Methods of

Flow Measurement

in Well Bores

GEOLOGICAL SURVEY WATER-SUPPLY PAPER 1544-C

Prepared in cooperation with the 

Pennsylvania Geological Survey, 

Department of Internal Affairs, 

Commonwealth of Pennsylvania
Methods of

Flow Measurement

in Well Bores

By EUGENE P. PATTEN, JR. and GORDON D. BENNETT

GENERAL GROUND-WATER TECHNIQUES

GEOLOGICAL SURVEY WATER-SUPPLY PAPER 1544-C

Prepared in cooperation with the 

Pennsylvania Geological Survey, 

Department of Internal Affairs, 

Commonwealth of Pennsylvania

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1962
UNITED STATES DEPARTMENT OF THE INTERIOR 

STEWART L. UDALL, Secretary

GEOLOGICAL SURVEY 

Thomas B. Nolan, Director

For sale by the Superintendent of Documents, U.S. Government Printing Office 

Washington 25, D.C.
CONTENTS

	Page 

Abstract __________________________________________________________ C-1

Introduction. _____________________________________________________ 1

Brine-tracing method ______________________________________________ 2

Instrumentation and equipment..._____________-_____--_-_--__-_ 3

Theoretical considerations______________________________________ 3

Report of field tests.___________________________________________ 6

Summary.. ___________________________________________________ 9

Thermal flowmeter._______________________________________________ 9

Instrumentation and equipment_____-________-_____--_-_-__--_ 10

Theoretical considerations______________________________________ 12

Calibration and reliability. ___________________________---_----._ 15

Summary_ _ _ ________________________________________________ 18

Au deep-well current meter.________________________________________ 18

Instrumentation, equipment, and theory________________-_-____--- 18

Calibration and reliability._____________________________________ 20

Summary.... _________________________________________________ 23

Review of other methods of flow measurement________________________ 23

Flowmeters in use in the oil industry.-.^______________-----___--- 23

Radioactive-tracer methods.___-______________----_---_--_-_---- 25

Concentration-time methods _____-____-_-_____-_-_-___---------- 25

References.--___________________________________-_-_-_-__---_----- 28
IV CONTENTS

ILLUSTKATIONS

Page 

FIGURE 1. Diagram of brine-injection apparatus___--____-.__-_-_____ C 4

2. Diagram showing probable form of velocity profile of flow in a

well_-____-____-___--___--_--_-__---______-____-__- 5

3. Graph showing resistivity of borehole fluid obtained in

measurement of internal flow by brine-tracing method__-_ 6

4. Graph showing comparison of brine-tracing results with

average borehole velocities---------------------------- 8

5. Photograph of thermal flowmeter and related equipment.-_- 10

6. Schematic diagram of thermal flowmeter tube and electrical

components--________-_____-___--_-_-_--__-___--_-__- 11

7. Photograph of thermal flowmeter equipped with centering and

flow-channeling devices------------------------------- 11

8. Diagram of thermal flowmeter as used without flow-channeling

device, showing Pitot effect_i__________-___ r -____-____- 14

9. Typical calibration curves for thermal flowmeter used without

flow-channeling device--_-_------------_-.---------_--_- 16

10. Typical calibration curves for thermal flowmeter used with

flow-channeling device--_-_--------_---_-------- ______ 17

11. Schematic diagram of Au deep-well current meter and recording circuit ___________________________________________ 19

12. Photograph of Au deep-well current meter equipped with 

rubber flow guides. Reel, cable, and accessory equipment 

are shown___________________________________________ 21

13. Calibration curve for Au deep-well current meter-__-__-___ 22

TABLE

TABLE 1. Results of brine-tracing field tests-_-___-_____-__-__-______ C-7
GENERAL GROUND-WATER TECHNIQUES

METHODS OF FLOW MEASUREMENT IN WELL BORES

By EUGENE P. PATTEN, JR., and GORDON D. BENNETT

ABSTRACT

Three techniques of borehole-flow measurement are particularly suitable for 

use in a water well: the brine-tracing method, use of the thermal flowmeter, and 

use of the Au current meter. Each of these methods was tested by the authors, 

and the results of these tests, together with certain general comments on the 

use of each method, are reported in this, paper.

The brine-tracing method is the most troublesome to use, because both logging and brine-injection equipment must be in the well. It is unsatisfactory for 

measurement of flow at a single point in the well bore, or at a single instant of 

time; a finite time and depth interval are always necessary. The method is. well 

suited, however, to a problem such as the measurement of very slow flow through 

a long interval of borehole.

The thermal flowmeter is a relatively new instrument, but tests indicate that 

its use holds forth the most promise for precise flowmetering in the future. The 

response of the meter is an electric current that is proportional to the flow 

velocity in the well bore, which makes it highly suited to incorporation into a 

well-logging unit. The thermal flowmeter tested by the authors gave reliable results in the velocity range from 2 to 75 feet per minute, and it is believed that 

with slight modifications in design, meters can be developed that will measure 

either higher or lower velocities.

The Au current meter has been used by the Geological Survey for many 

years, and is a convenient and fairly reliable instrument for measuring discharges in the range commonly observed in pumping wells. Its disadvantages 

include the fact that instantaneous recordings of velocity are not possible, and 

that the meter will not respond below a certain low velocity.

A brine-dilution technique that has been used successfully for pipe and channel 

flow is discussed also. The authors believe that this method might be modified, 

with the development of suitable equipment, to deal with borehole flow.

Seven other methods of flow measurements presently in use in the oil industry are reviewed briefly.

INTRODUCTION

This report discusses the results of an investigation of the methods 

for measuring the flow of water within a borehole. It represents one 

phase of an investigation into the application of borehole geophysics 

to hydrology that was made by the U.S. Geological Survey in cooperation with the Pennsylvania Topographic and Geologic Survey.

C-l
C-2 GENERAL GROUND-WATER TECHNIQUES

As the use of quantitative hydrologic methods has increased the need 

for accurate methods of measuring flow within a borehole has also 

increased. For example, a quantitative study of a well penetrating 

several aquifers has small value unless some means of measuring the 

discharge from each aquifer is available.

