Diffusion Coefficients in Hydrocarbon Systems Methane-Decane-Methanein Liquid Phase H. H. REAMER, J. B. OPFELL, AND B. H. SAGE California Institute of Technology, Pasadena, Calif.
In three articles presented by B. H. Sage and associates of the California Institute of Technology, a n analysis is given of the evaluation of the Fick diffusion coefficient from measurements of the transport of a gas into a liquid phase under conditions suoh that the effect of the change i n volume of the liquid phase cannot be neglected. Their results indicate that the Fick diffusion coefficient for methane is a function of the composition of the liquid phase in these systems, the coefficient undergoing as much as a threefold change within the ranges of composition covered by their work. Diffusion coefficients for the lighter hydrocarbons i n the liquid phase are useful in predicting the nonequilibrium behavior of petroleum during production and refining operations.
A
LTHOUGH many of the conditions encountered in nature involve hydrocarbon systems which are not at equilibrium, there has been but little experimental work on the transport characteristics of hydrocarbons. Pomeroy and coworkers ( 1 7 ) applied the Fick proposition (6) to the transport of the lighter hydrocarbons in quiescent liquids. Hill and Lacey (9, 10) investigated the rate of solution of methane and of propane in a number of hydrocarbon liquids. The effect of solid-liquid interfaces on the transport of methane in liquid phases was studied by Bertram and Lacey (4). Subsequent t o these early studies, attention was focused on the equilibrium behavior of hydrocarbons. At equilibrium the thermodynamic properties of hydrocarbon mixtures, involving components of low molecular weight, can now be predicted with reasonable accuracy by use of an equation of state (1-3). Little progress has been made in studying the nonequilibrium behavior ( 8 ) . Such phenomena can be conveniently divided into two classes. One relates t o strained ('7) thermodynamic systems and the second to the transport within and between phases not a t equilibrium (12, 15, 16). Drickamer and coworkers (20, 27, 81-33) investigated the diffusion of gases a t elevated pressures as well as the transport between liquid and gas phases. They reported (27, 32, 33) resistance at the interface in liquid-liquid systems, indicating that under transport the conditions on the two sides of the interface do not correspond to equilibrium. Emmert and Pigford ( 5 ) proposed interfacial reEistance as an explanation for the deviation of their results from predicted behavior. Schrage (26)predicted that interfacial resistance would only be of importance a t low pressure. The present investigation relates t o the measurement of the diffusion coefficients for the transport of methane in the liquid phase of the methane-decane system. Studies were made a t temperatures between 40" and 280" F. for pressures up t o 4000 pounds per square inch. The results were interpreted on the basis that no interfacial resistance existed. However, expressions based upon the assumption that a resistance directly proportional to the transfer rate was involved a t the interface also are presented.
METHODS A N D A P P A R A T U S
In principle, the method involved the introduction of methane in the gas phase of a quiescent heterogeneous mixture of methane and decane which was a t equilibrium. The quantity of methane necessary t o maintain the resulting nonequilibrium system a t constant pressure under isothermal conditions was determined as a function of time. Figure 1 is a schematic diagram of the equipment employed. The isochoric vessel, A , contained the heterogeneous mixture of methane and decane initially a t equilibrium a t a predetermined pressure. This vessel was connected by means of the small diameter tubing, B, t o the injector, C. Vessel A was immersed in an agitated liquid bath, D,which in turn was surrounded by the radiation shield, E. The pressure in the system was determined by means of the balance, F ( 2 4 ) , which was connected t o tubing B through the oil-mercury-gas interfaces in the steel U-tube, G. An electrical contact was provided in the U-tube, G, t o permit t h e maintenance of the oil-mercury interface at a constant elevation by adjustment of the manual injector, H . The plunger of injector C was located within an agitated oil bath, I , kept a t a temperature of 100' F. The injector was driven through the precision gear box, J, by the motor, K , the speed of which was controlled by means of a predetermined electronic counter driven by a quartz oscillator (19). With the combination of gear box J and motor K , the rate of change in volume of injector C could be determined with a probable error of not more than 0.05% for a 500-fold range in displacement rates. The rate of injection could be varied by steps of O.Ol%, and the speed of rotation was known within 0.02%. The probable angular deviation of motor K was 5" from the neutral control point. The plunger in bath 1 was packed with a fluorinated, solid hydrocarbon which was located in a gland (Figure 1). This gland could be adjusted through a worm and pinion drive, 0, from outside the agitated bath, I . The details of vessel A of Figure 1 are shown in Figure 2. This chamber was constructed of Type 416 stainless steel and was provided with the unsupported area seal, 0', on which was mounted the perforated glass disk, P. The methane was intro-
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duced through the small diameter tubing, S, and was permitted t o flow through the perforated disk, P , into the gas space of the heterogeneous, quiescent system, R. The tube, Q, with the associated valve, T , allowed the system t o be evacuated and t o be filled with decane. The vessel, A , was supported on the trunnions, U and U ' , so that it might be oscillated within the bath, D, of Figure 1 in order to bring the mixture of methane and decane to equilibrium before the introduction of methane for the diffusion measurements. The agitated bath, D , of Figure 1 was provided with a centrifugal type impeller in the lower part of the bath and a deflection shield, L , which afforded effective toroidal circulation of the liquid in the bath. An electrical heater n-ith low hrat capacity was provided within the agitated bath, and the energy supplied to it was modulated by an electronic circuit (1.9) controlled through a photoelectric cell. The light intensity from a galvanometer mirror falling on the cell was controlled by the indications of a platinum iesistance thermometer of the strain-free type. The details of this temperature control and measuring equipment have been described (25). Local temperature variations were less than 0.02" F. from place to place in the bath, and the changes in temperature with time a t a single point were less than 0.003' F. The strain-free platinum resistance thermometer ( 14) was compared with an instrument calibrated by the Bureau of Standards, and the temperature of the bath surrounding vessel A was known within 0.02" F. of the temperature on the international platinum scale. During measurements, the temperature of the adiabatic shield, E, of Figure 1 mas adjusted so that the control circuit of the bath used less than 50 watts of electric power, accounting for the small variation found in temperature from point to point within the nearly adiabatic system. Figure 3 shows the details of injector C of Figure 1. Plunger B was 1 inch in diameter and had a travel of approximately 8 inches. -4relatively heavy screw, A , was provided t o move plunger R. This smew engaged nut C which was mounted
1 i
Figure 1.
Schematic diagram of apparatus
Vol. 48,'No. 2
Nomenclature f o r Diffusion Coefficients in Hydrocarbon Systems DF = Fick diffusion coefficient, sq.ft./sec. = weight of component 12 a d d e d per u n i t a r e a of i n t e r -
mk
f a c e , lb./sq. ft.
A,+
= weight r a t e of transport of component k , Ib./(sec.)
P
= pressure,lb./sq.ft. = r e s i s t a n c e at interface, s e c . / f t .
T
=
u
= hydrodynamic velocity of a p h a s e i n r direction, ft./sec. = hydrodynamic velocity of a phase resulting f r o m dif-
(sq.ft.)
t/
