiliary dimensionless pressure difference
a¼ Fig. 1. Schematic illustration of the liquid flow leakage.
Fig. 2. Schematic illustration of the gas flow leakage.
Pg;i Patm Pg;i þ Patm
ð10aÞ
and the time constant
Fig. 3. Schematic illustration of the gas leakage, through the same leak geometry as the liquid leakage in Fig. 1.
4
V.A.F. Costa / Measurement 151 (2020) 107135
s ¼ Patm
p R4 1 1 8 L lg V g
!1 ð10bÞ
Eq. (9) allows obtaining the (absolute) pressure P g ðtÞ at any instant t after the beginning of the pressure-decay process as
1 þ aexpðt=sÞ Pg ðt Þ ¼ Patm 1 aexpðt=sÞ
ð11Þ
It is to be noted that as the geometry of the system through which the leakage occurs is not well known nor well defined, parameter s is not well defined, and Eq. (11) is not useful for practical purposes. It is useful only as it indicates how the pressure of the gas in the test chamber decays with time. Another way to express Eq. (9) is
" # et=s et=s 1 Pg ðt Þ Patm t=s ¼e þ 1 t=s P g;i Patm ae
ð12Þ
This equation shows that the gas pressure decay does not follow a first order decay [12], et=s , but that it includes the additional term inside square brackets of Eq. (12). This additional term is negative, smaller than the first order exponential decay given by et=s , but even so it is not null. 4. Relating the liquid and gas leakage flow rates To relate the liquid and gas leakage flows through the same leak geometry, it is assumed that the liquid pressure Pl remains essentially constant and that the liquid leakage is driven by the pressure difference ðP l Patm Þ. Dividing Eqs. (7) and (2) leads to
Q_ g Q_ l
x
ll Pg Patm 1 Pgþ Patm lg Pl Patm 2 Pg x
¼
ð13Þ
and only if the involved pressures P g , Pl , and Patm are very close is the volumetric flow rate ratio Q_ g =Q_ l essentially given by the x
dynamic viscosity ratio ll =lg . Dividing Eqs. (9) and (2) side by side and rearranging results in
Q_ l ¼
lg 1 ðPl Patm Þ 1 Pg ðtÞ Patm V ln ll g t Patm a Pg ðtÞ þ Patm
ð14Þ
It is to be noted that the geometry of the leak is absent from the obtained Eqs. (13) and (14), once it is the same for the liquid and gas leakages. Previous developments were made considering both liquid and gas leakages occurring through a circular channel of uniform cross section; however, when relating the liquid and gas leakage flow rates the particular geometry of the leak is irrelevant, as it is eliminated when obtaining Eqs. (13) and (14). Eq. (14) relates the liquid flow rate leakage Q_ with the gas presl
sure change from P g;i to P g ðtÞ into the gas chamber during the measurement time t. Both liquid and gas leakages occur through the same leak geometry, even if they are forced by different pressure differences, ðP l P atm Þ for the liquid leakage and (instantaneously)
P g ðtÞ P atm for the gas leakage. Once set the time period Dtg for the gas pressure decay, the volume of the test chamber V g , and the initial gas pressure Pg;i , there is a gas pressure Pg;min for which it is Q_ ¼ Q_ . Thus, criterion l
bm ¼
ll Dtg Patm _ Q lg V g ðPl Patm Þ l;max
ð15Þ
it is obtained from Eq. (14) that the lower limit (absolute) pressure Pg;min is
Pg;min ¼ P atm
1 þ aexpðbm Þ 1 aexpðbm Þ
ð16Þ
It is to be noted that parameter bm is well defined, evaluated from Eq. (15), that it does not depend on the geometry through which the liquid or gas leakages occur, and that Eq. (16) is very useful for practical purposes, allowing fast and accurate evaluation of the lower limit (absolute) pressure Pg;min . It can also be used to conduct the uncertainty analysis of the liquid leakage estimation through the pressure decay associated to the gas leakage occurring through the same leak geometry. Another way to express Eq. (16), in a form similar to that of Eq. (12), is
" # Pg;min Patm ebm ðebm 1Þ bm ¼e þ 1 bm Pg;i Patm ae
ð17Þ
which can also be used to evaluate P g;min once known bm , P g;i and Patm . P atm . Fig. 5 presents a possible graphical form of Eq. (17) considering some ranges of practical interest for the liquid (water) and gas (air) pressures. It is to be retained that when relating the liquid and gas leakage flow rates, flowing through the same leak system, they must occur in the same direction as some geometries and assemblies present some kind of diode characteristics for fluid flow, imposing different resistances depending on the fluid flow direction. 5. Validation tests Validation tests of Eq. (17) can be made considering water leakage from a system and its assessment through the air pressure decay measurement. The system under analysis, with constant volume V g ¼ 0:928 L, has some threaded pipes intentionally left incompletely screwed to originate the experimentally measured liquid leakage and its assessment using Eq. (17). The water leakages were measured for some liquid pressures, P l , and the measured value taken as the maximum admissible liquid leakage, Q_ . It is to be noted from Eq. (2) that it is l;max
Q_ l;max =ðPl Patm Þ ¼ constant in Eq. (15). For the particular system =ðP l P atm Þ ¼ under analysis it was obtained Q_ l;max
3:067 1012 m3/(Pa.s). For a liquid 4 bar relative pressure this corresponds to a liquid leakage of 1:213 106 m3/s. Water and air properties (dynamic viscosities) were taken for the temperature of 20 °C. Pressure decay tests with air corresponded to the same leakage geometry as for the liquid leakages measurements, from some
l;max
expressed by Eq. (4) requires that Pg P Pg;min for t ¼ Dt g to have Q_ l 6 Q_ l;max , and this is the way how a gas leakage measurement procedure can be used for liquid leakage evaluation or assessment. This is illustrated in Fig. 4. Given the dimensionless pressure difference a defined through Eq. (10a), and defining the additional dimensionless parameter
Fig. 4. Schematic illustration of the gas pressure decay test.
