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A novel oil–water separator design and its performance prediction
Author’s Accepted Manuscript A novel oil-water separator design and its performance Prediction Quanshu ZENG, Zhiming WANG, Xiaoqiu WANG, Yanlong ZHAO, Xiao GUO www.elsevier.com/locate/petrol
PII: DOI: Reference:
S0920-4105(16)30092-4 http://dx.doi.org/10.1016/j.petrol.2016.03.015 PETROL3392
To appear in: Journal of Petroleum Science and Engineering Received date: 6 September 2015 Revised date: 4 November 2015 Accepted date: 22 March 2016 Cite this article as: Quanshu ZENG, Zhiming WANG, Xiaoqiu WANG, Yanlong ZHAO and Xiao GUO, A novel oil-water separator design and its performance P r e d i c t i o n, Journal of Petroleum Science and Engineering, http://dx.doi.org/10.1016/j.petrol.2016.03.015 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
A Novel Oil-Water Separator Design and Its Performance Prediction Quanshu ZENG, Zhiming WANG*, Xiaoqiu WANG, Yanlong ZHAO, Xiao GUO State Key Laboratory of Petroleum Resources and Prospecting, College of Petroleum Engineering, China University of Petroleum, 102249 Beijing, China *
Corresponding author: Zhiming WANG. Address: China University of Petroleum, No. 18, Fuxue Road,
Changping, Beijing, China. Phone: (86)010-89734958, E-mail: [email protected].
Abstract Numerous oil wells, especially in their middle-late periods, are becoming less economic due to the high lifting costs and reduced recoveries. The downhole oil-water separation (DOWS) system is aimed to reduce the production cost, mitigate the environment impact, and enhance the oil recovery. However, current separators are of either poor separation effects or poor separation efficiencies. In this paper, a novel oil-water separator design is proposed based on the combination of two different flow resistance mechanisms and pipe serial-parallel theory, with the restrictive path restricting the heavier water, while the frictional path impeding the more viscous oil. Based on the combination of the flow pattern transformation criterion, homogenous model, two-fluid model, and pipe serial-parallel theory, a unified model of oil-water two-phase flow is developed to predict both the flow rate and water content distributions in different paths, which is then compared with the computational fluid dynamics (CFD) results. Unlike the CFD results, each path has a specific flow rate and water content, and as a consequence, specific flow regime and flow pattern. Both the CFD and model results show that the flow rate distributions in different paths of the separator will be adjusted automatically according to the fluid’s property, while the model can also predict the water content distributions at the same time. And the average relative deviation between the CFD and model results for flow rate distribution is 14.24%, while that for water content distribution is 42.03%. Specifically, oil, being more viscous, mainly takes the restrictive path; while water, being heavier, tends to take the frictional path instead. To sum up, this autonomous function directs oil and water to different paths, hence oil and water is well separated.
Keywords: Oil-Water Separator; Novel Design; Oil-Water Two-Phase Flow; Unified Model; Numerical Simulation
Nomenclature A = cross section area, m2 C = coefficient, dimensionless d = hydraulic diameter, m f = Moody wall friction coefficient, dimensionless g = gravitational acceleration, m/s2 L = length of pipe, m n = number, dimensionless p = pressure, Pa Q = flow rate, m3/day R = bending radius of the elbow, m Re = Reynolds number, dimensionless S = wetted perimeter, m v = velocity, m/s α = pipe inclination angle from horizontal, degree γ = half the radian corresponds to the wetted perimeter of lower water layer, rad △p = pressure drop, Pa η = volumetric fraction, dimensionless θ = bending angle of the elbow, rad μ = viscosity, Pa·s ρ = density, kg/m3 σ = tension, N/m τ = wall friction, Pa
Subscript c = continuous phase con = contraction cross section cono = contraction cross section oil conw = contraction cross section water cr = critical state d = dispersed phase D = downstream Do = downstream oil Dw = downstream water e = elbow f = frictional path fp = pipe in the frictional path i = interface between oil and water layers inc = inclination m = mixture o = oil p = pipe r = restrictive path rpe = expanded pipe in the restrictive path rps = shrunken pipe in the restrictive path sef = sudden expanded fitting ssf = sudden shrunken fitting U = upstream Um = upstream mixture Uo = upstream oil Uw = upstream water v = velocity w = water
1 Introduction Numerous oil wells, especially in their middle-late periods, are encountering the high water content and becoming less economic. Much of the cost is in managing the ever increasing volumes of water that must be lifted to the surface, separated, treated, pipelined, and re-injected back into the formations (Peachey and Matthews, 1994). In addition, once a region is producing fluids with high water content, fast track will be generated, and then oil production may severely decrease due to the limited flow contribution from the other regions (Denney, 2003). The downhole oil-water separation (DOWS) system, which installed at the bottom of oil wells, has the aim of production cost reduction (Blanco and Davies, 2001; Jokhio et al., 2002; Peachey, 1997), environment impact mitigation (Stuebinger and Elphingstone, 2000), and oil recovery enhancement (Alhoni et al., 2003; Paul, 2010). Three basic types of DOWS systems have been developed and widely used, referring to the gravity separator, hydrocyclone, and membrane separation technology, respectively. The gravity separator (Denney, 2004; Joe, 1982; Kenawy et al., 1997; Lockwood and Norris, 1971) uses the gravity difference caused by density difference between oil and water to separate, which will settle the heavier water while float the lighter oil. Instead of gravity difference, the hydrocyclone (Belaidi et al., 2003; Gomez et al., 2002; Meldrun, 1988) uses the centrifugal force difference to achieve the separation, with the heavier water threw to the boundary, spirals downward and leaves from the underflow port, while the lighter oil generates oil core around the center axis, and leaves from the overflow port. The induced gas flotation technology (Bridson et al., 2005; Frankiewicz et al., 2005; Leech et al., 1980), which injects/generates gas bubbles adhering to the suspended matter, is commonly combined with the previous two to improve their performances. Last but not least, the membrane separation technology (Duong and Chung, 2014a, 2014b; Fernandez et al., 2001; Padaki et al., 2015) uses the semipermeable membrane to separate the molecules with different particle sizes selectively, hence oil and water are well separated. However, current separators are still of either poor separation effects (the gravity separator, and the hydrocyclone) or poor separation efficiencies (the membrane separation technology) in the limited wellbore space, which limit their applications in heavy oil reservoir, deep water development, and high temperature & high pressure environment. In this paper, a novel oil-water separator design is proposed to overcome the limitations of current separators, and the development of such design concept is then described in detail. To better understand the separation performance of oil-water two-phase flow through the separator, a unified model is developed, which is then
compared with the computational fluid dynamics (CFD) results.
2 Novel Oil-Water Separator Design The novel oil-water separator (Fig. 1), consisting of two parallel-connected paths with pipes and fittings in series, is developed based on the combination of the local resistance mechanism, frictional resistance mechanism, and pipe serial-parallel theory. As it can be observed from Fig. 1, the separator comprises two parallel flow paths from top to bottom, the restrictive path, and the frictional path. The restrictive path, which has expanded and shrunken pipes alternately in series, is mainly of the local resistance loss, while the frictional path, which has a much longer path, is mainly of the frictional resistance loss. Since the local loss depends on the flow rate, fluid density, and local loss coefficient, while the frictional loss depends on the flow rate, fluid viscosity, and path length, both local loss coefficient and frictional path length are key structure parameters that determine the separation performance. And the structure parameter optimization will be discussed in Section 4.1. In addition, flow rate, viscosity, and density are key fluid factors to determine the flow distributions in different paths of the optimized separator. Specifically, water, being of high density and low viscosity, has higher local resistance through the restrictive path, and tends to mainly take the frictional path. In contrast, oil, with its low density and high viscosity, will mainly take the restrictive path instead due to the remarkable resistance increment in the frictional path. That is to say, the fluid through separator will be separated automatically according to its specific property. And this autonomous function of oil-water two-phase flow through separator will be simulated and deduced in detail, which will be shown in Section 3.
