United States Patent
`
`[11] Patent Number:
`5,317,928
`Young
`[45] Date of Patent:
`Jun. 7, 1994
`
`[191
`
`||I||llllIlIlIlllllllllllllIIIIIIIIIHIIIIIIIIIlllllllIlllllllllIlIllllllll
`U5005317928A
`
`[54] METHOD FOR MEASURING THE FLOW
`RATE OF A COMPONENT OF A
`TWO-COMPONENT FLUID MIXTURE
`
`(iii) determining a temperature ratio value according
`to the relationship
`
`Inventor:
`
`Alan M. Young, Los Gatos, Calif.
`
`Assignee:
`
`Exac Corporation, San Jose, Calif.
`
`T—Tz
`Ti—Tz
`
`[75]
`
`[73]
`
`I21]
`
`[22]
`
`[51]
`[52]
`
`[58]
`
`[56]
`
`Appl. No.: 6,800
`
`Filed:
`
`Jan. 21, 1993
`
`Int. Cl.5 .......................... G01F 1/74; GOIN 9/00
`US. Cl. ................................. 73/32 R; 73/861.04;
`364/577
`Field of Search ................. 73/32 R, 61.43, 61.44,
`73/861.04, 861.38; 364/510, 558, 577
`References Cited
`
`U.S. PATENT DOCUMENTS
`
`3/1977 Herzl .............................. 73/32 R X
`4,010,645
`4,689,989 9/1987 Aslesen et a1. ............... 73/861.04 X
`
`Primary Examiner—Herbert Goldstein
`Attorney, Agent, or Firm—Claude A. S. Hamrick
`
`[57]
`
`ABSTRACT
`
`A method for determining the relationship between the
`density of a multi-component fluid mixture comprising
`a number of known components and the concentration
`of one of the components of the fluid mixture. The
`method comprises the steps of:
`(i) determining a first and a second density-concentra-
`tion relationship to define the relationship between
`the density of the fluid mixture and the concentra-
`tion of the component at first and second known
`temperatures T1 and T2, respectively;
`(ii) measuring the temperature T of the mixture;
`
`(iv) choosing a component concentration value C,-,
`(v) determining first and second density values p(C.-,
`T1) and p(C,-, T2) by inputing the component con-
`centration value C,into said first and second densi-
`ty—concentration relationships to yield the first and
`second density values respectively;
`(vi) subtracting the second density value from the
`first density value to produce a density difference
`value Apngz;
`(vii) processing the results from steps (iii), (v) and (vi)
`according to the equation
`
`P(Ciy7) = P(Cin2) + [
`
` 2
`T2 :LAPn'"
`Tl —
`
`to produce a density-concentration value p(C.-, T) for
`said fluid mixture;
`(viii) incrementing the component concentration to
`provide a new component concentration value Cr,
`(ix) repeating steps (v) and (viii) until sufficient densi-
`ty-concentration values have been produced to
`define the relationship between the density of a
`muIti-component fluid mixture comprising a num-
`ber of known components and the concentration of
`one of the components of said fluid mixture.
`
`6 Claims, 5 Drawing Sheets
`
`DERIVE DENSITY-
`CONCENTRATION ('l IRVE
`OF A TWO-COMPONENT
`FLUID MIXTURE AT TI
`
`DERIVE DENSITY-
`CONCENTRATION CURVE
`OF A TWO-COMPONENT
`FLUID MIXTURE AT T,
`
`COMPLETED INCREMENT
`
`DERIVE
`DENSITY-
`DIFFERENCE
`FUNCTION
`
`DETERMINE
`DENSITY AT r2
`AND
`CONCENTRATION
`VALUE
`
`s
`
`4
`
`3
`
`DERIVE PARTIAL DENSITY - CONCENTRATION CURVE @ r
`
`so
`
`CHECK IF DENSITY-
`CONCENTRATION
`CURVE @ r
`
`SET
`CONCENTRATIO
`N VALUE
`
`MEASURE
`TEMPERATURE
`OF FLUID
`
`CALCULATE
`TEMPERATURE
`RATIO
`
`CONCENTRATION
`VALUE
`
`Micro Motion 1025
`
`1
`
`Micro Motion 1025
`
`

