Fluid flow control process

A method is disclosed for controlling flow rates of a primary fluid including aspirating, mixing, and metering the primary fluid with a secondary fluid. The secondary fluid has a high relative vapor pressure to form a gaseous mixture consisting essentially of vapor at constant volume fraction of primary fluid independent of flow rates. In one aspect, the invention includes passing a secondary fluid of diluent gas through a venturi having specified proportions including discharge coefficient; and pumping primary fluid through venturi suction to pass through a primary fluid orifice of specified discharge coefficient wherein the venturi discharge coefficients of the venturi and the liquid orifice form a substantially linear proportionality over a wide range of flow rates through the venturi.

BACKGROUND OF THE INVENTION 
This invention relates to a method for controlling fluid flow. In one 
aspect, the invention relates to a method for pumping and metering a 
corrosive, volatile, high density liquid at low flow rates. 
Fluids can be moved through a conduit or tube by various methods including 
by centrifugal force, by volumetric displacement, by transfer of momentum 
from one fluid to another fluid, or by gravity. 
Design criteria for selecting pumps for a particular service include design 
factors such as the physical and chemical properties of the liquid to be 
handled, the total head or pressure increase to be achieved, and other 
factors such as the service temperature range. Centrifugal pumps and 
positive displacement pumps, e.g., of the reciprocating or piston type, 
are widely used but are not particularly suited for pumping corrosive 
fluids in a production environment. These types of mechanical pumps 
require close tolerances and dynamic seals which break down over time in 
pumping corrosive fluids. 
An acceleration of one fluid to transfer momentum to a second fluid is a 
principle commonly used in handling corrosive materials. Jet pumps such as 
jets and eductors are in this category. These types of momentum pumps, 
also sometimes called siphons or exhausters, usually are designed for 
pumping against a low head, e.g., pressures less than the pressure of the 
fluid used for pumping. The injector is a specialized type of jet pump 
which is operated by steam for boiler feed and other similar applications. 
In injectors, the pumped fluid is transferred to a space under the same 
pressure as the steam used in the injector. 
Venturi nozzles are typically used to develop a suction from the momentum 
of a pumping fluid. The suction can be used to pull or pump a second fluid 
into the stream of flow. 
Carburetors are well known liquid and gas contacting apparatus using a 
venturi to pump and to mix fuel with air. The resulting fuel mixture 
typically is used in an automobile internal combustion engine. A 
sub-atmospheric pressure on the engine side of the throttle provides the 
low pressure against which the carburetor operates as one type of eductor. 
A good source of background information in this area is found in Perry's 
Chemical Engineering Handbook. For example, standard venturi meters are 
described, and standard dimensional proportions are recommended, including 
entrance and exit cone angles as well as throat length. Discharge 
coefficients for venturi meters are described in Perry's as the ratio of 
actual flow to theoretical flow taking into allowance stream contraction 
and frictional effects in the venturi. The discharge coefficient depends 
upon Reynolds Number and to a minor extent upon the size of the venturi, 
increasing with diameter. 
Conventional fluid flow measurement is accomplished by velocity meters 
which can take the form of pitot tubes, radial vane meters, turbine flow 
meters, and others. Another fluid flow measurement device is a head meter 
which includes the venturi meter. The rate of discharge from the head 
meter can be calculated after determining pressure reduction, flow area at 
the constriction, fluid density, and the coefficient of discharge. Area 
meters are another fluid flow measurement device, and these include 
rotameters. Perry's describes rotameters as capable of covering over a 
tenfold range of flow, and by providing "floats" of different densities, a 
200-fold range is practicable. Rotameters are available with pneumatic, 
electric, and electronic transmitters for actuating remote recorders, 
integrators, and automatic flow controllers. 
Corrosive and volatile high density liquids are very difficult and 
expensive to pump and meter through conventional pumps and meters. The 
corrosive nature of the fluids is damaging to conventional mechanical 
pumps. The volatile nature of the fluid typically creates problems when 
service temperatures at the point of application are higher than the 
boiling point of the fluid. Such fluids are difficult to handle and meter 
as liquids through conventional flow meters particularly where the liquid 
has a high density and must be pumped at low flow rates. 
