The deep sea is the largest habitat on earth, with at least 50% of the total biosphere lying below a depth of 1000 m in the ocean. Our knowledge of deep-sea ecosystems remains very limited compared to that for continental shelf ecosystems (Drazen and Yeh, 2012). This extreme environment is characterized by the absence of light, low temperature, and high hydrostatic pressure (Koyama et al., 2002; Pavithran et al., 2007). A variety of topographical features exist in deep-sea environments, such as hydrothermal vents, cold seeps, oceanic trenches, seamounts, and bathyal plains, which possess different physical and chemical properties (Zhang et al., 2018). Extremophiles could be sensitive to drastic changes in pressure and temperature and may be sensitive to changes in atmospheric pressure (Kim and Kato, 2010). Studies on microbes in extreme environments can deepen the understanding of deep-sea microbes’ survival principles and deep-sea microbes’ functions in the food chain (Huang et al., 2006). Humans currently do not understand the ecology and biology of the deep-sea biota because this remote environment is difficult and expensive to access and sample (Shillito et al., 2015). There are numerous methods to obtain samples from the deep sea, such as trawls, water samplers, microbe samplers, multi-bottle rosette samplers, bellows type samplers, box-core sediment samplers and grab samplers equipped with a camera (Koyama et al., 2002; Kim and Kato, 2010; Bianchi et al., 1999). Researchers have enabled investigations of seabed sulfides by developing near-bottom vehicles, including autonomous underwater vehicles (AUV), human-occupied vehicles (HOV), and remote-operated vehicles (ROV) (Wu et al., 2019).

Maintaining the in-situ pressure of a sample can prevent the chemical and biological properties of the sample from changing due to the release of dissolved volatile components caused by decompression (Huang et al., 2018; Rossel et al., 2017). International researchers have developed a variety of high-pressure instruments to collect samples at depth and to retrieve them to the surface under pressure, including isobaric fluid samplers, sediment samplers, pressure-stat aquarium systems, high-pressure fish trap-respirometers and the AbyssBox for permanent public exhibitions of live deep-sea hydrothermal fauna (Koyama et al., 2002; Shillito et al., 2015; Wu et al., 2010; Yamamoto, 2015; Drazen et al., 2005; McNichol et al., 2016; Peoples et al., 2019). These high-pressure sampling instruments are an inseparable part of pressure compensation technologies. The scientific community is willing to use sampling instruments with pressure-maintaining functions if the technology permits.

For a deep-sea sampler, an accumulator with compressed gas is usually used to compensate the pressure loss that is caused by small volume changes due to leakage, cubic deformation of the vessel and the compression of sealing materials (Huang et al., 2006; Jannasch and Wirsen, 1977). Previously, the parameters of the pressure compensation technique, such as the sample volume and sample pressure, were usually calculated by using the ideal gas state equation. Although most existing real gas state equations have quite good accuracy at pressures below 30 MPa, the calculation errors for these parameters increases as the pressure increases (as shown in Fig. 1), which makes them ill-suited for the samplers used for abyssal and hadal zones (Wu et al., 2018).

This paper presents an empirical real gas state equation and theoretical calculation method for deep-sea sampling equipment. The degree of deviation for some existing real gas state equations in ultrahigh pressures was analyzed and compared. The gas compression experiments were conducted according to the deep-sea gas pressure compensation range. We next proposed a simple gas state equation for pressures ranging from 15 to 120 MPa by fitting the data from the experiments. A theoretical calculation method for the sample volume and sample pressure of the sampler was proposed by combining with the real gas state equation. Finally, the calculation method was well verified by a high-pressure vessel experiment for the sampler under 115 MPa.

