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Heavy-organic particle deposition from petroleum fluid flow in oil wells and pipelines

Heavy-organic particle deposition from petroleum fluid flow in oil wells and pipelines of oil wells and pipelines. This is the major reason for fouling and arterial blockage in the petroleum industry. This report is devoted the study of the mechanism of migration of suspended heavy organic particles towards the walls in oil-producing wells and pipelines. In this report we present a detailed analytical model for the heavy organics suspended particle deposition coefficient corresponding to petroleum fl uids fl ow production conditions in oil wells. We predict the rate of particle deposition during various turbulent fl ow regimes. The turbulent boundary layer theory and the concepts of mass transfer are utilized to model and calculate the particle deposition rates on the walls of flowing conduits. The developed model accounts for the eddy diffusivity, and Brownian diffusivity as well as for inertial effects. The analysis presented in this paper shows that rates of particle deposition (during petroleum fl uid production) on the walls of the fl owing channel due solely to diffusion effects are small. It is also shown that deposition rates decrease with increasing particle size. However, when the process is momentum controlled (large particle sizes) higher deposition rates are expected. Asphaltene, Brownian deposition coefficient, diffusivity, diamondoids, heavy organic Key words: particles, paraffi n/wax, particle deposition, petroleum fl uid, prefouling behavior, production operation, suspended particles, turbulent fl ow In our recent reports we presented the various causes 1 Introduction and effects of phase behavior of petroleum fl uids containing A common problem faced by the oil industry is the heavy organic fractions and their depositions (Mansoori, deposition of heavy organics inside production wells, 2009a; 2009b). It is always preferred to prevent heavy storage vessels, and transfer pipelines. Our studies and organics deposition during petroleum fluid flows. In cases experiences have indicated that heavy organic deposition is when heavy organics precipitation can not be prevented one of the major factors that increase the cost of production we need to understand the fl uid fl ow behavior which is less and transportation of petroleum fluids (Mansoori, 1988; likely to cause fouling of a conduit. In these cases there is a Carpentier et al, 2007). Furthermore, miscible flooding of need for understanding how the precipitated and fl occulated petroleum reservoirs by lean gas, carbon dioxide, natural particles suspended in the oil will behave under certain gas, and other high pressure injection fluids has become an flow conditions. This motivated the research presented in economically viable technique for petroleum production. this report. Our main objective is to study the behavior of Introduction of a miscible fl uid in petroleum reservoirs, will, suspended heavy organic particles during fl ow conditions. in general, produce a number of alterations in petroleum fl uid As a preliminary step, the tendency of the crude oil to flow and phase behavior and reservoir rock characteristics. form solid particles, whenever a miscible solvent is injected One such alteration is the heavy organic precipitation, into the petroleum reservoir, must be determined. This may fl occulation and deposition (asphaltenes, diamondoids, etc.), be accomplished by using existing experimental techniques which in most of the observed instances result in plugging or (Mousavi-Dehghani et al, 2004; Mansoori et al, 2007) wettability reversal in the conduits (Escobedo and Mansoori, together with predictive models and packages (Branco et al, 1995a; 1995b; Branco et al, 2001; Mousavi-Dehghani et al, 2001). These combined experimental/predictive approaches 2004; Mansoori et al, 2007). have proven to be a useful tool for design of production and transportation schemes for crude oils prone to heavy organics precipitation, fl occulation and deposition. *Present address: Case Western Reserve University, 10900 Euclid Ave, The study of the behavior of suspended heavy-organic Cleveland, OH 44106. email: joelescobedo1@gmail.com particles during flow conditions has been focused on the ** Corresponding author. email: mansoori@uic.edu production well since fl ow through a pipeline is only a special Received May 15, 2009 Pet.Sci.(2010)7:502-508 503 503 case of this more general one. A typical production well may Substantial work has been done by many researchers be divided into two distinct sections (See Fig. 1): on the topic of particle deposition on the walls of channels (I) The pressure region above the bubble point (single- or pipes in turbulent flow by many researchers (Lin et al, phase) is the emphasis of the present report. Understanding of 1953; Laufer, 1954; Friedlander and Johnstone, 1957; Beal, deposition of particles in this region is especially important 1970; Chen and Ahmadi, 1997; Derevich and Zaichik, 1988; for particles which enter into the oil well from the reservoir. Johansen, 1991). The model presented here is a combination (II) The analysis of the region below the bubble-point of the work performed by the authors mentioned above, pressure (two-phase flow) is the subject of our ongoing modifi ed to be applicable to the deposition of heavy organic research. particles in turbulent petroleum fl uid fl ow. A key assumption in the development of this model is that fully developed petroleum turbulent flow has