**1. Introduction**

Petroleum is a mixture of organic compounds formed by the anaerobic decomposition of organic sediments in natural geological cavities or wells. The extraction techniques significantly modify its composition, adding an aqueous phase not miscible with the organic mixture and producing a complex emulsion [1]. Water is a contaminant in all oil derivatives, decreasing the quality of the resulting fuels [2], also implying higher pollution, which is a hindrance to the processes of transport, storage, and distillation. In addition, the water carries a wide variety of mineral solutes (sea salt, magnesium, and silicon, mainly) that damage pipes, valves, and pumps. The water is withdrawn from the raw oil, inducing coalescence, a process that consists of merging two or more droplets during contact to form a larger droplet [3,4]. This process may be enhanced by chemical substances. The final water content is a critical parameter in the subsequent petrochemical processing.

Characterization techniques for emulsions include electron and light microscopy, light and neutron scattering, electrical conductivity, and nuclear magnetic resonance [5,6]. Most of these techniques are only suitable for diluted and non-opaque emulsions, conditions not met by water-in-crude oil emulsions [6]. Other common methods for determining water content in crude oil, such as centrifugation [7], Karl Fisher's distillation, and grinding methods [8], require extracting a sample from the pipeline for further processing in a laboratory. These laboratory tests are time consuming and delay the processing and transportation of crude oil.

The real-time monitoring of water concentration before and after the coalescence process is of particular interest to the petrochemical industry [1]. Ultrasound can be useful for characterizing emulsions because it is robust, relatively inexpensive, easy to operate,

**Citation:** Reyna, C.A.B.; Franco, E.E.; Durán, A.L.; Pereira, L.O.V.; Tsuzuki, M.S.G.; Buiochi, F. Water Content Monitoring in Water-in-Oil Emulsions Using a Piezoceramic Sensor. *Machines* **2021**, *9*, 335. https://doi.org/10.3390/ machines9120335

Academic Editor: Dan Zhang

Received: 17 October 2021 Accepted: 2 December 2021 Published: 6 December 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

allows characterizing opaque liquids and it provides in-line and real-time monitoring of emulsion stability evolution using a multi-backscattering sensor [9] and sand production monitoring using a wideband vibration sensor [10]. Ultrasound-based techniques have been used for characterizing liquids, such as edible oils, honey, polymer resins and motor oils [11–13], as well as for process monitoring, such as polymer and concrete curing [14,15]. As regards wave generation and reception methods, the literature reports the use of compact thick-film piezoelectric transducers [16], laser techniques for both the generation and reception of ultrasonic pulses [17] and conventional ultrasonic transducers [18].

In the case of multi-phase fluids, ultrasonic techniques have been used to characterize and to monitor some physical properties of emulsions, suspensions and slurries [19–21]. Other interesting works deal with the monitoring of a multiphase oil-water-gas flow directly in a pipe [18] and the detection of oily contaminants in water courses [22]. These works show the interest in the subject and the variety of possible approaches.

Water-in-crude oil emulsions showed a water concentration in a volume of 40% for droplet size distribution ranging from 0.4 μm to 40 μm [23] and a water concentration in a volume of up to 30% for droplet size distribution from 1 μm to 10 μm [1,5]. This characteristic, in addition to a high variation in their chemical composition, could lead to a dispersive medium with high attenuation. Under these conditions, the best approach must be the monitoring of an average acoustic parameter at a suitable operating frequency. Ultrasonic spectroscopy allows the determination of the distribution of droplet sizes and concentration by measuring the propagation velocity and attenuation spectra [24,25]. This is a well-established technique, useful in monomodal droplet size distribution, and restricted to diluted emulsions (volume fraction of the dispersed phase is less than 1%) [26]. In a recent work [27], the authors used acoustic models and measured attenuation spectra to estimate the droplet size distribution in water-in-sunflower oil emulsions. They reported droplet size distributions of 0.4–5, 0.4–8, 0.4–15, 0.4–12 and 0.4–100 μm for water volume fractions of 0.1, 0.2, 0.3, 0.4 and 0.5, respectively. The droplet size distribution results of the ultrasonic spectroscopy for emulsions of moderate concentrations up to 20% were very close to the experimental data obtained by using laser diffraction.

The measurement of the propagation velocity of ultrasonic waves has been used to infer the physical properties of water-in-crude oil emulsions. In 2021, a novel multibackscattering sensor with a simple signal processing methodology, which allows the measurement of the propagation velocity, was proposed to monitor water-in-crude-oil emulsions [28]. The ultrasonic multiple-backscattering sensor consists of a 3.5-MHz transducer and a set of thin cylindrical scatterers located in the near field. The results from this experimental arrangement showed an almost linear behavior of the propagation velocity over a volumetric water concentration from 0% to 50%. This interesting result was corroborated in the present work.

This paper presents an ultrasonic technique to estimate water concentration in waterin-crude oil emulsions. The working principle is the determination of the time of flight of ultrasonic waves between two custom-made transducers. The sensing device developed was initially tested with static samples to establish the measurement methodology. Other measurements were carried out with the sample being stirred by a laboratory mixer. This was done to maximize the droplet interaction, accelerating the coalescence process. The main motivation is the development of compact, inexpensive, and chemically and mechanically resistant devices, which could be attached to pipes or valves in the oil process lines for on-line and real-time monitoring.

#### **2. Theoretical Background**

Although emulsions are classified as continuous materials, they have local effects that generate a complex acoustic behavior. If the mean diameter of the dispersed phase droplets is smaller than the wavelength, the local acoustic phenomena converge to a wavefront traveling through the mixture with constant velocity. In this case, a simple acoustic propagation model relates the propagation velocity and the concentration, establishing that the total propagation time of an ultrasonic wave through a heterogeneous mixture is the sum of the times in each phase [29] (see Figure 1):

$$t\_e = t\_w + t\_o = \frac{X\_w}{c\_w} + \frac{X\_o}{c\_o} = \frac{X\_e}{c\_e} \,\tag{1}$$

where *t* is the propagation time, *X* is the wave path length, *c* is the propagation velocity and subscripts *e*, *w* and *o* refer to emulsion, water and oil, respectively. The relationship between propagation velocity *c* in the emulsion and water volume fraction *φ* is:

$$\mathcal{L}\_t = \frac{1}{\frac{\phi}{c\_{tr}} + \frac{1-\phi}{c\_{\theta}}}.\tag{2}$$

**Figure 1.** Measurement scheme, showing the mixture model for the propagation velocity in the emulsion (Urick's model) and the arrangement of the ultrasonic transducers and the transmitted *a*(*t*) and reflected *b*(*t*) signals.

Figure 1 also shows the ultrasonic transducer arrangement, composed of an emitter/receiver (Tx) and a receiver (Rx) and reflector. Transducer Tx is used in pulse-echo mode while transducer Rx operates as a receiver. The excitation of Tx generates wave *a*(*t*) that propagates through the sample and reaches Rx. The part of the wave reflected from the Rx face generates signal *b*(*t*), which returns to Tx. This configuration allows the correlation of *a*(*t*) and *b*(*t*) with a shortest path (*Xe*) between them and minimizes the insertion loss reflections by using other materials (steel or aluminum). As distance *Xe* is known, time delay *te* between signals *a*(*t*) and *b*(*t*) allows the determination of propagation velocity *ce* in the emulsion.

#### **3. Materials and Methods**