5
V.A.F. Costa / Measurement 151 (2020) 107135
Fig. 5. A possible graphical presentation of Eq. (17).
Table 1 Validation results for a ¼ 0:1979. P g [Pa G]
t [s]
bm
50,000 40,000 30,000 20,000 10,000
0 12 28 49 87
0.2117 0.4941 0.8646 1.5351
P g [Pa G]
t [s]
bm
40,000 30,000 20,000 10,000
0 16 37 75
0.2823 0.6529 1.3234
Pg;min P atm Pg;i Patm Eq: ð17Þ
0.773 0.557 0.369 0.180
Pg;min Patm Pg;i P atm exp
error (%)
3.4 7.2 7.9 9.8
0.80 0.60 0.40 0.20
Table 2 Validation results for a ¼ 0:1648.
initial air pressures up to the corresponding minimum air pressures, and predicted and measured results compared. Some results are summarized in Tables 1, 2 and 3 for a ¼ 0:1979, a ¼ 0:1648, and a ¼ 0:1289, respectively. Evaluation of percent errors takes the experimental values as the references. From Tables 1–3 it can be seen that the obtained results using Eq. (17) are in good agreement with the experimental results, with percent errors lower than 10%, results predicted through Eq. (17) being always below the experimental ones. It is also observed that the percent error decrease as decreases the initial gas pressure, P g;i .
Pg;min Patm Pg;i Patm Eq: ð17Þ
0.719 0.476 0.233
Pg;min Patm Pg;i P atm exp
error (%)
4.1 4.9 7.0
0.75 0.50 0.25
It is to be retained that the gas pressure measurements in the gas pressure decay tests must be made using a gas pressure sensor/ meter with a short time response, in order to obtain accurate experimental gas pressures. If the gas pressure decay is already occurring when starts the gas pressure measurements, a gas pressure sensor/meter with a short time response is crucial not only for accurate pressure measurements but also for the accurate setting of the zero for the time counter. Errors reported in Tables 1–3 can even be smaller if shorter time response gas pressure sensors/meters are used.
Table 3 Validation results for a ¼ 0:1289. P g [Pa G]
t [s]
bm
30,000 20,000 10,000
0 21 59
0.3706 1.0411
Pg;min Patm Pg;i Patm Eq: ð17Þ
0.660 0.322
Pg;min Patm Pg;i Patm exp
0.67 0.33
error (%)
1.0 3.3
6
V.A.F. Costa / Measurement 151 (2020) 107135
6. Gas leakage volumetric flow rate Gas leakage volumetric flow rate depends on the local pressure, and the usual practice is to refer it to the atmospheric pressure. Noting from Eq. (5) that [11]
_ g ¼ qg Q_ g ¼ qg Q_ g m
P atm
¼
Patm Q_ g
P atm
Rg T atm
ð18Þ
which combined with Eq. (8) leads to
Q_ g
Patm
¼
V g dPg P atm dt
ð19Þ
Declaration of Competing Interest
the average outlet gas leakage volume flow rate, referred to the atmospheric pressure, corresponding to the 0 ! Dtg time period, is evaluated as
Q_ g
Patm
¼
V g DP g P atm Dt g
ð20Þ
Patm
3 cm =min ¼
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements
where SI units are used for all the involved variables. Eq. (20) is many times used with units of cm3/min to express the outlet average gas leakage volume flow rate, referred to the atmospheric pressure, and units of cm3 to express the volume of the gas test chamber. For that purpose Eq. (20) can be rewritten as
Q_ g
test, conducted through a gas pressure decay test, and that the gas pressure decay does not follow a first order decay, contrarily to what is mentioned in some literature. Explicit analytical expressions obtained relate all the governing variables, which can be used for the intended/convenient purposes. Developments and ready to use analytical expressions fulfill a gap of the literature concerning liquid evaluation and testing using gases, and complement the usual leak of scientific information of the users’ manuals of the leak testing equipment. This allows better equipment use, increased confidence to conduct leakage tests, and more supported results analyses and criticism.
