A METHOD AND SYSTEM FOR DETECTING DEPOSIT BUILDUP WITHIN AN ULTRASONIC FLOW METER

BACKGROUND

[0001] After hydrocarbons have been removed from the ground, the fluid stream (such as crude or natural gas) is transported from place to place via pipelines. It is desirable to know with accuracy the amount of fluid flowing in the stream, and particular accuracy is demanded when the fluid is changing hands, or "custody transfer." Even where custody transfer is not talcing place, however, measurement accuracy is desirable,

10001] Ultrasonic flow meters may be used in situations such as custody transfer, In an ultrasonic flow meter, acoustic signals are sent back and forth across the fluid stream to be measured between one or more pairs of transducers. Each transducer pair is positioned within the meter body, or spool piece, such that an acoustic signal traveling from one transducer to the other intersects fluid flowing through the meter at an angle. Electronics within the meter measure the difference between the transit time required for an acoustic signal to travel from the downstream transducer to the upstream transducer and the transit time required for an acoustic signal to travel from the upstream transducer to the downstream transducer. The difference in the transit times is then used to calculate the average velocity and the volumetric flow rate of fluid passing through the meter.

[0002J During operation of an ultrasonic flow meter in a pipeline, deposits may form over the inner surfaces of the meter. For example, liquid ultrasonic flow meters may be used to meter crude oils that often contain waxes. Over time, wax deposits build up on the inner surfaces of the meter. The deposit buildup may cause inaccuracies in measured transit times for the acoustic signals and reduce the effective cross-sectional flow area of the meter, both of which create error in the computed volumetric flow rate through the meter.

SUMMARY

[0003] The problems noted above are addressed, at least in part, by a method and system for detecting deposit buildup within an ultrasonic flow meter. At least some of the illustrative embodiments are systems comprising an ultrasonic flow meter and electronics, The ultrasonic flow meter comprises a spool piece configured to couple within a flow of fluid, a first transducer pair mechanically mounted to the spool piece and configured to fluidly couple to the flow of fluid, and electronics electrically coupled to the first transducer pair. The first transducer pair comprises an upstream transducer and a downstream transducer in operational

relationship to the upstream transducer and defines a first chord there between. The electronics is configured to determine diagnostic data based on acoustic signals transmitted between the first transducer pair, including a speed of sound through the fluid. The electronics is further configured to detect deposit buildup over an inner surface of the spool piece based on a trend of the speed of sound through the fluid.

[0004] Other illustrative embodiments are methods comprising determining diagnostic data based on acoustic signals transmitted between a transducer pair of an ultrasonic flow meter, including a speed of sound through a fluid flowing through the ultrasonic flow meter. These methods further comprise trending the speed of sound through the fluid with time and detecting deposit thickness over an inner surface of the ultrasonic flow meter using the trended speed of sound through the fluid.

[0005] Still other illustrative embodiments are computer-readable media comprising a plurality of instructions that, when executed by a processor, cause the processor to deposit buildup within an ultrasonic flow meter using a trend of diagnostic data based on acoustic signals transmitted between a transducer pair, the diagnostic data comprising a speed of sound through a fluid flowing through the ultrasonic flow meter.

[0006] The disclosed systems and methods comprise a combination of features and advantages that overcome deficiencies of the prior art. The various characteristics described above, as well as other features, will be readily apparent to those skilled in the art upon reading the following detailed description, and by referring to the accompanying drawings,

BRIEF DESCRIPTION OF THE DRAWINGS

[0007] For a detailed description of the various embodiments, reference will now be made to the accompanying drawings in which:

[0008] FIG. 1 illustrates a cut-away top view of an ultrasonic flow meter; [0009] FIG. 2 illustrates an end view of an ultrasonic flow meter in accordance with at least some of the embodiments comprising a spool piece and chordal paths A-D; [0010] FIG. 3 illustrates a top view of an ultrasonic flow meter in accordance with at least some embodiments comprising a spool piece housing several pairs of transducers; [0011] FIG. 4 depicts an illustrative method embodiment for detecting deposit buildup; [0012] FIGS. 5A and 5B schematically depict radial and axial cross- sectional views of an ultrasonic flow meter with deposit buildup; and

[0013] FIG. 6 depicts an illustrative method embodiment for quantifying deposit buildup and correcting the volumetric flow rate to account for the deposit buildup.

