Dynamic Efﬁciency Analysis of an Off-Shore Hydrocyclone System, Subjected to a Conventional PID- and Robust-Control-Solution

: There has been a continued increase in the load on the current offshore oil and gas de-oiling systems that generally consist of three-phase gravity separators and de-oiling hydrocyclones. Current feedback control of the de-oiling systems is not done based on de-oiling efﬁciency, mainly due to lack of real-time monitoring of oil-in-water concentration, and instead relies on an indirect method using pressure drop ratio control. This study utilizes a direct method where a real-time ﬂuorescence-based instrument was used to measure the transient efﬁciency of a hydrocyclone combined with an upstream gravity separator. Two control strategies, a conventional PID control structure and an H ∞ robust control structure, both using conventional feedback signals were implemented, and their efﬁciency was tested during severely ﬂuctuating ﬂow rates. The results show that the direct method can measure the system’s efﬁciency in real time. It was found that the efﬁciency of the system can be misleading, as ﬂuctuations in the feed ﬂow affect the inlet concentration more than the outlet oil concentration, which can lead to a discharge of large oil quantities into the ocean.


Introduction
In current oil and gas production facilities, water handling is an increasing challenge, as maturing fields result in an ever-increasing water cut; in some cases up to 98% [1][2][3]. Due to high costs of equipment installation and maintenance, updates in the current facilities are preferred [4,5]. The system considered in this study is the most common type of oil and water separation facility in the Danish sector of the North Sea, consisting of a gravity separator with a downstream hydrocyclone system. The separation efficiency of the oil and water in the gravity separator is controlled by manipulating the interface level (l) of the oil and water. The manipulation of l facilitates a specific residence time that determines the separation rate of oil droplets, which then surface and get skimmed over a weir, the placement of the weir is illustrated in Figure 1. The level is governed by the underflow valve V u , which regulates the flow from the gravity separator (F i ) to the hydrocyclone. The separating efficiency of the hydrocyclone ( ) is controlled by manipulating the overflow valve V o , which manipulates the flow of liquid through the overflow F o , which under the optimal operating conditions is assumed to consist of a high oil concentration. The overflow oil concentration is defined as (C o ). This high oil concentration occurs as a centripetal force is generated due to the cylindrical shape of the hydrocyclone and the tangential injection of the liquid. The oil is thus forced to the center of the hydrocyclone forming what is known as the oil core [6,7], which is similar to the working principle of a solid-liquid hydrocyclone [7][8][9]. The feedback parameter for the control loop, is the pressure drop ratio (PDR), which is calculated using Equation (1) [10]. In previous studies, a proportionality between the PDR and the flow split F s has been shown, where F s = F u /F i , and F u is the hydrocyclone's underflow flow rate [6,[11][12][13][14]: The PDR is thus governed by controlling V o , but in a previous study it was shown that V u negatively influences the performance of the PDR and is more dominant in comparison to V o [15]. The physical location of V u and V o can be seen in Figure 1. The location of the valves results in a physical coupling in the system, where V u has a cross-sectional area that is 25 times larger than that of V o and is therefore dominant with respect to the flow rate [12,16], which in turn influences the PDR.
In subsequent studies [17,18], this issue with the dominance of V u was addressed by updating the prevalent control strategy: currently comprising of two independent PID controllers, one for each control objective: level and PDR control. In these studies, an H ∞ robust control solution was proposed and resulted in an improved performance of the de-oiling system. In [18], reducing the fluctuation of the flow through the hydrocyclone and reducing the saturation of the control valves was believed to increase the system's performance. The premise for this was based on previous studies [13,14,19], where it was shown through oil-in-water (OiW) measurements (manual sampling) that fluctuating flows reduced the efficiency of a hydrocyclone. The de-oiling efficiency of the hydrocyclone ( ) is calculated through Equation (2) [20].
where C u is the concentration of oil in the underflow, and C i is the concentration of the oil in the inlet. The determination of based on the OiW concentration has been investigated in previous studies [6,21], where relationships between the PDR and F i were compared to . In both studies, was investigated from a static perspective and did not deal with the dynamic changes, which is important if during fluctuating flow rates is to be investigated. This was later done in [13,22], where, in the latter study, was measured in real-time and its dynamics were observed for different operating conditions. In [22], it was observed that was not influenced by the PDR as long as PDR was kept within a specific range, which is dependent on the operating conditions. was shown to be proportional to F i where the proportionality was reduced as F i increased. This is consistent with the steady state results from [6], where increases with F i following an S-curve shape, and reaches steady state, which was found to be up to 99% in [6]. A potential conclusion from this is that keeping the PDR and the F i relatively stable within a desired operating range will result in a high . Another aspect is that relates only to the efficiency of the oil separated from the water, but it does not quantify water in the oil exiting through the overflow. This is defined as the de-watering efficiency, see Equation (3), where C w u and C w i are the water concentrations in the underflow and inlet, respectively. The latter is undesirable, as this results in the pollution of oil with water, which has to be handled at a cost in downstream processes or recirculation.
E is an important factor as water in the overflow will eventually have to be separated from the oil before the oil can be used, thus being a negative cost factor. In addition, as the hydrocyclone cannot achieve 100% de-oiling efficiency ( ), the total amount of oil in the underflow is extremely important. For example, in 2015, the Danish oil sector discharged approximately 193 tons of dispersed oil into the sea, coming very close to the governmental limit of 202 tons [23,24]. The real-time measurement is crucial in evaluating the de-oiling performance of the hydrocyclone, which in current installations is based on manual samples and subsequent calculations performed twice a day following the OSPAR reference method [25,26]. Successful OiW measurements in the scaled pilot plant, specifically measurements of transients, have a potential for use in feedback control.
This study starts by evaluating the measurement technique used in [22] in measuring the OiW concentration in real time on the inlet and on the underflow of the hydrocyclone and extends the scope of the study by including the upstream three-phase gravity separator. The oil injection method used in [22] is in the current study replaced by an OiW mixture method that ensures a more stable OiW concentration and a more evenly distributed oil droplet size, as can be seen in Figure A1.
Using the OiW measurements, the entire system's dynamic efficiency is evaluated during fluctuations in F in , where the fluctuating flow rate is crucial for several reasons. Firstly, it will enable us to evaluate if the instrument can track the transient behavior of the OiW concentration and thus the potential of using such instruments for feedback purposes. Secondly, it enables us to test the newly developed robust H ∞ control solution's performance when subject to a disturbance, such as a fluctuating F in .
Two control solutions are implemented: a newly developed robust H ∞ control solution and a conventional PID control solution that is similar to the one currently used in the offshore oil and gas industry. Both controllers were developed in [18]. The goal of this is to investigate changes in the performance of by applying advanced control in comparison to a conventional control solution. The advanced control in [18] was shown to have the potential to improve the efficiency of the de-oiling system. This was based on the fact that, by reducing the impact of the fluctuation, which reverberates through the system and negatively influences , the efficiency can be improved. In the current study, this hypothesis is investigated directly through OiW measurements, thus evaluating directly.

