Industrial wastewaters are produced in ever-increasing quantities, and their treatment by conventional technologies is sometimes problematic and harmful to the environment. Among high temperature and pressure processes, Supercritical Water Oxidation (SCWO) is a powerful wastewater treatment technology that always operates above the critical point of pure water (Tc = 374 ºC and Pc = 221 bar), thus allowing the very effective destruction of a wide range of dangerous wastewaters [1]. A typical SCWO process involves several steps in which it is necessary to work at high pressure and temperature [2], including pressurization, heating, reaction, cooling, depressurization, and phase separation. Almost all studies reported in the literature in the last few decades were performed on the laboratory and pilot plant scales, where the depressurization step is easily carried out with a backpressure regulator valve. However, the use of this kind of valve is not particularly suitable when SCWO is applied on an industrial scale, where the high flowrates and the presence of solid particles, amongst other factors, may exacerbate the problems of valve erosion [3].

In this sense, an adequate control of pressure system is very important in the SCWO plant operation. The pressure operation in whole plant depends on the depressurization system, therefore, it must guarantee a stable and controllable operation, capable to absorb possible pressure changes produced. Especially in the reactor where temperature is higher, these pressure changes could exceed the material pressure limit, endangering the system performance. To solve this situation, Soria [4] suggested several steps to reduce the pressure, using different valves located in several lines. Thus, it is possible to diminish the flow in each line allowing a better regulation. However, when effluents contain suspended solids, valve erosion due to extreme velocities is produced when pressure decreases from 250 to 5 bar. For those cases, O’Regan et al. [5] proposed the use of coil pipes or even the combination of both coil pipes and valves in order to improve the operation. In this way, at industrial scale, several commercial SCWO plants of different companies like Hydroprocessing (HydroSolid, Texas), Hanwha Chemical Corporation (Korea), Chematur Engineering AB (AquaCritox, Sweden) have installed coil pipes as depressurization system [6]. However, there is a lack of scientific studies about the behavior and modeling of coil pipes in SCWO plants.

The use of coiled pipes provides a different way to achieve a gradual pressure change along the pipe length [7, 8]. Thus, it is possible to redistribute the mechanical stress along the length of a coiled pipe rather than producing an abrupt pressure change in a single valve. In addition, the installation and maintenance of coiled pipes are easier and more economical, thus making it possible to install different parallel coiled pipes to operate without stopping the process when maintenance is required due to erosion problems.

Coiled pipes have been used in a wide variety of industrial applications due to their many practical advantages, such as compactness, ease of manufacture, and high efficiency in heat transfer. In coiled pipes the pressure drop is higher than that produced in straight pipes at the same flowrate and pipe length. This fact can be explained by the secondary flow that is induced because of centrifugal forces, and different axial velocities. The presence of the secondary flow dissipates kinetic energy, thus increasing the resistance to flow. As a consequence, the transition from laminar to turbulent flow, which is marked by the critical Reynolds number (Re_cr), in coiled pipes is as high as 6000 to 8000 while in straight pipes Re_cr is approximately 2100. For that reason, the pipe’s diameter must be selected to achieve the necessary velocities to work in turbulent flow. In this way, it is possible to increase the pressure drop reducing the necessary length and at the same time, it is possible to avoid nucleation and solid deposition, preventing obstructions in pipes. Because of high velocities and centrifugal forces, erosion increases along the pipe wall. For that reason, different parallel coil systems can be installed to manage continuous operation even in the case of failure of a coil.

To obtain the critical Reynolds number in coiled pipes, Ito [9] suggested the following correlation.

(1)

Where d is the inner diameter of the pipe and D is the diameter of the coiled pipe.

The prediction of pressure drop in coiled pipes is an essential step in the design of a depressurization system for SCWO. In the present work, a system of coiled pipes was used in the depressurization step of a SCWO pilot plant where the pressure drop required was around 230–240 bar.

The pressure drop can be calculated using the Fanning friction factor according to the following equation:

(2)

Where ΔP is the pressure drop in bar, L is the coil section length in m, d is the diameter of the pipe in m, ρ is the density in kg m^-3, u is the velocity in m s^-1, and fc is the friction factor.