DP g ½Pa 60 V g cm3 Patm ½Pa Dt g ½ s
ð21Þ
where units of the involved variables are explicitly indicated within squared brackets, and it is to be retained that Patm ½Pa is the (absolute) atmospheric pressure expressed in Pascal. 7. Conclusions Information concerning the physics of the liquid and gas leakages, and the liquid and gas leakages relationship is absent from the literature and from the users’ manuals of the leak testing equipment. Developments are presented based on the physics of the pressure-difference driven liquid and gas leakages, leading to analytical expressions relating the involved variables and allowing relating the liquid and gas leakages occurring through the same leak geometry, even if driven by different pressure differences. Developments show how, and why, the particular geometry of the leak is not relevant when relating the liquid and gas leakages. Developments are made based on a circular leak of uniform cross section, but it is explained why the main results are independent of the particular geometry of the leak, which is unspecified and unknown in the usual situations of practical interest. It is shown that the liquid leakage can be evaluated based on a gas leak
Support from the UID/EMS/00481/2013-FCT Project, and from the CENTRO-01-0145-FEDER-022083 Project, are acknowledged. References [1] TM Electronics, Inc., Leak, Flow and Package Testing 101, 2008. [2] ATEC, ATEQ G520 User Manual, 5th Ed. www.ateq.com, Reference: UM19700E-U, 2006. [3] J. Amesz, Conversion of Leak Flowrates for Various Fluids and Different Pressure Conditions, eur 2982.e, European Atomic Energy CommunityEURATOM, 1966. [4] B. Lorenz, B.N.J. Persson, Leak rate of seals: effective-medium theory and comparison with experiment, Eur. Phys. J., E 31 (2010) 159–167, https://doi. org/10.1140/epje/i2010-10558-6. [5] P.-S. Murvaya, I. Silea, A survey on gas leak detection and localization techniques, J. Loss Prevent. Process Ind. 25 (6) (2012) 966–973, https://doi. org/10.1016/j.jlp.2012.05.010. [6] L. Grine, A.-H. Bouzid, Analytical and experimental studies of liquid and gas leaks through micro and nano-porous gaskets, Mater. Sci. Appl. 4 (2013) 32– 42, https://doi.org/10.4236/msa.2013.48a004. [7] G.P. Martinsanz, Sensors for fluid leak detection, Sensors 15 (2015) 3830–3833, https://doi.org/10.3390/s150203830. [8] R.O. Felix, T.P. Franchi, Automation and leak control system with use of clean energy supply (compressed air), J. Mech. Eng. Autom. 6 (6) (2016) 141–150, https://doi.org/10.5923/j.jmea.20160606.01. [9] K.B. Adedeji, Y.H. Bolanle, T. Abe, A.M. Abu-Mahfouz, Towards achieving a reliable leakage detection and localization algorithm for application in liquid piping networks: an overview, IEEE Access 5 (2017) 20272–20285, https://doi. org/10.1109/access.2017.2752802. [10] B.R. Munson, D.F. Young, T.H. Okiishi, Fundamentals of Fluid Mechanics, fourth ed., Wiley, New York, 2002. [11] M.J. Moran, H.N. Shapiro, D.D. Boettner, M.B. Bailey, Fundamentals of Engineering Thermodynamics, eighth ed., Wiley, New York, 2014. [12] J.P. Holman, Experimental Methods for Engineers, eighth ed., McGraw-Hill, New York, 2012.
Contents lists available at ScienceDirect
Measurement journal homepage: www.elsevier.com/locate/measurement
Liquid leakage assessment from gas leakage tests V.A.F. Costa TEMA – Centro de Tecnologia Mecânica e Automação, e Departamento de Engenharia Mecânica da Universidade de Aveiro, Campus Universitário de Santiago, 3810-193 Aveiro, Portugal
a r t i c l e
i n f o
Article history: Received 18 April 2019 Received in revised form 14 August 2019 Accepted 6 October 2019 Available online 11 October 2019 Keywords: Pressure difference driven leakage Liquid leakage assessment Gas leakage Pressure decay testing Liquid and gas leakages relationship
a b s t r a c t Liquid leakage assessment is usually difficult, what can be overwhelmed through leakage testing using gases. This happens in many situations of practical interest of pressure-difference driven liquid leakage. Starting from physical principles and laws, analytical expressions relate the liquid and gas leakages occurring through the same leak geometry. Pressure differences driven the liquid and gas leakages can be different. Process of obtaining the analytical expressions highlights the physics behind the process of leakage testing and the involved variables and principles. Obtained analytical expressions relate the governing variables, allowing calculations for results treatment, interpretation, correlation or uncertainty analysis. Developments and results presented in the paper fulfill a gap of the literature concerning the liquid leakage assessment and testing using gases, and of the users’ manuals of the leakage testing equipment. This additional knowledge and information allows equipment use and leak tests conduction with greater confidence, and supported results analyses, criticism and treatment. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Leakage detection, localization, measurement, evaluation and assessment are of major relevance in many activities and economic sectors. If this is true in general, it can be critical in many situations, and among them those characterized by low or even very low flow rate leakages, usually requiring more accurate analyses, methods, sensors and instruments. Leakages are usually unwanted, due to assemblies or sealing defects, the leak geometry through which leakages occur being not well defined, and remaining usually unknown. Liquids leakage tests are usually conducted subjecting the parts or assemblies to the operating conditions. However, liquids leakage tests have a considerable number of disadvantages, some of them being: (i) Liquid leakages correspond to low or even very low liquid flow rates, requiring long time periods for their evaluation or assessment, usually incompatible with fast/high production rates, and requiring highly accurate sensors for the liquid amount evaluation; (ii) It can be pernicious that some liquid belongs with the product after the leakage tests; (iii) Liquid remaining with the product can damage paper packing, and also the writings and/or printed matters over the packing; (iv) Liquid leakages always lead to some liquids waste and/or potential pollution. Leakage tests using gases, and specially those using air, have a lot of advantages, namely: (i) They can be fast, and thus compatible with
E-mail address: [email protected] https://doi.org/10.1016/j.measurement.2019.107135 0263-2241/Ó 2019 Elsevier Ltd. All rights reserved.