3 Methodology 3.1 Numerical Simulation Since numerical simulation has been widely used on the complex flow studies with the developments of both computer competency and CFD technology, the rules of oil-water two-phase flow through the separator are first studied numerically and then compared with the proposed unified model. The structure parameters of the separator are shown in Table 1. The three-dimensional mechanical model of the separator is first developed, which then the hydraulic model is obtained by Boolean operation and subsequently
the mesh is generated. All the inlets are set as velocity-inlet, while the outlets are set as pressure-outlet and the rest as wall. The inlet and outlet boundary conditions of the separator are shown in Table 2. For better understand the rules of oil-water two-phase flow through the separator at both stratified and dispersed flows while their flow mechanisms and rules are quite different, both 30 m3/day and 3000 m3/day are chosen. Since water content and oil viscosity have a wide range and great impact on the properties of oil-water mixtures, both parameters are considered as the main variables. And the inlet water content range of 0 - 100% covers all the oil-water ratio situations, while the oil viscosities of 0.001, 0.01, and 0.1 Pa·s are representative of low, medium, and high viscosity oil respectively. The laminar model is selected on simulating the laminar flow while the standard k model is selected on simulating the turbulent flow. In addition, the Eulerian model is selected on simulating the oil-water two-phase dispersed flow while the VOF model is selected on simulating the stratified flow. 3.2 Modeling However, current studies on the modeling and simulation of multi-outlet flow field are still limited to the case with same fluid composition in the whole flow field or the case with the fluid composition of each outlet known (Zeng et al., 2015). Moreover, neither homogenous model nor two-fluid model alone can determine the flow mechanisms and rules of both flow patterns perfectly. To solve this, a unified model of oil-water two-phase flow through the separator is developed on the combination of the flow pattern transformation criterion, homogenous model, two-fluid model, and pipe serial-parallel theory. Unlike the CFD results, each path has a specific flow rate and water content, and as a consequence, specific flow regime and flow pattern. Since this paper mainly focus on the design concept and standalone performance prediction of the novel oil-water separator, and pressure has little impact on either the liquid viscosity (Alshmakhy and Maini, 2012; Freitas et al., 2014; Yan et al., 2014) or liquid density (Abdulagatov et al., 2014; Hussein and Amin, 2010), oil, water, and their mixture are assumed as Newtonian and incompressible fluids. And assume that there is no heat exchange or work between the fluid and environment, the system remains isothermal. The interface between the oil and water layers is assumed as a flat surface. In addition, the flows of pipes and fittings have no obvious interaction on each other. 3.2.1 Flow Pattern Transformation Criterion The flow pattern transformation among the oil-water stratified flow (o&w), water in oil dispersed flow (w/o), and oil in water dispersed flow (o/w) is shown in Fig. 2. The transition from the stratified flow to dispersed flow is based on the balance of the total turbulent energy of continuous phase and the total surface free energy of dispersed
phase, and water (or oil) can be assumed to be dispersed in oil (or water) when the total turbulent energy is greater than the total surface free energy (Atmaca et al., 2009; Zhang et al., 2006). In addition, the transition between the w/o and o/w depends on the interface free energy, and the inversion point is where the system has the largest interface free energy (Brauner and Ullmann, 2002; Decarre and Fabre, 1997; Tidhar et al., 1986). As shown in Appendix A, one liquid will become dispersed in the other liquid phase when the mixture velocity is larger than a certain value (Eq. 1), while the dispersed phase will become the continuous when the volume content of dispersed phase is larger than another certain value (Eq. 2).
6.325Cinc d i w o g 1/ 2 vm f m m
1/ 2
w cr w cr
d w o
(1)
(2)
3.2.2 Flow through the Horizontal Pipe The control volumes of oil-water two-phase dispersed and stratified flows through the horizontal pipe are shown in Fig. 3. The pressure drop derivation processes of both dispersed and stratified flows through the horizontal pipe are present in Appendix A. The pressure loss of dispersed flow through the horizontal pipe is shown in Eq. 3, while that of stratified flow is shown in Eq. 4.
p p p p
4 m L d
o So w S w A
(3)
(4)
L
3.2.3 Flow through the Elbow The control volumes of oil-water two-phase dispersed and stratified flows through the elbow are shown in Fig. 4. Similar to the flow through the horizontal pipe, the general pressure drop equations of both dispersed and stratified flows through the elbow can be obtained respectively with re-integrating the pressure gradient equations along the radial, as shown in Eqs. 5&6.
pe
4 m R d
R pe o So w S w A
(5)
(6)
3.2.4 Flow through the Sudden Expanded Fitting The control volumes of oil-water two-phase dispersed and stratified flows through the sudden expanded fitting are shown in Fig. 5. Both the interface friction and gravity are ignored, and no mass exchange between the upper and lower layers is considered. The general pressure drop equation of oil-water two-phase dispersed flow through the sudden expanded fitting can be obtained on the basis of the homogenous model (Ahmed et al., 2007; Gundigdu et al., 2009; Hwang et al., 1997). 2
psef
A v2 1 U Um m AD 2
(7)
However, the settling phenomenon will occur whenever the dispersed flow transforms to the stratified, thus the momentum equation should be re-derived on the basis of the two-fluid model (Ahmed et al., 2007; Gundigdu et al., 2009).
pU AU pD AD p' AD AU oQo vUo vDo wQw vUw vDw
(8)
Where, p is the pressure in front of the sudden expanded fitting, Pa. According to Che and Li (2007), the pressure at U-U cross-section equals to that in front of the sudden expanded fitting, thus the general pressure drop equation of oil-water two-phase stratified flow through the sudden expanded fitting can be obtained.
psef oQo Uo Do wQw Uw Dw AD
(9)
3.2.5 Flow through the Sudden Shrunken Fitting The control volumes of oil-water two-phase dispersed and stratified flows through the sudden shrunken fitting are shown in Fig. 6. The assumption is the same with that of the sudden expanded fitting. The fluid will accelerate its speed and the pressure energy will translate to kinetic energy whenever the fluid flows from the U-U section to the minimum contraction section C-C, thus there is almost no frictional loss during this process (Che and Li, 2007). However, once the fluid has passed the C-C section, the rule is similar to that of the sudden expanded fitting and the frictional loss is generated. Thus the general pressure drop equation of oil-water two-phase dispersed flow through the sudden shrunken fitting can be obtained on the basis of the homogenous model (Hwang et al., 1997; Oertel et al., 2004).
pssf
2 1 2 vDm 1 2 2 m Cv Ccon Ccon 2
Ccon
(10)
A con AD
(11)
vc v
(12)
Cv
Where, vc is the actual average velocity cross the contraction cross-section, m/s; v is the ideal average velocity cross the contraction cross-section, m/s. Similarly, the settling phenomenon will occur whenever the dispersed flow transforms to the stratified, thus its momentum equation should be re-derived on the basis of the two-fluid model (Chen et al., 2009).
pcon Acon pD AD p' ( AD Acon ) oQo cono Do wQw conw Dw
(13)
And the pressure at C-C cross-section equals to that in front of the sudden shrunken fitting, thus the general pressure drop equation of oil-water two-phase stratified flow through the sudden shrunken fitting can be obtained.
pssf oQo cono Do wQw conw Dw AD
(14)
3.2.6 Pipe Serial-Parallel Theory Two important rules can be obtained for pipes and fittings connected in series, as shown in Eqs. 15&16; while another two rules obtained for pipes and fittings connected in parallel, as shown in Eqs. 17&18 (Minzer et al., 2006).
Q Q1 Q2 Qn
(15)
p p1 p2 pn
(16)
Q Q1 Q2
Qn
p p1 p2 pn
(17) (18)
Thereby both the flow distributions and pressure drops of oil-water two-phase flow through the separator can be obtained coupling Eqs. 15-18. 3.2.7 Model Solution The unified model is solved numerically and the flow chart is shown in Fig. 7. First, the initial basic
parameters are inputted, including the separator structure parameters, fluid property, and flow rate. And both oil and water flow rates in the restrictive path are initialized with a small value, then oil and water flow rates in the frictional path can be obtained according to the pipe serial-parallel theory. Then, the flow pattern transformation criterion is verified to determine whether the flow of each path is dispersed flow. For the dispersed flow, the model parameters and pressure drop are calculated on the basic of homogenous model. For the stratified flow, the model parameters and pressure drop are calculated on the basic of two-fluid model. Next, since both paths are in parallel, loop water flow rate in the restrictive path until the pressure drops of both paths equal to each other. Finally, since a system tends to be stable at the minimum energy (Sharma et al., 2011), loop oil flow rate in the restrictive path until the system has the minimum energy.