Several correlations of friction factors were studied in order to analyze the pressure drop behavior and to compare the predicted results with the experimental data. Typical pressure drop values for fluids circulating through these types of systems have been widely reported in the literature for both single-phase and two-phase systems under turbulent conditions [10]. The correlations chosen for this work are summarized in Tab. 1 and outlined below.

a) Correlations that consider single-phase flow:

In single-phase, the Fanning friction factor in coiled pipes (fc) was calculated using correlations proposed by different authors. White [11] suggested the first correlation for smooth pipes, which is useful as a first approximation.

(3)

Ito [9] suggested a theoretical equation:

(4)

Mishra and Gupta [12] also proposed a correlation for a coiled pipe:

(5)

b) Correlations to consider two-phase flow.

For two-phase flow, the Lockhart–Martinelli [13] correlation is most commonly used to determine pressure drop in straight pipes. Pressure drops of individual phases are calculated assuming that each phase is circulating alone through the pipe. The pressure drop multipliers for gas and liquid (ɸ_G² and ɸ_L²) are the ratios between the two-phase pressure drop

((ΔP/ Δz)_TP) and each individual phase pressure drop ((ΔP/ Δz)_G and (ΔP/ Δz)_L):

(6)

(7)

The Lockhart–Martinelli parameter (χ²) links liquid and gas pressure drop to obtain the two-phase pressure drop.

(8)

The following equations were proposed to determine the liquid and gas multipliers:

(9)

(10)

Where C is a parameter with values ranging from 5 to 20 depending on the flow regime for liquid and gas phases.

Based on the Lockhart–Martinelli correlation, Awwad et al. [14] and Xin et al. [15] proposed new correlations for horizontal coiled pipes with an air/water flow. Awwad et al. [14] found that the superficial velocities (u_L) had a significant effect and therefore, proposed a new equation in which this effect is considered to calculate the multipliers:

(11)

(12)

where C and n values depend on non-dimensional parameter; if F_d ≤ 0.3, C = 7.79 and n = 0.576, else F_d>0.3, C = 13.56 and n = 1.3.

However, Xin et al. [15] found a value of C = 10.646 in the Lockhart–Martinelli equation to adapt it for coiled pipes.

In the work described here, the study of a system of coiled pipes as an alternative depressurization system for the SCWO process is carried out. All the correlations included in Table 1 were studied with the aim of calculating a friction factor that represents the depressurization step from supercritical to ambient pressure. The value obtained was consistent with the experimental data obtained in the tests carried out. It is important to note that the correlations that appear in the literature where used with pressure drops of less than 20 bar, in processes completely different to SCWO. In the case considered in this work, the pressure drop is markedly higher, with a value of around 250 bar, therefore all correlations have been applied to conditions never studied before.

Table 1. Summary of correlations for friction factor considered for single phase and two-phase flow.

Authors	Correlation		Conditions
Correlations for Friction factor coiled pipes considering single-phase flow
White [11]	fc=0.08∙Re-0.25+0.012∙(d/D)0.5		Smooth pipes, empirical, turbulent flow 15000<Re<100000
Ito [9]	fc=0.076∙Re-0.25+0.00725∙(d/D)0.5		Theoretical ,turbulent flow 0.034<Re(d/D)2<300
Mishra and Gupta [12]	fc=0.079∙Re-0.25+0.0075∙(d/D)0.5		Empirical, turbulent 4500<Re<105
Correlations for Friction factor considering two-phase flow
Lockhart-Martinelli [13]			Gas-liquid
Awwad et al. [14]			Air-water 12.7<d<38.1 mm 330<D<670 mm 0.008<UL<2.2 m s-1 0.2<UG<50 m -1
Xin et al. [15]			Air-water 12.7<d<38.1 mm 305<D<609 mm 0.008<UL<2.2 m-1 0.2<UG<50 m-1

Fig. (1) shows the schematic diagram of the pilot plant in which the experiments were carried out. The performance of this pilot plant has been satisfactorily tested for the SCWO process using different wastes [16-19]. In a normal operation for wastewater oxidation, the liquid feed, which is composed of water and organics, is pumped at a flowrate in the range 250–420 g min^-1 at 250 bar, which is the normal operating pressure. The oxidant stream (air is used) is stored and pressurized by a compressor in an accumulating tank before adding to the system. The two streams are preheated separately in liquid and gas heat exchangers, respectively, taking advantage of the reactor effluent energy. In addition, it is necessary the use of electrical heater during the start-up step until the autothermal state is achieved. When operating conditions are reached, the two streams are mixed before entering the reactor, where the waste is oxidized by exothermic reactions and the effluent temperature increases. The temperature reached ranged from 450 to 550°C before entering into the heat exchangers, where the effluent temperature decreases up to 150ºC. However, another cooling is necessary to reduce the temperature below 50ºC. Then, the depressurization system reduces the pressure from operating conditions (250 bar) to ambient pressure. Finally, gas and liquid stream are separated in a gas-liquid separator