a structure as proposed by Lin et al. From experimental observations, they proposed a Annular- generalized velocity distribution for turbulent fl ow of fl uids in mist flow pipes comprised of three main regions: - A sublaminar (wall) layer 0 ≤ r ≤ 5, - A buffer layer 5 ≤ r ≤ 30, - A turbulent core 30 ≤ r , Slug flow where rD (/ V f2/Q) is a dimensionless distance iavg measured from the wall. This dimensionless distance is a function of the inner pipe diameter, D , fl uid average velocity, Transition flow i V , the Fanning friction factor, f, and the fluid kinematic avg viscosity, ν. The model presented here is for a system of constant density and viscosity. Therefore, it is applicable only Bubble flow to a single phase petroleum fluid flow. This theory can be extended to the region below the bubble point pressure (gas- Sublaminar liquid slug fl ow, etc.) using reliable expressions for petroleum layer Turbulent Bubble point viscosity and density versus pressure and temperature. The core assumption of constant viscosity and constant density is Single-phase justified since density changes are not appreciable until the turbulent flow bubble point pressure is reached inside the well (or tubing). It is also assumed that suspended particles are of uniform diameter, and that, due to their rather low concentration we can neglect particle-particle interactions. We assume the thickness of the boundary layer is quite small compared to the radius of the pipe as a result we can neglect the wall curvature Transition (buffer) effects in our model. region Oil reservoir We start with reporting the equation which is used to describe the particle fl ux, N , in terms of the diffusivities and the concentration gradient (Von Karman, 2004), i.e., Fig. 1 Illustration of velocity distribution and different fl ow regimes in the prefouling single-phase turbulent fl ow condition in the oil well dC BE ND D (1) dr In this report we present an analytical model for the B E heavy organic suspended particle deposition coefficient where D is the Brownian diffusivity; D is the eddy prior to deposition corresponding to petroleum fluids flow diffusivity; C is the particle concentration; and r is the radial in producing wells condition. In our previous publications distance. (Escobedo and Mansoori, 1995a; 1995b; 2010) we The Brownian diffusivity is defined by the following reported various segments of this analytical model some equation: of which contained typographical errors. For the sake of kT comprehensiveness and to provide the readership with the D (2) 3ʌ d P details of the algebraic manipulations involved we report here the details of the model in its entirety. where k is the Boltzmann constant (k =1.38066×10 J/K); T is the absolute temperature; d is the particle diameter; and μ 2 Development of the analytical model is the liquid viscosity of the suspending medium (petroleum fl uid). Equation (1) is subject to the boundary condition: The theory presented here is for a turbulent petroleum PP at r = S CC = fl uid system of constant density and viscosity. For petroleum where C is the particle concentration at r = S and S is S d d fluid flow in wells this is the case for the region above the d the particle “stopping distance” measured from the wall. A bubble pressure where only the liquid phase is the medium particle needs to diffuse only within one stopping distance for the suspended particles. 504 Pet.Sci.(2010)7:502-508 from the wall, and from this point on, due to the particle following equation: momentum, it would coast to the wall. For small particles ªº Vf /2 avg the stopping distance is small compared with the boundary (8) SS «» dd «» layer thickness and consequently diffusion dominates. The ¬¼ proposed correlation for the particle stopping distance is For the sublaminar layer Equation (1) may be integrated (Friedlander and Johnstone, 1957): following the procedure for the calculation of temperature drop across a composite wall. We will fi nd the concentration 0.05U Vd f /2 Pavg P (3) profiles from point to point across the boundary layer. That P 2 is, we will calculate the concentration differences through the where is the density of particles; V is the average sublaminar layer, the buffer region and the turbulent core. By avg velocity of petroleum fluids; and f is the Fanning friction adding these concentration differences we can fi nd the overall factor. particle fl ux in terms of the average and wall concentrations. Equation (1) may be integrated following the procedure Note that Equation (4) is only valid for dimensionless radial for the calculation of temperature drop across a composite distances smaller than 5, which is the limit of the sublaminar wall. We will find the concentration profiles from point to layer. point across the boundary layer. That is, we will calculate Introducing all the new dimensionless variables and the the concentration differences through the sublaminar layer, expressions for N and D into Equation (1), considering that the buffer region and the turbulent core. By adding these ªº Q concentration differences we can fi nd the overall particle fl ux Q we get: dd rr «» in terms of the average and wall concentrations. Before we Vf /2 «» avg P ¬¼ integrate Equation (1) for C , we need to have expressions *B * P for N and D as functions of the radial distance (r) for each ªº §· §· 2d rD r C NN 1/ «»  V f2 of the three main regions in the oil well and pipeline, i.e. ¨¸ (9) Po ¨¸ avg ** D Q 11.15 dr «» ©¹ i ©¹ sublaminar layer, buffer layer and turbulent core. ¬¼ 1) Sublaminar Layer subject to the following boundary