`

`US. Patent
`
`June 7, 1994
`
`Sheet 1 of 5
`
`5,317,928
`
`
`
`
`
`(PriorArt)
`
`2
`
`

`

`US. Patent
`
`June 7, 1994
`
`Sheet 2 of 5
`
`5,317,928
`
`DERIVE DENSITY-
`CONCENTRATION CURVE
`OF A TWO-COMPONENT
`FLUID MIXTURE AT Tl
`
`20
`
`
`
`DERIVE DENSITY-
`CONCENTRATION CURVE
`
`
`OF A TWO-COMPONENT
`
`
`FLUID MIXTURE AT T2
`
`22
`
`p (cl’Tl)
`
`24
`
`p (cpTz)
`
`26
`
`DERIVE DENSITY-CONCENTRATION
`CURVE OF A
`
`TWO-COMPONENT FLUID MIXTURE AT T
`
`28
`
`9 (cl)
`
`DERIVE
`
`CONCENTRATION OF A /30
`FLUID COMPONENT
`:
`
`CALCULATE MASS
`
`FLOW RATE OF A If 32
`FLUID COMPONENT 1
`
`mC
`
`Fig.2
`
`3
`
`

`

`US. Patent
`
`June 7, 1994
`
`Sheet 3 of 5
`
`5,317,928
`
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`

`

`US. Patent
`
`June 7, 1994
`
`Sheet 4 of 5
`
`5,317,928
`
`
`
`5
`
`

`

`US. Patent
`
`June 7, 1994
`
`Sheet 5 of 5
`
`5,317,928
`
`m.”m
`
`M
`mm
`
`DETERMINE FLUID
`COMPONENT
`CONCENTRATION
`
`92
`
`30
`
`iiiiv-----s!--.z-:
`
`wWWm
`RATE OF A TWO -
`COMPONENT FLUID
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`