4 Results and Analysis 4.1 Structure Parameter Optimization To ensure the separation performance, oil (870 kg/m3, 0.01 Pa·s) flow rate in the restrictive path should be at least larger than that in the frictional path, while water (998.2 kg/m3, 0.001003 Pa·s) flow rate is just the opposite. Based on this principle, the separator structure is optimized. As it can be observed from Fig. 1, the pressure drops of oil/water through both paths can be obtained with the adding of those through each pipes and fittings (Eqs. 19&20). Since the restrictive path consists of expanded and shrunken pipes alternately in series, all the values of nrps, nssf, and nsef are set as an uncertain integer n, while nrpe as n+1. Moreover, the pressure drops generated by parallel paths equal to each other (Eq. 21), which enables the fluid to be separated automatically according to its specific property.
pr nrpeprpe nrpsprps nssf pssf nsef psef
(19)
p f p fp ne pe
(20)
pr p f
(21)
As shown in Table 1, Af equals to Arpe, and is four times of Arps, then Ccon is 0.637, Cv is 0.985 in this case (Oertel et al., 2004). Since an oil-water treating capacity of 3000 m3/day can almost meet the maximum requirements of all situations (Alhoni et al., 2003; Belaidi et al., 2003; Blanco and Davies, 2001; Gomez et al., 2002; Jokhio et al., 2002; Paul, 2010), the flow rate is selected. And the relationship between vrpe and vf at 3000 m3/day is obtained.
vrpe v f 4.421m / s
(22)
Based on the optimization principle and selected parameters, both oil and water flow distributions with varying n and Lf can be obtained coupling Eqs. 19-22, which are shown in Fig. 8. The intersection of oil and water flow distribution ratios with same n value is defined as the critical flow distribution ratio, while the corresponding Lf is defined as the optimal frictional path length. As it can be observed, oil and water flow rates in the restrictive path will increase as Lf increases, while those in the frictional path will decrease. In order to direct more oil into the restrictive path, Lf should be as large as possible. In order to direct more water into the frictional path, on the contrary, Lf should be as small as possible. Therefore, the shunt effect will get worse whether Lf increases or decreases. Simultaneously, the critical flow distribution ratio will increase with a small gradient as n increases, while Lf will increase greatly. However, the separator will become too complex and unsteady if Lf is too long. Therefore, n is valued 1 and Lf is valued 119.36 m in this consideration. 4.2 Oil-Water Separation Performance To better understand the rules of oil-water two-phase flow through the separator, the flow rate and water content distributions in different paths with varying fluid properties can be obtained by both the numerical simulation and proposed unified model, which are shown in Fig. 9, and Fig. 10 respectively. As can be observed, the average relative deviation between the CFD and model results for flow distribution is 14.24%, while that for water content distribution is 42.03%. Since CFD can only describe the flow rate distributions while the proposed model can describe both the flow rate and water content distributions in different paths, the average relative deviation for water content distributions is higher than that that for flow rate distributions. The deviations are mainly due to the following reasons. First, the water contents in different paths remain the same during simulation, but in fact they are different in most cases, as considered in the united model. Second, the flow regimes and flow patterns in whole flow field remain the same during simulation, but in fact they are different in most cases, as considered in the united model. Next, only three patterns (o&w, w/o, and o/w) are considered in the unified model, which is simplified from the actual flow. Finally, oil, water, and their mixture are considered as Newtonian and incompressible fluids, but in fact they are non-Newtonian and slight-compressible fluids. As shown in Fig. 9 and Fig. 10, all the curves have several key turning points which are mainly caused by the flow regime transition, flow pattern transition, or flow re-distribution. The flow regime would transform among the laminar flow, transition flow, and turbulent flow, while the flow pattern would transform among the o&w, w/o, and o/w as previously described. Since both paths are in parallel, the change of either water content or oil viscosity will
re-distribute the flow rates and water contents in both paths, lead to the flow regime and flow pattern transition, and as a consequence, re-distribute the kinetic energy and surface free energy of system. At the flow rate of 30 m3/day, the flow patterns in both paths will remain stratified according to the flow pattern transform criterion while the flow regimes will remain laminar according to their Reynolds numbers. Since the kinetic energy of a stratified system is much smaller than the surface free energy, and the frictional path has a much longer path than the restrictive path, the surface free energy change of frictional path induced by the change of either water content or oil viscosity is much more remarkable. Therefore, to ensure the system has the minimum energy, none of the water will be directed into the frictional path until the water content of restrictive path has reached 100%. As a result, the flow rate and water content distributions in both paths with 30 m3/day are shown in Fig. 9(a), Fig. 9(b), and Fig. 10(a) respectively. As can be observed, the flow rate and water content changes in both paths with varying fluid viscosity are similar, and the changes can divide into two stages. Stage I, water will be only directed into restrictive path to ensure the system has the minimum energy. Stage II, once the water content of restrictive path reaches 100%, the water content of frictional path will begin to increase. That is, the separator has excellent separation performance at both stages. Simultaneously, the higher the oil viscosity is, the more fluid will be directed into the restrictive path, and the turning point between the stages would occur at higher water content. Overall, the separation effect is excellent with various inlet water contents in the situation of stratified flow. At the flow rate of 3000 m3/day, the flow patterns in both paths will remain dispersed according to the flow pattern transformation criterion while the flow regimes will remain turbulent according to their Reynolds numbers. Since the kinetic energy of a dispersed system is much greater than the surface free energy, the kinetic energy change of frictional path induced by the change of either water content or oil viscosity is much more remarkable. Since a system tends to be stable at the minimum energy, the fluid viscosity of frictional path should be as large as possible, which will direct more fluid into the restrictive path, and result in the minimum system energy. The flow rate and water content distributions in both paths with 3000 m3/day are shown in Fig. 9(c), Fig. 9(d), and Fig. 10(b) respectively. As can be observed, the flow rate and water content changes in both paths with varying oil viscosity are similar, and the changes can divide into four stages. Stage I, since the fluid viscosity increases with water content at low water content, water will be only directed into the frictional path to make sure that the viscosity of frictional path is as large as possible, and more fluid will be directed into the restrictive path. Stage II, the viscosity of frictional path will be the largest once its water content reaches the critical water content, and the water content of restrictive path begins to increase while that of frictional path remains the critical, as shown in Fig. 11. In this
case, the flow rate in restrictive path decreases while that in frictional path increases. Stage III, once the water content of restrictive path reaches the critical value, the water content of restrictive path will continue to increase while that of frictional path remain the critical. Since the phase inversion has occurred in the restrictive path, the flow rate in frictional path will increase instead while that in restrictive path is just the opposite. Stage IV, once the water content of restrictive path reaches 100%, the water content of frictional path begins to increase, and the flow rate of restrictive path increases, while that of frictional path is just the opposite. That is, the separator has excellent separation performance at both stage I and IV. For stage I, water will be only directed into the frictional path, and the water content of restrictive path remain 0. For stage IV, none of oil will be directed into the restrictive path, and the water content of restrictive path remain 100%. Simultaneously, the phase inversion point would occur at lower water content due to lower critical volumetric water content generated by higher viscosity oil, as shown in Fig. 11. And the scope of stage I will widen while that of stage IV will narrow as the oil viscosity increases. To sum up, this autonomous function directs oil and water to different paths, hence oil and water is well separated. Only when the water content of either path reaches 0 or 100%, the separation efficiency for this path is considered 100%. The separator has no minimum oil-water treating capacity limited, while its maximum oil-water treating capacity depends on inlet water content and oil viscosity. Of special interest is the connections of different outlets and storage tanks that the relative magnitude of water contents in both path may just reversal as the water content increases. Overall, the novel oil-water separator design has a small size, no movable parts, no additional energy supply, good separation effect and efficiency with reasonable parameters.
5 Conclusions In this paper, a novel oil-water separator design is proposed, which is then verified and predicted by both the numerical simulation and proposed unified model. The following conclusions and recommendations can be obtained on the basis of the study. (1) Based on the combination of the flow pattern transformation criterion, homogenous model, two-fluid model, and pipe serial-parallel theory, a unified model of oil-water two-phase flow through the separator is developed and then compared with the CFD results. The proposed unified model can not only describe the flow rate and water content distributions in different paths of the separator, but also predict the flow rate and water content re-distributions, flow pattern transform, and flow regime transform as the fluid properties change.
(2) Both the CFD and model results show that the flow rate distributions in different paths of the separator will be adjusted automatically according to the fluid’s property, while the model results show that the water content distributions will also be self-adjusted. And the average relative deviation for flow rate distribution is 14.24%, while that for water content distribution is 42.03%. (3) Overall, the novel oil-water separator design has a small size, no movable parts, no additional energy supply, good separation effect and efficiency with reasonable parameters.
Acknowledgments This study was supported by the 111 Project (Grant No.: B12033), National Science and Technology Major Project (Grant No.: 2016ZX05044005-001), National Natural Science Foundation of China (Grant No.: 51474225), and State Key Laboratory Foundation of Offshore Oil Exploitation (Grant No.: CCL2013RCPS0239GNN). Simultaneously, the reviewers of the original manuscript are greatly appreciated; their comments and suggestions help improve this paper.