Pilot Plant
The experiments were performed on a scaled pilot plant of a typical offshore de-oiling system, a simplified P&ID of this system is shown in Figure 1. Table 1 lists the description of equipment used in the pilot plant and Table 2 lists all the materials used in the experiments. The system comprises of a pump which pumps a mixture of oil and water into a mixer, where air is injected using an air compressor. This mixture is sent through a pipeline which is connected to a riser pipeline. The riser pipeline is upstream of the gravity separator, and they are separated by a topside choke valve [27][28][29]. The gravity separator is a scaled three-phase separator with a diameter of 0.6 m and an operating flow of 1 L/s (at 10 bars) and a residence time of ≈3 min, when using a weir height of 0.33 m. The gravity separator's gas pressure is controlled using V gas around a set point of 7 bars, which is limited by the gas pressure of the compressor. From the gravity separator, the water is sent to a single three-section 35 mm hydrocyclone liner from Vortoil [30]. The water level is measured using a differential pressure transmitter, and this measurement is used as the feedback parameter for the level control loop. The PDR is measured by the three pressure transmitters (P i , P o , and P u ) and is used as the feedback parameter for the PDR control loop. The liquid flows from the hydrocyclone's overflow and underflow are controlled by the two valves (V o and V u ), which are used in the PDR and level control loops, respectively. The OiW instruments are located at the hydrocyclone inlet and underflow, and they are referred to as OiWT in Figure 1.