NOTATION AND NOMENCLATURE

[0014] Certain terms are used throughout the following description and claims to refer to particular system components. This document does not intend to distinguish between components that differ in name but not function.

[0015] In the following discussion and in the claims, the term "comprises" and "comprising" are used in an open-ended fashion, and thus should be interpreted to mean "including, but not limited to...". Also, the term "couple" or "couples" is intended to mean either an indirect or direct connection. Thus, if a first device couples to a second device, that connection may be through a direct connection, or through an indirect connection via other devices and connections.

DETAILED DESCRIPTION

[0016] FIG. 1 illustrates an ultrasonic flow meter suitable for measuring fluid flow, such as liquids or gases, in accordance with at least some embodiments. Spool piece 100, suitable for placement between sections of a pipeline, has a predetermined size and defines a measurement section. A pair of transducers 120 and 130, and their respective housings 125 and 135, are located along the length of spool piece 100. Transducers 120 and 130 are ultrasonic transceivers, meaning that they both generate and receive ultrasonic signals. "Ultrasonic" in this context refers to acoustic signals, in some embodiments having frequencies above about 20 kilohertz. In some embodiments, the ultrasonic signals may have a frequency of approximately 125 kilohertz (for gas meters), and 1 megahertz (for liquid meters).

[0017] Regardless of the frequency, acoustic signals may be generated and received by a piezoelectric element in each transducer. To generate an ultrasonic signal, the piezoelectric element is stimulated electrically, and it responds by vibrating. The vibration of the piezoelectric element generates an ultrasonic signal that travels across the spool piece 100 through the fluid to the corresponding transducer of the transducer pair. Upon being struck by an ultrasonic signal, the receiving piezoelectric element vibrates and generates an electrical signal that is detected, digitized, and analyzed by electronics associated with the meter. [0018] A path 110, sometimes referred to as a "chord," exists between transducers 120 and 130 at an angle θ to a centerline 105. The length of "chord" 110 is the distance between the face of transducer 120 to the face of transducer 130. Points 140 and 145 define the locations where acoustic signals generated by transducers 120 and 130 enter and leave fluid flowing through the spool piece 100. The position of transducers 120 and 130 may be defined by the angle θ, by a first length L measured between transducers 120 and 130, a second length X corresponding to

the axial distance between points 140 and 145, and a third length D corresponding to the pipe or spool piece diameter. In most cases distances D, X and L are precisely determined during meter fabrication. Further, transducers such as 120 and 130 are usually placed a specific distance from points 140 and 145, respectively, regardless of meter size {i.e. spool piece diameter).

[0019] Initially, downstream transducer 120 generates an ultrasonic signal that propagates to and strikes the upstream transducer 130. Some time later, the upstream transducer 130 generates a return ultrasonic signal that propagates to and strikes the downstream transducer 120. Thus, the transducers 120 and 130 play "pitch and catch" with ultrasonic signals 115 along chordal path 110. During operation, this sequence may occur thousands of times per minute for each transducer pair.

[0020] A fluid flows in the spool piece 100 in a direction 150 with a velocity profile 152. Velocity vectors 153-158 illustrate that the velocity through spool piece 100 increases toward centerline 105. The transit time of the ultrasonic signal 115 between transducers 120 and 130 depends in part upon whether the ultrasonic signal 115 is traveling upstream or downstream with respect to the fluid flow. A transit time for an ultrasonic signal 115 traveling downstream {i.e. in the same direction as the flow) is less than the transit time when traveling upstream {i.e. against the flow). The upstream and downstream transit times can be used to calculate the average velocity along the chordal path 110, and may also be used to calculate the speed of sound in the fluid flow. Given the cross-sectional measurements of the meter carrying the fluid and the average velocity, the volume of fluid flowing through the spool piece 100 may be calculated.