In the original pilot plant, the depressurization system consisted of a backpressure regulator valve, which took all of the mechanical stress produced by the great pressure change. In this work, a series of coiled pipes was installed in order to study an alternative approach to enhance the operation and to facilitate maintenance by achieving a gradual pressure change. In this way, with the backpressure valve fully open, the coil system must reduce the operating pressure through the pressure drop produced.

A schematic diagram of the new depressurization system is shown in Fig. (2). It can be seen that this system was designed with different coil sections to allow effluent circulation through each one, either individually or in series. All coil sections were made of stainless steel (AISI 316L) pipe with an inner diameter of 1.0795 mm and a coil diameter of 16.5 cm. In addition, the valves and bypass in the system make it is possible to circulate the fluid through one, two, or three sections of coiled pipe depending on the length required to achieve the desired pressure drop. The inlet and outlet pressure of each coiled pipe was monitored using four pressure transmitters (PI00 to PI03 in Fig. (2)) linked to a data acquisition system.

Fig. (1). Schematic of the SCWO pilot plant apparatus.

Fig. (2). New coil system.

Several blocks of experiments were carried out in order to obtain the pressure drop data for different coil lengths. The coil pipes used in each block had different lengths, making it possible to obtain the pressure at different distances from the beginning of the coil system. The blocks of experiments are shown in Table 2 along with the corresponding lengths of coil pipes used. The length of each section of coil pipe is shown in the middle column and the coil pipe lengths in the right-hand column are those where pressure data were obtained using the pressure gauge in (Fig. 2).

Pressure data measurements were repeated in duplicates and a good reproducibility of the results was verified. In these cases, an average value was taken as the final result.

Moreover, in order to assess the influence that the air and water flowrate had on the pressure drop, several tests were carried out for each block of experiments. In total, 16 tests were performed in each block, i.e., four different water flowrates (257, 307, 357 and 410 g min^-1) and four air flowrates (70, 80, 90, and 100 g min^-1) for each block. In this way, it was possible to obtain the pressure drop as a function of coil pipe length for each test.

It should be noted that in all tests carried out in this study the pilot plant reactor was at supercritical conditions, where the circulating fluids are very compressible. This fact is really important to adequately represent the behavior of a SCWO plant. In other words, despite the depressurization system is not at supercritical conditions (because temperature is below 50ºC), the behavior of a flowing system under pressure is strongly affected by the presence of a compressible medium in a part of the plant. On the other hand, a wastewater was not fed into the system to ensure that the flowrate of air and water remained constant when they reached the depressurization system, achieving an accurate characterization model. However, the performance of coil pipes will be the same in those cases in which oil emulsions (oil in water or gas in oil) are fed, since in a supercritical water oxidation plant, most of the oil present will be completely oxidized along the reactor generating gases as CO2, so the oil amount would be drastically reduced in the effluent. For this reason, when emulsions are fed to a SCWO plant, the effluent before the depressurization step will be a mixture of gas and water with similar properties to those of the air-water mixture tested in this work. The pressure of the mixture of gas and water contained in the effluent is gradually reduced along the coils length and therefore the formation of bubbles in the system is not a problem.

The study presented here demonstrates that it is possible to efficiently use a system of coiled pipes instead of a backpressure regulator valve for the depressurization step in an SCWO pilot plant. The length of coiled pipe can be selected by three coils in series, therefore adjusting the pressure drop needed for different liquid and gas flowrates. This approach ensures stable and controlled system operation, in spite of the fluid compressibility because of supercritical conditions in the reactor.

In order to predict the behavior of the depressurization step from supercritical to ambient pressures, friction factor correlations were used to fit the experimental data. An assessment of correlations from the literature showed that single phase correlations are not applicable. Instead, the Lockhart–Martinelli correlation, which is used for two-phase flow in straight pipe, shows a good fit with the experimental data. An analysis was carried out to determine the optimum value of the C parameter and an average of 6.260 ± 0.1 was appropriate to achieve good agreement between simulated results and experimental data.

Fig. (8). Experimental data and simulated results with both the optimum and average C values for all tests.