conditions: Johansen (1991) proposed the following correlation to *P P express the eddy diffusivity as a function of radial distance (r) ­ at rS C C ° d for the sublaminar layer: *P P at rC 5 C ¯ 5 3 3 r* r* §· S  5 §· Dv for r*d 5 or ¨¸ ¨¸ Rearranging Equation (9), integrating and applying the 11.15 Q 11.15 ©¹ ©¹ above boundary conditions we arrive at the following integral (4) form: In this equation v is the kinematic viscosity of the fl owing * P 1/3 2/3 ªº petroleum fluid, r is the dimensionless radial distance and 2 11.15 N 11.15N PP 0 Sch Sch CC «» F F 51 2 * S E d Vf /2 33D D represents the sublaminar layer (r ≤ 5) eddy diffusivity. «» * avg ¬¼ S  5 (10) The particle molar flux, N , is assumed to vary linearly In the above equation N is the Schmidt number defi ned from the wall to the center line of the channel, as proposed by Sch as: Beal (1970): §· Q 2r PP N { (11) NN  1 (5) ¨¸ Sch o B ©¹ i and F and F are defi ned by the following expressions: In this equation N is the particle flux at the wall; r is 1 2 a dimensionless radial distance and D is the dimensionless 2 * ªº ªº 1 S I inner well (or tubing) diameter, both defi ned by the following 15  I 11 d «» F  ln«» ln equations: 2 2 «» 2(1 5I ) 2 «» 1 S I ¬¼ d (12) ¬¼ ªº Vf /2 avg §· 10I  1 §· 21 S I rr «» (6) 3tan  3tan ¨¸ ¨¸ «» 33 ©¹ ©¹ ¬¼ ªº Vf /2 * ªº * avg ªº 1 S I 1(1 5I ) 1 d DD «» (7) ii «» F  ln ln «» Q 2 «» ¬¼ «» «» 15  I 1 S I ¬¼ d ¬¼ (13) where D is the inner diameter of the well (or tubing); V i avg * §· §· 10I  1 21 S I 11 d is the average fl uid velocity; f is the Fanning friction factor; 3tan  3tan ¨¸ ¨¸ and v is kinematic viscosity of the fl owing fl uid, m /s. Let us ©¹ ©¹ also define the dimensionless stopping-distance, by the where for simplicity we have defi ned: d Pet.Sci.(2010)7:502-508 505 506 Pet.Sci.(2010)7:502-508 Pet.Sci.(2010)7:502-508 507 This is shown in Fig. 5 where we can notice that deposition Kinematic viscosity coefficients decrease with increasing particle size due to the fact that Brownian diffusion is inversely proportional IE-2 1.91cSt to the particle size of the diffusing species. However, with 3.17cSt increasing particle size (or mass) the momentum increases, IE-4 4.97cSt 12.16cSt so that particle momentum effects become more important. 32.12cSt It is expected a minimum deposition rate for a given particle IE-6 size, beyond which the process is essentially momentum controlled, resulting in higher deposition rates. For a radius IE-8 of 270 nm, we still notice very small values (see Fig. 4), this 0 1000 2000 3000 means that heavy organic particle size must become much Oil roduction rate, m /day larger in order to exhibit high deposition rates. Fig. 3 Effect of petroleum production rate on the deposition coeffi cient of 1 micron (1000 nm) diameter suspended particles in petroleum fl uids Particle size of various kinematic viscosities ranging from 1.91 - 32.12 cSt 2nm 3nm 4nm is less than 1,000 nm. Fig. 2 indicates a decrease in the 5nm 6nm deposition coefficients with increasing kinematic viscosity and an increase in the deposition coeffi cient with increasing production rate. The lighter the petroleum fl uid, the higher the probability of having particle deposition. Fig. 4 shows the predicted deposition coefficients for particles as a function of the crude oil production rate for two extreme particle sizes, 3.5 nm (corresponding to asphaltene steric-colloidal particles in original crude oil) and 270 nm (corresponding to flocculated asphaltene aggregates). As it was mentioned the present analysis is for the single-phase 100 1000 10000 region of the well-tubing (region before the bubble point Oil production rate, m /day pressure is reached). One can notice from this fi gure the very Effect of particle size on deposition coeffi cient for Fig. 5 small values of deposition coefficients for 3.5 nm particles, a 37.8 °API petroleum fl uid for the volumetric fl ow rates of up to 3,000 m /day. Fig. 4 also indicates that deposition coeffi cients increase with increasing We performed model predictions varying the kinematic velocities. However, when the oil production rate is about viscosity of the crude oil to study the effect of this parameter 10,000 m /day, deposition coeffi cient is roughly 0.06 cm/min. on the deposition coefficient. This was done because Therefore we would expect sizeable amounts of deposition at kinematic viscosity decreases with increasing temperature, high production rates. and because it is a function of the API gravity of the crude oil. Fig. 6 shows the predicted values, and we can see a decrease in the deposition coefficient with increasing kinematic Particle size viscosity. This means that the lighter the petroleum fluid is the higher the probability of having heavy organic deposition will be. However, these predicted values are still very small. 3.5 nm Kinematic viscosity 0.03cSt 1.0 270 nm 0.04cSt 0.05cSt 0.1 100 1000 10000 0.06cSt Oil production rate, m /day 0.07cSt Fig. 4 Predicted deposition coeffi cients as a function of the crude oil production rates. It is calculated for particles with a diameter of 3.5 nm suspended in a 37.8 °API petroleum fl uid 0 1000 2000 With the idea in mind of finding another factor that Oil production rate, m /day could increase the tendency of the particles to deposit, we Fig. 6 Effect of kinematic viscosity on deposition coeffi cient examined the effect of particle size on deposition coeffi cient. Deposition coefficient K ×10 , cm/min Deposition coefficient, cm/min 3 Deposition coefficient K ×10 , cm/min Deposition coefficient K ×10 , cm/min d d 508 508 Pet.Sci.