The increase in use of electric well logging in hydrology has also 

emphasized the need for such measurements, as the lithologic data 

provided by the logs becomes much more valuable if it can be correlated with flow data. Certain methods of flow measurement have 

been developed, moreover, which utilize conventional logging equipment; in addition, some flowmeters now in use separately will probably be incorporated into logging units in the future.

This report is not intended to be a comprehensive discussion of all 

types of flow measurement, as certain techniques have been described 

adequately elsewhere and, therefore, are treated only briefly here.

The authors conducted field tests of the brine-tracing method, the 

thermal flowmeter, and the Au current meter. In each case the borehole-flow measurements were made in the cased part of a well as the 

well was discharged at different rates. A gasoline-driven centrifugal 

pump was used, with the pump intake set well above the interval of 

measurement.

Independent determinations of the flow were made at the surface 

by measuring with a stopwatch the time required to fill a 55-gallon 

drum. In testing the brine-tracing technique the results of these 

surface measurements were compared with the flow rates computed 

from the tracing results. In testing the flowmeters the results of these 

surface measurements were used to construct calibration curves for the 

instruments. The merits of the instruments are discussed on the basis 

of the general characteristics of these calibration curves.

In the case of the thermal flowmeter the calibration curves obtained 

in field testing are supplemented by a set of curves obtained in the 

laboratory.

BRINE-TRACING METHOD

The brine-tracing method of measuring the movement of water 

has been used extensively in pipe and open-channel flow. Its use in 

borehole flow was a natural consequence of the introduction of fluidconductivity logging equipment. It is hardly possible to say who 

first applied the technique it seems to have come into use gradually, 

in a variety of places, without specific mention in the literature. 

However, U.S. patents were granted for such techniques as early as 

1925.

The technique used during this investigation was to inject a discrete slug of brine into the flow and then trace its movement with
METHODS OF FLOW MEASUREMENTS IN WELL BORES C-3

the fluid-conductivity device. The flow velocity was then calculated 

from the time and distance intervals separating the two recorded 

positions of the brine slug.

INSTRUMENTATION AND EQUIPMENT

The equipment necessary for this method of flow measurement 

includes a fluid-conductivity logging apparatus, a suitable brineinjection device, and a clock or stopwatch for timing the movement of the brine. Most of the commercially available fluid-conductivity devices are satisfactory for this work. The primary requirements which they must meet are accurate depth control, and sufficient 

sensitivity to detect the brine.

The brine-injection device may take one of several forms and can 

usually be improvised in the field. The only requirement is that the 

device be capable of injecting a discrete slug of brine at the desired 

depth. The authors have used a device of the sort diagrammed in 

figure 1 by which air is pumped into the brine container by a small 

hand pump. The air, in turn, forces brine through a ^4-inch plastic 

hose to the desired depth of release. Once flow has been established 

in the hose the brine will siphon, and injection can be controlled 

merely by opening and closing the valve leading into the plastic 

hose.

Another device used by the authors consists of a cylindrical metal 

brine container whose ends are sealed with sheet gelatin. The container is not filled until immediately prior to measurement, as the 

sheet gelatin dissolves after being in contact with water for a short 

time. The device is suspended beneath the logging probe, and the 

probe and container are lowered to the desired depth. The probe 

is then moved up and down until a deflection of the fluid-resistivity 

log indicates that the gelatin has dissolved and the brine has been 

released.

Obviously, many other devices may be used for brine injection. 

Some workers have obtained successful results simply by suspending 

a bottle of brine beneath the probe and breaking it against the wall 

of the hole. Any method which is convenient may be used if a 

discrete and easily recognizable brine slug is produced.

THEORETICAL CONSIDERATIONS

In a cylindrical conduit of the diameter of a typical water well 

and at the flow rates commonly found in well discharge, the flowvelocity profile will generally have the form shown in figure 2. The 

velocity falls off rapidly near the wall, but maintains a fairly constant rate, vm , across the middle of the conduit. Because the velocity 

vm prevails over most of the cross-sectional area of the flow, the prob-
C-4 GENERAL GROUND-WATER TECHNIQUES

Brine tank

Valve

Air pump

Plastic hose

FIGURE 1. Diagram of brine-injection apparatus.

ability is greatest that an individual fluid particle injected into the 

conduit will move with this velocity. Therefore, most of the injected 

brine particles must move with the velocity vm, and the point of 

maximum concentration will appear to move with this velocity.
METHODS OF FLOW MEASUREMENTS IN WELL BORES C-5

EXPLANATION

Length of arrow indicates relative magnitude of flow 

velocities

FIGURE 2. Diagram showing probable form of velocity profile of flow in a well.

In most tests this velocity will be close enough to the average velocity 

to be used without correction in discharge calculations. In some tests, 

however, it may be necessary to estimate or empirically evaluate a 

correction factor. About the only way that such a factor can be evaluated in a well is by injecting brine in the casing, or at least above the 

uppermost yielding zone, while operating the pump at a known discharge. To determine the necessary correction the velocity obtained 

by tracing the point of maximum conductivity can be compared with 

the quantity computed by the following equation.

Average A , ., , , pump discharge (cfs) velocity (ips) =f ~-. f ^rr2 

& j v r- / borehole area (sq ft)

The correction obtained by this method is actually no more than an 

estimate, as the flow-velocity profile may have a different form in the 

casing than elsewhere in the borehole. However, the correction itself will normally be small, and an estimate obtained by this method 

should be satisfactory in most cases.

Settling of the brine slug due to gravity will usually be a negligible 

factor. If uncertainty exists on this point, brine can be injected in 

the casing when no pumping is in progress, and the effects of settling

644520 O 62 2
C-6 GENERAL GROUND-WATER TECHNIQUES

can be observed by conductivity tracing. If appreciable settling is 

observed a correction can be established. It is important to note that 

this type of control should be established in tightly cased intervals, 

as flow between aquifers may be present in uncased intervals of the 

well when pumping is not in progress, and this flow might in some 

cases be mistaken for settling.