fast/high production rates, fastness of the tests being increased as increases the gas pressure; (ii) Parts remain dry and clean during and after the leakage tests; (iii) Leakage tests can be easily automated, and/or included in an automated processes; (iv) Gas leakage tests do not induce any damage of both the product and the packing; (v) If air is used for the gas leakage tests no additional costs and/or pollution exist related with the air losses due to the gas leakage. This work deals with pressure-driven leakage flows. Molecular flows due to Fick or Knudsen diffusion are not considered, as the mean free path of the molecules is significantly lower than the characteristic dimension of the leak geometry. Leakage tests using gases can be made subjecting the gas to a pressure greater than the atmospheric pressure (overpressure tests) or lower than the atmospheric pressure (under-pressure tests). The first option is usually cheaper, as the compressor equipment and operation are usually cheaper than those of a vacuum pump. Additionally, if a pressure greater than the atmospheric pressure is used it is easy to filtrate the gas contacting the part to be tested, while if a pressure lower than the atmospheric pressure is used gas can enter the part from the ambient at unspecified points, and it is not so easy to filtrate it. If gas leakage tests are faster, cheaper, cleaner, and easier than liquid leakage tests, it is tempting to assess the liquid leakages from gas leakage tests, and specially from air leakage tests. Present work shows that this is possible, and how are related the liquid and gas leakages flowing through the same leak geometry, even if the liquid and gas leakages are driven by different pressure differences.
2
V.A.F. Costa / Measurement 151 (2020) 107135
Nomenclature L m _ m P Q_ R R t T V x
Length of the leakage channel [m] mass [kg] Mass flow rate [kg/s] Pressure [Pa] Volumetric flow rate [m3/s] Radius of the leak channel [m] Particular gas constant [J/(kg.K)] Time [s] Temperature (absolute) [K] Volume [m3] Length coordinate, along the leakage [m]
Dt
l q s
Testing time period [s] Dynamic viscosity [kg/(m.s)] Density [kg/m3] Time constant [s]
Subscripts atm Atmospheric value g Gas i Initial l Liquid max Maximum value min Minimum value
Greek letters a Dimensionless auxiliary pressure [] b Dimensionless auxiliary variable []
This is not a new issue and equipment exist to do that, examples being those referred in [1] and [2]. Concerning available equipment for leakage measurements/assessment, some information is available on how to use the equipment on the respective users’ manual. However, few reliable information is available concerning the involved physical principles and laws, the involved variables, the relationships between the involved variables, the pressures’ scales, the variables’ units, etc. It is also unclear how to relate the liquid and gas leakage flow rates, and how to relate them for different operating and test conditions. This work aims to fulfill this leak of analysis and information, joining in a concise and grounded way the issues concerning the physics of the involved processes, and the relationships between the involved variables, including the additional complexity associated with the gas compressible character. If the equipment’s manuals are not of great help concerning the aspects referred above, the scientific literature on the leak measurement/assessment is also not very rich. Amesz [3] reports the development of rules for conversion of gas and liquid leakages, as in many cases leakage is tested by means of a gaseous medium for systems that operate with a liquid medium. Some correlations, instead of analytical closed relationships, are proposed to relate liquid and gas leakage flows. This is the work whose main objectives are closer to those of the present work, but the approach, results and readability are considerably different. Lorenz and Persson [4] present a medium theory of the leak rate of rubber seals, based on a contact mechanics theory, emphasis being given to the particular nature of the rubber seals. Emphasis of the work by Murvaya and Silea [5] is on the state-of-the-art in leak detection and localization methods, based on the principle that gas leakage detection can avoid the major incidents resulting from gas leakages. However, no emphasis is given to the relationship between the liquid and gas leakage flow rates through the same leak geometry Work by Grine and Bouzid [6] develops an analytical leak rate prediction methodology applying for the particular case of gasketed joints, including the estimation of the leak porous structure through a pseudo analytical-experimental approach. The analytical model is validated by comparison with experimental results. Work by Martinsanz [7] is devoted to the technological developments and methods of sensors based on physical, chemical or biological principles aiming fluid leak detection, starting from the point that leakage is a problem that can cause important economic losses and environmental pollution, putting human, animal or plant lives at risk. Work by Felix and Franchi [8] deals with a sealing system designed to perform simulations of air leaks. Air leakage is measured using a mass flow sensor, directly indicating the volumetric
leakage. The automation of the process has been developed and implemented on an open-source platform using low-cost controller. Adedeji et al. [9] deal with the leakage detection and localization in pipelines of large-scale potable water distribution networks, relying mainly on wireless sensor networks for leakage detection purposes. Even if few, no any of the works found in the literature follows the approach, answers the questions, and leads to the results as proposed by the present work. 2. Fluid flow through a leak 2.1. Base formulation for the laminar fluid flow through a leak The basis for the evaluation of the laminar fluid flow driven by a pressure difference against a given resistance dependent on the leak geometry and on the fluid viscosity, is the Hagen-Poiseille Law. In the differential form, for a leakage through a circular duct, it sets that locally [10].