(2010)7:502-508 Car pentier B, Wilhelms A and Mansoori G A. Reservoir organic 4 Conclusions geochemistry: Processes and applications. Journal of Petroleum Science and Engineering. 2007. 58(3-4): 341-343 The model developed for the particle deposition onto Che n S K and Ahmadi G. Deposition of particles in a turbulent pipe the walls of a pipe from a turbulent petroleum fluid stream fl ow. Journal of Aerosol Science. 1997. 28(5): 789-796 in oil wells and pipelines was used to predict the deposition Der evich I V and Zaichik L I. Particle deposition from a turbulent fl ow. coefficient from turbulent flow production operations. The Fluid Dynamics. 1988. 23(5): 722-729 effect of particle size on the deposition coefficient was Esc obedo J and Mansoori G A. Solid particle deposition during turbulent investigated, finding that when the deposition process is flow production operations. Paper SPE 29488 presented at SPE diffusion-controlled (particles with a diameter < 1,000 nm) Production Operations Symposium, 2-4 April 1995a, Oklahoma City, the predicted values are very small. However, when the Oklahoma deposition process is momentum controlled (particles with a Esc obedo J and Mansoori G A. Asphaltene and other heavy-organic diameter > 1,000 nm) the predicted values for the deposition particle deposition during transfer and production operations. Paper coefficient increase more rapidly with increasing particle SPE 30672 presented at SPE Annual Technical Conference and Exhibition, 22-25 October 1995b, Dallas, Texas diameter. We also investigated the effect of petroleum fluid Esc obedo J and Mansoori G A. Prefouling behavior of suspended kinematic viscosity on the deposition coefficient. We found particles in petroleum fluid flow. scientia Ir., Transactions C: that the deposition coefficient decreases with increasing Chemistry and Chemical Engineering. 2010. 17: (to appear) petroleum fl uid kinematic viscosity. For kinematic viscosity Fri edlander S K and Johnstone H F. Deposition of suspended particles of 12.16 cSt the predicted deposition coeffi cient is negligible from turbulent gas streams. Industrial and Engineering Chemistry. for suspended particles of 1,000 nm. We also found that the 1957. 49(7): 1151-1156 deposition coefficient increases with increasing production Joh ansen S T. The deposition of particles on vertical walls. International rate. This is due to the fact that at larger production rates the Journal of Multiphase fl ow. 1991. 17(3): 355-362 amount of eddy diffusion is bigger. The proposed model can Lau fer J. The structure of turbulence in fully developed pipe flow. be used for various cases of the behavior of heavy organics NACA 1174, National Advisory Committee for Aeronautics, 1954 particle deposition from turbulent petroleum flows so long (Available from NASA as TR-1174). Lin C S, Moulton R W and Putnam G L. Mass transfer between solid as the particles are neutral, their sizes are stable, there are no wall and fl uid streams. Industrial and Engineering Chemistry. 1953. particle-particle interactions and there are no phase transitions 45(3): 636-646 occurring in the fl ow. However, in cases where such changes Man soori G A. Asphaltene deposition: An economic challenge in heavy are occurring in the system this model will require appropriate petroleum crude utilization and processing. OPEC Review. 1988. modifi cations as presented and applied elsewhere (Mansoori 103-113 G A, ASPHRAC: A comprehensive package of computer Man soori G A, Vazquez D and Shariaty-Niassar M. Polydispersity programs and database which calculates various properties of heavy organics in crude oils and their role in oil well fouling. of petroleum fluids containing heavy organics. www.uic. Journal of Petroleum Science and Engineering. 2007. 58(3-4): 375- edu/~mansoori/ASPHRAC_html). Man soori G A. A unified perspective on the phase behaviour of Acknowledgements petroleum fluids. International Journal of Oil, Gas and Coal Technology. 2009a. 2(2): 141-167 The authors would like to thank Aly Hamouda, Diogo Man soori G A. Phase behavior in petroleum fluids, petroleum Melo Paes, Paulo Ribeiro, Kamy Sepehrnouri and Mahdy engineering – Downstream section of encyclopedia of life support Shirdel for taking time to read the manuscript and suggesting systems. 33 pages. UNESCO, UN, Paris, France, 2009b very useful corrections. To receive the executable computer Man soori G A. ASPHRAC: A comprehensive package of computer package and the set of related equation for our proposed programs and database which calculates various properties of petroleum fluids containing heavy organics. www.uic. model please contact the corresponding author. edu/~mansoori/ASPHRAC_html Mou savi-Dehghani S A, Riazi M R, Vafaie-Sefti M and Mansoori G A. References An analysis of methods for determination of onsets of asphaltene Bea l S K. Deposition of particles in turbulent fl ow on channel or pipe phase separations. Journal of Petroleum Science and Engineering. walls. Nuclear Science and Engineering. 1970. 40: 1-11 2004. 42 (2-4): 145-156 Bra nco V A M, Mansoori G A, De Almeida Xavier L C, et al. Asphaltene Von Karman T. Aerodynamics: Selected Topics in the Light of Their fl occulation and collapse from petroleum fl uids. Journal of Petroleum Historical Development. www.doverpublications.com, 2004 Science and Engineering. 2001. 32: 217-230 (Edited by Sun Yanhua) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Petroleum Science Springer Journals

Heavy-organic particle deposition from petroleum fluid flow in oil wells and pipelines

Escobedo, Joel; Ali Mansoori, G.