[0021] To more precisely determine the average velocity over the meter cross-section, ultrasonic flow meters comprise a plurality of paths. FIG. 2 illustrates a multi-path ultrasonic flow meter. In these embodiments spool piece 100 comprises a chordal path A 225, a chordal path B 230, a chordal path C 235, and a chordal path D 240 at varying levels through the fluid flow. In alternative embodiments, the multi-path flow meter may comprise a different number of chordal paths. Each chordal path A-D corresponds to two transducers behaving alternately as a transmitter and a receiver. Also shown are control electronics 160, which acquire and process the data from the four chordal paths A-D. Hidden from view in FIG. 2 are the four pairs of transducers that correspond to chordal paths A-D.

[0022] The arrangement of the four pairs of transducers may be more easily understood by reference to FIG. 3. Four pairs of transducer ports are mounted on spool piece 100. Each pair

of transducer ports corresponds to a single chordal path 110 of FIG. 2. The spool piece 100 has mounted thereon a first pair of transducer ports 125 and 135 as well as associated transducers. Another pair of transducer ports comprising ports 165 and 175 (only partially in view) as well as associated transducers is mounted so that its chordal path loosely forms an "X" with respect to the chordal path 110 of transducer ports 125 and 135. Similarly, transducer ports 185 and 195 are placed parallel to transducer ports 165 and 175 but at a different "level" {i.e., a different radial position in the pipe or meter spool piece). Not explicitly shown in FIG. 3 is a fourth pair of transducers and transducer ports.

[0023] Taking FIGS. 2 and 3 together, the pairs of transducers are arranged such that the upper two pairs of transducers corresponding to chords A and B form an "X", and the lower two pairs of transducers corresponding to chords C and D also form an "X". Based on the transit times, the flow velocity of the fluid may be determined at each chord A-D to obtain chordal flow velocities, and the chordal flow velocities may be combined to determine an average flow velocity over the entire pipe or meter spool piece 100. The volumetric flow rate through the meter spool piece 100 may then be determined as the product of the average flow velocity and the cross-sectional area of the meter spool piece 100.

[0024] The chordal flow velocities are based on a batch of transit times received from the four pairs of transducers. For a chord i, the batch of transit times comprise a batch of a difference AT; in transit time between an upstream transit time Tg and a downstream transit time T _21I generated by substantially the following equation:

^T = T ₁ . - T _2t! (1)

A batch of 20 values of ATi may be used to determine an average value of ATj, hi alternative embodiments, a different number of values of δTj may be used.

[0025] Based on the average value of ATi, & ⁿ average chordal flow velocity Vj may be determined as defined by substantially the following equation:

F> -≤— ^- (2,

wherein i is indicative of the particular chord, V, is the chordal flow velocity being determined (i.e., V _A , V _B , V _C , or V _D corresponding to chords A-D, respectively), Lj is the distance or chord length between the transducers, and X ₁ is the axial distance in the flow. Further, based on the average chordal velocities Vi, an average flow velocity V of the flow of fluids through the pipe or meter spool piece 100 may be determined by substantially the following equation:

V = I ₁ W ₁ V ₁ (3) wherein Wj is a chord-dependent weighting factor for chord i.

[0026] Using the average flow velocity V, the volumetric flow rate Q through the meter spool piece 100 may be determined by:

Q = VA ₀ (4) wherein A ₀ is the cross-sectional flow area of the meter spool piece 100. The cross-sectional flow area A ₀ may be determined by:

wherein D is the inner diameter of the meter spool piece 100 and is usually measured when the spool piece 100 is first fabricated.

[0027] During ultrasonic flow meter operation, electronics associated with the meter perform a number of functions, which may include causing a transducer to fire, receiving output from one or more transducers, and computing the average chordal velocity Vj for each chord, the average flow velocity V and the volumetric flow rate Q through the meter. Parameters calculated by the electronics may then be transmitted to electronic device(s) external to the meter, such as a Supervisory Control and Data Acquisition (SCADA) system, and used as input for further computations, Alternatively, all computations may be performed by electronics associated with the meter or by electronics remote to the meter.