Appendix A. United Model of Oil-Water Two-Phase Flow through the Horizontal Pipe A.1 Flow Pattern Transformation Criterion The oil-water interfacial tension is low due to the small difference between oil and water densities, thus the oil-water interface is difficult to maintain stability, also the stratified flow is easy to transform to the dispersed flow. The transition from stratified flow to dispersed flow is based on the balance of the total turbulent energy of the continuous phase and the total surface free energy of the dispersed phase, while the transition between the w/o and o/w depends on the interface free energy. The dispersed phase is dispersed as spherical drops in the continuous phase which will collide and coalesce with one another due to the turbulent movement. Simultaneously, the drops will be broken up by the turbulent forces exerted on them if the sizes are larger than a certain value. Moreover, the drop coalescence of continuous phase and the drop broken of dispersed phase will lead to the phase inversion. Therefore, the amount of dispersed phase per unit can hold depends on the turbulent intensity of the continuous phase. Water (or oil) can be assumed to be dispersed in oil (or water) when the total turbulent energy is greater than the total surface free energy, that is, the mixture velocity should be larger than a certain value (Atmaca et al., 2009; Zhang et al., 2006). In addition, the inversion point is where the system has the largest interface free energy, the dispersed phase will become the continuous when the volume content of dispersed phase is larger than another
certain value (Brauner and Ullmann, 2002; Decarre and Fabre, 1997; Tidhar et al., 1986).
6.325Cinc d i w o g 1/ 2 vm f m m
1/ 2
d w o
(A-1)
w cr w cr
(A-2)
Where,
Cinc
2.5 sin
(A-3)
2
64 Re m 0.0122Re m 2320 fm 1680 0 . 3164 Re 0m.25
Re m 2320 2320 Re m 4000
4000 Re
m
105
(A-4)
(A-5)
v d Re m m m m
(A-6)
cr
1 1 o w
0.4
o w
0.6
The density and velocity of the dispersion can be calculated on the properties of both continuous and dispersed phases (Awad and Muzychka, 2008), while its viscosity mainly depends on the continuous phase (Brinkman, 1952; Roscoe, 1952), as shown in Fig. 11.
m cc dd
(A-7)
vm vc vd
(A-8)
m cc2.5
(A-9)
A.2 Dispersed Flow Model The momentum equation of oil-water two-phase dispersed flow through the horizontal pipe, developed on the basis of the homogenous model (Awad and Muzychka, 2008; Hasan and Kabir, 2002; Ouyang and Aziz, 2000), is shown in Eq. A-10.
dp 4 m dx d
(A-10)
Where,
m
(A-11)
1 f m m vm2 8
Thus the general pressure drop equation of oil-water two-phase dispersed flow through the horizontal pipe can be obtained with the integration of Eq. A-10.
p p
4 m L d
(A-12)
A.3 Stratified Flow Model However, the settling phenomenon will occur whenever the dispersed flow transforms to the stratified, thus the general pressure drop equation should be re-derived on the basis of the two-fluid model (Barnea and Taitel, 1994; Brauner et al., 1998; Taitel et al., 1995; Zhang et al., 2006). The volume flow rates of both layers are shown in Eqs. A-13&A-14, while the momentum equations shown in Eqs. A-15&A-16.
Qo Ao vo
(A-13)
Qw Awvw
(A-14)
Ao
dp o S o i Si 0 dx
(A-15)
Aw
dp w S w i Si 0 dx
(A-16)
Where, Si is the cross section chord length of oil-water interface, m. Thus the general pressure drop equation of oil-water two-phase stratified flow through the horizontal pipe can be obtained with the addition and integration of Eqs. A-15&A-16, while the combinational momentum equation obtained with the subtraction of Eqs. A-15&A-16.
p p
o So w S w A
(A-17)
L
w S w o So 1 1 i Si 0 Ao Aw Aw Ao
(A-18)
However, several key parameters are required to close the stratified flow model, which contain the geometric parameters and friction parameters (Ullmann and Brauner, 2006).
The geometric parameters, which are shown in Fig. 3(b), contain the wetted perimeters and cross section areas. The wetted perimeters of both layers are shown in Eqs. A-19&A-20, while the cross section areas occupied by both layers shown in Eqs. A-21&A-22, and the cross section chord length of oil-water interface shown in Eq. A-23. (A-19)
So d S w d
(A-20)
d2 Ao ( sin cos ) 4
(A-21)
Aw
d2 ( sin cos ) 4 Si d sin
(A-22)
(A-23)
The friction parameters mainly consider the wall friction which is referred to the concept of friction coefficient (Ullmann et al., 2004).
o
1 f o o vo2 8
(A-24)
w
1 f w wvw2 8
(A-25)
The effective Reynolds numbers of both layers are shown in Eqs. A-26&A-27.
vd Re o o o o o
(A-26)
w vw d w w
(A-27)
Re w
The hydraulic diameter formulas of oil and water layers differ a lot according to the velocity of each layer (Ullmann et al., 2004; Ullmann and Brauner, 2006).
dw
4 Aw S w Si
(vo vw )
4 Aw Sw
(vo vw )
4 Ao S S o i do 4 Ao So
(vo vw ) (vo vw )
(A-28)
(A-29)
The interface friction between the oil and water layers is shown in Eq. A-30 (Kamel and Renee, 2010).
i
1 f i i (vo vw ) 2 sgn( vo vw ) 8
(A-30)
Where,
fo f i 0 f w
o i 0 w
(vo vw )
(A-31)
(vo vw ) (vo vw )
(vo vw ) (vo vw )
(A-32)
(vo vw )
Thereby the pressure drop of oil-water two-phase flow through the horizontal pipe can be obtained coupling Eqs. A-1, A-2, A-12, and A-17.
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Figures
Fig. 1 Structure Diagram of the Novel Oil-Water Separator Design
Fig. 2 Flow Pattern Transformation
(a) Dispersed Flow
(b) Stratified Flow Fig. 3 Control Volumes of Oil-Water Two-Phase Flows through the Horizontal Pipe
(a) Dispersed Flow
(b) Stratified Flow Fig. 4 Control Volumes of Oil-Water Two-Phase Flows through the Elbow
(a) Dispersed Flow
(b) Stratified Flow Fig. 5 Control Volumes of Oil-Water Two-Phase Flows through the Sudden Expanded Fitting
(a) Dispersed Flow
(b) Stratified Flow Fig. 6 Control Volumes of Oil-Water Two-Phase Flows through the Sudden Shrunken Fitting
Fig. 7 Solving Procedure for the Proposed Oil-Water Two-Phase Unified Model
Fig. 8 Oil/Water Flow Distributions versus Lf with Varying n Values
(a) 30 m3/day, Restrictive Path
(b) 30 m3/day, Frictional Path
(c) 3000 m3/day, Restrictive Path
(d) 3000 m3/day, Frictional Path Fig. 9 Flow Rate Distributions in Different Paths with Varying Fluid Properties
(a) 30 m3/day
(b) 3000 m3/day Fig. 10 Water Content Distributions in Different Paths with Varying Fluid Properties
Fig. 11 Mixture Viscosities in Different Paths with Varying Fluid Properties
Tables Table 1 Structure Parameters of the Separator Structure Parameters
Value
Units
Restrictive Path Total Length of the Restrictive Path
4.9
m
Number of the Expanded Pipe
n+1 (uncertain)
Dimensionless
Diameter of the Expanded Pipe
0.1
m
Number of the Shrunken Pipe
n (uncertain)
Dimensionless
Diameter of the Shrunken Pipe
0.05
m
Number of the Sudden Expanded Fitting
n (uncertain)
Dimensionless
Number of the Sudden Shrunken Fitting
n (uncertain)
Dimensionless
Total Length of the Frictional Path
Lf (uncertain)
m
Diameter of the Frictional Path
0.1
m
Number of the Elbow
12
Dimensionless
Bending Angle of the Elbow
90
degree
Bending Radius of the Elbow
0.3
m
Frictional Path
Table 2 Inlet and Outlet Boundary Conditions of the Separator Fluid Properties
Value
Units
Inlet Flow Rate
30, 3000
m3/day
Volume Water Content
0 - 100
%
Oil Density
870
kg/m3
Oil Viscosity
0.001, 0.01, 0.1
Pa·s
Water Density
998.2
kg/m3
Water Viscosity
0.001003
Pa·s
0
Pa
0
Pa
Outlet 1 Pressure Outlet 2 Pressure
Highlights 1. An oil-water separator is proposed with combination of two resistance mechanisms. 2. A unite model of oil-water two-phase flow through the separator is developed. 3. The flow rate and water content distributions through both paths are auto-adjusted. 4. The proposed model can predicted both the flow rate and water content distributions. 5. The separator design has a small size, good separation effect and efficiency.