Petroleum Science , Volume 7 (4) – Nov 10, 2010
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Publisher
Springer Journals
Copyright
Copyright © 2010 by China University of Petroleum (Beijing) and Springer-Verlag Berlin Heidelberg
Subject
Earth Sciences; Mineral Resources; Industrial Chemistry/Chemical Engineering; Industrial and Production Engineering; Energy Economics
ISSN
1672-5107
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1995-8226
DOI
10.1007/s12182-010-0099-4
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Abstract

of oil wells and pipelines. This is the major reason for fouling and arterial blockage in the petroleum industry. This report is devoted the study of the mechanism of migration of suspended heavy organic particles towards the walls in oil-producing wells and pipelines. In this report we present a detailed analytical model for the heavy organics suspended particle deposition coefficient corresponding to petroleum fl uids fl ow production conditions in oil wells. We predict the rate of particle deposition during various turbulent fl ow regimes. The turbulent boundary layer theory and the concepts of mass transfer are utilized to model and calculate the particle deposition rates on the walls of flowing conduits. The developed model accounts for the eddy diffusivity, and Brownian diffusivity as well as for inertial effects. The analysis presented in this paper shows that rates of particle deposition (during petroleum fl uid production) on the walls of the fl owing channel due solely to diffusion effects are small. It is also shown that deposition rates decrease with increasing particle size. However, when the process is momentum controlled (large particle sizes) higher deposition rates are expected. Asphaltene, Brownian deposition coefficient, diffusivity, diamondoids, heavy organic Key words: particles, paraffi n/wax, particle deposition, petroleum fl uid, prefouling behavior, production operation, suspended particles, turbulent fl ow In our recent reports we presented the various causes 1 Introduction and effects of phase behavior of petroleum fl uids containing A common problem faced by the oil industry is the heavy organic fractions and their depositions (Mansoori, deposition of heavy organics inside production wells, 2009a; 2009b). It is always preferred to prevent heavy storage vessels, and transfer pipelines. Our studies and organics deposition during petroleum fluid flows. In cases experiences have indicated that heavy organic deposition is when heavy organics precipitation can not be prevented one of the major factors that increase the cost of production we need to understand the fl uid fl ow behavior which is less and transportation of petroleum fluids (Mansoori, 1988; likely to cause fouling of a conduit. In these cases there is a Carpentier et al, 2007). Furthermore, miscible flooding of need for understanding how the precipitated and fl occulated petroleum reservoirs by lean gas, carbon dioxide, natural particles suspended in the oil will behave under certain gas, and other high pressure injection fluids has become an flow conditions. This motivated the research presented in economically viable technique for petroleum production. this report. Our main objective is to study the behavior of Introduction of a miscible fl uid in petroleum reservoirs, will, suspended heavy organic particles during fl ow conditions. in general, produce a number of alterations in petroleum fl uid As a preliminary step, the tendency of the crude oil to flow and phase behavior and reservoir rock characteristics. form solid particles, whenever a miscible solvent is injected One such alteration is the heavy organic precipitation, into the petroleum reservoir, must be determined. This may fl occulation and deposition (asphaltenes, diamondoids, etc.), be accomplished by using existing experimental techniques which in most of the observed instances result in plugging or (Mousavi-Dehghani et al, 2004; Mansoori et al, 2007) wettability reversal in the conduits (Escobedo and Mansoori, together with predictive models and packages (Branco et al, 1995a; 1995b; Branco et al, 2001; Mousavi-Dehghani et al, 2001). These combined experimental/predictive approaches 2004; Mansoori et al, 2007). have proven to be a useful tool for design of production and transportation schemes for crude oils prone to heavy organics precipitation, fl occulation and deposition. *Present address: Case Western Reserve University, 10900 Euclid Ave, The study of the behavior of suspended heavy-organic Cleveland, OH 44106. email: joelescobedo1@gmail.com particles during flow conditions has been focused on the ** Corresponding author. email: mansoori@uic.edu production well since fl ow through a pipeline is only a special Received May 15, 2009 Pet.Sci.(2010)7:502-508 503 503 case of this more general one. A typical production well may Substantial work has been done by many researchers be divided into two distinct sections (See Fig. 1): on the topic of particle deposition on the walls of channels (I) The pressure region above the bubble point (single- or pipes in turbulent flow by many researchers (Lin et al, phase) is the emphasis of the present report. Understanding of 1953; Laufer, 1954; Friedlander and Johnstone, 1957; Beal, deposition of particles in this region is especially important 1970; Chen and Ahmadi, 1997; Derevich and Zaichik, 1988; for particles which enter into the oil well from the reservoir. Johansen, 1991). The model presented here is a combination (II) The analysis of the region below the bubble-point of the work performed by the authors mentioned above, pressure (two-phase flow) is