Valves of piping systems that use sealing devices (such as packed stuffing boxes) are prone to leakage failure, which may lead to the release of toxic substances that can cause environmental harm, health hazards, and loss of revenue. Advancements in the field of sealing technology have been overlooked because of the need to continuously develop new machinery to fulfill various demands in different industries. More emphasis has been placed on efforts to avoid catastrophic leak failure; little to no consideration has been given to minimizing leaks and reducing fugitive emissions [1
]. From this standpoint, it was unrealistic to study the prediction of leak rates at micro/nano levels at a time when sealing was considered adequate if leakages were neither seen nor heard. Although some improvement has been observed in refineries that have implemented maintenance programs in accordance with revised standards on tightness procedures and tightening sequences (ASME PCC1) [2
]—and provisions were made to better train pipe fitters—leakage is still a major issue in pressure vessels and the piping industry. However, with today’s focus on green consciousness and increasingly strict environmental regulations worldwide, achieving adequate tightness has taken on a different meaning [3
]. In fact, leak rate is becoming a design criterion that has been implemented in standards such as EN and JIS and is under adoption by ASME BPVC. While zero-leak of pressurized equipment is a myth, the challenge for design engineers is to reduce leakage to a minimum. Few standard test procedures have been developed in recent years to certify valves [5
], limit leakage failures, or reduce fugitive emissions [8
], but there is a need to better understand fluid flow through sealing materials at the micro and nano levels in order to be able to predict leaks and improve tightness.
Over the past few decades, there has been some progress toward understanding the leakage behavior of packed stuffing boxes and bolted flange gasketed joints through analysis of the fluid flow through porous sealing materials. Analytical models have been developed to predict leaks [9
]. However, the developed models are not representative of the true porous material behavior over the wide range of compressive loads, and thus have some limitations in their use. Some parameters to consider in any model development might include: the identification of the flow regime as a function of the applied load, the determination of the porosity parameters inherent to the sealing material, their variation in service, and the effect of the fluid type. A limited research work was published on liquid leak rates of porous gasket materials [14
]. The difficulty of measuring small quantities of liquid leak (as compared to gas leak) has been scientifically recognized; there is no commercially available instrument that can directly measure liquid flow rates below 0.001 mL/s. Conversely, gas leaks are measured down to 10−8
mL/s with instruments based on spectrometry. For these reasons, most research has concentrated on the study of gas leaks. The researchers in [18
] conducted tests with different gases to understand the behavior of porous gaskets and packing materials. Others predicted flow through porous media based on sophisticated modelling and simulations using the Monte Carlo method [20
], with no practical use for gaskets and packing seals. The various existing analytical models and their experimental validations deal with the mass flowrate of liquids in a single capillary tube of known dimensions at room temperature. In addition, models described in the literature [21
] treat gaseous flow in a capillary of a specific size and do not consider different-sized capillaries in order to cover macro- and nanoflows. Experimental studies conducted on packing seals with different gases at room temperature are reported in [23
]. The current method used to correlate between different fluids (including liquids) is the simple viscosity ratio method, which is based on leaks conducted with a reference gas (usually helium). There are other more accurate methods that are based on porous structures, difficult to obtain for gaskets and packing seals under different operating conditions. Changes in the size and shape of the porous structure under load and temperature are difficult to measure in a test rig [26
]. In addition, the prediction of leakage requires the operating conditions, flow regime and fluid properties to be known. The pressure, temperature, fluid density, dynamic viscosity, surface tension, and multiphase flow are to name a few.
In this study, an analytical model based on experimental determination of the porosity parameters used to accurately predict leak rates in packing seals under different operating conditions was proposed. The analytical model was based on fluid flow in capillaries, using the theory of Navier–Stokes, with the first slip boundary condition. The internal structure of the packing was simulated with rectilinear capillaries of unknown size and number, oriented in the stem axial direction. The objective was to predict liquid leak rates based on leakage measurements conducted on the same batch of packing seals under similar conditions, but with a reference gas (helium), from which the porosity parameters of the set of packing were deduced under isothermal steady-state conditions. In the last part of the study, liquid leaks at room temperature—measured experimentally—were compared to the predictions. A homemade liquid leak measuring device was developed to measure down to 0.0001 mL/s. Water and kerosene were selected for the experiments because they have different viscosities and are easy to manipulate.