[0028] As fluid passes through the meter spool piece, deposits may begin to form over its inner surfaces. Over time, the deposit buildup can cause errors in the computed average chordal velocity Vj, a function of measured transit times T _1, ,, T _2; i, the cross-sectional flow area A _c of the meter, and therefore the computed volumetric flow rate Q through the meter. As deposits buildup, an acoustic signal fired by a transducer must pass through deposit material before being received by another transducer. Thus, measured transit times Ti ^, T _2j i are affected by the deposit buildup, creating an error in the computed average chordal velocity Vi. Moreover, deposit buildup reduces the effective cross- sectional area A ₀ of the meter. Both of these errors create error in the computation of the volumetric flow rate Q through the meter. [0029] The inability to detect and quantify deposit buildup over the inner surfaces of an ultrasonic flow meter necessitates maintenance of the meter at regular intervals. This often leads to time consuming and costly unneeded maintenance operations. Furthermore, in the related art, there is no way to adjust reliably the computed volumetric flow rate to account for deposit buildup between maintenance procedures. The present disclosure is directed to

methods and systems for detecting and quantifying deposit buildup in ultrasonic flow meters. The disclosed methods and systems provide diagnostic data, both measured and computed, that permits maintenance to reduce deposit buildup when needed, rather than on fixed schedule. In the event that maintenance procedures are not immediately performed, the disclosed methods and systems also permit the computed volumetric flow rate to be corrected to account for deposit buildup.

[0030] In accordance with some embodiments, errors in transit times T _ljl5 T _2,! , and thus deposit buildup, may be detected using a function η (Eta). The background and derivation of error indicator η are presented in U, S, Patent No. 6,816,808, which is incorporated herein by reference. For two chords A and B having substantially different chord lengths L _A and L _B , respectively, error indicator ηAB is expressed:

^ = -^- ' ^^ (6)

^B ^A ^C B ^C A where C _A is the computed speed of sound through fluid along chord A and C _B is the computed speed of sound through fluid along chord B. Similar expressions maybe written for other pairs chords having substantially different lengths, such as for chords B and D, chords C and A, and chords C and D of FIG. 2. [0031] The speed of sound C _A for chord A is determined by: where Ti _1A is the upstream transit time along chord A and T _2JA is the downstream transit time along chord A. The speed of sound associated with chord B, as well as other chords, may be expressed similarly.

[0032] If the speed of sound through fluid in the meter is homogenous and no errors occur in the measurement of transit times T^ _A , T _2;A , T _{I >B} and T^ _B , ηAB will be zero. However, if there is an error in any of these measured transit times, η _AB will be nonzero. As discussed above, deposit buildup may create errors in measured transit times, and thus cause ηAB to be nonzero. Therefore, by monitoring the value of η _AB over time, deposit buildup within the ultrasonic flow meter may be detected.

[0033] When calculating η _A B over time for the purpose of detecting deposit buildup, the fluid flow regime should be considered. Temperature stratification may occur, meaning fluid temperature is nonuniform within the meter, when there is little to no fluid flow through an ultrasonic flow meter. For example, fluid near the top of the meter may be warmer than fluid

near the meter base. Because the speed of sound through the fluid is temperature dependent, the speed of sound within the fluid will not be homogeneous in the presence of temperature stratification. Moreover, differing speeds of sound through the fluid will cause a variation in the value of ηAB from one chord to the next.

[0034] Temperature stratification may be minimized, however, when the fluid is well mixed, such as when there is turbulent fluid flow through the meter. Therefore, when calculating ηAB over time for the purpose of detecting deposit buildup, it is preferable to measure transit times Ti _1A , T ₂ , A, Ti _jB and T ₂ , _B when fluid is flowing through the ultrasonic flow meter. [0035] FIG. 4 shows a flow diagram for an illustrative method of detecting deposit buildup within an ultrasonic flow meter. The method 400 begins when electronics associated with the meter periodically measure transit times Ty, T _2,! between at least two pairs of transducers positioned within the meter (block 405). hi some embodiments, transit times T _ljl5 T^i may be measured for all transducer pairs, while in other embodiments transit times T _{1 J} , T ₂ ,; may be measured for only select pair(s).

