Unlted States Patent [19]
`Liu et al.
`
`[11] Patent Number:
`[45] Date of Patent:
`
`5,029,482
`Jul. 9, 1991
`
`[5,4] GAS/LIQUID FLOW MEASUREMENT
`USING CORIOLIS-BASED FLOW METERS
`
`[56]
`
`References Cited
`U_S_ PATENT DOCUMENTS
`
`'
`
`_
`
`_ -
`
`-
`
`-
`
`.
`
`[75] Invemms' g‘ T‘e" llg‘“l’l€temt‘l’i;gmfhcva'l.f
`“Ye”, ‘1 e °“'
`°
`1 '
`
`4,662,219 5/1987 Nguyen .......................... .. 73/861.04
`
`4,689,989 9/1987 Aslesen =1 11].
`4,773,257 9/1988 Aslesen =1 a1. .
`
`.... .. 73/86l.04
`.... .. 73/61.1 R
`
`[73] Assignee: Chevron Research Company, San
`Francisco’ Cahf'
`
`[21] Appl‘ No‘: 414’034
`22 F} d
`s 28 1989
`[
`]
`1 e .
`ep.
`,
`
`[63]
`
`_
`.
`Related {15- Apphcmo“ Du‘ _
`Continuation-impart of Ser. No. 307,156, Feb. 3, 1989,
`abandoned, which is a continuation ‘of Ser. No.
`112,350, Oct. 22, 1987, abandoned
`
`[51] Int. Cl.5 .............................................. .. GOlF l/74
`[52] U5. C1. .......................... .. 73/861114; 73/6100 R;
`‘
`73/61.1O R; 73/831313
`[58] Field of Search I .......... .. 73/861.04, 861.38, 61 R,
`73/61.1 R
`
`4,823,613 4/1989 Cage et a1. . . . . .
`. . . . .. 73/861.38
`4,872,351 10/1989 Ruesch ........................... .. 73/86l.04
`Primary Examiner-Huron E. Williams
`Assistant Examiner—Craig Miller
`Attorney, Agent, or Firm-Edward J. Keeling; David J.
`Power; Robert D. Touslee
`[57]
`AB
`
`Cr
`
`A method of determining mass ?ow rate and phase
`distribution of gas/liquid two-phase ?ows is disclosed.
`The method 11565 a Coriolis-b35611 mass flow meter.
`Flow streams Of known mass flow rate and phase distri
`bution are directed through the meter and correlation
`factors are obtained ‘using an apparent mass flow rate
`output and an apparent density output from the Coriolis
`meter. The true mass flow rate and phase distribution of
`unknown ?ow streams can then be determined.
`1
`7 Claims, 2 Drawing Sheets
`
`FLUID MASS m
`VELOCITY V
`
`FLUID MASS m
`
`VELOCITY V
`O
`
`1
`
`Micro Motion 1019
`
`

`
`US. Patent
`
`July 9, 1991
`
`Sheet 1 of 2
`
`5,029,482
`
`
`
`
`
`n. my v? @r... 211...‘
`
`
`o\ /1 e m2: 231.
`1 Ba. .0 >.:oo.._u>
`
`
`
`E was‘ 05.:
`
`2
`
`

`
`US. Patent
`
`July 9, 1991
`
`Sheet 2 of 2
`
`5,029,482
`
`‘CALCULATED vs MEASURED QUALITY
`
`an METER PRESSURE BETWEEN
`'
`as AND'5O PSIA
`-
`/
`.. o Auo+= REPEATED RUNS AT KNOWN
`PRESSURE DF 54 TO 76y .
`
`'ngblqam I
`
`-
`..
`
`XCALC
`
`,
`
`/
`
`_
`
`'
`
`oauouE LINE REPRESENTS IDEAL
`_ GRAPHICAL RELATIONSHIP OF
`"°TE' CALCULATED VALUES BEING
`TRUE REPRESENTATION OF
`ACTUAL VALUES
`1
`1
`1
`1
`1
`1
`|
`l"
`l
`1
`1
`1
`.2 .25 ,3 .35 .4 .45 .5 .55 .6 .65 .7 .75 .8
`X MEASURE
`
`FIG_3
`
`CALCULATED vs MEASURED F LOW RATES
`
`32 —
`30
`
`an uETER PRESSURE BETWEEN
`36 AND 50 PSIA
`- o Ann+= REPEATED RUNS AT KNOWN
`PRESSURE OF 54 1'0 76 PSIA ’
`
`/
`
`
`
`2a - 2o
`
`f
`9.