The brine-tracing method is strictly applicable only over intervals 

in which the flow is constant that is, in the intervals between points 

of water entry to the borehole. If the flow is gradually changing due 

to inflow or outflow through the wall of the borehole, the best result 

that can be obtained is an average velocity for the zone of measurement. Even this result may be difficult to achieve because the radial 

inflow or outflow will tend to disrupt the shape of the brine slug. The 

brine-tracing method is best suited to wells in which the water-yielding 

zones are separated by wide nonyielding intervals. In such wells the 

movement of the brine may be traced over relatively long distances, 

and the errors in measurement of velocity can be held to a minimum.

REPORT OF FIELD TESTS

Field testing of the method consisted of a series of brine-tracing 

runs made in a well casing 10.2 inches in diameter, as the well was 

pumped at several different rates. The logging device, or sonde, used 

was 3 inches in diameter. The tracing interval in this series was never 

longer than 14 feet, as shown in table 1. Results were good in spite 

of this relatively short, interval, but longer intervals should give 

correspondingly better results, as errors in distance measurement will 

be relatively smaller. Figure 3 shows a typical resistivity log obtained in the field tests of the brine-tracing method.

Depth

(feet)

20

Fluid resistivity ohm-meters 

20 30

FIGDBE 3. Graph showing resistivity of borehole fluid obtained in measurement 

of internal flow by brine-tracing method.
METHODS OF FLOW MEASUREMENTS IN WELL BORES C-7 

TABLE 1. Results of brine-tracing field tests

Distance between 

deflections (feet)

3.5

12. 5

13

14

14

13. 5

14. 0

11. 5

11. 5

Time interval between 

deflections (seconds)

615

419

160

120

92

79

47

30

24

Veloci 

mu 

(fee

;y of point minim resistivity 

; per minute)

0.34

1.79

4.88

7.00

9. 13

10.25

17.87

23.00

28.75

Velocity computed from 

pumpage (feet per 

minute)

0. 52

2.0

5.2

7.9

9. 1

11. 0

17.3

24. 3

31. 1

The measurements were made by the following procedure. The 

logging sonde, in this case a fluid-resistivity instrument, was suspended below the point of injection. A. slug of brine was injected 

using the plastic-hose device described previously. The sonde was 

drawn up through the slug, and a notation was made of the time 

at which the point of minimum resistivity was passed. The sonde 

was then drawn up another 10 to 15 fee[t and held stationary. When 

the recorder indicated that the point of minimum resistivity had 

almost reached the sonde's position, the sonde was lowered through 

the slug, and again a notation was made of the time at which the 

point of minimum resistivity was passed. The total time of the slug's 

travel was then obtained by subtracting the two recorded times, and 

the depth measurement was taken directly from the resistivity log. 

The prevailing borehole velocity was (Obtained from these measurements and was then compared with th^ average velocity, which was 

determined by dividing the measured pump discharge by the borehole area. The results of several such comparisons are summarized 

in table 1 and figure 4.

Figure 4 indicates that the errors are random and do not increase 

or decrease regularly with increasing velocity. The authors believe 

that the most probable source of error was the distortion of the slug 

caused by mixing by the measuring device as it moved through the 

brine slug. The difference in velocities; across the well bore, as illustrated by figure 2, apparently had njo appreciable effect, because 

errors due to this effect would be consistently positive and would tend 

to decrease as velocities increased.

The greatest percentage error occuifs at the lowest velocity, for 

which the distance between resistivity^ minima was 3.5 feet. The 

authors believe that the poor results in this case indicate that this 

interval is too short relative to the disturbances in the position of 

the slug caused by the motion of the s^nde. A positive error due to
C-8 GENERAL GROUND-WATER TECHNIQUES 

36 i32

UJ

3 

Z

5

K 28

UJ

a.

» 

UJ 

UJ " 24

z

h-~

UJ

5 20

o

S

UJ

I 16

00

>-

00

a

£ 12

8 12 16 20 24 28 32 

VELOCITY COMPUTED BY PUMPAGE, IN FEET PER MINUTE

36

FIGURE 4. Graph showing comparison of brine-tracing results with average borehole 

velocities. All measurements made in cased part of one well at different rates of 

discharge.

the difference in velocities across the borehole probably was in this 

measurement, but was obscured by the large negative error due to 

the movement of the probe.

The greatest error in the remaining measurements amounts to 

about 11.5 percent. The authors believe that much greater accuracy 

can be achieved when a longer interval of measurement is available, 

because the errors due to disturbance by the logging sonde will constitute a smaller fraction of the interval. Errors of about 10 percent 

can be expected when conventional logging equipment and a measuring interval of 10 to 15 feet are used.
METHODS OF FLOW MEASUREMENTS IN WELL BORES C-9 

SUMMARY

The brine-tracing method involves field procedures which are 

considerably more troublesome than those involved in the use of 

flowmeters that consist of a single device in the well. The method 

cannot be used when the measurements must be made at a precise 

depth rather than over an interval of borehole; it will not give satisfactory results when used in an interval of borehole in which fluid 

is entering the well; and it is not suitable in applications which require a number of measurements in rapid succession.

The method has certain advantages, however, that use of the directmeasuring instruments lacks, and it should, therefore, remain an 

important technique in the foreseeable future. For example, brine 

tracing requires little instrumental calibration, and errors because 

of equipment failure or deterioration are uncommon. Also, a high 

degree of accuracy can probably be achieved when a long interval 

of borehole is available for measurement. Finally, brine tracing can 

be relied upon to indicate direction of flow clearly at velocities so low 

that a flowmeter may not indicate any flow.

Some of the disadvantages of the brine-tracing technique might be 

eliminated by designing specialized equipment for the purpose. Two 

fixed conductivity electrodes, suspended at a known separation on a 

single cable, would be very much superior to the single movable logging sonde as the need for traversing the brine slug with the instrument would be eliminated. An automatic brine release system 

(incorporated into the same downhole unit as the pickup electrodes) 

would add greatly to the convenience of the method. Finally, an 

automatic system in the control unit for recording the time required 

for the brine to move from one electrode to the other would probably 

result in greater accuracy and might permit relatively close spacing 

of the pickup electrodes.