`

`1
`
`5,317,928
`
`METHOD FOR MEASURING THE FLOW RATE
`OF A COMPONENT OF A TWO-COMPONENT
`FLUID MIXTURE
`
`BACKGROUND OF THE INVENTION
`
`1. Field of the Invention
`The present invention relates generally to a method
`for measuring the flow rate of fluids and, more particu-
`larly, to a method for measuring the flow rate of a com- 10
`ponent of a two-component fluid mixture.
`2. Brief Description of the Prior Art
`In industrial processes involving fluids which are
`considered to be two-component fluid mixtures, a need
`exists to accurately measure the concentration of one of 15
`the components of the two-component fluid mixture.
`Typically a two-component fluid mixture consists of
`either a solid component fully or partially dissolved
`within a liquid carrier fluid, or a liquid component
`mixed with a liquid carrier fluid. In addition to measur- 20
`ing the concentration of one of the components of the
`two-component mixture, a need exists to accurately
`measure the flow rate corresponding to the measured
`component.
`In the beverage industry, for example, there is a need 25
`to accurately measure and control the concentration of
`sugar in water and to determine the associated total
`amount of sugar used. In the pulp and paper industry,
`knowledge of the concentration of TiOz and its associ-
`ated flow rate is valuable in accurately controlling 30
`paper coating processes. Similarly, in oil production,
`there is a need to accurately measure the oil and water
`concentrations and determine the associated oil produc-
`tion rates for royalty calculation purposes.
`There are several known prior art methods of mea- 35
`suring the flow rate and/or the concentration of a com-
`ponent of a two-component fluid mixture. One of these
`methods is described in US. Pat. No. 4,689,989 to
`Aslesen et al. This method is also described in “EXAC
`Mass Flow Meter Applications Manual (8300 EX, 8310 40
`EX)”, pages 2—14 to 2—16.
`The method described in these publications is based
`on the fact that, at a known temperature, a determinable
`relationship between the density of a two-component
`mixture and the concentration of one of the components 45
`of that mixture exists.
`The relationship between the density of the two-com-
`ponent mixture and the concentration of one of the
`components of that mixture can be plotted graphically
`as is illustrated by curve 10 in FIG. 1 of the accompany- 50
`ing drawings. In this figure, the density p of the two-
`component mixture is plotted on the vertical axis 12 and
`the concentration C of one of the components of that
`mixture is plotted on the horizontal axis 14.
`One method of determining the density concentration 55
`curve 10 is to create a mixture in which the concentra-
`tion of one of the components is known. The sample is
`then heated to a known temperature and its density is
`measured. If the known component concentration, say
`C1 and the measured density, say p1, are plotted on the 60
`vertical and horizontal axes 12 and 14, respectively, a
`point (C1; p1) is defined in the C-p plane between the
`axes 12 and 14.
`
`The above step is then repeated by producing a dif-
`ferent sample of the mixture with a different component 65
`concentration, say C2, and its measuring density, say p2,
`at the same temperature at which the first concentration
`C1 and density p1 values were measured. This second
`
`2
`measurement will yield a further point (C2; p2) in the
`C-p plane.
`The above process is repeated until sufficient points
`(typically 15) have been determined to plot the curve
`10.
`Once this curve has been determined, it can be used
`to measure the concentration of a component of a two-
`component fluid mixture. The way this is done is by first
`measuring the density of a two-component fluid mix-
`ture. Typically, this density of the fluid mixture can be
`measured by using devices such as a pycnometer, a
`vibrating tube densitometer, gamma ray density gauges,
`hygrometers, or any other suitable apparatus or tech-
`nique. This measured density is then plotted on the
`vertical axis 12, read across to curve 10 and, from curve
`10, down to determine the concentration value from the
`horizontal concentration axis 14.
`A major problem with this method is that the curve
`10 is derived at a single known temperature and can
`only be used to determine concentrations in a mixture at
`that temperature. If this curve 10 is used to determine
`the concentration of the component of a two-compo-
`nent fluid mixture which is at a different temperature to
`which the curve 10 was produced, erroneous results
`will occur.
`
`This can be illustrated by considering the following
`hypothetical situation: If the density of a two-compo-
`nent fluid mixture is p1, the concentration of the mea-
`sured component of the two-component fluid will, ac-
`cording to curve 10, be equal to C]. This is true, as is
`described above, only if the temperature of the fluid
`under consideration is the same as that for which a
`curve 10 is derived. If that same fluid is now heated to
`a greater temperature, its density would decrease to a
`value, say p3. If we use curve 10 to determine the con-
`centration of the component of the mixture, this will
`yield a concentration C3. However, this concentration
`C3 is clearly incorrect because the concentration of the
`component has not changed and is still at a value C1.
`This is because concentration, on either a mass or a
`weight basis, does not change with the temperature of
`the fluid, even though the fluid’s density does. Concen-
`tration on a mass basis is simply proportional to the ratio
`of the concentrate mass divided by the sum of the con-
`centrate mass plus the carrier mass. Mass does not
`change with temperature and, therefore, neither does
`concentration on a mass basis. However, density, which
`defined as mass per volume, does change with tempera-
`ture since volume typically increases with increasing
`temperature.
`In fact, with the change in density with the change in
`temperature, a change in the density-concentration rela-
`tionship has occurred. This changed relationship is indi-
`cated by the broken-line curve 16 in FIG. 1 which is
`drawn through the intersection point between a vertical
`line drawn up from concentration C1 and the horizontal
`line drawn from density p3. What this second curve 16
`illustrates is that, for an accurate concentration determi-
`nation at the second temperature a different curve (in
`this case curve 16) should be used.
`A seemingly straightforward solution to this problem
`would be to accurately account
`for
`temperature
`changes. One way of doing this would be to make al-
`lowance for the changes in a fluid’s density based on its
`coefficient of thermal expansion. However, a mixture of
`two components cannot accurately be characterized as
`having a single, constant coefficient of thermal expan-
`
`7
`
`