PII: DOI: Reference:
S0920-4105(16)30092-4 http://dx.doi.org/10.1016/j.petrol.2016.03.015 PETROL3392
To appear in: Journal of Petroleum Science and Engineering Received date: 6 September 2015 Revised date: 4 November 2015 Accepted date: 22 March 2016 Cite this article as: Quanshu ZENG, Zhiming WANG, Xiaoqiu WANG, Yanlong ZHAO and Xiao GUO, A novel oil-water separator design and its performance P r e d i c t i o n, Journal of Petroleum Science and Engineering, http://dx.doi.org/10.1016/j.petrol.2016.03.015 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
A Novel Oil-Water Separator Design and Its Performance Prediction Quanshu ZENG, Zhiming WANG*, Xiaoqiu WANG, Yanlong ZHAO, Xiao GUO State Key Laboratory of Petroleum Resources and Prospecting, College of Petroleum Engineering, China University of Petroleum, 102249 Beijing, China *
Corresponding author: Zhiming WANG. Address: China University of Petroleum, No. 18, Fuxue Road,
Changping, Beijing, China. Phone: (86)010-89734958, E-mail: [email protected].
Abstract Numerous oil wells, especially in their middle-late periods, are becoming less economic due to the high lifting costs and reduced recoveries. The downhole oil-water separation (DOWS) system is aimed to reduce the production cost, mitigate the environment impact, and enhance the oil recovery. However, current separators are of either poor separation effects or poor separation efficiencies. In this paper, a novel oil-water separator design is proposed based on the combination of two different flow resistance mechanisms and pipe serial-parallel theory, with the restrictive path restricting the heavier water, while the frictional path impeding the more viscous oil. Based on the combination of the flow pattern transformation criterion, homogenous model, two-fluid model, and pipe serial-parallel theory, a unified model of oil-water two-phase flow is developed to predict both the flow rate and water content distributions in different paths, which is then compared with the computational fluid dynamics (CFD) results. Unlike the CFD results, each path has a specific flow rate and water content, and as a consequence, specific flow regime and flow pattern. Both the CFD and model results show that the flow rate distributions in different paths of the separator will be adjusted automatically according to the fluid’s property, while the model can also predict the water content distributions at the same time. And the average relative deviation between the CFD and model results for flow rate distribution is 14.24%, while that for water content distribution is 42.03%. Specifically, oil, being more viscous, mainly takes the restrictive path; while water, being heavier, tends to take the frictional path instead. To sum up, this autonomous function directs oil and water to different paths, hence oil and water is well separated.
Keywords: Oil-Water Separator; Novel Design; Oil-Water Two-Phase Flow; Unified Model; Numerical Simulation
Nomenclature A = cross section area, m2 C = coefficient, dimensionless d = hydraulic diameter, m f = Moody wall friction coefficient, dimensionless g = gravitational acceleration, m/s2 L = length of pipe, m n = number, dimensionless p = pressure, Pa Q = flow rate, m3/day R = bending radius of the elbow, m Re = Reynolds number, dimensionless S = wetted perimeter, m v = velocity, m/s α = pipe inclination angle from horizontal, degree γ = half the radian corresponds to the wetted perimeter of lower water layer, rad △p = pressure drop, Pa η = volumetric fraction, dimensionless θ = bending angle of the elbow, rad μ = viscosity, Pa·s ρ = density, kg/m3 σ = tension, N/m τ = wall friction, Pa
Subscript c = continuous phase con = contraction cross section cono = contraction cross section oil conw = contraction cross section water cr = critical state d = dispersed phase D = downstream Do = downstream oil Dw = downstream water e = elbow f = frictional path fp = pipe in the frictional path i = interface between oil and water layers inc = inclination m = mixture o = oil p = pipe r = restrictive path rpe = expanded pipe in the restrictive path rps = shrunken pipe in the restrictive path sef = sudden expanded fitting ssf = sudden shrunken fitting U = upstream Um = upstream mixture Uo = upstream oil Uw = upstream water v = velocity w = water
1 Introduction Numerous oil wells, especially in their middle-late periods, are encountering the high water content and becoming less economic. Much of the cost is in managing the ever increasing volumes of water that must be lifted to the surface, separated, treated, pipelined, and re-injected back into the formations (Peachey and Matthews, 1994). In addition, once a region is producing fluids with high water content, fast track will be generated, and then oil production may severely decrease due to the limited flow contribution from the other regions (Denney, 2003). The downhole oil-water separation (DOWS) system, which installed at the bottom of oil wells, has the aim of production cost reduction (Blanco and Davies, 2001; Jokhio et al., 2002; Peachey, 1997), environment impact mitigation (Stuebinger and Elphingstone, 2000), and oil recovery enhancement (Alhoni et al., 2003; Paul, 2010). Three basic types of DOWS systems have been developed and widely used, referring to the gravity separator, hydrocyclone, and membrane separation technology, respectively. The gravity separator (Denney, 2004; Joe, 1982; Kenawy et al., 1997; Lockwood and Norris, 1971) uses the gravity difference caused by density difference between oil and water to separate, which will settle the heavier water while float the lighter oil. Instead of gravity difference, the hydrocyclone (Belaidi et al., 2003; Gomez et al., 2002; Meldrun, 1988) uses the centrifugal force difference to achieve the separation, with the heavier water threw to the boundary, spirals downward and leaves from the underflow port, while the lighter oil generates oil core around the center axis, and leaves from the overflow port. The induced gas flotation technology (Bridson et al., 2005; Frankiewicz et al., 2005; Leech et al., 1980), which injects/generates gas bubbles adhering to the suspended matter, is commonly combined with the previous two to improve their performances. Last but not least, the membrane separation technology (Duong and Chung, 2014a, 2014b; Fernandez et al., 2001; Padaki et al., 2015) uses the semipermeable membrane to separate the molecules with different particle sizes selectively, hence oil and water are well separated. However, current separators are still of either poor separation effects (the gravity separator, and the hydrocyclone) or poor separation efficiencies (the membrane separation technology) in the limited wellbore space, which limit their applications in heavy oil reservoir, deep water development, and high temperature & high pressure environment. In this paper, a novel oil-water separator design is proposed to overcome the limitations of current separators, and the development of such design concept is then described in detail. To better understand the separation performance of oil-water two-phase flow through the separator, a unified model is developed, which is then
compared with the computational fluid dynamics (CFD) results.
2 Novel Oil-Water Separator Design The novel oil-water separator (Fig. 1), consisting of two parallel-connected paths with pipes and fittings in series, is developed based on the combination of the local resistance mechanism, frictional resistance mechanism, and pipe serial-parallel theory. As it can be observed from Fig. 1, the separator comprises two parallel flow paths from top to bottom, the restrictive path, and the frictional path. The restrictive path, which has expanded and shrunken pipes alternately in series, is mainly of the local resistance loss, while the frictional path, which has a much longer path, is mainly of the frictional resistance loss. Since the local loss depends on the flow rate, fluid density, and local loss coefficient, while the frictional loss depends on the flow rate, fluid viscosity, and path length, both local loss coefficient and frictional path length are key structure parameters that determine the separation performance. And the structure parameter optimization will be discussed in Section 4.1. In addition, flow rate, viscosity, and density are key fluid factors to determine the flow distributions in different paths of the optimized separator. Specifically, water, being of high density and low viscosity, has higher local resistance through the restrictive path, and tends to mainly take the frictional path. In contrast, oil, with its low density and high viscosity, will mainly take the restrictive path instead due to the remarkable resistance increment in the frictional path. That is to say, the fluid through separator will be separated automatically according to its specific property. And this autonomous function of oil-water two-phase flow through separator will be simulated and deduced in detail, which will be shown in Section 3.