THERMAL FLOWMETER

The thermal flowmeter was developed by H. E. Skibitzke of the 

Ground Water Branch, U.S. Geological Survey (1955). Several 

experimental models of the meter were furnished the Harrisburg 

office of the Ground Water Branch for field testing. Some of the results of these tests are given in the following discussion. Emphasis 

will be placed upon the performance of the meter itself rather than 

upon the recording circuit or logging reel, as these components will 

probably be modified in many respects as the meter comes into general use.
C-10 GENERAL GROUND-WATER TECHNIQUES 

INSTRUMENTATION AND EQUIPMENT

The thermal flowmeter consists of a small brass tube, five-eighths 

of an inch in diameter and about 6 inches long as shown in figure 5.

FIGUEE 5. Photograph of thermal flowmeter and related equipment.

Two thermistors and an electrical heating element are arranged as 

shown in figure 6, which also shows a schematic diagram of the control and recording unit used by the authors. The two wires leading 

from the heating element are connected to an AC power supply at the 

surface. The thermistors constitute two branches of a wheatstone 

bridge circuit, and the other branches of this bridge are variable resistors in the control box.

The tests described here were made with a recording unit in which 

the galvanometer current of the bridge is fed into a simple amplifying circuit whose output is then recorded as a microammeter deflection. The five-conductor cable, which terminates in special plugs for 

connection to the flowmeter and control box, was carried on a hand 

reel. The flowmeters were equipped with centering devices and, 

when used for low velocities, with devices for channeling flow into the 

tube. Both these devices are on the flowmeter shown in figure 7. The 

recording unit and power supply operate on an ordinary 110-volt 60- 

cycle supply.
METHODS OF FLOW MEASUREMENTS IN WELL BORES C-ll

Electrode 

FIGURE 6. Schematic diagram of thermal flowmeter tube and electrical components.

FIGUEE 7. Photograph of thermal flowmeter equipped with centering and flow-channeling

devices.
C-12 GENERAL GROUND-WATER TECHNIQUES 

THEORETICAL CONSIDERATIONS

The operation of the flowmeter depends upon a sequence of effects, 

through which the flow velocity in the well bore outside the meter is 

related to the response of the recording unit. The flow velocity outside the meter is related to the velocity through the tube in a manner 

which will be discussed below. The amount the water is warmed as 

it passes the heater is an inverse function of the flow velocity. The 

amount of warming is measured by two thermistors, one of which, 

upstream from the heater, is approximately at the ambient temperature of the well water; the other, downstream from the heater, is 

approximately at the temperature of the warmed water. The response of the thermistors is such that a change of temperature causes 

a change in the electrical resistance, which in turn unbalances the 

wheatstone bridge and causes a change in the amount of current flowing through the galvanometer and recording circuits. In practice 

the instrument is calibrated empirically by recording the final galvanometer deflection as a function of known external velocities, thus 

leapfrogging the various intermediate variables. A brief discussion 

of the interdependence of these variables, however, may help to explain certain characteristics of the meter's response.

The thermistors in the flowmeter tube possess high negative temperature coefficients of resistance. They show large decreases in resistance as temperature is increased, and large increases in resistance 

as temperature is decreased. Neither the temperature-resistance 

curve nor the current-voltage curve of a typical thermistor is linear. 

The current-voltage curve is nonlinear because a thermistor, like any 

other resistor, is heated to some degree by the current passing through 

it. This heating lowers resistance, so that a larger current can pass 

than might have been predicted by the linear form of Ohm's Law. 

These relatively complex characteristics make it difficult to predict 

exactly what the electrical response of the measuring circuit will be 

to a given temperature difference between flowmeter thermistors.

The relation between the flow velocity within the flowmeter tube 

and the temperature difference between thermistors has as many complicating factors as the relation between thermistor temperatures and 

electrical response. When there is no flow through the flowmeter 

tube, heat is transferred from the heater to the thermistors by conduction through the water and the walls of the tube. The bridge 

circuit of the meter is generally balanced for this condition of zero 

flow; any additional transfer of heat will then throw the bridge out 

of balance, unless this transfer is equal in both directions and the 

characteristics of the two thermistors are identical. Flow of fluid in 

the tube creates an additional heat transfer by convection.
METHODS OF FLOW MEASUREMENTS IN WELL BORES C-13

The results of the convective process are difficult to predict in view 

of the many ways in which it can affect the device. The process increases the rate of heat transfer in the direction of flow and decreases 

it in the opposite direction, thus tending to bring the temperature of 

the upstream thermistor to the temperature of the well water. At the 

same time, the flow cuts down the ability of the heater to increase the 

temperature of the surrounding water and interferes with conduction 

through the walls of the tube by providing greater opportunity for 

heat loss from the walls to the water passing through. It is clear, 

therefore, that the difference in thermistor temperatures will not 

generally be a linear function of the flow velocity within the tube.

The velocity within the flowmeter tube is, of course, quite different 

from the velocity outside the tube. For velocities above 10 fpm (feet 

per minute) the meter is generally used without a flow-channeling 

device and acts somewhat in the manner of a Pitot tube, as shown in 

figure 8. The velocity along the streamline A-B falls rapidly toward

v2 

zero as point B is approached, so that an increase in head of-^ (where

v is the fluid velocity that existed at point B prior to insertion of the 

flowmeter, and g is the gravitational constant) occurs at the lower 

end of the tube. A decrease in head, ht, occurs at the upper end of 

the tube owing to turbulence. The flow velocity through the tube dev2 

pends upon the head differential,-^ A.t , and upon the frictional

resistance of the tube. Thus the flow velocity within the tube is much 

smaller than the velocity in the well. When the meter is used in this 

way, it measures the velocity at a particular point in the cross section 

of the well. If the velocity profile has the form illustrated in figure 2, 

a simple centering device will insure that the quantity measured is vm, 

the velocity in the central part of the well bore.

For velocities lower than 10 fpm the meter does not usually respond 

well when used as shown in figure 8. The authors were able to obtain 

useful results in this velocity range, however, by attaching a funnelshaped, flow-channeling device to the end of the tube. A sizeable 

fraction of the well flow is thus diverted through the flowmeter tube. 

