energies Article Liquid-Liquid Flow Pattern Prediction Using Relevant Dimensionless Parameter Groups Olusegun Samson Osundare 1,* , Gioia Falcone 1 , Liyun Lao 2 and Alexander Elliott 1 1 James Watt School of Engineering, University of Glasgow, Glasgow G12 8QQ, UK; [email protected] (G.F.); [email protected] (A.E.) 2 Centre for Thermal Energy Systems and Materials, Cranfield University, Bedford MK43 0AL, UK; l.lao@cranfield.ac.uk * Correspondence: [email protected]; Tel.: +44-7466878853 Received: 15 June 2020; Accepted: 17 August 2020; Published: 24 August 2020 Abstract: Accurate predictions of flow patterns in liquid-liquid flow are critical to the successful design and operation of industrial and geo-energy systems where two liquids are jointly transported. Unfortunately, there is no unified flow pattern map, because all published maps are based on limited ranges of dimensional parameters. Dimensional analysis was performed on oil-water horizontal flows, to obtain some relevant dimensionless parameter groups (DPG) for constructing flow pattern maps (FPM). The following combinations of DPG were used: (i) the ratio of mixture Reynolds number to Eötvös number versus water fraction, (ii) the ratio of Weber number to Eötvös number versus water fraction, (iii) the mixture Froude number versus water fraction, (iv) the water Froude number versus oil Froude number, (v) the ratio of gravity force to viscous force versus water fraction. From twelve published experimental studies, 2696 data points were gathered and analysed covering a variety of flow patterns including stratified, stratified mixed, dispersed oil in water, dispersed water in oil, annular and slug flows. Based on the performed analysis, it was found that flow patterns could occupy more than one isolated region on the DPG-based flow pattern map. None of the combinations of DPG can mark out all the considered flow patterns, however, some combinations of DPG are particularly suitable for marking out the regions associated with some flow patterns. Keywords: oil-water; flow regime; geo-energy; dimensionless numbers; oil-viscosity; pipe diameter 1. Introduction Due to their applicability in various process industries, horizontal liquid-liquid flows have been extensively studied. Such research is particularly important in the energy sector, where oil and water are usually co-produced and transported jointly. However, despite the importance of liquid-liquid flows, they have not been studied to the same extent of the gas-liquid flows [1,2] and there is no unified flow pattern map for the liquid-liquid flows [3]. In most cases, the flow pattern maps available for the liquid-liquid flow are limited to the conditions for which the flow maps were constructed [4]. Figure1 presents a liquid-liquid flow pattern map developed for mineral oil and tap water, featuring superficial phase velocities. Various other parameters have been employed in the construction of flow pattern maps, as discussed in Section 2.2. The use of dimensionless groups to develop flow pattern maps would lead to a wider range of applicability [5]. Therefore, this project focuses on the construction of flow pattern maps using various combinations of relevant dimensionless parameter groups to ensure wider usage in horizontal pipes. The earliest research into liquid-liquid flow targeted the improvement of transportation of crude oil in pipelines [6–9], but liquid-liquid flow research is also important for flow in oil well production tubing, enhanced oil recovery (EOR) methods, and the design of chemical reactors and separators [10]. Energies 2020, 13, 4355; doi:10.3390/en13174355 www.mdpi.com/journal/energies Energies 2020, 13, 4355 2 of 26 Energies 2020, 13, x FOR PEER REVIEW 2 of 28 Figure 1. Graph of superficial water velocity versus superficial oil velocity modified after Trallero et al. [11] 3 developedFigure for1. Graph an inner of pipe superficial diameter water of 50.1 velocity mm, with versusµo = superficial0.0288 Pa s, oilµw velocity= 0.00097 modified Pa s, ρo =after884 Trallero kg/m , et 3 ( ) 3 ρw =al.997 [11] * kgdeveloped/m and σ for= 0.036an inner N/m pipe at 25.5 diameter◦C. Note: of 50.1 for datamm, withwith *µ o, the= 0.0288 authors Pa recordeds, µ w = 0.00097 1037 kg Pa/m s, ρo = for tap884 waterkg/m3 at, ρw25.5 = 997C. * kg/m3 and σ = 0.036 N/m at 25.5 °C. Note: for data with (*), the authors recorded ≈ ◦ 1037 kg/m3 for tap water at ≈25.5 °C. 1.1. Importance of Flow Patterns in the Industrial Sector 1.1.Understanding Importance of Flow thenature Patterns and in the behaviour Industrial of Sector liquid-liquid flow is critically important but also challenging,Understanding as many physical the nature and, and sometimes, behaviour chemical of liquid mechanisms-liquid flow govern is critically the formation important of but flow also patterns.challenging, Once a as flow many pattern physical is determined, and, sometimes, some key chemical process mechanisms parameters, govern such as the pressure formation gradients of flow andpatterns. phase fractions Once a flow of that pattern particular is determined, flow system some could key be process estimated. parameters, such as pressure gradients andIn oil-waterphase fractions pipelines, of that stratified particular flow existsflow system at low velocitiescould be estimated. with oil flowing at the top while water flows atIn the oil bottom-water in pipelines, a horizontal stratified pipe. The flow bottom exists section at low of velocities the pipeline with is oil prone flowing to corrosion at the top due while to thewater continuous flows flowat the of bottom water [in12 a,13 horizontal] and the dissolutionpipe. The bottom of gases, section such of as the CO pipeline2 and H2 isS inprone water, to whichcorrosion are attributed as the cause of corrosion. 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Before transporting such crude, its high viscosityAt ambient is usually conditions, reduced, viscous by either heavy heating oil does it, addingnot flow a diluent,easily. Before or both. transporting Charles et al. such [7] and crude, Shiits et al.high [16 viscosity] found that is usually the introduction reduced, ofby water either into heating a heavy it, adding oil pipeline a diluent, can reduce or both. both Charles the pressure et al. 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