3 Methodology 3.1 Numerical Simulation Since numerical simulation has been widely used on the complex flow studies with the developments of both computer competency and CFD technology, the rules of oil-water two-phase flow through the separator are first studied numerically and then compared with the proposed unified model. The structure parameters of the separator are shown in Table 1. The three-dimensional mechanical model of the separator is first developed, which then the hydraulic model is obtained by Boolean operation and subsequently
the mesh is generated. All the inlets are set as velocity-inlet, while the outlets are set as pressure-outlet and the rest as wall. The inlet and outlet boundary conditions of the separator are shown in Table 2. For better understand the rules of oil-water two-phase flow through the separator at both stratified and dispersed flows while their flow mechanisms and rules are quite different, both 30 m3/day and 3000 m3/day are chosen. Since water content and oil viscosity have a wide range and great impact on the properties of oil-water mixtures, both parameters are considered as the main variables. And the inlet water content range of 0 - 100% covers all the oil-water ratio situations, while the oil viscosities of 0.001, 0.01, and 0.1 Pa·s are representative of low, medium, and high viscosity oil respectively. The laminar model is selected on simulating the laminar flow while the standard k model is selected on simulating the turbulent flow. In addition, the Eulerian model is selected on simulating the oil-water two-phase dispersed flow while the VOF model is selected on simulating the stratified flow. 3.2 Modeling However, current studies on the modeling and simulation of multi-outlet flow field are still limited to the case with same fluid composition in the whole flow field or the case with the fluid composition of each outlet known (Zeng et al., 2015). Moreover, neither homogenous model nor two-fluid model alone can determine the flow mechanisms and rules of both flow patterns perfectly. To solve this, a unified model of oil-water two-phase flow through the separator is developed on the combination of the flow pattern transformation criterion, homogenous model, two-fluid model, and pipe serial-parallel theory. Unlike the CFD results, each path has a specific flow rate and water content, and as a consequence, specific flow regime and flow pattern. Since this paper mainly focus on the design concept and standalone performance prediction of the novel oil-water separator, and pressure has little impact on either the liquid viscosity (Alshmakhy and Maini, 2012; Freitas et al., 2014; Yan et al., 2014) or liquid density (Abdulagatov et al., 2014; Hussein and Amin, 2010), oil, water, and their mixture are assumed as Newtonian and incompressible fluids. And assume that there is no heat exchange or work between the fluid and environment, the system remains isothermal. The interface between the oil and water layers is assumed as a flat surface. In addition, the flows of pipes and fittings have no obvious interaction on each other. 3.2.1 Flow Pattern Transformation Criterion The flow pattern transformation among the oil-water stratified flow (o&w), water in oil dispersed flow (w/o), and oil in water dispersed flow (o/w) is shown in Fig. 2. The transition from the stratified flow to dispersed flow is based on the balance of the total turbulent energy of continuous phase and the total surface free energy of dispersed
phase, and water (or oil) can be assumed to be dispersed in oil (or water) when the total turbulent energy is greater than the total surface free energy (Atmaca et al., 2009; Zhang et al., 2006). In addition, the transition between the w/o and o/w depends on the interface free energy, and the inversion point is where the system has the largest interface free energy (Brauner and Ullmann, 2002; Decarre and Fabre, 1997; Tidhar et al., 1986). As shown in Appendix A, one liquid will become dispersed in the other liquid phase when the mixture velocity is larger than a certain value (Eq. 1), while the dispersed phase will become the continuous when the volume content of dispersed phase is larger than another certain value (Eq. 2).
6.325Cinc d i w o g 1/ 2 vm f m m
1/ 2
w cr w cr
d w o
(1)
(2)
3.2.2 Flow through the Horizontal Pipe The control volumes of oil-water two-phase dispersed and stratified flows through the horizontal pipe are shown in Fig. 3. The pressure drop derivation processes of both dispersed and stratified flows through the horizontal pipe are present in Appendix A. The pressure loss of dispersed flow through the horizontal pipe is shown in Eq. 3, while that of stratified flow is shown in Eq. 4.
p p p p
4 m L d
o So w S w A
(3)
(4)
L
3.2.3 Flow through the Elbow The control volumes of oil-water two-phase dispersed and stratified flows through the elbow are shown in Fig. 4. Similar to the flow through the horizontal pipe, the general pressure drop equations of both dispersed and stratified flows through the elbow can be obtained respectively with re-integrating the pressure gradient equations along the radial, as shown in Eqs. 5&6.
pe
4 m R d
R pe o So w S w A
(5)
(6)
3.2.4 Flow through the Sudden Expanded Fitting The control volumes of oil-water two-phase dispersed and stratified flows through the sudden expanded fitting are shown in Fig. 5. Both the interface friction and gravity are ignored, and no mass exchange between the upper and lower layers is considered. The general pressure drop equation of oil-water two-phase dispersed flow through the sudden expanded fitting can be obtained on the basis of the homogenous model (Ahmed et al., 2007; Gundigdu et al., 2009; Hwang et al., 1997). 2
psef
A v2 1 U Um m AD 2
(7)
However, the settling phenomenon will occur whenever the dispersed flow transforms to the stratified, thus the momentum equation should be re-derived on the basis of the two-fluid model (Ahmed et al., 2007; Gundigdu et al., 2009).
pU AU pD AD p' AD AU oQo vUo vDo wQw vUw vDw
(8)
Where, p is the pressure in front of the sudden expanded fitting, Pa. According to Che and Li (2007), the pressure at U-U cross-section equals to that in front of the sudden expanded fitting, thus the general pressure drop equation of oil-water two-phase stratified flow through the sudden expanded fitting can be obtained.
psef oQo Uo Do wQw Uw Dw AD
(9)
3.2.5 Flow through the Sudden Shrunken Fitting The control volumes of oil-water two-phase dispersed and stratified flows through the sudden shrunken fitting are shown in Fig. 6. The assumption is the same with that of the sudden expanded fitting. The fluid will accelerate its speed and the pressure energy will translate to kinetic energy whenever the fluid flows from the U-U section to the minimum contraction section C-C, thus there is almost no frictional loss during this process (Che and Li, 2007). However, once the fluid has passed the C-C section, the rule is similar to that of the sudden expanded fitting and the frictional loss is generated. Thus the general pressure drop equation of oil-water two-phase dispersed flow through the sudden shrunken fitting can be obtained on the basis of the homogenous model (Hwang et al., 1997; Oertel et al., 2004).
pssf
2 1 2 vDm 1 2 2 m Cv Ccon Ccon 2
Ccon
(10)
A con AD
(11)
vc v
(12)
Cv
Where, vc is the actual average velocity cross the contraction cross-section, m/s; v is the ideal average velocity cross the contraction cross-section, m/s. Similarly, the settling phenomenon will occur whenever the dispersed flow transforms to the stratified, thus its momentum equation should be re-derived on the basis of the two-fluid model (Chen et al., 2009).
pcon Acon pD AD p' ( AD Acon ) oQo cono Do wQw conw Dw
(13)
And the pressure at C-C cross-section equals to that in front of the sudden shrunken fitting, thus the general pressure drop equation of oil-water two-phase stratified flow through the sudden shrunken fitting can be obtained.
pssf oQo cono Do wQw conw Dw AD
(14)
3.2.6 Pipe Serial-Parallel Theory Two important rules can be obtained for pipes and fittings connected in series, as shown in Eqs. 15&16; while another two rules obtained for pipes and fittings connected in parallel, as shown in Eqs. 17&18 (Minzer et al., 2006).
Q Q1 Q2 Qn
(15)
p p1 p2 pn
(16)
Q Q1 Q2
Qn
p p1 p2 pn
(17) (18)
Thereby both the flow distributions and pressure drops of oil-water two-phase flow through the separator can be obtained coupling Eqs. 15-18. 3.2.7 Model Solution The unified model is solved numerically and the flow chart is shown in Fig. 7. First, the initial basic
parameters are inputted, including the separator structure parameters, fluid property, and flow rate. And both oil and water flow rates in the restrictive path are initialized with a small value, then oil and water flow rates in the frictional path can be obtained according to the pipe serial-parallel theory. Then, the flow pattern transformation criterion is verified to determine whether the flow of each path is dispersed flow. For the dispersed flow, the model parameters and pressure drop are calculated on the basic of homogenous model. For the stratified flow, the model parameters and pressure drop are calculated on the basic of two-fluid model. Next, since both paths are in parallel, loop water flow rate in the restrictive path until the pressure drops of both paths equal to each other. Finally, since a system tends to be stable at the minimum energy (Sharma et al., 2011), loop oil flow rate in the restrictive path until the system has the minimum energy.