When used in this manner, the velocity through the flowmeter is 

no longer directly dependent on the velocity in the well, as the response 

of the meter will be affected by the percentage of the total well flow 

that is diverted through it by the channeling device. This percentage 

will, of course, vary as the ratio of the cross-sectional areas of 

the well and the flow-channeling device. Therefore, the meter must 

be calibrated separately for each well diameter that may be encoun644520 O 62 3
C-14 GENERAL GROUND-WATER TECHNIQUES

B

Fluid movement

Turbulent zone

Point of near-zero 

pipe velocity

FIGURE 8. Diagram of thermal flowmeter as used without 

flow-channeling device, showing Pitot effect.
METHODS OF FLOW MEASUREMENTS IN WELL BORES C-15

tered by relating total discharge past the meter to the response of the 

device.

This discussion of the variables through which flow velocity is related to meter response should illustrate that the response will not 

be a linear function of the velocity. In general, rather, the velocityresponse curve will be difficult to describe mathematically. This, of 

course, has no bearing upon the utility of the instrument, as the only 

requirements are that a certain response correspond to a certain flow 

velocity within the well bore and that empirical methods can establish 

the necessary correlation.

Differences in water temperature in the range normally found in 

ground-water work have no measurable effect upon the operation of 

the meter. Since the thermistors constitute two arms of a bridge circuit, the response of the device is controlled by the difference in their 

temperatures rather than by the absolute magnitude of these temperatures. The downstream thermistor adjusts approximately to the temperature of the well water, and the difference between this temperature 

and that of the upstream thermistor is governed by the heat-transfer 

processes described previously.

CALIBRATION AND RELIABILITY

Figures 9 and 10 show typical calibration curves for the thermal 

flowmeter. Each figure shows two curves, corresponding to constant 

heater currents of different magnitudes. Figure 9 shows the response 

of a meter used as diagrammed in figure 8. The tests from which these 

curves were constructed were made in the laboratory and cover a relatively wide velocity range. The meter was highly unstable at velocities lower than 10 f pm.

Figure 10 shows the response of another meter which was tested in 

the field and was equipped with the simple flow-channeling device. 

The curves are scaled in terms of average velocity and apply only for 

the well size in question; the data was taken by suspending the meter 

in a casing 13 inches in diameter and pumping at several different 

rates. The curves indicate that this device will give reliable results for 

average flow velocities as low as 2 f pm.

Each calibration curve represents the most reasonable, smoothest fit 

that could be made to the experimental data. The accuracy and reliability that can be expected from the device may be estimated from 

the relation between the slope of the calibration curve and the accuracy 

with which the recording meter can be read.

The possible error in reading the meter on the recording unit used by 

the authors was ±1 microampere. Figures 9 and 10 indicate that by 

proper selection of the heat input it is possible to obtain a curve having
C-16 GENERAL GROUND-WATER TECHNIQUES

140

130 -

10 20 30 40 50 60 

MICROAMPERES

70 80 90 100

FIGURE 9. Typical calibration curves for thermal flowmeter used without flow-channeling

device.

a slope of less than 1 fpm per microampere for any velocity interval 

between 2 and 75 f pm. At the lower velocities, slopes of less than 0.5 

fpm per microampere were obtained. Errors greater than ±1 fpm
METHODS OF FLOW MEASUREMENTS IN WELL BORES C-17 

18

16

Heater current, 100

iu 14

12

S! 10

z

uj 8

Heater current, 200

0 10 20 30 40 50 60 70 80 90 100

MICROAMPERES

FIGURE 10. Typical calibration curves for thermal flowmeter used with flow-channeling

device.

are, therefore, unlikely at the higher velocities, and errors greater 

than 0.5 f pm are unlikely at the lower velocities.

The devices tested by the authors showed a flattening of the calibration curves at velocities above 75 fpm and a corresponding reduction 

in accuracy. It would be possible to construct probes to give accurate 

results in this velocity range. Flow velocities in a borehole are not 

generally that high, however, and the meters tested by the authors 

seemed adequate to handle most situations that are likely to be encountered in the field.

It should be noted that separate calibration curves must be run for 

downward flow, because the cable and connections extending upward 

from the meter may obstruct the flow into the upper end of the tube. 

In general, some sort of flow-channeling device attached to the upper 

end of the tube is necessary for reliable measurement of downward discharges, and the calibration must, therefore, be in terms of discharge 

for the well size in question. The design of the meter is such that the
C-18 GENERAL GROUND-WATER TECHNIQUES

galvanometer current of the bridge circuit will be reversed as the flow 

is reversed, so that any recording system based upon direct amplification of this current will indicate flow direction by a positive or a negative response.

SUMMARY

The thermal flowmeter method seems to be the most promising 

method of borehole flow measurement currently in use. Although 

the instruments tested by the authors were experimental models, good 

results were achieved both in the laboratory and in the field. It was 

found that by adjusting the heat input to obtain a favorable calibration curve for the velocity interval in question, and by using a flowchanneling device for the lower velocities, reasonably accurate measurements could be mad© over a very wide range.

The small size of the probe represents an advantage over most other 

instruments of measurement, in that the necessity for lowering bulky 

metering or tracing equipment in the well is eliminated, and the 

danger of fouling is thus greatly reduced. Measurements generally 

can be made much more rapidly than by any of the other methods; 

however, a minute or so may be required for the thermistors to reach 

equilibrium after a large change in flow has occurred, and because 

of this the authors found that measurement with the meter in a fixed 

position was preferable to continuous logging.

In accuracy and range of reliable measurement, the thermal flowmeter method tested by the authors was comparable to the other 

methods tested. The meters tested were experimental models, and 

future improvements in the meters will probably result in improved 

accuracy and reliability. The thermal flowmeter method is the most 

convenient method of measurement tested, and it appears to be the 

method best suited for incorporation into a well-logging unit. Of 

the three methods tested, therefore, it seems to hold the best prospects 

for the future.

AU DEEP-WELL CURRENT METER

The U.S. Geological Survey has used the Au deep-well current 

meter for borehole flow measurement for a number of years. This 

meter was designed by C. H. Au of the Geological Survey and was 

described by Fiedler (1927). It is described here chiefly for the sake 

of comparison with other methods.