`5 24 r
`g
`
`2o _
`
`'
`
`-/
`
`ODLIOUE LINE REPRESENTS IDEAL
`' '
`22 - / NOTE. CRAPHICAL RELATIONSHIP OF
`/ ' CALCULATED VALUES BEING
`,
`TRUE REPRESENTATION OF
`.
`ACTUAL VALUES
`/ |
`|
`1
`1
`I8
`20
`26
`28
`24
`WT MEASURE
`
`'
`
`1
`22
`
`1
`3D
`
`1
`32
`
`FIG-4
`
`3
`
`

`
`1
`
`5,029,482
`
`2
`the Coriolis-based mass ?ow meter to determine a set
`of correlation equations;
`flowing a second gas/liquid stream through the Corio
`lis-based mass ?ow meter;
`obtaining a second apparent mass flow rate output and
`a second apparent density output from the Coriolis
`based mass flow meter; and
`calculating the total mass ?ow rate and phase distribu
`tion of the second gas/liquid stream based on the
`aforementioned correlation equations.
`Knowing total mass ?ow rate and phase distribution
`of the gas/liquid stream, the individual amounts of gas
`and liquid phases can also be determined arithmetically,
`if desired.
`The generalized form of the correlation equations can
`be expressed as:
`
`GAS/LIQUID FLOW MEASUREMENT USING
`CORIOLIS-BASED FLOW METERS
`
`CROSS REFERENCE TO RELATED
`APPLICATIONS
`This is a continuation-in-part of U.S. application Ser.
`No. 307,156, ?led Feb. 3, 1989, which is a continuation
`of U.S. application Ser. No. 112,350, ?led Oct. 22, 1987,
`now abandoned.
`
`5
`
`25
`
`BACKGROUND OF THE INVENTION
`The present invention relates to the ?eld of two
`phase ?ow measurement. In particular, the present in
`vention provides a method and apparatus for measuring
`the relative quantities of gas and liquid in a ?owing ?uid
`stream, especially for the measurement of wet steam.
`One method of enhancing recovery of hydrocarbons
`in, for example, oil-bearing reservoirs, is to inject steam.
`In order to properly manage this enhanced recovery
`technique, it is necessary to know the “quality” and the
`mass flow rate of steam that is injected, wherein the
`“quality” is de?ned as the ratio of vapor to vapor plus
`liquid of the injected steam.
`-
`Many methods have been proposed for the measure
`ment of steam quality in surface steam lines. For exam
`ple, U.S. _Pat. No. 4,662,219, to Nguyen, incorporated
`by reference herein for all purposes and assigned to the
`30
`assignee of the present invention, discloses a method of
`using two ori?ce plates in series to determine steam
`quality. However, such methods actually provide only
`an indirect determination of steam quality because they
`are not directly measuring the mass and/or density of
`35
`the liquid stream. They are in many cases only accurate
`over a limited range of conditions.
`U.S. Pat. Nos. 4,689,979 and 4,773,257 to Aslesen et
`al., also assigned to the assignee of the present invention
`and incorporated herein by reference for all purposes,
`discloses a method of measuring the relative amounts of
`oil and water in a liquid stream. However, no method of
`determining steam quality is shown or suggested.
`A “Q-Bar” device has also been described as being
`useful in the measurement of two phase streams. For
`45
`' example, the “Steamcheck Energy Monitor” sold by
`_ Baker Packers uses the “spike” resonant frequency of a
`resonating tube to determine steam quality. This device
`uses only a sample of the steam and has found to have
`only limited accuracy.
`It is desirable, therefore, to devise an improved
`method of measuring wet steam.