p 1 dP Q_ x ¼ R4 8 l dx
ð1Þ
Geometries other than the circular duct for the leak can be considered, but this particular geometry is not relevant for the present purposes, once it is the same for the liquid and gas leakages, by the reasons explained below. 2.2. Liquid flow leakage Liquid is considered to be incompressible, its volumetric flow rate being independent of the local pressure, no liquid storage/ accumulation occurs in leak system, and the surface tension effects are neglected when compared with the pressure difference forces. It is also assumed that no liquid-vapor phase change occurs as the liquid pressure decreases along the leak. Under the above referred conditions, for the situation illustrated in Fig. 1, Eq. (1) set for the liquid can be integrated along the whole length of the leak to give
p R4 1 ðP l Patm Þ Q_ l ¼ 8 L ll
ð2Þ
where on the right-hand side are observed, from left to right, the influence of the geometry of the leak system, the liquid viscosity, and the pressure difference forcing the liquid leakage (Fig. 1).
3
V.A.F. Costa / Measurement 151 (2020) 107135
In general, the geometry of the leak system is not well known nor well defined. It can be a straight circular channel, a straight rectangular cross section channel, a straight circular or rectangular annular cross section channel, tortuous circular or rectangular cross section channels, tortuous channels with variable cross sections, a series association of tortuous channels with variable cross sections, a parallel association of tortuous channels with variable cross sections, etc. Conceptually, any particular geometry can be condensed in a geometry factor G, with units of m3, and Eq. (2) reads, for a generic leak system
1 Q_ l ¼ G ðPl P atm Þ
ð3Þ
ll
In practical situations of liquid leakage evaluation and assessment, some kind of criterion sets the limit Q_ of the admissible
Pg
dPg 8 1 _ l PQ ¼ dx p R4 g g g x
ð6Þ
Using Eq. (5) to take P g Q_ g ¼ constant, Eq. (6) can be intex
grated along the leak and the result arranged as
1 Pg þ P atm p R4 1 Q_ g ¼ Pg Patm x 2 8 L lg Pg x
ð7Þ
which is the Hagen-Poiseille Law for an isothermal (Ideal Gas) compressible flow, noting that pressures in Eq. (7) are absolute pressures. 3. Pressure decay associated with the gas leakage from a test chamber
l;max
volume flow rate for the liquid leakage, as
Q_ l 6 Q_ l;max
ð4Þ
In some situations the admissible liquid leakage is specified through the number of liquid drops that escape during a given time period. In these situations attention needs to be given to the liquid volume corresponding to some drops that holds attached to the solid parts due to the surface tension effects, the number of drops that escaped through the leakage differing from the number of drops that fall from the part being tested during the specified time period. 2.3. Gas flow leakage Contrarily to the liquid, the gas is compressible and locally its volumetric flow rate depends on the local pressure. If the gas can be assumed to behave as an Ideal Gas, it is [11]
P Q_ _ g ¼ qg Q_ g ¼ g g m Rg T
ð5Þ
If no gas storage/accumulation occurs in the leak system and assuming the temperature of the gas is constant along the leak, it _ ¼ constant at any point of the leak [11], and from Eq. (5) it is m g ¼ Pg ¼ constant at any point of the leak. is P g Q_ Q_ g
x
x
g
x
Starting with Eq. (1), in this case for the gas as presented in Fig. 2, rearranging and multiplying both sides by P g results in
Gas flow leakage is usually measured through a pressure decay method, as illustrated in Fig. 3: a chamber of volume V g (constant, corresponding to the whole volume filled with the gas that experiences the pressure decay due to the gas leakage) filled with gas initially at pressure P g;i . During a given test period Dt g , after a pressure stabilization period, gas pressure decreases in volume V g , and it is from this gas pressure decay with time that the gas flow leakage is evaluated. It is assumed that the geometry through which the gas leakage occurs is the same as that through which the liquid leakage occurs, in order to allow the evaluation/assessment of the liquid leakage from the measurement of the gas leakage through a pressure decay test. It is assumed that the gas behave as an Ideal Gas, and that the expansion process experienced by the gas filing volume V g is sufficiently slow to be considered isothermal, at absolute temperature T. From the Ideal Gas Law it is [11]