INSTRUMENTATION, EQUIPMENT, AND THEORY

The meter consists of a roughly helical turbine, or rotor, mounted 

on a vertical axis in a metal cylinder, as shown in figure 11. The 

axis of the rotor coincides with that of the cylinder, and is mounted
METHODS OF FLOW MEASUREMENTS IN WELL BORES C-19

Electrical 

contact

Battery <O) Shielded cable

_ . / Earphones

 Helical rotor

FIGURE 11. Schematic diagram of Au deep-well current meter and recording circuit.

between supports extending from the cylinder wall. The interior 

of the cylinder is unobstructed except for the rotor, rotor supports, 

and electrical contacts.
C-20 GENERAL GROUND-WATER TECHNIQUES

The meter is suspended on a two-conductor electrical cable. One 

conductor is connected to the cylinder wall and, thus, to the metal 

axis of the rotor; the other is separated from the body of the meter 

by an insulating support and terminates in a light, flexible strip of 

metal extending toward the axis. With each revolution of the rotor, 

a slight protrusion on the axis makes contact briefly with the metal 

strip. The cable is actually part of a simple electrical circuit which 

includes, at the surface, a battery and a pair of earphones, as shown 

in figure 11. Thus, with each revolution of the blade the circuit is 

closed for an instant, and a click is heard in the earphones. A record 

of the number of clicks heard in a given time interval indicates the 

number of revolutions that occurred in that interval.

The relation between fluid velocity and the rate of rotation of the 

turbine blade is difficult to analyze theoretically. It depends upon 

the design and inertia of the blade, the friction in the bearings, and 

the relation between the total flow through the well bore and the flow 

through the cylindrical turbine housing. In general, increases in 

the velocity of flow in the well produce increases in the rate of revolution of the turbine blade, but the response is not necessarily linear. 

The relation between velocity and meter response is determined by empirical calibration. A centering device attached to the meter insures 

that the meter response is a measure of the prevailing velocity, vm 

(% 2).

The meter tested by the authors shown in figure 12 was equipped 

with flexible rubber flow guides designed to channel maximum flow 

into the turbine housing. Thus equipped, the meter must be calibrated in terms of volumetric discharge, or average borehole velocity, 

for each well diameter in which it is to be used.

CALIBRATION AND RELIABILITY

A calibration curve for the meter tested by the authors is shown 

in figure 13. The curve shows the performance of the meter for flows 

of 2 to 8 f pm in a casing 13 inches in diameter. It represents the most 

reasonable fit that could be made to plots of the experimental data. 

The maximum deviation of plotted measurements from the curve is 

approximately 0.2 fpm, which indicates that errors greater than 3 

or 4 percent are not likely in the use of this meter in a 13-inch well. 

This is true, of course, only if the flow velocity in the borehole is in 

the ranges covered by figure 13, the instrument is centered in the well 

as it was during calibration, and the measurements of revolutions per 

minute are at least as accurate as those made during calibration.

In obtaining the data for figure 13 the time necessary for 30 revolutions was measured by a stopwatch. The watch was started at a click,
METHODS OF FLOW MEASUREMENTS IN WELL BORES C-21

FIGURE 12. Photograph of Au deep-well current meter equipped with rubber flow guides. 

Reel, cable, and accessor}- equipment are shown.

and stopped at the 30th following click. The time intervals involved 

were more than 1 minute in all cases, and random errors in time measurement should, therefore, be quite small. If the meter is used where
C-22 GENERAL GROUND-WATER TECHNIQUES

7

LU

1 6

C£L

LU

t 5 LU 

LU

5 4

LU

= 3

e

S 2 LJJ

> 

1

0

i i i i i r

5 7 9 11 13 15 17 19 21 

CLICKS PER MINUTE

FIGURE 13. Calibration curve for Au deep-well-current meter.

rapid measurements of discharge are required, the time interval available for each measurement may be considerably less than 1 minute, 

and the reliability of the measurements will be lessened correspondingly.

The meter tested by the authors gave no response to flows of less 

than 2 fpm. This fact illustrates a defect common to all turbinetype meters; there is always a limiting velocity below which the rotor 

will not turn. This limit should always be determined during calibration. There are various factors which will cause a meter of this 

type to have an upper limiting velocity above which the device fails 

to indicate further increases in flow reliably. In general, however, 

the flow velocities in wells are relatively low, and the upper operating 

limit of a meter is seldom exceeded in the field.

It should be noted that because of the cable and supports above the 

rotor, and because of the presence of packers or flow deflectors in some 

instruments, calibration may be different for downward flow than for 

upward flow. If possible, therefore, calibration curves for downward flow should be constructed by suspending the meter in a well 

casing, beneath the water level, and pumping water into the well. 

During flow measurement in the field, direction can be determined 

by raising or lowering the meter. If the revolutions per minute of 

the rotor decreases as the instrument is raised, the flow is upward; 

if they increase as the meter is raised, the flow is downward. When 

the direction of flow is known, the velocity can be determined by
METHODS OF FLOW MEASUREMENTS IN WELL BORES C-23

holding the meter in a fixed position and consulting the proper calibration curve.

SUMMARY

The Au meter is probably the most widely used flowmeter in the 

U.S. Geological Survey. With suitable centering and flow-channeling 

equipment it gives good results for discharge measurements in which 

the average flow velocity within the well bore exceeds 2 fpm. Its 

simplicity of design minimizes equipment failure in the field and contributes greatly to the reliability of the instrument.

The Au meter is unsatisfactory, however, for the measurement of 

slow flows and in applications which require a rapid series of flow 

measurements. Also, it is generally impossible to log continuously 

with the device, as each measurement must be made with the meter 

in a fixed position. Despite these disadvantages the Au meter remains one of the best available methods of borehole flow measurement 

available.

REVIEW OF OTHER METHODS OF FLOW MEASUREMENT

FLOWMETERS IN USE IN THE OIL INDUSTRY

Various turbine-type meters, generally more complex than the Au 

meter, have been used by the oil industry. The basic principle is 

the same some sort of rotor is driven by moving water at an angular 

rate which is proportional to the flow velocity within the well bore 

but refinements have been introduced in the methods of recording, in 

the design of the housing, and in other respects. Rumble and others 

(1959) describe a turbine-type meter that records by making and 

breaking an electric circuit three times during each revolution of the 

rotor. The device indicates the direction of flow as well as the rate, 

as the circuit actuators are unevenly spaced, and different pulse 

sequences are obtained for different directions of rotor revolution. 