The state of a certain amount of pure gas can be determined when two of P, V and T are given. This functional equation is called an equation of state (EOS), namely, f(P, V, T)=0 (Smith et al., 2005). The simplest realistic model equation of state is the ideal gas equation of state, which is acceptable at low pressures. Under high pressure, an actual gas is increasingly resistant to compression as the molecules move closer together (Priede, 2018). To represent the PVT behavior of both liquids and vapors, it is essential to obtain an equation of state that encompasses a wide range of temperatures and pressures with no limitation (Halder, 2014). In this regard, numerous such equations have been proposed (Hempert et al., 2017). The compression factor, Z, which accounts for the deviation from ideal gas behavior, is defined by Z=PV/RT (also known as the Virial Equation), where Z=1 for an ideal gas (Monago, 2010). The PVT relations of real gases have been elaborately discussed, with some better-known equations involving large-scales of pressures and temperatures, such as the van der Waals (vdW), Peng-Robinson (PR), Redlich-Kwong (RK), Soave-Redlich-Kwong (SRK), and Martin-Hou (MH) equations of state (Redlich and Kwong, 1949; Martin and Hou, 1955; Soave, 1972; Peng and Robinson, 1976). Descriptions of these EOSs are shown in Table 1. These types of equations are complicated in form but are very capable of providing accurate results. Therefore, these equations are successfully and widely used in different areas.

To examine whether the existing real gas state equations are well-suited for full ocean depths, a gas compression experiment ranging from 15 to 120 MPa was designed according to the deep-sea gas pressure compensation range. More details of the experiment are introduced in Section 3.2. Experimental data were accounted for in existing real gas state equations to calculate theoretical gas pressure values. The relative errors of the theoretical values were obtained by comparing them with the experimental pressure values (as shown in Fig. 1).

Most existing real gas state equations have small errors at pressures ranging from 15 to 30 MPa, but these deviations increase gradually as the pressure increases. Therefore, an appropriate gas state equation should be chosen to deal with high pressures of up to 120 MPa and should calculate the deep-sea sampler parameters conveniently and precisely.

A high-pressure vessel experiment of a deep-sea pressure-maintaining sampler was conducted to verify the accuracy of the theoretical calculation method. The sampler mainly consisted of a sampling cylinder, a sampling valve and an actuator, which has the typical structure as has been reported previously (Fig. 8) (Wu et al., 2018). Six sets of these samplers were put into a high-pressure vessel for conducting water sampling (Fig. 9). The sampling pressure of the experiment was set to 115 MPa for simulating the full ocean depth environment.

After the initial and the final parameters of P, V and T of the experiment were recorded, the theoretical sample volume and pressure were calculated by using the equations in Section 4. As shown in Tables 3 and 4, the results of the calculations are very close to the practical values, which prove the precision of this calculation method. Compared to the ideal gas state equation, the calculation method presented in Section 4 provides a better calculation of the pressure and volume of the sampler sample.

For the sampler, we need to explore an appropriate usage rule to better meet the needs of scientific investigations. The sample volume and pressure of the sampler operating at 115 MPa pressure are calculated by setting different precharged pressures, as shown in Fig. 10. As the precharged pressure increases, the sample volume gradually decreases and the pressure of the sample increases. To better meet the requirements of the sample, scientists generally require that the pressure of the sample be closer to the in situ pressure. However, it is difficult for the sampler to ensure the in situ pressure. The better the pressure holding effect of the sampler is, the smaller the sample volume obtained. During actual applications, the pressure value of precharged gas is usually set to be 10%~20% of the bottom pressure. This requires the users to set an appropriate precharged pressure for the gas according to the actual needs of the scientific investigation.

The calculation errors of the existing gas state equations increase as the pressure increases over 30 MPa. We proposed an empirical gas state equation based on the compression factor Z which was obtained by quadratic polynomial regression of the experimental data. It shows adequate accuracy for compressed nitrogen gas with a pressure ranging from 15 to 120 MPa. Furthermore, the theoretical calculations of the pressure and volume of the deep-sea sampler combined with the proposed gas state equation were described in detail. Water sampling experiments inside the high-pressure vessel were constructed, and the results demonstrated the accuracy of the theoretical calculation method. The theory of pressure compensation can provide theoretical guidance not only for the design and operation of deep-sea samplers but also for other high-pressure instruments associated with compressed gases.

We thank Bo Zhang and Xun Wang for previous laboratory experiment. We also thank Guorui Zhong and Zhiwei Zhu for their support in the high-pressure vessel experiments.