Pg V g ¼ mg Rg T )
dmg V g dPg _g ¼ ¼m dt Rg T dt
ð8Þ
Introducing Eqs. (8) into (7) leads to an equation that can be integrated for the pressure of the gas filling volume V g changing from Pg;i to P g ðtÞ, during the time t, from which results
2
3
P g ðt ÞP atm P ðt ÞþP atm 5 ln4 Pg Patm g;i Patm P g;i þP atm
1
¼
p R4 1 1 t 8 L lg V g
ð9Þ
On the left-hand side of this equation is present, in a nonlinear form, the pressure variation experienced by the gas filling volume V g . On the right-hand are observed, from left to right, the influence of the geometry of the leak, the gas viscosity, the volume of the chamber from which the gas escapes, and the time period t during which pressure in the chamber changes from P g;i to P g ðtÞ. It is to be retained that pressures in this equation are absolute pressures. Defining the auxiliary dimensionless pressure difference
a¼ Fig. 1. Schematic illustration of the liquid flow leakage.
Fig. 2. Schematic illustration of the gas flow leakage.
Pg;i Patm Pg;i þ Patm
ð10aÞ
and the time constant
Fig. 3. Schematic illustration of the gas leakage, through the same leak geometry as the liquid leakage in Fig. 1.
4
V.A.F. Costa / Measurement 151 (2020) 107135
s ¼ Patm
p R4 1 1 8 L lg V g
!1 ð10bÞ
Eq. (9) allows obtaining the (absolute) pressure P g ðtÞ at any instant t after the beginning of the pressure-decay process as
1 þ aexpðt=sÞ Pg ðt Þ ¼ Patm 1 aexpðt=sÞ
ð11Þ
It is to be noted that as the geometry of the system through which the leakage occurs is not well known nor well defined, parameter s is not well defined, and Eq. (11) is not useful for practical purposes. It is useful only as it indicates how the pressure of the gas in the test chamber decays with time. Another way to express Eq. (9) is
" # et=s et=s 1 Pg ðt Þ Patm t=s ¼e þ 1 t=s P g;i Patm ae
ð12Þ
This equation shows that the gas pressure decay does not follow a first order decay [12], et=s , but that it includes the additional term inside square brackets of Eq. (12). This additional term is negative, smaller than the first order exponential decay given by et=s , but even so it is not null. 4. Relating the liquid and gas leakage flow rates To relate the liquid and gas leakage flows through the same leak geometry, it is assumed that the liquid pressure Pl remains essentially constant and that the liquid leakage is driven by the pressure difference ðP l Patm Þ. Dividing Eqs. (7) and (2) leads to
Q_ g Q_ l
x
ll Pg Patm 1 Pgþ Patm lg Pl Patm 2 Pg x
¼
ð13Þ
and only if the involved pressures P g , Pl , and Patm are very close is the volumetric flow rate ratio Q_ g =Q_ l essentially given by the x
dynamic viscosity ratio ll =lg . Dividing Eqs. (9) and (2) side by side and rearranging results in
Q_ l ¼
lg 1 ðPl Patm Þ 1 Pg ðtÞ Patm V ln ll g t Patm a Pg ðtÞ þ Patm
ð14Þ
It is to be noted that the geometry of the leak is absent from the obtained Eqs. (13) and (14), once it is the same for the liquid and gas leakages. Previous developments were made considering both liquid and gas leakages occurring through a circular channel of uniform cross section; however, when relating the liquid and gas leakage flow rates the particular geometry of the leak is irrelevant, as it is eliminated when obtaining Eqs. (13) and (14). Eq. (14) relates the liquid flow rate leakage Q_ with the gas presl
sure change from P g;i to P g ðtÞ into the gas chamber during the measurement time t. Both liquid and gas leakages occur through the same leak geometry, even if they are forced by different pressure differences, ðP l P atm Þ for the liquid leakage and (instantaneously)
P g ðtÞ P atm for the gas leakage. Once set the time period Dtg for the gas pressure decay, the volume of the test chamber V g , and the initial gas pressure Pg;i , there is a gas pressure Pg;min for which it is Q_ ¼ Q_ . Thus, criterion l
bm ¼
ll Dtg Patm _ Q lg V g ðPl Patm Þ l;max
ð15Þ
it is obtained from Eq. (14) that the lower limit (absolute) pressure Pg;min is
Pg;min ¼ P atm
1 þ aexpðbm Þ 1 aexpðbm Þ
ð16Þ