An inflatable packer serves to center the instrument and to force all 

flow through the turbine chamber. Dale (1949) describes a turbine 

instrument in which the revolutions of the rotor are recorded through 

an optical-electrical system as a series of dashes on a moving film. 

The instrument may be equipped with flow guides of various diameters 

to center it, as well as to channel flow into the rotor housing. The 

helical rotor is extremely light in weight, and will respond to the 

flow of both gases and liquids.

A thermistor flowmeter has been described by Morgan and others 

(1948). The measurement of flow is made by a single thermistor 

which is heated by an electric current. This current is held nearly 

constant. Moving liquid or gas cools the thermistor and causes a
C-24 GENERAL GROUND-WATER TECHNIQUES

change in resistance, which results in a change in the voltage required 

to maintain the heating current at a constant level. These voltage 

changes are recorded and indicate the flow rate. The instrument 

contains a second thermistor, in an essentially separate circuit, which 

is used to measure fluid temperature. The meter has been used successfully in the measurement of gas flow.

Vincent and others (1948) described a meter that utilizes a hot-wire 

anemometer as the flow-detecting element. The anemometer constitutes one branch of a wheatstone bridge circuit. A second branch of 

the bridge is placed in the flow stream to compensate for temperature 

variations in the well fluid. The bridge circuit permits accurate 

measurement of the resistance of the hot wire, which varies owing to 

the cooling effect of the moving fluid, and the change in resistance 

provides a means of measuring the fluid flow. The authors report the 

use of the device in determining the producing ability of gas sands.

Piety and Wiley (1952) described another instrument that utilizes 

the hot-wire principle. The meter consists of a cylinder divided into 

two coaxial flow tubes. A packer extends from the exterior of this 

cylinder to the borehole wall, so that all fluid moving in the borehole 

must pass through one of the two flow tubes. The interior tube contains a small pump, and the outer tube contains the hot-wire element. 

The pump is controlled from the surface and is calibrated in terms 

of rotational speed versus fluid discharge. Continuity requires that 

when the pump is operating at the particular discharge that exist? 

in the well bore, no flow will pass through the outer tube. Cooling 

of the hot wire will obviously be at a minimum in this condition. 

Flow measurements are made by adjusting the pump speed until an 

indicator shows that the hot-wire temperature has reached a maximum. Then, the borehole flow is equal to the calibrated output of 

the pump. At lower pump speeds a part of the borehole flow passes 

through the outer tube, and at higher pump speeds a fraction of the 

pump output recirculates through this tube. Under either of the 

latter two conditions there will be cooling of the hot-wire element. 

The meter has been used successfully for water injectivity profiling.

Bardeen and Teplitz (1956) described a meter that responds to the 

pressure differential between the interior and exterior of a tube that 

has wide flow-inlet openings but a restricted outlet opening. The 

pressure differential causes a proportional deflection in a diaphragm 

in the wall of the tube. This deflection is recorded electrically by placing a potential electrode on the diaphragm and recording voltage differences as the position of this electrode varies between two fixed current electrodes. The instrument is designed to detect zones of lost
METHODS OF FLOW MEASUREMENTS IN WELL BORES C-25

mud circulation; the inlet openings are at the upper end of the 

cylinder.

RADIOACTIVE-TRACER METHODS

Radioactive tracers have been used in the oil industry for flow measurements within the well bore and could easily be used in water wells 

for the same purpose. Bird and Dempsey (1955) reported two methods of measuring flow by using beads of a plastic material in which a 

radioactive isotope has been dissolved. One method is exactly analogous to the brine-tracing technique, except that a group of these 

radioactive particles is released in place of the brine slug, and a radioactivity-logging device is used in place of the conductivity-logging 

device.

The second method, used in the water-injection wells of secondary 

recovery projects, makes use of the fact that as water containing these 

radioactive particles enters a porous medium, the particles are filtered 

out on the face of the medium. A container of the particles is broken 

in the well during the flooding process, and the relative number of 

particles that filter out on the face of each sand zone is proportional 

to the fraction of the well input that is entering that zone. A radioactivity log run shortly after the slug injection indicates the relative 

amounts of the tracer that have filtered out at each zone.

CONCENTRATION-TIME METHODS

Barbagelata (1928) described a method of flow measurement involving the use of injected brine, which has yielded excellent results in 

application to channel flow. A variation of this method might be used 

in a well where certain difficult measurement problems exist. For example, if velocities are too low for detection with any type of flowmeter, and if the depth interval of measurement is too short for safe 

application of the brine-tracing procedure, the method may prove 

useful.

The method depends upon the equation

N=Q ft2 C(t)dt (1) Jla

in which N is the total number of particles of a certain type injected 

into a flow, Q is the fluid discharge (volume/time), C(t) is the concentration of the injected particles (particles/volume) at a given 

instant at the point of measurement, and t is time. C(t] is a function 

of time and is considered constant across the flow cross section at the 

point of measurement; and ti and t2 are two times chosen so that all the 

injected particles pass the point of measurement between ti and £2 , Q is
C-26 GENERAL GROUND-WATER TECHNIQUES

considered constant during the interval (t^ t2 }. The equation 

sums the products

each of which gives the number of particles that have passed the 

point of measurement during the interval A£.

The application of equation 1 to the measurement of flow requires 

first, knowledge of the total number of injected particles; second, a 

determination of C(t) in sufficient detail to permit evaluation of the 

integral, and finally, some method of insuring that the concentration 

at a given instant is uniform across the flow area at the point of 

measurement.

In the technique under discussion, a salt solution of some sort is 

injected into the interval of measurement. It is convenient, in this 

case, to consider the injected quantity of brine as divided into small 

units of volume for example, cubic millimeters each of which constitutes a particle of the sort referred to in the preceding paragraphs. 