The Measurement of OiW
The measurement of OiW follows the design presented in [22], where the OiW concentration is measured on the inlet and underflow of the hydrocyclone using a fluorescence based instrument, the TD-4100XDC (TD-4100) from Turner Designs. The instruments are placed on a side stream, and they are connected with a T-junction. A choke valve V bp is used to divert some of the flow through the instruments. The instruments are calibrated to operate within a concentration range of [0-5000] ppm.

Oil-in-Water Mixture
The water and oil mixture was created by continuous stirring using two propeller stirrers to stir 2 m 3 mixture, the propeller stirrer have a maximal capacity of 1469 m 3 /h, but they were operated at approximately 1/3 of their maximal capacity.
A hydrocyclone's performance is related to the droplet size at the inlet [31,32]. In order to quantify the droplet sizes in the OiW mixture, the mixture was scanned using video microscopy, using the Jorin VIPA (VIPA) instrument. The VIPA instrument was placed in the inlet side-stream and a constant flow was pumped through the system. The particles were recorded with a frame rate of 30 images/s and the particles counted using the Jorin VIPA software. For more information on the instrument refer to [33]. The droplet size distribution analysis is shown in Appendix A. The correct oil droplet distribution is difficult to evaluate, and little information on the oil droplet size distribution on the hydrocyclone inlet exists. This is because the oil droplet size distribution varies significantly between the different offshore installations and reliable measurements for offshore use have not matured. However, the general range of the droplet size has been reported to be between 1 and 1000 µm in offshore untreated produced water, where most of the droplets lie in the range between 5 µm and 50 µm [34].
In [21], the reported droplet distribution lies between 5 and ≈120 µm for a concentration of 4100 mg/L and between 3 and 70 µm for a concentration of 435 mg/L. It is noteworthy that the concentration in [21] was created in the lab and is therefore not directly representative of an offshore scenario. From the histogram in Figure A1, we show that the majority of our droplets lie between 5 and 60 µm, and thus we can safely say that it lies in a realistic range.
In [12], it was shown that reaching the droplet size of 60 µm resulted in close to 100% efficiency. A similar result was shown in [21], where migration probability of 100% was seen when the droplet sizes were above 60 µm. This indicates that, if our mixture had a significantly larger droplet size range, it would facilitate an improved separation efficiency, this could be explained as per the Stokes law, where larger droplet sizes facilitate better separation.

Experiment Design
A series of tests were designed to test the measurement technology and using the measurements for evaluating the performance of the control structures. The different tests are shown in Table 3 and described in the following. Table 3. List of experiments performed in this paper.

Dynamic-Tracking Capability
Evaluate the instruments dynamic and static performance Controller Evaluation 1 Evaluate the de-oiling efficiency ( ) during fluctuating flow Controller Evaluation 2 Evaluate the instruments dynamic and static performance

Dynamic-Tracking Capability
The initial experiment is a dynamic tracking capability analysis, with the objective to check whether the deployed OiW sensor could reliably track the dynamically varying flow conditions. The experiment is performed by running the PID controller at the same operating conditions two times and comparing the results. During the experiment, the system is subjected to a varying inlet flow rate, which is designed such that it emulates severe fluctuating flow rates. The fluctuating flow rates are discussed in [18,35]. The operating conditions, i.e., the inlet flow rate to the gravity separator are shown in the bottom plot in Figure 2. By varying the flow rate, it is possible to evaluate the dynamic performance of the instruments. The results are shown in the top three plots in Figure 2.

Controller Evaluation 1
The OiW measurements are evaluated on the de-oiling system, where the system is controlled using two different control strategies: (1) a PID control solution which was designed to emulate control solution from the Danish sector of the North Sea (see [18] for details) and (2) an H ∞ robust controller, which was developed in [18] and is expected to improve the system's disturbance rejection, making the system robust towards fluctuating inlet flow rates F in . In this experiment, the inlet flow rate is the same as in the Dynamic-Tracking Capability experiment, which is challenging for the conventional PID control solution, and this experiment aims at investigating the two controllers disturbance rejection and de-oiling efficiency. Being able to measure the OiW concentration in real time can illuminate the benefit of using the robust controller, and we can identify the parameters that are linked to the system's de-oiling efficiency .