It is to be noted that parameter bm is well defined, evaluated from Eq. (15), that it does not depend on the geometry through which the liquid or gas leakages occur, and that Eq. (16) is very useful for practical purposes, allowing fast and accurate evaluation of the lower limit (absolute) pressure Pg;min . It can also be used to conduct the uncertainty analysis of the liquid leakage estimation through the pressure decay associated to the gas leakage occurring through the same leak geometry. Another way to express Eq. (16), in a form similar to that of Eq. (12), is
" # Pg;min Patm ebm ðebm 1Þ bm ¼e þ 1 bm Pg;i Patm ae
ð17Þ
which can also be used to evaluate P g;min once known bm , P g;i and Patm . P atm . Fig. 5 presents a possible graphical form of Eq. (17) considering some ranges of practical interest for the liquid (water) and gas (air) pressures. It is to be retained that when relating the liquid and gas leakage flow rates, flowing through the same leak system, they must occur in the same direction as some geometries and assemblies present some kind of diode characteristics for fluid flow, imposing different resistances depending on the fluid flow direction. 5. Validation tests Validation tests of Eq. (17) can be made considering water leakage from a system and its assessment through the air pressure decay measurement. The system under analysis, with constant volume V g ¼ 0:928 L, has some threaded pipes intentionally left incompletely screwed to originate the experimentally measured liquid leakage and its assessment using Eq. (17). The water leakages were measured for some liquid pressures, P l , and the measured value taken as the maximum admissible liquid leakage, Q_ . It is to be noted from Eq. (2) that it is l;max
Q_ l;max =ðPl Patm Þ ¼ constant in Eq. (15). For the particular system =ðP l P atm Þ ¼ under analysis it was obtained Q_ l;max
3:067 1012 m3/(Pa.s). For a liquid 4 bar relative pressure this corresponds to a liquid leakage of 1:213 106 m3/s. Water and air properties (dynamic viscosities) were taken for the temperature of 20 °C. Pressure decay tests with air corresponded to the same leakage geometry as for the liquid leakages measurements, from some
l;max
expressed by Eq. (4) requires that Pg P Pg;min for t ¼ Dt g to have Q_ l 6 Q_ l;max , and this is the way how a gas leakage measurement procedure can be used for liquid leakage evaluation or assessment. This is illustrated in Fig. 4. Given the dimensionless pressure difference a defined through Eq. (10a), and defining the additional dimensionless parameter
Fig. 4. Schematic illustration of the gas pressure decay test.
5
V.A.F. Costa / Measurement 151 (2020) 107135
Fig. 5. A possible graphical presentation of Eq. (17).
Table 1 Validation results for a ¼ 0:1979. P g [Pa G]
t [s]
bm
50,000 40,000 30,000 20,000 10,000
0 12 28 49 87
0.2117 0.4941 0.8646 1.5351
P g [Pa G]
t [s]
bm
40,000 30,000 20,000 10,000
0 16 37 75
0.2823 0.6529 1.3234
Pg;min P atm Pg;i Patm Eq: ð17Þ
0.773 0.557 0.369 0.180
Pg;min Patm Pg;i P atm exp
error (%)
3.4 7.2 7.9 9.8
0.80 0.60 0.40 0.20
Table 2 Validation results for a ¼ 0:1648.
initial air pressures up to the corresponding minimum air pressures, and predicted and measured results compared. Some results are summarized in Tables 1, 2 and 3 for a ¼ 0:1979, a ¼ 0:1648, and a ¼ 0:1289, respectively. Evaluation of percent errors takes the experimental values as the references. From Tables 1–3 it can be seen that the obtained results using Eq. (17) are in good agreement with the experimental results, with percent errors lower than 10%, results predicted through Eq. (17) being always below the experimental ones. It is also observed that the percent error decrease as decreases the initial gas pressure, P g;i .
Pg;min Patm Pg;i Patm Eq: ð17Þ
0.719 0.476 0.233
Pg;min Patm Pg;i P atm exp
error (%)
4.1 4.9 7.0
0.75 0.50 0.25
It is to be retained that the gas pressure measurements in the gas pressure decay tests must be made using a gas pressure sensor/ meter with a short time response, in order to obtain accurate experimental gas pressures. If the gas pressure decay is already occurring when starts the gas pressure measurements, a gas pressure sensor/meter with a short time response is crucial not only for accurate pressure measurements but also for the accurate setting of the zero for the time counter. Errors reported in Tables 1–3 can even be smaller if shorter time response gas pressure sensors/meters are used.