It is an object of this invention to provide a method for the simple and 
accurate flow control of corrosive and volatile liquids. 
A further object of this invention is to provide a method for pumping and 
metering a corrosive and volatile high density liquid at low flow rates. 
It is another object of the present invention to provide a method for 
pumping a fluid by employing the momentum of a first fluid through an 
aspirator to pump a second fluid and to produce a controllable mixture of 
the first and second fluids in a predetermined composition independent of 
flow rates. 
Other objects of this invention will become apparent from an inspection of 
the Summary and Detailed Description of the invention which follow. 
SUMMARY OF THE INVENTION 
The present invention includes a method for pumping, mixing, and metering a 
primary fluid with a secondary fluid. A secondary fluid is selected having 
a high vapor pressure relative to the primary fluid. The secondary fluid 
is passed through a venturi having a specified discharge coefficient to 
pump the primary fluid by venturi suction through a primary fluid orifice 
of specified discharge coefficient. The invention includes thoroughly 
mixing the primary and secondary fluids to form a mixture having a 
constant volume fraction independent of flow rate and consisting 
essentially of vapor. The invention further includes measuring the vapor 
mixture to determine primary fluid flow rate.

DETAILED DESCRIPTION 
The process of the present invention provides controlled pumping and 
metering of a primary fluid with a secondary fluid or diluent. The 
invention includes aspirating and mixing the primary fluid into the 
secondary fluid or diluent such that the mixture is maintained in a vapor 
state and in a predetermined concentration. 
In one embodiment, the present invention provides a method for controlling 
low rates of flow of a corrosive, volatile liquid, including aspirating 
and mixing the liquid into a diluent gas of high relative vapor pressure 
to form a gaseous mixture consisting essentially of a vapor and having a 
substantially constant volume fraction independent of flow rates, and 
metering the flow rate of the vapor mixture produced. The invention 
includes passing the diluent gas through a venturi of specified 
proportions including discharge coefficient and pumping the liquid by 
venturi suction to pass through a liquid orifice of specified discharge 
coefficient and to pass into the venturi, wherein the venturi discharge 
coefficient relative to the liquid orifice discharge coefficient forms a 
substantially linear proportionality over a wide range of flow rates 
through the venturi. 
The present invention requires a secondary fluid, e.g., of a diluent gas, 
having a high relative vapor pressure. High relative vapor pressure is 
defined in this context as a vapor pressure substantially in excess of the 
vapor pressure of the primary fluid. In this way, the mixture of primary 
and secondary fluids forms a gaseous mixture consisting essentially of 
vapor. Otherwise, undesirable entrained droplets of liquid will remain in 
the fluid mixture. Such entrained droplets or condensation will defeat the 
essential character of the present invention by altering the constant 
ratio of primary fluid to secondary fluid achieved through the method and 
apparatus of the present invention. 
The venturi aspirator used in the process of the present invention provides 
for a constant proportion mixing of the primary fluid and secondary fluid, 
e.g., such as liquid SiCl.sub.4 and argon gas. The essentially constant 
ratio of primary fluid to secondary fluid can be established by properly 
selecting the cross-sectional areas of the venturi and/or liquid orifice. 
This can be accomplished only if the venturi discharge coefficient 
C.sub.DV and the discharge coefficient for the liquid orifice C.sub.D2 
form a substantially linear proportionality over a wide range of flow 
rates through the venturi. The flow rates through the venturi can be 
related by the Reynolds Numbers parameter. A constant ratio primary fluid 
to secondary fluid is achieved through the present invention irrespective 
of flow rates. That is, flow rates of secondary fluid through the venturi 
can vary high or low from a reference flow rate, and yet the fraction of 
primary fluid in the final mixture will remain essentially constant. 
In one embodiment, the method of the present invention requires a venturi 
having specified proportions including discharge coefficient and specified 
venturi entrance orifice area, entrance and exit cone angles, and throat 
length as it applies to a particular liquid to be pumped, e.g., such as 
silicon tetrachloride. 