[0036] Error indicator η may be calculated for any two pairs of transducers having substantially different chord lengths therebetween and for which transit times Ty, T _2, ! are measured. For example, there are four pairs of transducers contained within the ultrasonic flow meter depicted in FIG. 2. If transit times Ty, T _2] j are measured for each pair of transducers, then η may then be calculated for pairs of transducers associated with chords A and B, B and D, A and C ₃ and C and D.

[0037] In some embodiments, transit times Ty ₅ T ₂ ,; are repeatedly measured over a period of time and then averaged over that time period, thereby yielding averaged transit times Ty _iavg and T _2, i _,avg (block 410). The averaged transit times Ty _>avg , T _2> i _]avg may then be used to calculate the speed of sound c, by substituting the averaged transit times Ty _iavg , and chord length L[ into equation (7) (block 415). In turn, the speed of sound cj and appropriate chord lengths are then substituted into equation (6) to calculate η (block 420). In a sense, the computed η is an averaged η, or η _avg , because it is determined using averaged transit times Ty _,avg , T ₂ J^ _V g- [0038] Alternatively, the speed of sound C ₁ may be calculated by substituting the measured transit times Ty, T ₂ ^ and chord length Lj into equation (7) (block 425). In turn, the speed of sound Cj and appropriate chord lengths are then substituted into equation (6) to calculate η (block 430). These calculations may be repeated over a period of time and the computed values of η averaged, thereby yielding an averaged η, or η _avg (block 435),

[0039] Next, each calculated η _avg may be evaluated to determine whether there is detectable deposit buildup within the ultrasonic flow meter (block 440). One basis for determining that deposit buildup exists is the assumption that each calculated η _avg will drift by substantially the same amount and exceed a pre-defined threshold.

[0040] If no deposit buildup is detected, no remedial action may be required at that time. Electronics associated with the ultrasonic flow meter may continue to sample transit times Tj ₁ J ₅ T _2j i and compute η _avg for the two or more transducer pairs uninterrupted until deposit buildup is detected. In the event mat deposit buildup is detected, remedial action may be talc en at that time. Depending on the circumstances, operation of the ultrasonic flow meter may be discontinued to allow for maintenance to reduce, or eliminate, the deposit buildup (block 445). Alternatively, electronics may perform additional computations to determine an adjusted or corrected volumetric flow rate through the meter that accounts for the deposit buildup (block 450). [0041] The ability to detect deposit buildup in accordance with methods disclosed herein, including method 400, may permit maintenance of the ultrasonic flow meter when needed, rather than on a fixed schedule. Furthermore, the ability to quantify the deposit buildup and account for that buildup by correcting computed volumetric flow rates through the meter may allow maintenance to be delayed indefinitely. In at least some embodiments, η provides the basis for quantifying deposit buildup and correcting volumetric flow rates through the meter. [0042] Referring again equation (6), η _AB is a function of the speed of sound C _A and the speed of sound C _B . Assuming there is a timing error δT _A in the measurement of either transit time Ti _1A or T _2JA due to deposit buildup, the resulting error δC _A in the computed speed of sound CA is: c ² Ac _A = -~AT _A (8)

Thus, the speed of sound C _A for chord A may be written as: c ² c _A = c + Ac _A = c AT _x (9)

Similar expressions may be written for other chords, such as chords B, C and D of FIG. 2. [0043J By substituting equation (9) and a similar expression for chord B into equation (6) and neglecting higher order terms, meaning the product of δT _A and δT _B , ηAB may be expressed as:

_!]M __ L ₁ AT - L AT, ₍₁₀₎

[0044] If deposits form on the faces of transducers at opposite ends of a chord, such deposits will cause an error in the fluid speed of sound c. One way to quantify this error is to consider that the deposits cause an error in the measured transit time T. Assuming the deposit material has a speed of sound C _depO sit and the deposit on each transducer face has a thickness tdeposit, the error δT in transit time caused by deposit buildup may be defined as:

δγ = 2^ (— -) (H) c deposit ^c

[0045] As shown by equation (11), the error δT in transit time caused by deposit buildup depends on the deposit thickness t _llepOs i _t ) the speed of sound through the fluid c, and the speed of sound through the deposit material C _depos i _t , but not chord length. Moreover, assuming deposits buildup uniformly within the ultrasonic flow meter, the error δT in transit time caused by deposit buildup is independent of the chord. Thus, δT _A and δT _B of equation (10) are independent of chords A and B, respectively, and maybe designated simply δT. Equation (10) then simplifies to:

V _M = ^AT ( ¹² )

[0046] Combining equations (11) and (12), η _A β and the error δT in transit time due to deposit buildup maybe expressed in terms of the deposit thickness t _d epo _s it

η _M = AT = It^ i- -) (13) deposit

Through algebraic manipulation of equation (13), the deposit thickness t _de p _os i _t ^ma Y b ^e expressed:

_ Aγ C c _thposil

¹ deposit - ~ \ ^l V

^ ^c ^deposit

[0047] As described above in reference to FIG. 4, η _AB may be calculated using measured transit times Tij, T^i. Having determined η _A B and knowing from equation (13) that ηAB equals the timing error δT, the deposit thickness t _de p _os i _t may then be determined using equation (14). Thus, equation (14) permits deposit buildup within an ultrasonic flow meter to be quantified. [0048] In some embodiments, the decision to perform maintenance on the ultrasonic flow meter to reduce deposit buildup may depend on the deposit thickness t _d ep _o si _t - F° ^r example, a threshold value may be defined such that maintenance is performed when the deposit thickness t _de p _os it exceeds that threshold. In the event that maintenance is not performed to reduce or eliminate deposit buildup, the volumetric flow rate through the meter may be corrected to account for the deposit buildup.

[0049] The volumetric flow rate through the meter is given by:

Q = VA, (15) where A _c is the cross-sectional flow area and V is the average flow velocity. As previously discussed, deposit buildup will create errors in both the average flow velocity V and the cross- sectional flow area A ₀ . Thus, the relative uncertainty in the volumetric flow rate δQ/Q may be expressed by:

M = ^ + ^ (16)

Q V A, where δV/V and δA _c /A ₀ are the relative uncertainties in the average flow velocity V and cross- sectional flow area A ₀ , respectively. To determine the relative uncertainty in the volumetric flow rate δQ/Q and thus the error δQ created in the volumetric flow rate Q caused by the deposit buildup, the relative uncertainties in the average flow velocity and cross-sectional flow area δV/V, δA _c /A _c , respectively, are evaluated. [0050] The cross-sectional flow area A _c is: πD'

(17)

4 wherein D is the inner diameter of the meter spool piece measured in the absence of deposit buildup. Deposit buildup reduces the effective inner diameter of the meter spool piece. Thus, the relative uncertainty in the cross-sectional flow area δ A ₀ ZA ₀ may be expressed as:

^ = 1- . ^AD (18)

A _c A _c 3D

Substituting for A _c in terms of D using equation (17) and noting that δD equals -2l _depoS i _t , the relative uncertainty in the cross-sectional flow area δA _c /A _c is:

[0051] The average flow velocity V is given by:

V = ZW ₁ V ₁ (20) wherein Wj is a chord-dependent weighting factor for chord i. Thus, the relative uncertainty in the average flow velocity δV/V may be expressed as:

The average chordal flow velocity V ₁ is given by:

2 T - T

F = -^- ¹ '' ² '' (22)

2X, V ₂ , wherein L, is the length of chord i, X ₁ is the axial component of L ₁ , Ti ₁₁ is the upstream transit time (meaning transit time for an acoustic signal to travel from the downstream transducer along chord i to the upstream transducer), and T _2jl is the downstream transit time. Thus, the relative uncertainty in the flow velocity δV/V for chord i may be expressed as: where the errors in transit times T^ ₁ and T _2jl are δT, as previously discussed. Using equation (22), the above expression may be simplified:

AV, AX, 2c

AT (24)