`

`5,317,928
`
`4
`tration value Ci into said first and second density-con-
`centration relationships to yield said first and second
`density values respectively;
`(vi) subtracting said second density value from said
`first density value to produce a density difference value
`Apnn;
`.
`(vii) processing the results from steps (iii), (v) and (vi)
`according to the equation
`
`p(C.;T) = #012) + I:
`
`T—Tz
`filwm
`
`to produce a density-concentration value p(C.-, T) for
`said fluid mixture;
`(viii) incrementing the initial component concentra-
`tion to provide a new component concentration value
`C5 and
`(ix) repeating steps (v) to (viii) until sufficient density-
`concentration values have been produced to define said
`relationship between the density of a multi-component
`fluid mixture comprising a number of known compo-
`nents and the concentration of one of the components of
`said fluid mixture.
`The method of the invention can further be used to
`
`determine the mass flow rate of the component of the
`multicomponent fluid mixture. This is done by the fol-
`lowing additional steps:
`(i) measuring the density of the multi-component
`fluid;
`(ii) using the relationship between density and con-
`centration as determined above, to determine the con-
`centration of the component;
`(iii) measuring the mass flow rate of the multi-compo-
`nent fluid mixture; and
`(iv) multiplying said mass flow rate of the fluid mix-
`ture by the determined concentration of the component
`to determine said mass flow rate of the component.
`
`3
`sion because the two components will behave differ-
`ently as temperature changes and will depend on the
`relative amendment of the two components present
`which, of course are a priori, unknown. This is primar-
`ily because each component of the mixture will exhibit
`different rates of thermal expansion.
`Furthermore, it is not always possible to know or
`obtain the expansion coefficient for each fluid compo-
`nent. For example, in the case of a sugar solution, one
`would have to know the expansion coefficient for both 10
`water (which is known) and that of sugar in solution
`(which is not known).
`Another way of making allowances for changes in
`temperature would be to plot a large number of density-
`concentration curves over a large range of different 15
`temperature conditions. Unfortunately, this is not al-
`ways practical to do for each and every type of solution
`that one would wish to measure. Furthermore, certain
`density-concentration measurements are required to be
`so accurate that temperature differences of only a few 20
`degrees Fahrenheit could lead to unacceptable inaccu-
`racies. To produce a curve for each possible tempera-
`ture range is similarly impractical.
`For the above reasons, therefore, the prior art meth-
`ods of determining density concentration relationships
`and, more particularly, the concentration of a compo-
`nent of a two-component fluid mixture and its associ-
`ated flowrate are insufficient for providing for situa-
`tions where the temperature of the mixture varies.
`SUMMARY OF THE INVENTION
`
`5
`
`25
`
`30
`
`35
`
`Object of the Invention
`
`It is, therefore, an object of this invention to provide
`a method for determining the concentration and flow
`rate of a component of a two-component fluid mixture
`over a range of different temperatures.
`Another object of the present invention is to provide
`a method for measuring the concentration and flow rate
`of a component of a two-component fluid mixture with-
`out having any information about the fluid mixture’s
`thermal expansion coefficient.
`Yet another object of this invention is to provide a
`method of characterizing the density concentration
`relationship of a two-component fluid mixture over of
`range of different temperatures.
`SUMMARY OF THE INVENTION
`
`Briefly, this invention provides for a method for de-
`termining the relationship between the density of a
`multicomponent fluid mixture comprising a number of 50
`known components and the concentration of one of the
`components of the fluid mixture. The method comprises
`the steps of:
`(i) determining a first and a second density-concentra-
`tion relationship to define the relationship between the 55
`density of the fluid mixture and the concentration of
`said component at first and second known temperatures
`T] and T2, respectively;
`(ii) measuring the temperature T of the mixture;
`(iii) determining a temperature ratio value according 60
`to the relationship
`
`Advantages of this Invention
`
`A primary advantage of the method of this invention
`is that it provides an accurate manner of determining
`the relationship between the density of a two-compo-
`nent fluid mixture and the concentration of a compo-
`nent fluid of that mixture.
`
`45
`
`Another advantage of the method of this invention is
`that temperature changes are properly accounted for
`when determining this density concentration relation-
`ship.
`Yet another advantage of the method of this inven-
`tion is that knowledge of the thermal expansion coeffici-
`ents for each component of the twocomponent fluid
`mixture is not required in order to accurately derive the
`density-concentration relationship.
`These and other objects and advantages of the pres-
`ent invention will no doubt become apparent to those
`skilled in the art after having read the following detailed
`description of the preferred embodiment illustrated in
`the several figures of the drawing.
`BRIEF DESCRIPTION OF THE DRAWINGS
`
`T — T2
`T1 — T2
`
`;
`
`(iv) choosing a component concentration value Cf,
`(v) determining first and second density values p(C,',
`T1) and p(C,~, T2) by inputing said component concen-
`
`65
`
`In the accompanying drawings:
`FIG. 1 illustrates a prior art method of determining
`the density-concentration relationship for a two—com-
`ponent fluid mixture; FIG. 2 is a flow chart illustrating
`the primary steps of the method of this invention;
`
`8
`
`