The invention is suitable for pumping and metering fluids similar to 
SiCl.sub.4 such as TiCl.sub.4 or other volatile corrosive fluids. In place 
of argon as the secondary fluid, other non-reactive diluent gases can be 
substituted such as helium or any other inert or non-reactive gas having a 
high relative vapor pressure with respect to the primary fluid. 
By way of example, the invention is particularly suited for mixing liquid 
silicon tetrachloride into an inert gas stream, e.g., of argon, to form a 
mixture consisting essentially of vapor and having a concentration ratio 
of components which is essentially constant. The example is drawn from a 
metal treatment system as described in U.S. Pat. No. 4,392,888, which is 
hereby incorporated by reference. The referenced metal treatment system 
uses silicon tetrachloride as a fluorine acceptor in treating molten 
aluminum. The flow rate of the silicon tetrachloride is low so that the 
amount of silicon introduced into molten aluminum will be only relatively 
miniscule. SiCl.sub.4 liquid has a high specific gravity, i.e., about 
1.48. The SiCl.sub.4 is a liquid at room temperature but quickly vaporizes 
upon ingestion into the moving stream of argon, O.sub.2, and C.sub.2 
Cl.sub.2 F.sub.2 as employed in the process of U.S. Pat. No. 4,392,888. 
However, the temperature of the metal treatment plant typically is higher 
than that commonly referred to as room temperature, i.e., higher than 
about 70.degree. F. SiCl.sub.4 is considered a corrosive fluid and will 
vigorously attack containment materials. In this way, a system is 
described in which very small amounts of a volatile and corrosive high 
density liquid are required to be pumped in a metered form at an elevated 
temperature. The SiCl.sub.4 flow has been found to be extremely difficult 
to control through conventional pumps and variable area meters, 
particularly at low flow rates. 
The present invention involves pumping and mixing a primary fluid with a 
secondary fluid such as a diluent gas to form a vapor mixture at a 
substantially constant predetermined volume fraction such that 
condensation does not occur at the pressure and temperature conditions 
under which the mixture is used. In the case of a primary fluid of 
SiCl.sub.4, a volume (mole) fraction of 0.2 SiCl.sub.4 in a secondary 
fluid of argon gas will maintain a completely vaporous phase at ambient 
temperatures at and above 90.degree. F. and at system pressures of 16 psig 
and below. In the case of primary fluids other than SiCl.sub.4, a 
preliminary step involves determining a mole fraction of primary fluid in 
the secondary fluid at selected service temperatures and pressures which 
will remain completely in the vapor state. Condensation or entrained 
droplets of liquid in the mixture of primary and secondary fluids are not 
acceptable for the reason that the mixture must have a constant and 
predetermined volume fraction. Such a constant volume fraction mixture is 
required so the mixture can be metered through conventional variable area 
rotameter apparatus to determine or measure primary fluid flow rates. The 
process of the present invention further includes providing a constant 
proportion mixing of the primary fluid in the secondary fluid through a 
venturi aspirator. 
A complete description and understanding of the invention will be 
facilitated by reference to the illustrations presented in the figures and 
the description which follows. 
Referring to FIG. 1, a primary fluid which can be a corrosive and volatile 
high density liquid, e.g., silicon tetrachloride, is introduced at 1 and 
is passed through conduit 2 to reservoir vessel 3. The liquid level is 
maintained at 4 through conventional level maintenance techniques such as 
by float valves or electromechanical level controllers (not shown). Liquid 
level 4 is maintained at an elevation above the inlet orifice 6 of liquid 
conduit 7. 
The primary fluid, e.g., in this case being a liquid, is raised or elevated 
through conduit 7 by suction or vacuum. Liquid rises in conduit 7 and 
enters flow casing 9. Liquid is received from conduit 7 into flow casing 9 
through channel 11. Channel 11 can have a constricted throat 12 to provide 
a smooth transition from a larger to smaller pipe diameter. Liquid flowing 
through channel 11 is viewed as the primary fluid. The vacuum or suction 
used to raise or elevate the primary fluid is provided by the flow of a 
secondary fluid through casing 9. Secondary fluid in the form of gas in 
this example enters flow casing 9 at 13 and is directed into venturi 
insert 14. The venturi facilitates the suction applied on the primary 
fluid. 