the subject of our ongoing modifi ed to be applicable to the deposition of heavy organic research. particles in turbulent petroleum fl uid fl ow. A key assumption in the development of this model is that fully developed petroleum turbulent flow has a structure as proposed by Lin et al. From experimental observations, they proposed a Annular- generalized velocity distribution for turbulent fl ow of fl uids in mist flow pipes comprised of three main regions: - A sublaminar (wall) layer 0 ≤ r ≤ 5, - A buffer layer 5 ≤ r ≤ 30, - A turbulent core 30 ≤ r , Slug flow where rD (/ V f2/Q) is a dimensionless distance iavg measured from the wall. This dimensionless distance is a function of the inner pipe diameter, D , fl uid average velocity, Transition flow i V , the Fanning friction factor, f, and the fluid kinematic avg viscosity, ν. The model presented here is for a system of constant density and viscosity. Therefore, it is applicable only Bubble flow to a single phase petroleum fluid flow. This theory can be extended to the region below the bubble point pressure (gas- Sublaminar liquid slug fl ow, etc.) using reliable expressions for petroleum layer Turbulent Bubble point viscosity and density versus pressure and temperature. The core assumption of constant viscosity and constant density is Single-phase justified since density changes are not appreciable until the turbulent flow bubble point pressure is reached inside the well (or tubing). It is also assumed that suspended particles are of uniform diameter, and that, due to their rather low concentration we can neglect particle-particle interactions. We assume the thickness of the boundary layer is quite small compared to the radius of the pipe as a result we can neglect the wall curvature Transition (buffer) effects in our model. region Oil reservoir We start with reporting the equation which is used to describe the particle fl ux, N , in terms of the diffusivities and the concentration gradient (Von Karman, 2004), i.e., Fig. 1 Illustration of velocity distribution and different fl ow regimes in the prefouling single-phase turbulent fl ow condition in the oil well dC BE ND D (1) dr In this report we present an analytical model for the B E heavy organic suspended particle deposition coefficient where D is the Brownian diffusivity; D is the eddy prior to deposition corresponding to petroleum fluids flow diffusivity; C is the particle concentration; and r is the radial in producing wells condition. In our previous publications distance. (Escobedo and Mansoori, 1995a; 1995b; 2010) we The Brownian diffusivity is defined by the following reported various segments of this analytical model some equation: of which contained typographical errors. For the sake of kT comprehensiveness and to provide the readership with the D (2) 3ʌ d P details of the algebraic manipulations involved we report here the details of the model in its entirety. where k is the Boltzmann constant (k =1.38066×10 J/K); T is the absolute temperature; d is the particle diameter; and μ 2 Development of the analytical model is the liquid viscosity of the suspending medium (petroleum fl uid). Equation (1) is subject to the boundary condition: The theory presented here is for a turbulent petroleum PP at r = S CC = fl uid system of constant density and viscosity. For petroleum where C is the particle concentration at r = S and S is S d d fluid flow in wells this is the case for the region above the d the particle “stopping distance” measured from the wall. A bubble pressure where only the liquid phase is the medium particle needs to diffuse only within one stopping distance for the suspended particles. 504 Pet.Sci.(2010)7:502-508 from the wall, and from this point on, due to the particle following equation: momentum, it would coast to the wall. For small particles ªº Vf /2 avg the stopping distance is small compared with the boundary (8) SS «» dd «» layer thickness and consequently diffusion dominates. The ¬¼ proposed correlation for the particle stopping distance is For the sublaminar layer Equation (1) may be integrated (Friedlander and Johnstone, 1957): following the procedure for the calculation of temperature drop across a composite wall. We will fi nd the concentration 0.05U Vd f /2 Pavg P (3) profiles from point to point across the boundary layer. That P 2 is, we will calculate the concentration differences through the where is the density of particles; V is the average sublaminar layer, the buffer region and the turbulent core. By avg velocity of petroleum fluids; and f is the Fanning friction adding these concentration differences we can fi nd the overall factor. particle fl ux in terms of the average and wall concentrations. Equation (1) may be integrated following the procedure Note that Equation (4) is only valid for dimensionless radial for the calculation of temperature drop across a composite distances smaller than 5, which is the limit of the sublaminar wall. We will find the concentration profiles from point to layer. point across the boundary layer. That is, we will calculate Introducing all the new dimensionless variables and the the concentration differences through the sublaminar layer, expressions for N and D into Equation (1), considering that the buffer region and the turbulent core. By adding these ªº Q concentration differences we can fi nd the overall particle fl ux Q we get: dd rr «» in terms of the average and wall concentrations. Before we Vf /2 «» avg P ¬¼ integrate Equation (1) for C , we need to have expressions *B * P for N and D as functions of the radial distance (r) for each ªº §· §· 2d rD r C NN 1/ «»  V f2 of the three main regions in the