`
`50
`
`BRIEF SUMMARY OF THE INVENTION
`A method of determining total mass ?ow rate and
`phase distribution of the individual component in a
`flowing gas/liquid stream is disclosed. The method
`comprises the steps of
`?owing at least a ?rst gas/liquid stream through a Cori
`olis-based ?owmeter, the ?rst gas/liquid stream hav
`ing a ?rst known total mass ?ow rate and individual
`component phase distribution;
`obtaining a ?rst apparent total mass ?ow rate output
`and a ?rst apparent density output from the Coriolis
`based mass flow meter;
`correlating the ?rst known total mass flow rate and
`phase distribution with the apparent mass ?ow rate
`output and the apparent density output obtained from
`
`60
`
`65
`
`Wnpp=f(Wl ; y)
`
`and
`
`(2)
`Dapp=8 (‘VI ; y)
`where Wu”, and Dam, are apparent mass flow rate output
`and apparent density output obtained from the Coriolis
`based mass flow meter. W, and y denote the true total
`mass flow rate and true phase distribution parameter of
`the gas/liquid flow stream.
`In the step of calculating, the use of the above simul
`taneous correlation equations provides a means to com
`pute two unknown variables, W, and y, based on the
`two known outputs, WW9 and D0”, obtained from the
`Coriolis-based mass flow meter.
`Note that the term “phase distribution parameter” or
`the symbol “y” as used herein can be uniquely charac
`terized by a variety of engineering parameters; such as
`homogeneous mixture density (p,,,), no-slip liquid
`holdup (A) and homogeneous vapor mass fraction (X).
`The adjectives, “homogeneous” and “no-slip", as used
`herein refer to a physical state in which the gas-liquid
`?ow stream is perfectly mixed and both phases are
`?owing at the same velocity in the flow line.
`These three parameters are inter-related; knowing
`one of the parameters, the other parameters can be
`determined. In wet steam measurement application, the
`parameter “X” is commonly referred to as “steam qual
`ity”.
`BRIEF SUMMARY OF THE DRAWINGS
`FIG. 1 illustrates the Coriolis-based flow meter.
`FIG. 2 illustrates the experimental equipment used to
`test the utility of the device.
`FIG. 3 is a graph comparing actual quality with cal
`culated quality using the invention described herein.
`FIG. 4 is a graph comparing actual total mass flow
`rate with calculated total mass flow rate using the in
`vention described herein.
`
`DETAILED DESCRIPTION OF THE
`INVENTION
`In the discussion herein, two-phase steam is used by
`way of example, but it is clear that the method could be
`applied to other gas/liquid streams such as natural gas/
`natural gas liquid streams. Referring to FIG. 1, the
`Coriolis-type mass flow meter of the present invention
`measures a very small force generated by steam ?uid as
`it moves through a U-shaped sensor tube (1). This force
`results from the acceleration or deceleration of the ?uid
`particles as the tube vibrates perpendicular to the direc
`tion of ?ow. The force is analogous to the Coriolis force
`which causes air currents to circulate around the rotat
`
`4
`
`

`
`V
`sin0=-2—‘At
`
`I
`
`10
`(
`)
`
`5,029,482
`4
`3
`of travel (V ,), multiplied by At, is geometrically related
`ing earth, and to gyroscopic forces employed in naviga
`to 6 by:
`tion systems of ships and aircraft.
`The forces induced by ?uid ?ow on the sensor tube
`are the Coriolis or gyroscopic-type forces. FIG. 1
`shows, a tube with a ?uid with mass (m) and velocity
`(V) moving through the tube which is rotating with
`angular velocity (u) about axis 0-0. 1
`'
`The magnitude of the ?ow-induced Coriolis force is
`described by the following equation:
`
`If 6 is small, sin 0 is nearly equal to 0. Also for small
`rotation angles, V, is the product of w and the tube
`0 length (L), so:
`
`9 =
`
`LwAt
`2r
`
`Combining equations 7 and 9 gives:
`
`KsLw
`' srlaz.
`
`K, A,
`_ 8:1
`
`(11)
`
`(12)
`
`The mass ?ow rate Q is therefore proportional only
`to the time interval and geometric constants. Note that
`Q is independent of m, and therefore independent of the
`vibration frequency of the sensor tube.
`The vibrating U-tube method of measurement also
`produces an output which is proportional to the density
`of the ?uid in the meter. The output is a square wave at
`the natural frequency of the vibrating system. The natu
`ral frequency (f) of a spring system can be calculated
`directly from the mass (m) and a spring constant (k):
`
`(13)
`
`In the case of the ?ow tube, the vibrating system can
`be divided into the tube mass (m!) and ?uid mass
`(mf= pV). The ?uid mass is in turn proportional to the
`?uid density (p) since the tube volume is constant.