The primary and secondary fluids meet in chamber 16 and proceed to flow 
through exit cone 17. By the time the primary and secondary fluids are 
discharged from exit cone 17, the fluids are thoroughly mixed. Such a 
mixture is achieved by adhering to prescribed dimensions and angles for 
the venturi. 
Venturi insert is a term used to refer to a machined piece such as venturi 
insert 14 which can be readily inserted into flow casing 9 as shown in 
FIG. 1. The insert can be machined in such a way to alter the dimensions 
of the venturi. In this way, different venturi dimensional systems are 
adaptable for various fluid systems. Venturi dimensions have been found to 
be critical in the sense that standard dimensions when held constant are 
inoperative for particular fluid systems. For example, very low flow rates 
have been found to be inoperative at standard entrance cone angles of 
21.degree..+-.2.degree.. 
Venturi insert 14 is more completely illustrated in FIG. 2. The entrance 
cone angle is indicated in FIG. 2 by Y.degree.. In accordance with the 
present invention, secondary fluid enters venturi insert 14 through 
entrance orifice 41 having diameter D.sub.o. The entrance orifice 
optionally can be countersunk at an angle of Z.degree. which typically 
will range from about 40.degree. to 80.degree.. Fluid passes through the 
entrance orifice, passes through entrance cone 43, and forms a vena 
contracta at about position 44 in throat 45. Throat 45 of the venturi has 
diameter D.sub.T and length S.sub.T. The total length of the insert is 
indicated by S.sub.I. 
In one embodiment of the present invention, silicon tetrachloride liquid is 
the primary fluid and an inert gas such as argon serves as the secondary 
fluid or diluent. Very low flow rates of silicon tetrachloride are 
required to be pumped and metered for supplying downstream metal 
treatment. The final mixture of fluids will contain SiCl.sub.4 in a 
predetermined mole fraction of about 0.2. Flow rates of argon gas entering 
flow casing 9 range from about 180 to 200 standard cubic feet per hour. An 
efficient vacuum is achieved through a venturi as established by venturi 
insert 14 having an entrance cone angle Y.degree. in the range of about 
15.degree..+-.3.degree.. Entrance orifice areas can range from about 0.003 
in..sup.2 to about 0.03 in..sup.2. For establishing a mole fraction of 0.2 
SiCl.sub.4 in argon, the entrance orifice area should be about 0.009. For 
components other than SiCl.sub.4 in argon, the D.sub.V /D.sub.2 area ratio 
can be calculated, and the appropriate discharge coefficients then can be 
obtained experimentally. The throat length of the venturi should range 
from about 0.5 to about 8 throat diameters depending on flow rate. Exit 
cone angle should be in the range of about 10.degree..+-.3.degree., and 
the exit cone length should be about 5 to 20 diameters, also flow rate 
dependent. 
Fluid leaving exit orifice 18 and proceeding left to right as indicated in 
FIG. 1 enters outlet chamber 19 of flow casing 9. The fluid channel 
connecting venturi exit orifice 18 having exit orifice diameter D.sub.E 
and exit chamber 19 of the float casing can be tapered as shown at 21. The 
mixed fluid passes through exit chamber 19 and exits flow casing 9. In 
this example where SiCl.sub.4 has a high heat of vaporization, makeup heat 
is added to prevent condensation. The fluid mixture subsequently is 
metered through conventional fluid measuring devices such as by rotameter 
22. 
Rotameter 22 has controlling means 23 for controllably adjusting fluid 
flow. In this manner, the primary fluid in the mixture flowing through 
rotameter 22 is adjusted in response to proportional mixture flow rate 
through the rotameter. 