Controller Evaluation 2
In this experiment, the system is operated first at a steady state, where the inlet flow rate is 0.47 L/s during the 1000-2000 s period. At 2000 s, the inlet flow rate is linearly decreased for 1000 s, from 0.47 to 0.37 L/s. The aim of this experiment is to investigate the system's steady state de-oiling efficiency at different operating conditions.

Experiment Discussion: Dynamic-Tracking Capability
From the third plot in Figure 2, the efficiency of the two experiments appear relatively similar, except for some small deviations. The reason for the deviations are (1) a slightly alternating inlet concentration as can be seen in Plot 4 in Figure 2 and (2) the controller's performance, which is reflected in the position of the valves in particular from 1400 to 2000 s. Nevertheless, the outlet concentration for both experiments is almost identical as seen in the bottom plot in Figure 2.

Experiment Discussion: Controller Evaluation With a Fluctuating Flow Rate
The efficiency of the hydrocyclone is calculated through Equation (2), but we find the total discharged oil concentration to be equally important, as it gives a good representation of the system's polluting effects, in particular the total amount of discharged oil as mentioned earlier, and thus we present these results in Figure 3. The total discharged oil concentration throughout the experiment is shown in Table 4. In this initial analysis, the PID controller performs worse than the H ∞ control solution, discharging 6.95% more oil through the water. The relative larger amount of oil is related to the larger inlet flow rate, as can be seen in Figure 4, where C u is similar for both controllers, but F i is larger for the PID control solution where the total volume of the inlet mixture is 13.62% larger.
Comparing the total oil discharge to the efficiency, we see a different picture, where the PID control solution has a higher mean efficiency that the H ∞ control solution, as shown in Table 4. The higher efficiency is thought to be facilitated by the overflow valves being saturated at 100%, which occurs in many of the instances where the efficiency is above 80%. From the principles of the hydrocyclones operation [10], we can expect that, when the overflow valve is saturated at 100% opening, the flow through the overflow will be high. This causes the majority or all of the oil to flow through the overflow and thus not the underflow, which ensures good de-oiling efficiency, but at the consequence of poor de-watering separation. The negative side of this is that the overflow can potentially, in addition to the oil, contain water and thus result in poor de-watering separation (E). Another interesting fact is that the PID control solution returns a higher average efficiency of ≈78.92% than the H ∞ control solution with a mean of ≈71.8%. These results are similar to what was observed [21], where higher was observed in [6,21] while running at higher flow rates. This efficiency was achieved at a mean PDR value of 1.38, which is considered to be outside of the nominal operating range of the de-oiling hydrocyclone according to [6,13]. Instead it is more evident that the dynamic and static efficiency is more related to the inlet flow rate, as was concluded in a previous study [22].
To analyze the dynamics of the efficiency in more detail, the controller evaluation experiment was investigated in a shorter time range (2050-2550 s), and the results are plotted in Figure 5. This particular range was chosen as the PID control solution results in valves to severely oscillate and influences the efficiency without reducing the efficiency to 0. A relationship between the efficiency, the underflow concentration, and the inlet concentration of the PID control solution is evident, with an inverse relationship with respect to the underflow concentration. When observing the H ∞ control solution, the is closely following the C i , but unlike the PID control solution the C u is steady, which is most likely caused by a more steady F u .  Table 4. Total volume of the inlet mixture, total volume of oil discharged, and mean de-oiling efficiency . In the experiment (controller evaluation with fluctuating inlet flow rate F i ), the duration was 1900 s.  To further emphasize the relationship between the efficiency and the flow rates, a correlation coefficient has been calculated for all relevant system parameters from 2050 to 2550 s and plotted in a correlation matrix in Figure 6, where a numeric version is attached in the appendix in Figure A2. The relationship between and F i and that between and F u for the PID control solution is high, with 0.75 and 0.74 correlation coefficients, respectively, but so is the link to C i and C u , which consists of 0.78 and −0.86 correlation coefficients, respectively. This coincides with observations from Figure 5. When considering the H ∞ control solution, the lack of relationship between and C u is indicated by a correlation coefficient of −0.2. This value is not a true correlation but stems from the oscillations in the signals, as can be seen in Figure 5. The influence of the flow rates on is clear, as 's relationships with both F i and F u for the H ∞ control solution present 0.18 and 0.24 correlation coefficients, respectively. As discussed earlier, C u has a significant impact on the amount of oil in the underflow, and from this analysis it can be seen that by using the H ∞ control solution C u is decoupled from many of the parameters, resulting in a consistent oil flow rate through the underflow during fluctuating inlet flow rates. The larger correlations between the flow and the valve actuation and between C u and suggest that the PID control solution leaves the hydrocyclone vulnerable towards fluctuating inlet flow rates.