Concentration of injected particles may then be expressed in terms 

of cubic millimeters of brine per gallon of borehole fluid. If the 

equipment described on page C-3 for the brine-tracing method is used, 

measurement of the quantity of brine in the reservoir before and 

after injection provides a simple method of determining the injected 

quantity. A uniform concentration of brine across the borehole 

area might be obtained by using an injection hose which is perforated 

radially over an interval of several feet. The greatest difficulty occurs 

in determining G(t] by use of fluid-conductivity data.

The fluid-conductivity electrode is held in a stationary position 

downstream from the interval of injection. The electrode and injection device should both lie in an interval from which it is reasonably 

certain that no water is leaving the borehole. As the brine is carried 

past the electrode, a record of conductivity as a function of time is 

made. This record must be converted into a record of concentration 

as a function of time by a previously established relation between 

conductivity and concentration.

It is difficult to theorize the nature of this relation between conductivity and the concentration of injected brine, other than to say that 

an increase in concentration will produce an increase in conductivity 

The main reason for this vagueness lies in the fact that the sodiumchloride solution is injected into water which generally contains some 

unknown original concentration of this salt, together with various 

unknown concentrations of other salts. Under these conditions it is 

impossible to make a precise theoretical prediction as to how the injected solution will affect the conductivity as very little quantitative 

data are available on the total conductivity of mixtures of electrolytes.
METHODS OF FLOW MEASUREMENTS IN WELL BORES C-27

While the conductivity of individual electrolytes may be known, the 

total conductivity of a mixture of these electrolytes cannot be predicted because of the complex interaction between ions. In cases where 

sodium chloride is the only salt present in appreciable quantity, a 

linear relationship between conductivity and concentration can be 

applied for a wide range of concentrations; however, the assumption 

that sodium chloride is the only important solute is usually not justified in dealing with ground water. Thus, an empirical relation between conductivity and the concentration of injected brine must be 

established. This empirical relation may be obtained in the laboratory if it is possible to obtain a water sample from the depth interval 

in which the measurement of flow within the well is to be made. A 

graph showing conductivity versus concentration of injected brine 

can be constructed, and it can be used to convert the field conductivity 

readings to brine concentrations.

A graphical evaluation of the integral in equation 1 is the most 

convenient solution. After the conductivity data has been converted 

to brine concentration, a plot of concentration versus time is prepared 

for the interval ti to t2 . The area under this graph is measured to 

give the value of the integral, and equation 1 may then be solved for Q.

The injected-brine method is, of course, troublesome. The development of more elaborate equipment specifically designed for this 

method might possibly increase the ease and efficiency of field operations, but at present both the operational difficulties and the possible 

sources of error are numerous. Using the equipment described in 

the discussion of brine tracing, the authors were unable to obtain acceptable results from the method; this failure may have been due to 

errors in the relation used to convert conductivities to brine concentrations. The method is included in this discussion because it is felt that 

it can be made to work, if experimental techniques are improved, 

and because there are a few measurement problems for which no other 

method seems adequate.

A radioactive-tracer method similar to the brine-dilution method 

of Barbagelata has been used in pipe-flow measurement (Hull, 1955). 

In this method a slug of tracer is substituted for the brine slug, and 

a counter is substituted for the conductivity bridge. The method 

might be adapted for well-bore measurements, using radioactivitylogging equipment, and could conceivably avoid certain of the disadvantages of the brine-dilution method.

The use of radioactive tracers in this connection emphasizes the 

generality of equation 1 and the methods based upon it. It is not 

necessary to use brine in measuring flow by this technique, as any 

substance which can be injected easily, and whose concentration can
C-28 GENERAL GROUND-WATER TECHNIQUES

be measured by an instrument suspended in the well, should be satisfactory. It may, in fact, be worthwhile to seek some injection substance whose detection is unaffected by natural substances in the well. 

The conductivity measurement, as indicated above, is affected by ions 

present naturally in the well water; a radioactivity measurement, in 

the same way, might be affected by the natural radioactivity of the 

wall rock. Difficulties of this sort would be avoided in a system in 

which the measuring device could respond only to injected material.

REFERENCES CITED

Barbagelata, A., 1928, Chemical-electric measurement of water: Am. Soc. Civil

Engineers Proc., v. 54, p. 789-802. 

Bardeen, T., and Teplitz, J. A., 1956, Lost circulation information with a new

tool for detecting zones of loss: Jour. Petroleum Technology, February,

p. 36-41. 

Bird, J. M., and Dempsey, J. C., 1955, The use of radioactive-tracer surveys in

water-injection wells: Kentucky Geol. Survey Spec. Pub. 8, p. 44-54. 

Chapman, H. T., and Robinson, A. E., 1962, A thermal flowmeter for measuring

velocity of flow in a well: U.S. Geol. Survey Water-Supply Paper 1544-E

E-l-E-2. 

Dale, C. R., 1949, Bottom hole flow surveys for determination of fluid and gas

movement in wells: Am. Inst. Mining Metall. Engineers1 Trans., Petroleum

Devel. Technology, v. 186, p. 205-210. 

Fiedler, A. G., 1927, The Au deep-well current meter and its use in the Roswell

artesian basin, New Mexico, in Methods of exploring and repairing leaky

artesian wells: U.S. Geol. Survey Water-Supply Paper 596-A, p. 24-32. 

Hull, D. E., 1955, Using tracers in refinery control: Nucleonics, v. 13, no. 4,

p. 18-21. 

Morgan, F., and others, 1948, Meter for measuring distribution of gas flow in

well bores: Am, Inst. Mining Metall. Engineers Trans., Petroleum Devel.

Technology, v. 174, p. 253-268. 

Peity, R. G., and Wiley, B. F., 1952, Flowmeter for injectivity profiling: World

Oil, May, p. 176-186,188. 

Rumble, R. C., and others, 1959, New subsurface flowmeter developed by Humble

research engineers: Oil and Gas Jour., May, p. 104-107. 

Skibitzke, H. E., 1955, Electronic flow meter: U.S. Patent No. 2,728,225. 

Vincent, R. P., and others, 1948, Well flowmeter for logging producing ability

of gas sands: Am. Inst. Mining Metall. Engineers Trans., Petroleum Devel.

Technology, v. 174, p. 305-314.

o