oil well and pipeline, i.e. ¨¸ (9) Po ¨¸ avg ** D Q 11.15 dr «» ©¹ i ©¹ sublaminar layer, buffer layer and turbulent core. ¬¼ 1) Sublaminar Layer subject to the following boundary conditions: Johansen (1991) proposed the following correlation to *P P express the eddy diffusivity as a function of radial distance (r) ­ at rS C C ° d for the sublaminar layer: *P P at rC 5 C ¯ 5 3 3 r* r* §· S  5 §· Dv for r*d 5 or ¨¸ ¨¸ Rearranging Equation (9), integrating and applying the 11.15 Q 11.15 ©¹ ©¹ above boundary conditions we arrive at the following integral (4) form: In this equation v is the kinematic viscosity of the fl owing * P 1/3 2/3 ªº petroleum fluid, r is the dimensionless radial distance and 2 11.15 N 11.15N PP 0 Sch Sch CC «» F F 51 2 * S E d Vf /2 33D D represents the sublaminar layer (r ≤ 5) eddy diffusivity. «» * avg ¬¼ S  5 (10) The particle molar flux, N , is assumed to vary linearly In the above equation N is the Schmidt number defi ned from the wall to the center line of the channel, as proposed by Sch as: Beal (1970): §· Q 2r PP N { (11) NN  1 (5) ¨¸ Sch o B ©¹ i and F and F are defi ned by the following expressions: In this equation N is the particle flux at the wall; r is 1 2 a dimensionless radial distance and D is the dimensionless 2 * ªº ªº 1 S I inner well (or tubing) diameter, both defi ned by the following 15  I 11 d «» F  ln«» ln equations: 2 2 «» 2(1 5I ) 2 «» 1 S I ¬¼ d (12) ¬¼ ªº Vf /2 avg §· 10I  1 §· 21 S I rr «» (6) 3tan  3tan ¨¸ ¨¸ «» 33 ©¹ ©¹ ¬¼ ªº Vf /2 * ªº * avg ªº 1 S I 1(1 5I ) 1 d DD «» (7) ii «» F  ln ln «» Q 2 «» ¬¼ «» «» 15  I 1 S I ¬¼ d ¬¼ (13) where D is the inner diameter of the well (or tubing); V i avg * §· §· 10I  1 21 S I 11 d is the average fl uid velocity; f is the Fanning friction factor; 3tan  3tan ¨¸ ¨¸ and v is kinematic viscosity of the fl owing fl uid, m /s. Let us ©¹ ©¹ also define the dimensionless stopping-distance, by the where for simplicity we have defi ned: d Pet.Sci.(2010)7:502-508 505 506 Pet.Sci.(2010)7:502-508 Pet.Sci.(2010)7:502-508 507 This is shown in Fig. 5 where we can notice that deposition Kinematic viscosity coefficients decrease with increasing particle size due to the fact that Brownian diffusion is inversely proportional IE-2 1.91cSt to the particle size of the diffusing species. However, with 3.17cSt increasing particle size (or mass) the momentum increases, IE-4 4.97cSt 12.16cSt so that particle momentum effects become more important. 32.12cSt It is expected a minimum deposition rate for a given particle IE-6 size, beyond which the process is essentially momentum controlled, resulting in higher deposition rates. For a radius IE-8 of 270 nm, we still notice very small values (see Fig. 4), this 0 1000 2000 3000 means that heavy organic particle size must become much Oil roduction rate, m /day larger in order to exhibit high deposition rates. Fig. 3 Effect of petroleum production rate on the deposition coeffi cient of 1 micron (1000 nm) diameter suspended particles in petroleum fl uids Particle size of various kinematic viscosities ranging from 1.91 - 32.12 cSt 2nm 3nm 4nm is less than 1,000 nm. Fig. 2 indicates a decrease in the 5nm 6nm deposition coefficients with increasing kinematic viscosity and an increase in the deposition coeffi cient with increasing production rate. The lighter the petroleum fl uid, the higher the probability of having particle deposition. Fig. 4 shows the predicted deposition coefficients for particles as a function of the crude oil production rate for two extreme particle sizes, 3.5 nm (corresponding to asphaltene steric-colloidal particles in original crude oil) and 270 nm (corresponding to flocculated asphaltene aggregates). As it was mentioned the present analysis is for the single-phase 100 1000 10000 region of the well-tubing (region before the bubble point Oil production rate, m /day pressure is reached). One can notice from this fi gure the very Effect of particle size on deposition coeffi cient for Fig. 5 small values of deposition coefficients for 3.5 nm particles, a 37.8 °API petroleum fl uid for the volumetric fl ow rates of up to 3,000 m /day. Fig. 4 also indicates that deposition coeffi cients increase with increasing We performed model predictions varying the kinematic velocities. However, when the oil production rate is about viscosity of the crude oil to study the effect of this parameter 10,000 m /day, deposition coeffi cient is roughly 0.06 cm/min. on the deposition coefficient. This was done because Therefore we would expect sizeable amounts of deposition at kinematic viscosity decreases with increasing temperature, high production rates. and because it is a function of the API gravity of the crude oil. Fig. 6 shows the predicted values, and we can see a decrease in the deposition coefficient with increasing kinematic Particle size viscosity. This means that the lighter the petroleum fluid is the higher the probability of having heavy organic deposition will be. However, these predicted values are still very small. 3.5 nm Kinematic viscosity 0.03cSt 1.0 270 nm 0.04cSt 0.05cSt 0.1 100 1000 10000 0.06cSt Oil production rate, m /day 0.07cSt Fig. 4 Predicted deposition coeffi cients as a function of the crude oil production rates. It is calculated for particles with a diameter of 3.5 nm suspended in a 37.8 °API petroleum fl uid 0 1000 2000 With the idea in mind of finding another factor that Oil production rate, m /day could increase the tendency of the particles to deposit, we Fig. 6 Effect of kinematic viscosity on deposition coeffi cient examined the effect of particle size on deposition coeffi cient. Deposition coefficient K ×10 , cm/min Deposition coefficient, cm/min 3 Deposition coefficient K ×10 , cm/min Deposition coefficient K ×10 , cm/min d d 508 508 Pet.Sci.