Experiment Discussion: Controller Evaluation with Constant Flow Rate Followed by a Linearly Decreasing Flow Rate
Subjecting the system to a constant inlet flow rate has a positive effect on the system's efficiency and its stability, especially when considering the PID control solution. The continuous flow into the system is reflected in the valve actuation considering the PID control solution in Figure 7, which now maintains the valves at a constant position until 2000 s, where the inlet flow rate is linearly decreasing from 0.47 to 0.37 L/s. After the linear decrease, the level controller starts to regulate the opening of V u , ending at an opening of ≈40%. This is a good indication of the dominance of V u , as the relatively small change in V u causes a fast closing action of V o , which towards the end of the experiments chatters between 10 and 20%. Through the experiment, the efficiency is stable for both controllers, and so are C u and C i . After 2450 s, C u , with respect to the PID control solution, starts increasing due to the choking of V o , while C o remains unaffected. This directly affects . This could be an indication that the hydrocyclone's separating mechanism is being compromised by the decreasing flow rate or that the flow of oil through the overflow is reducing; thus, an increased flow of oil is detected at the underflow. The reduced reference tracking of the robust H ∞ control solution here shows a positive effect, as the slower actuation of the valves results in a stable C u and thus . In cases where the inlet flow rate to the separator would be low for extensive periods, the robust H ∞ control solution would fare better than the conventional PID control solution. It is particularly in these situations, where the efficiency deviates, that OiW measurements are important, as they can be used as feedback to a controller or the operator to take the proper measures to restore maximal separation.

Conclusions
In this paper, we have investigated the OiW separation efficiency of a pilot scaled offshore de-oiling system consisting of a three-phase separator and a downstream hydrocyclone separator. The efficiency was measured using a novel method where two fluorescence-based oil-in-water monitors are used to measure the OiW concentration upstream and downstream of the hydrocyclone. The goal was to achieve real-time measurements of the hydrocyclones separation efficiency and investigate the potential of the measurements by the two instruments as a feedback parameter.
The system was injected with a mixture of OiW, which was stirred continuously in the buffer tank, which provided a consistent OiW concentration and droplet size distribution. Two control strategies were applied to the de-oiling system: a conventional PID control solution and a robust H ∞ control solution.
The OiW measurements were performed successfully with a good dynamic tracking capability in a wide variety of operating conditions, both with respect to steady-state and dynamic operating conditions.
In the controller evaluation, it is shown that, when the PID control solution is applied, it has a good performance while sacrificing the total oil discharge, which raises questions about the true value of . Instead, it directs more attention towards C u . This is especially true when the H ∞ control solution is applied, where its performance measured in is lower than that of the PID control solution, while achieving a lower C u and thus resulting in a lower pollutant discharge into the ocean. To elucidate, the system can perform well with respect to , while yet discharging large amounts of oil through the water fraction. In addition, the H ∞ control solution decoupled C u and from F i , which is a significant achievement, as it means that the system has become more robust towards fluctuating inlet flow rates.
Future studies will use OiW measurements in the control of the hydrocyclone, as and C u are the actual acclimatisation parameters, unlike the PDR or the flow split, and including them into the feedback loop will yield a better efficiency.

Conflicts of Interest:
The authors declare no conflict of interest.