Pressures can be equilibrated between exit chamber 19 and primary fluid 
reservoir 3 through pressure balance line 24. The pressure balance line is 
designed to equilibrate pressure at a position, e.g., at position 26, 
downstream from the vena contracta of the venturi. Pressure balance is 
required to maintain a flow of primary fluid from the reservoir to the 
venturi. The liquid reservoir pressure is equilibrated to a position 
downstream from the venturi for the purpose of maintaining flow 
proportionality in this closed system. 
A volume ratio of pumped liquid, e.g., such as silicon tetrachloride, to 
carrier diluent, e.g., such as a diluent gas of argon, can be calculated 
from liquid vapor pressure and system operating conditions of temperature 
and pressure. The Clausius Clapeyron or Antone equations can be used to 
calculate the vapor pressure of liquids for which this information is not 
directly tabulated. For the purpose of the present illustration, assume a 
ratio of 5 for the diluent to liquid (in vapor state). 
This volume ratio can be converted to a diluent to liquid (in liquid state) 
ratio by multiplying the volume ratio by the ratio of liquid-liquid phase 
density (.rho..sub.L) to liquid-vapor phase density (.rho..sub.V). In this 
illustrative embodiment, the liquid-liquid phase is 95 lbm/ft.sup.3 and 
the liquid-vapor phase density is 0.4 lbm/ft.sup.3. On a volumetric basis, 
the ratio of diluent gas to liquid is 1188 
##EQU1## 
wherein R.sub.V-L(L) =Diluent-Liquid (Liquid phase ratio) 
The process of the present invention includes introducing a diluent gas, 
e.g., such as argon, into a converging nozzle with a vena contracta of 
area A.sub.T, e.g., such as over circular area provided by diameter 
D.sub.T, depicted in FIG. 2, at a pressure P.sub.1. By the equations of 
energy and mass, a pressure drop, .DELTA.P.sub.v =P.sub.1 -P.sub.2 occurs 
at velocity V.sub.T through A.sub.T. In addition, the hydrostatic pressure 
P.sub.f at the liquid flow control orifice is given by P.sub.f 
=.rho..sub.f h.sub.f, where .rho..sub.f is the fluid density and h.sub.f 
is the height of the fluid over the flow control orifice. The total 
pressure drop .DELTA.P is the sum of .DELTA.P.sub.v and P.sub.f. Thus, 
.DELTA.P=.DELTA.P.sub.v +P.sub.f. The following expression relates 
.DELTA.P, A.sub.T, and diluent flowrate Q.sub.d. 
EQU Q.sub.d =A.sub.T V.sub.T (2) 
The velocity at A.sub.T can also be expressed as follows: 
##EQU2## 
where C.sub.DV =discharge coefficient at vena contracta, and 
EQU .rho.(diluent)=diluent density. 
Equations (2) and (3) can be combined as follows: 
##EQU3## 
A similar expression will describe the volume flowrate Q.sub.L of liquid to 
be pumped, e.g., silicon tetrachloride, the liquid orifice area A.sub.2, 
e.g., such as provided by diameter D.sub.2 shown in FIG. 1. 
##EQU4## 
The flowrates are expressed as a ratio as follows: 
##EQU5## 
In the present illustration, R.sub.V-L(L) is 1188. 
##EQU6## 
Two criteria are used to size the diluent venturi throat area. First, since 
the diluent gas velocity cannot exceed the speed of sound in this type 
venturi, a minimum A.sub.T (D.sub.V, min) exists. Secondly, C.sub.DV 
reaches an essentially constant value when the Reynolds number exceeds 
30,000. For the venturi to have an invariant C.sub.D.sbsb.2, a maximum 
value of A.sub.T (D.sub.V, max) is specified as follows: 
A.sub.T, min(D.sub.V, min): Maximum diluent flow, Q.sub.max =250 ft.sup.3 
-hr.sup.-1 speed of sound in diluent (argon), Vs=3.7.times.10.sup.6 
ft-hr.sup.-1 (at T=25.degree. C., P=40 psi a) minimum throat diameter, 
D.sub.V, min 
##EQU7## 
Thus, 
##EQU8## 
or A.sub.T, min=7.times.10.sup.-5 ft.sup.2 
Thus, the minimum venturi throat diameter is 0.0093 ft since diluent flow 
in the venturi is limited to sonic velocity. 