(2010)7:502-508 Car pentier B, Wilhelms A and Mansoori G A. Reservoir organic 4 Conclusions geochemistry: Processes and applications. Journal of Petroleum Science and Engineering. 2007. 58(3-4): 341-343 The model developed for the particle deposition onto Che n S K and Ahmadi G. Deposition of particles in a turbulent pipe the walls of a pipe from a turbulent petroleum fluid stream fl ow. Journal of Aerosol Science. 1997. 28(5): 789-796 in oil wells and pipelines was used to predict the deposition Der evich I V and Zaichik L I. Particle deposition from a turbulent fl ow. coefficient from turbulent flow production operations. The Fluid Dynamics. 1988. 23(5): 722-729 effect of particle size on the deposition coefficient was Esc obedo J and Mansoori G A. Solid particle deposition during turbulent investigated, finding that when the deposition process is flow production operations. Paper SPE 29488 presented at SPE diffusion-controlled (particles with a diameter < 1,000 nm) Production Operations Symposium, 2-4 April 1995a, Oklahoma City, the predicted values are very small. However, when the Oklahoma deposition process is momentum controlled (particles with a Esc obedo J and Mansoori G A. Asphaltene and other heavy-organic diameter > 1,000 nm) the predicted values for the deposition particle deposition during transfer and production operations. Paper coefficient increase more rapidly with increasing particle SPE 30672 presented at SPE Annual Technical Conference and Exhibition, 22-25 October 1995b, Dallas, Texas diameter. We also investigated the effect of petroleum fluid Esc obedo J and Mansoori G A. Prefouling behavior of suspended kinematic viscosity on the deposition coefficient. We found particles in petroleum fluid flow. scientia Ir., Transactions C: that the deposition coefficient decreases with increasing Chemistry and Chemical Engineering. 2010. 17: (to appear) petroleum fl uid kinematic viscosity. For kinematic viscosity Fri edlander S K and Johnstone H F. Deposition of suspended particles of 12.16 cSt the predicted deposition coeffi cient is negligible from turbulent gas streams. Industrial and Engineering Chemistry. for suspended particles of 1,000 nm. We also found that the 1957. 49(7): 1151-1156 deposition coefficient increases with increasing production Joh ansen S T. The deposition of particles on vertical walls. International rate. This is due to the fact that at larger production rates the Journal of Multiphase fl ow. 1991. 17(3): 355-362 amount of eddy diffusion is bigger. The proposed model can Lau fer J. The structure of turbulence in fully developed pipe flow. be used for various cases of the behavior of heavy organics NACA 1174, National Advisory Committee for Aeronautics, 1954 particle deposition from turbulent petroleum flows so long (Available from NASA as TR-1174). Lin C S, Moulton R W and Putnam G L. Mass transfer between solid as the particles are neutral, their sizes are stable, there are no wall and fl uid streams. Industrial and Engineering Chemistry. 1953. particle-particle interactions and there are no phase transitions 45(3): 636-646 occurring in the fl ow. However, in cases where such changes Man soori G A. Asphaltene deposition: An economic challenge in heavy are occurring in the system this model will require appropriate petroleum crude utilization and processing. OPEC Review. 1988. modifi cations as presented and applied elsewhere (Mansoori 103-113 G A, ASPHRAC: A comprehensive package of computer Man soori G A, Vazquez D and Shariaty-Niassar M. Polydispersity programs and database which calculates various properties of heavy organics in crude oils and their role in oil well fouling. of petroleum fluids containing heavy organics. www.uic. Journal of Petroleum Science and Engineering. 2007. 58(3-4): 375- edu/~mansoori/ASPHRAC_html). Man soori G A. A unified perspective on the phase behaviour of Acknowledgements petroleum fluids. International Journal of Oil, Gas and Coal Technology. 2009a. 2(2): 141-167 The authors would like to thank Aly Hamouda, Diogo Man soori G A. Phase behavior in petroleum fluids, petroleum Melo Paes, Paulo Ribeiro, Kamy Sepehrnouri and Mahdy engineering – Downstream section of encyclopedia of life support Shirdel for taking time to read the manuscript and suggesting systems. 33 pages. UNESCO, UN, Paris, France, 2009b very useful corrections. To receive the executable computer Man soori G A. ASPHRAC: A comprehensive package of computer package and the set of related equation for our proposed programs and database which calculates various properties of petroleum fluids containing heavy organics. www.uic. model please contact the corresponding author. edu/~mansoori/ASPHRAC_html Mou savi-Dehghani S A, Riazi M R, Vafaie-Sefti M and Mansoori G A. References An analysis of methods for determination of onsets of asphaltene Bea l S K. Deposition of particles in turbulent fl ow on channel or pipe phase separations. Journal of Petroleum Science and Engineering. walls. Nuclear Science and Engineering. 1970. 40: 1-11 2004. 42 (2-4): 145-156 Bra nco V A M, Mansoori G A, De Almeida Xavier L C, et al. Asphaltene Von Karman T. Aerodynamics: Selected Topics in the Light of Their fl occulation and collapse from petroleum fl uids. Journal of Petroleum Historical Development. www.doverpublications.com, 2004 Science and Engineering. 2001. 32: 217-230 (Edited by Sun Yanhua)

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Petroleum Science – Springer Journals

Published: Nov 10, 2010

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