`Therefore, the density can be expressed directly in
`terms of the tube frequency (f) and constants K1 and Kg:
`
`F=2m$Xl7
`
`(3)
`
`where 1-? is force and E, 5 and V are directional quanti
`ties and X is the vector cross product operator.
`' The angular velocity (to) of the sensor tube is not
`required to be constant, but can oscillate with a peak
`angular velocity (5,). The associated force is also oscil
`latory, with a peak valug(F,,), proportional to the ?uid
`mass (m) and velocity (V).
`Forces exerted by the ?uid on each leg (F1 and F2)
`20
`are opposite in direction (180 degrees out of phase). As
`the tube vibrates about axis 0——0, the forces create an
`' oscillating moment (AM) about axis R—R which is
`expressed by:
`
`25
`
`Since F1=F2 and r1=r2, from equations 1 and 2:
`
`AM=2Fr=4m Vwr
`
`(5)
`
`Now, in (unit mass/unit length) multiplied by V (unit
`length/unit time) yields AQ (unit mass/unit time), i.e.,
`the mass ?ow rate. Equation 3 then becomes:
`
`AM=4wrAQ
`
`35
`
`(6)
`
`The total moment (M) about axis R—R due to all of
`the ?uid particles is found by integrating Equation 4
`around the sensor tube.
`
`M= fAM=4wrQL
`
`<7)
`
`The moment M causes an angular de?ection or twist
`of the sensor about axis R—R, which is at its maximum
`at the midpoint of vibrating tube travel. There is no
`45
`twist at the upper and lower limits of travel since at
`these points a) is zero. The de?ection of 0 due to M is
`resisted by the spring stiffness (K;) of the sensor tube. In
`general, for any torsional spring, the torque (T) is de
`?ned by:
`-
`
`T=K,0
`
`(8)
`
`Since T=M, the mass ?ow rate (Q) can now be re
`lated to the de?ection angle 0 by combining Equations
`5 and 6.
`
`55
`
`.
`.
`Ki
`giving p = f—2 — K2
`
`(9) '
`
`The mass ?ow rate can be derived by measuring the
`de?ection angle (0) using the sensors 2 and 3 shown in
`FIG. 1. This measurement is accomplished by measur
`ing the relative times that each sensor detects the mid
`point crossing of the respective leg. The time difference
`at zero ?ow is nulled. As ?ow increases, causing an
`increase in 0, the time difference (At) between signals
`also increases. The velocity of the tube at' the midpoint
`
`65
`
`Constants K1 and K; can be determined by filling the
`sensor tube with two . ?uids of known densities (at the
`same temperature) and noting the resulting frequencies.
`~When a Coriolis-based mass ?ow meter is used to
`measure a liquid mixture stream containing two or more
`different types of liquids, the two fundamental outputs
`provided from the mass ?ow meter still represent the
`true values of the mass ?ow rate and the density of the
`liquid mixture stream being measured. US. Pat. No.
`4,689,979 and 4,773,257 to Aslesen, et al., have disclosed
`a method of using the above-mentioned ?ow meter to
`
`5
`
`

`
`5,029,482
`5 .
`determine individual amounts of two-phase liquid/liq
`uid streams. In this particular situation, the phase distri~
`bution can be computed directly from the true density
`output as provided from the mass ?ow meter.
`However, when the Coriolis-based mass flow meter
`is used to measure a gas/liquid two-phase flow stream,
`the flow meter behaves substantially differently. Al
`though the Coriolis-based mass flow meter still pro
`vides two fundamental outputs, neither of them give
`true mass flow rate and true density of the gas/liquid
`?ow as it does in a liquid/liquid mixture flow. It has
`been found that these two fundamental outputs, one is
`herein referred to as apparent mass ?ow rate output and
`the other as apparent density output, are simultaneously
`dependent upon both the true total mass flow rate and
`the true density of the gas/liquid flow stream. It has also
`been found that, for a given gas-liquid system, there
`exists an unique relationshipbetween the true values
`and the apparent outputs indicated by the Coriolis
`based mass flow meter.
`The generalized form of the correlation equations are
`shown in Equations (1) and (2). The choice of the spe
`cific form of correlation equations is virtually unlimited.
`For example, the following simultaneous correlation
`equations can be used:
`
`6
`
`We» = In Wimp}?