4 Results and Analysis 4.1 Structure Parameter Optimization To ensure the separation performance, oil (870 kg/m3, 0.01 Pa·s) flow rate in the restrictive path should be at least larger than that in the frictional path, while water (998.2 kg/m3, 0.001003 Pa·s) flow rate is just the opposite. Based on this principle, the separator structure is optimized. As it can be observed from Fig. 1, the pressure drops of oil/water through both paths can be obtained with the adding of those through each pipes and fittings (Eqs. 19&20). Since the restrictive path consists of expanded and shrunken pipes alternately in series, all the values of nrps, nssf, and nsef are set as an uncertain integer n, while nrpe as n+1. Moreover, the pressure drops generated by parallel paths equal to each other (Eq. 21), which enables the fluid to be separated automatically according to its specific property.
pr nrpeprpe nrpsprps nssf pssf nsef psef
(19)
p f p fp ne pe
(20)
pr p f
(21)
As shown in Table 1, Af equals to Arpe, and is four times of Arps, then Ccon is 0.637, Cv is 0.985 in this case (Oertel et al., 2004). Since an oil-water treating capacity of 3000 m3/day can almost meet the maximum requirements of all situations (Alhoni et al., 2003; Belaidi et al., 2003; Blanco and Davies, 2001; Gomez et al., 2002; Jokhio et al., 2002; Paul, 2010), the flow rate is selected. And the relationship between vrpe and vf at 3000 m3/day is obtained.
vrpe v f 4.421m / s
(22)
Based on the optimization principle and selected parameters, both oil and water flow distributions with varying n and Lf can be obtained coupling Eqs. 19-22, which are shown in Fig. 8. The intersection of oil and water flow distribution ratios with same n value is defined as the critical flow distribution ratio, while the corresponding Lf is defined as the optimal frictional path length. As it can be observed, oil and water flow rates in the restrictive path will increase as Lf increases, while those in the frictional path will decrease. In order to direct more oil into the restrictive path, Lf should be as large as possible. In order to direct more water into the frictional path, on the contrary, Lf should be as small as possible. Therefore, the shunt effect will get worse whether Lf increases or decreases. Simultaneously, the critical flow distribution ratio will increase with a small gradient as n increases, while Lf will increase greatly. However, the separator will become too complex and unsteady if Lf is too long. Therefore, n is valued 1 and Lf is valued 119.36 m in this consideration. 4.2 Oil-Water Separation Performance To better understand the rules of oil-water two-phase flow through the separator, the flow rate and water content distributions in different paths with varying fluid properties can be obtained by both the numerical simulation and proposed unified model, which are shown in Fig. 9, and Fig. 10 respectively. As can be observed, the average relative deviation between the CFD and model results for flow distribution is 14.24%, while that for water content distribution is 42.03%. Since CFD can only describe the flow rate distributions while the proposed model can describe both the flow rate and water content distributions in different paths, the average relative deviation for water content distributions is higher than that that for flow rate distributions. The deviations are mainly due to the following reasons. First, the water contents in different paths remain the same during simulation, but in fact they are different in most cases, as considered in the united model. Second, the flow regimes and flow patterns in whole flow field remain the same during simulation, but in fact they are different in most cases, as considered in the united model. Next, only three patterns (o&w, w/o, and o/w) are considered in the unified model, which is simplified from the actual flow. Finally, oil, water, and their mixture are considered as Newtonian and incompressible fluids, but in fact they are non-Newtonian and slight-compressible fluids. As shown in Fig. 9 and Fig. 10, all the curves have several key turning points which are mainly caused by the flow regime transition, flow pattern transition, or flow re-distribution. The flow regime would transform among the laminar flow, transition flow, and turbulent flow, while the flow pattern would transform among the o&w, w/o, and o/w as previously described. Since both paths are in parallel, the change of either water content or oil viscosity will
re-distribute the flow rates and water contents in both paths, lead to the flow regime and flow pattern transition, and as a consequence, re-distribute the kinetic energy and surface free energy of system. At the flow rate of 30 m3/day, the flow patterns in both paths will remain stratified according to the flow pattern transform criterion while the flow regimes will remain laminar according to their Reynolds numbers. Since the kinetic energy of a stratified system is much smaller than the surface free energy, and the frictional path has a much longer path than the restrictive path, the surface free energy change of frictional path induced by the change of either water content or oil viscosity is much more remarkable. Therefore, to ensure the system has the minimum energy, none of the water will be directed into the frictional path until the water content of restrictive path has reached 100%. As a result, the flow rate and water content distributions in both paths with 30 m3/day are shown in Fig. 9(a), Fig. 9(b), and Fig. 10(a) respectively. As can be observed, the flow rate and water content changes in both paths with varying fluid viscosity are similar, and the changes can divide into two stages. Stage I, water will be only directed into restrictive path to ensure the system has the minimum energy. Stage II, once the water content of restrictive path reaches 100%, the water content of frictional path will begin to increase. That is, the separator has excellent separation performance at both stages. Simultaneously, the higher the oil viscosity is, the more fluid will be directed into the restrictive path, and the turning point between the stages would occur at higher water content. Overall, the separation effect is excellent with various inlet water contents in the situation of stratified flow. At the flow rate of 3000 m3/day, the flow patterns in both paths will remain dispersed according to the flow pattern transformation criterion while the flow regimes will remain turbulent according to their Reynolds numbers. Since the kinetic energy of a dispersed system is much greater than the surface free energy, the kinetic energy change of frictional path induced by the change of either water content or oil viscosity is much more remarkable. Since a system tends to be stable at the minimum energy, the fluid viscosity of frictional path should be as large as possible, which will direct more fluid into the restrictive path, and result in the minimum system energy. The flow rate and water content distributions in both paths with 3000 m3/day are shown in Fig. 9(c), Fig. 9(d), and Fig. 10(b) respectively. As can be observed, the flow rate and water content changes in both paths with varying oil viscosity are similar, and the changes can divide into four stages. Stage I, since the fluid viscosity increases with water content at low water content, water will be only directed into the frictional path to make sure that the viscosity of frictional path is as large as possible, and more fluid will be directed into the restrictive path. Stage II, the viscosity of frictional path will be the largest once its water content reaches the critical water content, and the water content of restrictive path begins to increase while that of frictional path remains the critical, as shown in Fig. 11. In this
case, the flow rate in restrictive path decreases while that in frictional path increases. Stage III, once the water content of restrictive path reaches the critical value, the water content of restrictive path will continue to increase while that of frictional path remain the critical. Since the phase inversion has occurred in the restrictive path, the flow rate in frictional path will increase instead while that in restrictive path is just the opposite. Stage IV, once the water content of restrictive path reaches 100%, the water content of frictional path begins to increase, and the flow rate of restrictive path increases, while that of frictional path is just the opposite. That is, the separator has excellent separation performance at both stage I and IV. For stage I, water will be only directed into the frictional path, and the water content of restrictive path remain 0. For stage IV, none of oil will be directed into the restrictive path, and the water content of restrictive path remain 100%. Simultaneously, the phase inversion point would occur at lower water content due to lower critical volumetric water content generated by higher viscosity oil, as shown in Fig. 11. And the scope of stage I will widen while that of stage IV will narrow as the oil viscosity increases. To sum up, this autonomous function directs oil and water to different paths, hence oil and water is well separated. Only when the water content of either path reaches 0 or 100%, the separation efficiency for this path is considered 100%. The separator has no minimum oil-water treating capacity limited, while its maximum oil-water treating capacity depends on inlet water content and oil viscosity. Of special interest is the connections of different outlets and storage tanks that the relative magnitude of water contents in both path may just reversal as the water content increases. Overall, the novel oil-water separator design has a small size, no movable parts, no additional energy supply, good separation effect and efficiency with reasonable parameters.
5 Conclusions In this paper, a novel oil-water separator design is proposed, which is then verified and predicted by both the numerical simulation and proposed unified model. The following conclusions and recommendations can be obtained on the basis of the study. (1) Based on the combination of the flow pattern transformation criterion, homogenous model, two-fluid model, and pipe serial-parallel theory, a unified model of oil-water two-phase flow through the separator is developed and then compared with the CFD results. The proposed unified model can not only describe the flow rate and water content distributions in different paths of the separator, but also predict the flow rate and water content re-distributions, flow pattern transform, and flow regime transform as the fluid properties change.
(2) Both the CFD and model results show that the flow rate distributions in different paths of the separator will be adjusted automatically according to the fluid’s property, while the model results show that the water content distributions will also be self-adjusted. And the average relative deviation for flow rate distribution is 14.24%, while that for water content distribution is 42.03%. (3) Overall, the novel oil-water separator design has a small size, no movable parts, no additional energy supply, good separation effect and efficiency with reasonable parameters.
Acknowledgments This study was supported by the 111 Project (Grant No.: B12033), National Science and Technology Major Project (Grant No.: 2016ZX05044005-001), National Natural Science Foundation of China (Grant No.: 51474225), and State Key Laboratory Foundation of Offshore Oil Exploitation (Grant No.: CCL2013RCPS0239GNN). Simultaneously, the reviewers of the original manuscript are greatly appreciated; their comments and suggestions help improve this paper.