`

`5,317,928
`
`5
`FIG. 3 is a flow chart illustrating, in detail, two of the
`steps in FIG. 2;
`FIG. 4 is a graphical representation further illustrat-
`ing the steps in FIG. 3; and
`FIG. 5 is a flow chart illustrating, in detail, the final
`two steps of FIG. 2.
`BRIEF DESCRIPTION OF AN EMBODIMENT
`
`1. General Overview of the Method
`
`The primary steps of the method of this invention are
`illustrated in FIG. 2. It should be understood that this
`
`figure gives only an overview of the method of the
`invention and that a more detailed description thereof is
`presented in the description of FIGS. 3—5.
`The method of this invention, rather than using a
`single density concentration curve at a single tempera-
`ture (as shown in FIG. 1), uses two density concentra-
`tion curves, each determined at a different temperature,
`to define the density-concentration relationship of the
`two-component fluid mixture.
`The first density concentration curve is produced, at
`a first temperature T1, according to the method de-
`scribed above with reference to FIG. 1. This step is
`represented by the block marked 20 in FIG. 2. Simi-
`larly, the second curve is derived for the fluid at a sec-
`ond, different temperature T2 during a step represented
`by the block marked 22. The result of step 20 is a densi-
`ty-cOncentration relationship, derived at temperature
`Tland expressed as p(C, T1), and the result of step 22 is
`a similar relationship, derived at temperature T2, which
`can be expressed as p(C, T2).
`The next step in the method, represented by the block
`marked 28, is to derive a density concentration curve of
`the two-component fluid mixture at a temperature T,
`which is the actual measured temperature of the two-
`component mixture under investigation. This step will
`be described in greater detail below with reference to
`FIGS. 3 and 4 and yields a new density concentration
`relationship which can be expressed p(C, T).
`This new relationship p(C, T) is then used, in a fur-
`ther step represented by the block marked 30 to deter-
`mine the concentration of the fluid component of the
`two-component fluid mixture at
`the temperature T.
`This is done, as is explained above, by measuring the
`density of the fluid mixture and determining the concen-
`tration C using the new relationship p(C, T).
`Finally, the concentration C is processed in step 32 to
`calculate the mass flow rate mo of the fluid component
`under consideration.
`
`2. Derivation of the p-C Curve at Temperature T
`In FIG. 3, which is a flow diagram, the steps 28 and
`30 of FIG. 2 are further illustrated.
`Starting with an initializing substep 40, an initial con-
`centration value C; is set. This value C,- is input, along
`path 42, into substep 44 which derives a density value
`corresponding to the concentration value C; for both of
`the curves produced by steps 20 and 22, respectively.
`Substep 44 then produces a density difference value by
`subtracting the two different density values obtained in
`this way, in accordance with Equation (1):
`
`10
`
`15
`
`20
`
`25
`
`30
`
`35
`
`45
`
`50
`
`55
`
`60
`
`APn.n=P(Ci.TI) —P(Cin2)
`
`(1)
`
`65
`
`This substep 44 is graphically illustrated in FIG. 4 in
`which the density concentration curve p(C, T1), de-
`rived by step 20, is illustrated as curve 70 and the den-
`
`6
`sity concentration function p(C, T2), derived by step 22
`above, is represented by curve 72.
`the corre-
`For the initial concentration value C7,
`sponding density values p(C,; T1) and p(C,, T2) are read
`using the curves 70 and 72, respectively. The difference
`between these two values, i.e., Apn, 72 corresponds to
`a point 74 on the vertical line extending from concentra-
`tion point Ci. This point 74 also lies on a density differ-
`ence curve 78.
`
`Returning now to FIG. 3, it can be seen that the
`resulting density difference value Apn, 72 is input along
`path 46 to substep 48 in which a partial density concen-
`tration curve for the mixture at measured temperature T
`is derived. The substep 48 is further described below.
`Also as part of step 28, a substep 50 measures the
`temperature T of the two-component fluid mixture. The
`temperature T is then processed in substep 52 which
`calculates a temperature ratio according to the follow-
`ing Equation (2):
`
`T—Tz
`Tl—Tz
`
`(2)
`
`The resulting temperature ratio is then input along
`path 54 to be processed in substep 48, along with the
`density difference value Apn, 72 derived in this substep
`44.
`
`Yet another component of step 28 is substep 56 which
`utilizes the initially-set concentration Ciand determines,
`by using the results of step 22, its corresponding density
`p(C,, T2) for the fluid mixture at the second temperature
`T2. The resulting density value p(C,, T2), is input along
`path 58 to substep 48.
`Substep 48,
`therefore, uses the density difference
`value Apn, 72 produced by substep 44, the density
`value p(C,, T2) produced by substep 56 and the temper-
`ature ratio produced by substep 52. These values are
`then used to derive a partial density concentration value
`p( C1, T) at temperature accordance with Equation (3):
`
`T—T2
`p(CiJ) = P(Ci,T2) + [77:72-:I‘APng
`
`3
`()
`
`This value (Ci, T) is then input along path 60 and
`stored as indicated by substep 62. Substep 62 also
`checks whether or not enough partial density concen-
`tration values have been derived to adequately plot
`density concentration curve at temperature T. If this
`substep 62 finds that insufficient data points exist, sub-
`step 64 increments the concentration value C,to CH1,
`and the above process is repeated.
`This step is graphically illustrated in FIG. 4 in which,
`during the iteration represented by substep 64, the con-
`centration is incremented to a value C,-+ 1. This concen-
`tration Ci+1, following the method above, yields a fur-
`ther Apr], 72 point 76 on the vertical line extending
`from point CH1.
`The curve 78 drawn through points 74 and 76 and
`other derived points (not illustrated) is the graphical
`representation of the relationship defined by Equation
`(1) above.
`Once sufficient values for p(C,; T) have been pro-
`duced in terms of Equation (3), the resultant function
`p(C, T) is input along path 66 to step 30. This function
`p(C, T) is graphically represented by curve 80 in FIG.
`
`9
`
`