`
`and
`
`Dapp = b4 Wisp:
`
`(22)
`
`(23)
`
`where b1 through b6 are correlation constants. Equa
`tions (22) and (23) still conform the generalized form set
`forth by Equations (1) and (2), although Wvis used here
`in Equation (23) instead of Wt. This is because that Wy
`is a function of W, and X (i.e., W,.=W,* X), and X is a
`function of p,,I (Equation (21)), it therefore follows that
`- Dgpp is a function of W, and pm as de?ned in Equation
`(1)
`Similarly, still another example of correlation equa
`tions can be expressed as:
`
`20
`
`Wm, = q W? M3
`
`and
`
`0,,” = c4 W,‘S AC6
`
`(24)
`
`(25)
`
`where c1 through c6 are correlation constants.
`
`25
`
`EXAMPLE
`To test the utility of the above-described invention,
`the experimental apparatus illustrated in FIG. 2 was
`used. Air and water were used to test the two-phase
`?ow measurement abilities of a Coriolis-based mass
`?ow meter 3.
`where:
`In particular, a Model D-150 mass flow meter manu
`Wapp is the apparent mass ?ow rate output from the
`factured by Micro Motion, Inc. was used in the test.
`Compressed air flowed into the system via com
`Coriolis-based mass flow meter.
`Dappis the apparent density output from the Coriolis
`pressed air line 4 and water flowed into the system via
`based mass flow meter.
`a tank 5 and water line 6 through a pump 7. The ?ow
`W, is the true total mass ?ow rate of the gas/liquid
`rates of air and water were monitored with meters 8 and
`flow stream, and is equal to Wy+ WL.
`_
`9 respectively. The flow rates of air and water were
`W, is the true mass ?ow rate of vapor phase.
`regulated with valves 10 and 11 respectively. After
`W1, is the true mass flow rate of liquid phase.
`mixing, air and water were thoroughly agitated and
`p,,l is the homogeneous density of the gas/liquid ?ow.
`dispersed in static mixer 12.
`a1 through a6 are correlation constants.
`Flow tests were run at high air-water ratios to simu
`Note that an alternative form of correlation equations
`late steam tlow conditions. At this range of air-water
`can also be used by replacing the parameter p,,I in the
`rates, the flow is homogeneous with water droplets
`Equations (18) and (19) with either A or X,
`being entrained by the air stream.
`where:
`During each test run, air flow rate was kept constant
`A is the no-slip liquid holdup.
`and water flow rate was allowed to vary. Tests at the
`X is the homogeneous vapor mass fraction of the
`‘same air flow rate were then repeated at different line
`vapor phase; it is de?ned as Wy/Wb a ratio of true
`pressures. '
`50
`vapor mass flow rate to the true total mass flow
`‘Experiments were run for air rates ranging from 100
`rate.
`to 167 standard cu. ft. per minute, water rates ranging
`_ Any of these parameters sufficiently quantify the
`from 0.5 to 2.6 gallons per minute and line pressures
`gas-liquid phase distribution in the gas/liquid flows.
`ranging from 20 to 120 pounds per square inch absolute.
`They are also inter-related; knowing one parameter, the
`A data acquisition system 13 was used to record ?ow
`55
`other two parameters can then be computed. Some
`data comprising air and water flow rates, line static
`identity relationships of these parameters are shown
`- pressure and the apparent mass flow rate output and the
`below.
`apparent density output from the Coriolis-based mass
`?ow meter.
`Equations (22) and (23) were used to correlate the test
`data. A multi-variable least square analysis is utilized to
`determine the correlation constants b1 through b6, yield
`ing the following simultaneous correlation equations:
`
`WW = “I WP’?
`
`and
`
`D0”, = a4 wfspzf
`
`(13)
`
`30
`
`(19)
`
`35
`
`45
`
`Pm=PL. Mm’ (14)
`
`p,,,=1/ [x/p,+(1-x) / PL]
`
`(2°)
`
`(21)
`
`p, and p; are, respectively, the known densities of
`pure vapor phase and pure liquid phase under the oper
`ating condition.
`Another form of simultaneous correlation equations
`can also take the form of:
`
`65
`
`1.051101214
`
`(26)
`
`6
`
`

`
`7
`-continued
`—0.28050.0647
`Wv
`Pm
`
`.