Next, the Reynolds number at the minimum specified diluent flowrate and 
D.sub.V =0.0093 ft must be calculated: 
##EQU9## 
where .rho.=Diluent (argon) density=0.1 lbm-ft.sup.-3 
n=Diluent Newtonian viscosity=0.12 lbm-ft.sup.-1 -hr.sup.-1 
D.sub.V =Venturi throat diameter 
Q.sub.min =100 ft.sup.3 -hr.sup.-1 
Thus, 
##EQU10## 
Since Re&lt;30,000 C.sub.DV, immunity, or invariance, does not exist, and the 
functionality between Re and C.sub.DV is experimentally determined. The 
experimental procedure is to fabricate a venturi configured as depicted in 
FIG. 2. Since in this case A.sub.T max effectively does not exist, a 
D.sub.V =0.01 ft was selected to provide assurance that Vs would not be 
attained. The diluent flowrate range of 100-250 ft.sup.3 -hr.sup.-1 is 
used to calculate a Reynolds number range of 11,400 to 28,500. 
The functionality between C.sub.DV and Re is determined within this range. 
This is performed in the laboratory using argon and measuring the actual 
gas flowrate with a rotameter. The theoretical flowrate for a given 
pressure drop is given by: 
##EQU11## 
where .DELTA.P=Pressure drop at orifice 
.rho.=Gas density corrected for pressure. 
Since: 
##EQU12## 
where VA=Actual velocity (measured) 
Values of C.sub.D are experimentally determined as a function of Reynolds 
number. In the example, C.sub.D varied over a range of 0.89 to 0.94 for a 
Reynolds number range of 11,400 to 28,500, respectively. A 5% variation 
(2.5% about mean C.sub.D) in C.sub.D was accepted. Rigorously, a 
polynomial can be obtained that expresses C.sub.D as a function of 
Reynolds number of the secondary fluid orifice (exit-entrance angle, etc.) 
and can then be incrementally varied until the same functionality of 
C.sub.D and Reynolds number as the venturi orifice is obtained. 
Since A.sub.T is known (7.times.10.sup.-5) and the mean C.sub.DV is 0.92, 
the product A.sub.T C.sub.DV is known (6.4.times.10.sup.-5 ft.sup.2). 
Recall from equation (10) that: 
##EQU13## 
Thus, 
##EQU14## 
Assuming that C.sub.D2 =1, A.sub.2 =9.1.times.10.sup.-7 ft and D.sub.2 
=0.0011 ft, the diluent gas flowrate (Q.sub.d) range is 100-250 
ft-hr.sup.-1, and Q.sub.d =Q.sub.L /1188; where Q.sub.L is the liquid 
flowrate, and 1188 is obtained from equation (1). The range of Q.sub.d is 
then 0.08 ft-hr.sup.-1. Thus, the liquid orifice Reynolds number range 
(calculated) is 4040 to 10,600 (using the liquid kinematic properties of 
.eta.=0.9 cP and .rho.=95 lbm-ft.sup.-3. As in the previous step, C.sub.D2 
was found to vary from 0.78 to 0.81 over this Reynolds number range, and a 
mean value of C.sub.D2 =0.80 was selected. 
Finally, A.sub.2 can be calculated: 
##EQU15## 
A.sub.2, the liquid orifice area, is now known (1.1.times.10.sup.-6 
ft.sup.-2) as is A.sub.T (7.times.10.sup.-5 ft.sup.2). 
EQU A.sub.T /A.sub.2 =63.6 (19) 
Similarly, 
##EQU16## 
The process and apparatus of the present invention are particularly suited 
for pumping and metering very low flow rates of a volatile and corrosive 
high density liquid such as TiCl.sub.4 or such as silicon tetrachloride as 
used in the metal treatment system disclosed in U.S. Pat. No. 4,392,888. 
In this embodiment the apparatus of the invention can be constructed from 
metals such as austenitic stainless steels and nickel base alloys to 
withstand the corrosive nature of the SiCl.sub.4.