`

`7
`4 which, in fact, represents the density concentration
`value for the mixture under study at measured tempera-
`ture T.
`
`As illustrated in this FIG, measured temperature T is
`less than temperature T2, but is greater than T1, but it
`will be apparent that the method of this invention could
`be applied to the mixture at any temperature T, whether
`it was greater than or less than both temperatures T1 or
`T2.
`
`3. Derived Concentration of the Fluid Component
`
`The step of deriving the concentration C of the fluid
`component of the two-component mixture is illustrated
`in greater detail in the top half of FIG. 5.
`Initially, the density of the fluid mixture must be
`measured in connection with substep 90. This density
`value p is then input into substep 92 which uses the
`density concentration curve 80 illustrated in FIG. 4 to
`read off the fluid concentration value C.
`
`4. Calculation of the Mass Flow Rate
`
`Thereafter, the concentration value C is input into
`step 32, shown in the lower half of FIG. 5, to determine
`the mass flow rate of the fluid component under consid-
`eration.
`
`Step 32 is, in itself, a two-step procedure wherein, in
`the first substep 100, the mass flow rate m of the entire
`two-component fluid mixture is measured. This can be
`done using any convenient method, but a Coriolis flow
`meter, employing at least one vibrating tube, is a pre-
`ferred device for measuring flow rates and, for that
`matter, the fluid density in substep 90 described above.
`A suitable Coriolis mass flow of this type is described in
`US. patent application Ser. No. 07/833,767, the disclo-
`sure of which is incorporated herein by reference.
`Once the mass flow rate m has been determined, this
`is input into the final substep 102 where the mass flow
`rate of the fluid component Inc can be calculated ac-
`cording to the following Equation (4):
`
`mt: anr
`
`(4)
`
`5. Application of the Method of the Invention
`
`The method of this invention provides an accurate
`method of determining the concentration and the mass
`flow rate of a fluid component in a two-part fluid mix-
`ture.
`
`It will be appreciated by anyone skilled in the art that
`this method has many applications and can be used in
`any of a large number of industrial applications which
`require knowledge of the concentration and/or mass
`flow rate of a component in a two-part fluid mixture.
`Although a preferred embodiment of the present
`invention has been disclosed above, it will be appreci-
`ated that numerous alterations and modifications
`
`thereof will no doubt become apparent to those skilled
`in the an after having read the above disclosures. It is
`therefore intended that the following claims be inter-
`preted as covering all such alterations and modifications
`as fall within the true spirit and scope of the invention.
`What is claimed is:
`1. A method for defining the relationship between the
`density of a multi-component fluid mixture and the
`concentration of one of the components of said fluid
`mixture, the method comprising the steps of:
`(i) determining a first density-concentration relation-
`ship defining the relationship between the density
`
`5,317,928
`
`of said fluid mixture and the concentration of said
`component at a first known temperature T1;
`(ii) determining a second density-concentration rela-
`tionshipdefining the relationship between the den-
`sity of said fluid mixture and the concentration of