V ₁ X ₁ L ₁ wherein c is the speed of sound in the fluid. [0052] The axial component X ₁ is given by: where θ is the angle chord i makes with respect to the flow direction and f, is the relative fractional distance that the measuring plane of chord i is from the center plane of the meter. FIGS. 5A and 5B schematically illustrate the relative fractional distance f _t and the axial extent X ₁ for a chord i having chord length L ₁ . Deposit buildup creates errors in the effective diameter of the meter and the relative fractional distance fj that the measuring plane of chord i is from the center plane of the meter f,. Thus, the relative uncertainty in axial extent AX ₁ ZX ₁ may be expressed by:

As before, δD maybe expressed in terms of deposit thickness t _depos i _t :

δD = -2t _deposιl (27)

Also, the error in the relative fractional distance δf,/f, is:

δ/, _ It deposit

(28) f, D

Substituting for δD and Af ₁ Zf ₁ in equation (26) using equations (27) and (28), the relative uncertainty in axial extent AX ₁ ZX ₁ is:

AX, It deposit (29) x, D(i- /n

[0053] Further, substituting for δXj/Xj in equation (24) using equation (29), the relative uncertainty in the flow velocity δV;/V for chord i may be simplified:

^J- = 2t ( ^{1 2 c ~ CdeP} ° ^s » λ n$)

^V i ^U J l ) ^l ^C deposit

[0054] As described in reference to FIG. 4, η _AB may be calculated using measured transit times Xi _1J9 Using equation (13), the deposit thickness t _de p _os i _t may be determined as a function of η _AB - The deposit thickness tdep _o sit may then be used as input to equations (19) and (30) to determine δA _c /A _c and δVj/V;, respectively. Finally, the relative error in the volumetric flow rate δQ/Q may be evaluated using equation (16).

[0055] Accounting for the deposit buildup, the corrected volumetric flow rate Q ₀ through the meter is: β _e = β + δβ (31) wherein Q is the volumetric flow rate through the meter in the absence of deposit buildup and may be determined using equation (15).

[0056] FIG. 6 shows a flow diagram for an illustrative method 500 for quantifying deposit buildup within an ultrasonic flow meter and correcting the volumetric flow rate through the meter to account for the deposit buildup. The method 500 begins with detecting deposit buildup in accordance with method 400 discussed above in reference to FIG. 4 (block 505). One product of method 400 is η _avg , which may then be substituted into equation (13) and the deposit thickness calculated (block 510).

[0057] Next, method 500 uses the deposit thickness tdeposit to calculate the corrected volumetric flow rate Q ₀ through the meter in a series of steps. The relative uncertainty in cross-sectional flow area AA ₀ / A ₀ is calculated using equation (19) (block 515). The relative uncertainty in the average chorda! flow velocity δV/Vi for each chord i is calculated using equation (30) (block 520). The computed values of δVi/Vj for all chords i are then substituted into equation (21) to determine the relative uncertainty for the average flow velocity δV/V (block 525). The relative uncertainty in the volumetric flow rate δQ/Q is determined from the computed values of δA _c /A _c and δV/V using equation (16) (block 530).

[0058] The volumetric flow rate Q through the meter in the absence of deposit buildup may be determined using equation (15) (block 535). The computed values of δQ/Q and Q may then be

combined to arrive at the error in the volumetric flow rate due to deposit buildup δQ (block 540). Finally, the corrected volumetric flow rate Q ₀ through the meter may be determined using equation (31) (block 545).

[0059] From the description provided herein, those skilled in the art are readily able to combine the methods as described to create software that when combined with appropriate general purpose or special purpose computer hardware may be used to create a computer system and/or computer subcomponents embodying the invention, to create a computer system and/or computer subcomponents for carrying out the method of the invention, and/or to create a computer-readable media for storing a software program to implement the method aspects of the invention. Using such software, the methods described herein may be executed on a periodic basis or as needed.

[0060] The above discussion is meant to be illustrative of the principles and various embodiments of the present invention. Numerous variations and modifications will become apparent to those skilled in the art once the above disclosure is fully appreciated. It is intended that the following claims be interpreted to embrace all such variations and modifications.