Appendix A. United Model of Oil-Water Two-Phase Flow through the Horizontal Pipe A.1 Flow Pattern Transformation Criterion The oil-water interfacial tension is low due to the small difference between oil and water densities, thus the oil-water interface is difficult to maintain stability, also the stratified flow is easy to transform to the dispersed flow. The transition from stratified flow to dispersed flow is based on the balance of the total turbulent energy of the continuous phase and the total surface free energy of the dispersed phase, while the transition between the w/o and o/w depends on the interface free energy. The dispersed phase is dispersed as spherical drops in the continuous phase which will collide and coalesce with one another due to the turbulent movement. Simultaneously, the drops will be broken up by the turbulent forces exerted on them if the sizes are larger than a certain value. Moreover, the drop coalescence of continuous phase and the drop broken of dispersed phase will lead to the phase inversion. Therefore, the amount of dispersed phase per unit can hold depends on the turbulent intensity of the continuous phase. Water (or oil) can be assumed to be dispersed in oil (or water) when the total turbulent energy is greater than the total surface free energy, that is, the mixture velocity should be larger than a certain value (Atmaca et al., 2009; Zhang et al., 2006). In addition, the inversion point is where the system has the largest interface free energy, the dispersed phase will become the continuous when the volume content of dispersed phase is larger than another
certain value (Brauner and Ullmann, 2002; Decarre and Fabre, 1997; Tidhar et al., 1986).
6.325Cinc d i w o g 1/ 2 vm f m m
1/ 2
d w o
(A-1)
w cr w cr
(A-2)
Where,
Cinc
2.5 sin
(A-3)
2
64 Re m 0.0122Re m 2320 fm 1680 0 . 3164 Re 0m.25
Re m 2320 2320 Re m 4000
4000 Re
m
105
(A-4)
(A-5)
v d Re m m m m
(A-6)
cr
1 1 o w
0.4
o w
0.6
The density and velocity of the dispersion can be calculated on the properties of both continuous and dispersed phases (Awad and Muzychka, 2008), while its viscosity mainly depends on the continuous phase (Brinkman, 1952; Roscoe, 1952), as shown in Fig. 11.
m cc dd
(A-7)
vm vc vd
(A-8)
m cc2.5
(A-9)
A.2 Dispersed Flow Model The momentum equation of oil-water two-phase dispersed flow through the horizontal pipe, developed on the basis of the homogenous model (Awad and Muzychka, 2008; Hasan and Kabir, 2002; Ouyang and Aziz, 2000), is shown in Eq. A-10.
dp 4 m dx d
(A-10)
Where,
m
(A-11)
1 f m m vm2 8
Thus the general pressure drop equation of oil-water two-phase dispersed flow through the horizontal pipe can be obtained with the integration of Eq. A-10.
p p
4 m L d
(A-12)
A.3 Stratified Flow Model However, the settling phenomenon will occur whenever the dispersed flow transforms to the stratified, thus the general pressure drop equation should be re-derived on the basis of the two-fluid model (Barnea and Taitel, 1994; Brauner et al., 1998; Taitel et al., 1995; Zhang et al., 2006). The volume flow rates of both layers are shown in Eqs. A-13&A-14, while the momentum equations shown in Eqs. A-15&A-16.
Qo Ao vo
(A-13)
Qw Awvw
(A-14)
Ao
dp o S o i Si 0 dx
(A-15)
Aw
dp w S w i Si 0 dx
(A-16)
Where, Si is the cross section chord length of oil-water interface, m. Thus the general pressure drop equation of oil-water two-phase stratified flow through the horizontal pipe can be obtained with the addition and integration of Eqs. A-15&A-16, while the combinational momentum equation obtained with the subtraction of Eqs. A-15&A-16.
p p
o So w S w A
(A-17)
L
w S w o So 1 1 i Si 0 Ao Aw Aw Ao
(A-18)
However, several key parameters are required to close the stratified flow model, which contain the geometric parameters and friction parameters (Ullmann and Brauner, 2006).
The geometric parameters, which are shown in Fig. 3(b), contain the wetted perimeters and cross section areas. The wetted perimeters of both layers are shown in Eqs. A-19&A-20, while the cross section areas occupied by both layers shown in Eqs. A-21&A-22, and the cross section chord length of oil-water interface shown in Eq. A-23. (A-19)
So d S w d
(A-20)
d2 Ao ( sin cos ) 4
(A-21)
Aw
d2 ( sin cos ) 4 Si d sin
(A-22)
(A-23)
The friction parameters mainly consider the wall friction which is referred to the concept of friction coefficient (Ullmann et al., 2004).
o
1 f o o vo2 8
(A-24)
w
1 f w wvw2 8
(A-25)
The effective Reynolds numbers of both layers are shown in Eqs. A-26&A-27.
vd Re o o o o o
(A-26)
w vw d w w
(A-27)
Re w
The hydraulic diameter formulas of oil and water layers differ a lot according to the velocity of each layer (Ullmann et al., 2004; Ullmann and Brauner, 2006).
dw
4 Aw S w Si
(vo vw )
4 Aw Sw
(vo vw )
4 Ao S S o i do 4 Ao So
(vo vw ) (vo vw )
(A-28)
(A-29)
The interface friction between the oil and water layers is shown in Eq. A-30 (Kamel and Renee, 2010).
i
1 f i i (vo vw ) 2 sgn( vo vw ) 8
(A-30)
Where,
fo f i 0 f w
o i 0 w
(vo vw )
(A-31)
(vo vw ) (vo vw )
(vo vw ) (vo vw )
(A-32)
(vo vw )
Thereby the pressure drop of oil-water two-phase flow through the horizontal pipe can be obtained coupling Eqs. A-1, A-2, A-12, and A-17.
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Figures
Fig. 1 Structure Diagram of the Novel Oil-Water Separator Design
Fig. 2 Flow Pattern Transformation
(a) Dispersed Flow
(b) Stratified Flow Fig. 3 Control Volumes of Oil-Water Two-Phase Flows through the Horizontal Pipe
(a) Dispersed Flow
(b) Stratified Flow Fig. 4 Control Volumes of Oil-Water Two-Phase Flows through the Elbow
(a) Dispersed Flow
(b) Stratified Flow Fig. 5 Control Volumes of Oil-Water Two-Phase Flows through the Sudden Expanded Fitting
(a) Dispersed Flow
(b) Stratified Flow Fig. 6 Control Volumes of Oil-Water Two-Phase Flows through the Sudden Shrunken Fitting
Fig. 7 Solving Procedure for the Proposed Oil-Water Two-Phase Unified Model
Fig. 8 Oil/Water Flow Distributions versus Lf with Varying n Values
(a) 30 m3/day, Restrictive Path
(b) 30 m3/day, Frictional Path
(c) 3000 m3/day, Restrictive Path
(d) 3000 m3/day, Frictional Path Fig. 9 Flow Rate Distributions in Different Paths with Varying Fluid Properties
(a) 30 m3/day
(b) 3000 m3/day Fig. 10 Water Content Distributions in Different Paths with Varying Fluid Properties
Fig. 11 Mixture Viscosities in Different Paths with Varying Fluid Properties
Tables Table 1 Structure Parameters of the Separator Structure Parameters
Value
Units
Restrictive Path Total Length of the Restrictive Path
4.9
m
Number of the Expanded Pipe
n+1 (uncertain)
Dimensionless
Diameter of the Expanded Pipe
0.1
m
Number of the Shrunken Pipe
n (uncertain)
Dimensionless
Diameter of the Shrunken Pipe
0.05
m
Number of the Sudden Expanded Fitting
n (uncertain)
Dimensionless
Number of the Sudden Shrunken Fitting
n (uncertain)
Dimensionless
Total Length of the Frictional Path
Lf (uncertain)
m
Diameter of the Frictional Path
0.1
m
Number of the Elbow
12
Dimensionless
Bending Angle of the Elbow
90
degree
Bending Radius of the Elbow
0.3
m
Frictional Path
Table 2 Inlet and Outlet Boundary Conditions of the Separator Fluid Properties
Value
Units
Inlet Flow Rate
30, 3000
m3/day
Volume Water Content
0 - 100
%
Oil Density
870
kg/m3
Oil Viscosity
0.001, 0.01, 0.1
Pa·s
Water Density
998.2
kg/m3
Water Viscosity
0.001003
Pa·s
0
Pa
0
Pa
Outlet 1 Pressure Outlet 2 Pressure
Highlights 1. An oil-water separator is proposed with combination of two resistance mechanisms. 2. A unite model of oil-water two-phase flow through the separator is developed. 3. The flow rate and water content distributions through both paths are auto-adjusted. 4. The proposed model can predicted both the flow rate and water content distributions. 5. The separator design has a small size, good separation effect and efficiency.