`
`p,” = 11.1465
`
`(27)
`
`5
`
`5,029,482
`8
`based on the correlation equations and the second
`apparent mass ?ow rate output and the second
`apparent density output.
`'
`2. The method as recited in claim 1 wherein the step
`of correlating uses two simultaneous correlation equa
`tions to relate the ?rst apparent mass flow rate output
`and the ?rst apparent density output obtained from the
`Coriolis-based mass flow meter with a true mass ?ow
`rate and a component phase distribution parameter of
`the gas/liquid two-phase ?ow of the form:
`
`and
`
`15
`
`Dapp=8 (wt ; Y)
`
`wherein Wapp is the ?rst apparent mass flow rate output
`obtained from the Coriolis-based mass flow meter, Dam,
`is the ?rst apparent density output obtained from the
`Coriolis-based mass ?ow meter, W, is the true total mass
`flow rate of the gas/liquid ?ow stream, and y is the
`component phase distribution parameter of the gas/liq
`uid flow stream.
`3. The method as recited in claim 2 wherein the cor
`relation equations are of the form:
`
`where W, is the true total mass ?ow rate of air and
`water, was the true air mass ?ow rate, pm is the homo
`geneous mixture density of air/water, and Wm, and
`Dapp are, respectively, the apparent density and the 10
`apparent mass ?ow rate output from the Micro Motion
`mass ?ow meter.
`To verify the validity of the correlation equations,
`the calculated air quality (X calc) and the actual air
`quality (X meas) for all test data are compared in FIG.
`3. Also, the calculated total mass ?ow rate (W , calc) and
`the actual mass ?ow rate (W , meas) are compared in
`FIG. 4. FIG. 3 is constructed by generating the calcu
`lated and measured p"I values, then using the relation
`ship in Equation (21) to compute the corresponding X
`20
`values.
`This example illustrates the utility of the present in
`vention.
`It is to be understood that the above embodiments are
`intended to be illustrative and not restrictive. Most
`25
`notably, the invention could be used to measure the
`relative amounts of liquid and vapor in flow streams
`other than ai'r/ water mixture and wet steam. The scope
`ol' the invention, therefore, should be interpreted not
`with reference to the above description, but with refer
`ence to the appended claims, along with the full range
`of equivalents thereto.
`What is claimed is:
`wherein a;, a2, a3, a4, a5, and as are correlation con
`l. A method of determining total mass ?ow rate and
`stants, and Pm is homogeneous density of the gas/liquid
`phase distribution of individual components in a ?ow
`mixture.
`ing gas/liquid stream comprising the steps of:
`4. The method as recited in claim 3 wherein the ho
`?owing at least a ?rst'gas/liquid stream through a
`mogeneous density of the gas/liquid mixture parameter,
`Coriolis-based flow meter, the ?rst gas/liquid
`pm, in both correlation equations is substituted with a
`stream having a ?rst known total mass flow rate
`parameter “7t”, the no-slip liquid holdup.
`and component phase distribution;
`_
`.
`5. The method as recited in claim_3 wherein the ho
`obtaining a ?rst apparent total mass flow rate output
`mogeneous density of the gas/liquid, mixture parame
`and a ?rst apparent density output from the Corio
`ter, pm, in both correlation equations is substituted with
`lis-based mass ?ow meter;
`a parameter “X”, the homogeneous mass fraction of the
`correlating the fast known total mass ?ow rate and
`phase distribution with the ?rst apparent mass ?ow
`- vapor phase.
`,
`45
`6. The method as recited in claim 1 wherein said
`rate output and the ?rst apparent density output
`gas/liquid stream includes two-phase streams of vary
`obtained from the Coriolis-based mass flow meter
`ing composition.
`to determine a set of correlation equations;
`7. The method of claim 1, further comprising the step
`?owing a second gas/liquid stream through the Cori
`Of:
`olis-based mass ?ow meter;
`'
`determining the relative amount of gas and liquid in
`obtaining a second apparent mass flow rate output
`and a second apparent density output from the
`the second gas/liquid stream from the total mass
`flow rate and the second component phase distri
`Coriolis-based mass flow meter;
`bution.
`calculating a total mass flow rate and a component
`phase distribution of the second gas/liquid stream
`
`Wnpp = “1 Win P513
`
`and
`
`Dapp = "4 W115 P516
`
`# i $ $ $
`
`35
`
`40
`
`50
`
`55
`
`65
`
`7