Table 3 Validation results for a ¼ 0:1289. P g [Pa G]
t [s]
bm
30,000 20,000 10,000
0 21 59
0.3706 1.0411
Pg;min Patm Pg;i Patm Eq: ð17Þ
0.660 0.322
Pg;min Patm Pg;i Patm exp
0.67 0.33
error (%)
1.0 3.3
6
V.A.F. Costa / Measurement 151 (2020) 107135
6. Gas leakage volumetric flow rate Gas leakage volumetric flow rate depends on the local pressure, and the usual practice is to refer it to the atmospheric pressure. Noting from Eq. (5) that [11]
_ g ¼ qg Q_ g ¼ qg Q_ g m
P atm
¼
Patm Q_ g
P atm
Rg T atm
ð18Þ
which combined with Eq. (8) leads to
Q_ g
Patm
¼
V g dPg P atm dt
ð19Þ
Declaration of Competing Interest
the average outlet gas leakage volume flow rate, referred to the atmospheric pressure, corresponding to the 0 ! Dtg time period, is evaluated as
Q_ g
Patm
¼
V g DP g P atm Dt g
ð20Þ
Patm
3 cm =min ¼
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements
where SI units are used for all the involved variables. Eq. (20) is many times used with units of cm3/min to express the outlet average gas leakage volume flow rate, referred to the atmospheric pressure, and units of cm3 to express the volume of the gas test chamber. For that purpose Eq. (20) can be rewritten as
Q_ g
test, conducted through a gas pressure decay test, and that the gas pressure decay does not follow a first order decay, contrarily to what is mentioned in some literature. Explicit analytical expressions obtained relate all the governing variables, which can be used for the intended/convenient purposes. Developments and ready to use analytical expressions fulfill a gap of the literature concerning liquid evaluation and testing using gases, and complement the usual leak of scientific information of the users’ manuals of the leak testing equipment. This allows better equipment use, increased confidence to conduct leakage tests, and more supported results analyses and criticism.
DP g ½Pa 60 V g cm3 Patm ½Pa Dt g ½ s
ð21Þ
where units of the involved variables are explicitly indicated within squared brackets, and it is to be retained that Patm ½Pa is the (absolute) atmospheric pressure expressed in Pascal. 7. Conclusions Information concerning the physics of the liquid and gas leakages, and the liquid and gas leakages relationship is absent from the literature and from the users’ manuals of the leak testing equipment. Developments are presented based on the physics of the pressure-difference driven liquid and gas leakages, leading to analytical expressions relating the involved variables and allowing relating the liquid and gas leakages occurring through the same leak geometry, even if driven by different pressure differences. Developments show how, and why, the particular geometry of the leak is not relevant when relating the liquid and gas leakages. Developments are made based on a circular leak of uniform cross section, but it is explained why the main results are independent of the particular geometry of the leak, which is unspecified and unknown in the usual situations of practical interest. It is shown that the liquid leakage can be evaluated based on a gas leak
Support from the UID/EMS/00481/2013-FCT Project, and from the CENTRO-01-0145-FEDER-022083 Project, are acknowledged. References [1] TM Electronics, Inc., Leak, Flow and Package Testing 101, 2008. [2] ATEC, ATEQ G520 User Manual, 5th Ed. www.ateq.com, Reference: UM19700E-U, 2006. [3] J. Amesz, Conversion of Leak Flowrates for Various Fluids and Different Pressure Conditions, eur 2982.e, European Atomic Energy CommunityEURATOM, 1966. [4] B. Lorenz, B.N.J. Persson, Leak rate of seals: effective-medium theory and comparison with experiment, Eur. Phys. J., E 31 (2010) 159–167, https://doi. org/10.1140/epje/i2010-10558-6. [5] P.-S. Murvaya, I. Silea, A survey on gas leak detection and localization techniques, J. Loss Prevent. Process Ind. 25 (6) (2012) 966–973, https://doi. org/10.1016/j.jlp.2012.05.010. [6] L. Grine, A.-H. Bouzid, Analytical and experimental studies of liquid and gas leaks through micro and nano-porous gaskets, Mater. Sci. Appl. 4 (2013) 32– 42, https://doi.org/10.4236/msa.2013.48a004. [7] G.P. Martinsanz, Sensors for fluid leak detection, Sensors 15 (2015) 3830–3833, https://doi.org/10.3390/s150203830. [8] R.O. Felix, T.P. Franchi, Automation and leak control system with use of clean energy supply (compressed air), J. Mech. Eng. Autom. 6 (6) (2016) 141–150, https://doi.org/10.5923/j.jmea.20160606.01. [9] K.B. Adedeji, Y.H. Bolanle, T. Abe, A.M. Abu-Mahfouz, Towards achieving a reliable leakage detection and localization algorithm for application in liquid piping networks: an overview, IEEE Access 5 (2017) 20272–20285, https://doi. org/10.1109/access.2017.2752802. [10] B.R. Munson, D.F. Young, T.H. Okiishi, Fundamentals of Fluid Mechanics, fourth ed., Wiley, New York, 2002. [11] M.J. Moran, H.N. Shapiro, D.D. Boettner, M.B. Bailey, Fundamentals of Engineering Thermodynamics, eighth ed., Wiley, New York, 2014. [12] J.P. Holman, Experimental Methods for Engineers, eighth ed., McGraw-Hill, New York, 2012.