`said component at a second known temperature T2;
`(iii) measuring the temperature T of said mixture;
`(iv) determining a temperature ratio value according
`to the equation
`
`T—Tz
`Tl—Tz'
`
`(v) choosing a component concentration value Cr,
`(vi) inputing said component concentration value Ci
`into said first density-concentration relationship to
`determine a first density value p(C.', T1);
`(vii) inputing said component concentration value Ci
`into said second density-concentration relationship
`to determine a second density value p(C,~, T2);
`(viii) subtracting said second density value from said
`first density value to produce a density difference
`value Apnn;
`(ix) processing the results from steps (iv), (vii) and
`(viii) according to the equation
`
`T— T2
`NC”) = P(Ci.T2) + [-7-]—_ r2 :I‘Apruz
`
`to produce a density-concentration value p(C,-, T) for
`said fluid mixture;
`(x) incrementing the component concentration to
`provide a new component concentration value Cr,
`(xi) repeating steps (v) to (x) until sufficient density-
`concentration values have been produced to define
`said relationship between the density of said mix-
`ture and said concentration of one of the compo-
`nents of said fluid mixture.
`
`2. A method of determining the mass flow rate of a
`component of a multi-component fluid mixture com-
`prising the steps as set out in claim 1 and further com-
`prising the steps of:
`(i) measuring the density of said multi-component
`fluid;
`(ii) using said defined relationship between the den-
`sity of said mixture and the concentration of one
`component of said mixture to determine the con-
`centration of said component;
`(iii) measuring the mass flow rate of said mixture; and
`(iv) multiplying said measured mass flow rate by said
`determined concentration of said component to
`determine said mass flow rate of said component.
`3. The method of claim 2 wherein said mass flow rate
`of the fluid mixture is measured using a Coriolis mass-
`flow meter.
`4. The method of claim 3 wherein said mass flow rate
`of the fluid mixture is measured using a Coriolis mass-
`flow meter which includes at least one vibrating tube.
`5. The method of claim 1 wherein said first and sec-
`ond density—concentration relationships are each deter-
`mined according to a method comprising the steps of:
`(i) creating a sample of said multi-component fluid
`mixture in which the concentration of said compo-
`nent is known and heating said mixture to said
`known temperature;
`(ii) measuring the density of said fluid mixture;
`
`5
`
`10
`
`15
`
`20
`
`25
`
`30
`
`35
`
`4O
`
`45
`
`50
`
`55
`
`65
`
`10
`
`10
`
`

`

`9
`
`5,317,928
`
`10
`
`concentration values have been defined to deter-
`mine said density-concentration relationship.
`d 6' Tile snetliod or claim 5f :herjem. said. densaty IS
`etermine
`usmg any one o ,t e .ev1ces in a group
`conSistlng of a pycnometer, a Vibrating tube denSItome-
`ter, gamma ray density gauges, and hygrometers.
`*
`"‘
`"
`“
`*
`
`(iii) defining a density-concentration “11.13 represent-
`mg sald known concentratlon and said measured
`density;
`(iv) creating a different sample of said fluid mixture
`with a different concentration of said component
`and heating said fluid mixture to said known tern-
`perature; and
`(v) repeating steps (ii) to (iv) until sufficient density-
`
`5
`
`10
`
`15
`
`20
`
`25
`
`30
`
`35
`
`45
`
`50
`
`SS
`
`65
`
`11
`
`11
`
`