**by GH Nelson · Cited by 1 — FIG. 1- TYPICAL FIELD SETUP FOR WELL PRODUCTION TEST USING MANUAL BUBBLER SYSTEM IN PUMPED WELL. the water level in the glass cylinder to rise above the.
35 pages**

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REPORT OF INVESTIGATION NO. 23 1954 STATE OF ILLINOIS WILLIAM G. STRATTON, Governor Bubbler System Instrumentation For Water Level Measurement by Gerald H. Nelson DEPARTMENT OF REGISTRATION AND EDUCATION VERA M. BINKS, Director STATE WATER SURVEY DIVISION A. M. BUSWELL, Chief URBANA, ILLINOIS (Printed by the authority of the State of Illinois)

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REPORT OF INVESTIGATION NO. 23 1954 STATE OF ILLINOIS WILLIAM G. STRATTON, Governor Bubbler System Instrumentation For Water Level Measurement by Gerald H. Nelson DEPARTMENT OF REGISTRATION AND EDUCATION VERA M. BINKS, Director STATE WATER SURVEY DIVISION A. M. BUSWELL, Chief URBANA, ILLINOIS (Printed by the authority of the State of Illinois)

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TABLE OF CONTENTS Page ABSTRACT 1 ACKNOWLEDGMENT 1 INTRODUCTION 2 BUBBLER SYSTEM 4 Introduction and Description of Basic Components 4 Discussion of General Principle of Operation 4 Laboratory Studies for Development of Adapted Bubbler System 6 Flow Control 6 Equipment and Procedure 7 Results 8 Evaluation of Effective Bubble Pressure 9 Equipment and Procedure 9 Results .. 10 Frictional and Deformational Characteristics of Plastic Airline Tubing 10 Equipment and Procedure . 11 Results 11 Laboratory and Field Studies on Adapted Bubbler System 13 Description of Equipment Developed 13 Static Accuracy Tests 13 Equipment and Procedure 15 Analysis of Data 15 Results 16 Field Test 17 Equipment and Procedure 17 Analysis of Data 17 Results 20 Laboratory Tests of Field Methods of Water Level Measurement 20 Procedure 20 Results 20 CONCLUSIONS AND RECOMMENDATIONS 21 APPENDIX I: Calculation of Approximate Data Corrections 23 Assumptions 23 Required Data 23 Typical Data: Field Setup 23 Typical Data: Laboratory Setup.. 23 Correction of Field Data 23 (B + C) (WCO2): The Pressure Exerted by Vertical Column of CO2 in the Airline .. 23 Assumptions 23 Procedure and Example 23 hL: Airline Frictional Head Loss 25

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Assumptions 25 Procedure and Example 25 B(wair): Pressure Exerted by a Vertical Column of Air in the Casing Between the Datum and the Water Surface 26 Assumptions 26 Procedure and Example 26 Pb: Effective Bubbler Pressure 26 Summary 26 Correction of Laboratory Data 26 (D + E) (wCO2): Pressure Exerted by a Vertical Column of CO2 in the Airline 26 Assumptions 26 Example 27 hL: Frictional Head Loss 27 Assumptions 27 Example 27 (D + F) (wCO2): Pressure Exerted by Vertical Column of CO2 in the Pressure line 27 Assumptions 27 Example 27 Pb: Effective Bubble Pressure 27 Summary 27 APPENDIX II: Other Sources of Bubbler System Error 28 APPENDIX III: List of Symbols 30

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1 ABSTRACT To meet the frequent needs of engineers of the Illinois State Water Survey for a portable automatic water-level measuring instrument, a method for precise measurement of water levels in observation wells, utilizing bubbler system instrumentation, has been developed for well production tests. Since no summary of the possible sources of error in bubbler systems was found in the literature, these were investigated and the various forces affecting the accuracy of bubbler systems are discussed in this report. The material presented herein may be adapted to develop instrumentation for measuring liquid levels (or specific weights) for a number of industrial, chemical or hydrologic applications where basic data-gathering accuracy is of primary importance. A procedure based This Report of Investigation describes all significant research work and derived results from a project carried out by the staff of the Illinois State Water Survey Division’s Hydraulic Laboratory Section pursuant to a request from the Groundwater Section. Laboratory work on this project was done under the supervision of H. E. Hudson, Jr., Head of the Engineering Subdivision. A preliminary exploration of the problem was carried on by R. E. Roberts in the summer of 1952. The author on approximate formulas derived from hydrostatics was worked out for computing the required corrections to bubbler system data. Other field methods of water level measurement used by Survey engineers for production-test, water-level measurement were also checked to determine the accuracy obtainable. A laboratory comparison of bubbler system instrumentation with methods now in use showed the measurement errors, using the bubbler system, to be one-fourth to one-tenth those obtained with the usual field measuring devices. Field trial of the bubbler system gave favorable results. The linear accuracy of bubbler system data analyzed by the equations presented herein was found to be almost entirely dependent upon the accuracy of the pressure – indicating device used to measure airline pressure. wishes to acknowledge the contributions of Donald H. Schnepper, Professor V. T. Chow, and Professor J. C. Guillou, members of the University of Illinois Civil Engineering Department and also J. C. Buchta and Dr. Max Suter for technical review of this report and many valuable suggestions. Mr. G. A. Flom and Mrs. J. L. Abu-Lughod drafted the figures which appear in this report and Ray A. Schuster assisted with the editorial work. ACKNOWLEDGMENT

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2 INTRODUCTION Since 1895, the Illinois State Water Survey has provided services and conducted research for the citizens of the State of Illinois. The Groundwater Section of the Survey’s Engineering Subdivision has, as one of its functions, the responsibility to encourage and observe pumping tests on municipal and private water wells in the state. Over 1300 pumping tests have been completed to date under the direction of the Survey. The data taken during these pumping tests are analyzed by the Survey staff and sent to the engineer involved, to waterworks personnel and the State Department of Health, so that they may readily determine the yield potential of the aquifer tested. Except for state-owned property, the Survey does not evaluate the data for the well owner; rather it provides aid in securing the basic data and presenting it in a form that may be easily used by the engineer in charge, who is acquainted with the immediate problems on location. A pumping test is the everyday name for a “well production test.” When a new well has been drilled for a municipality, city officials are naturally interested in knowing how good the well is. This knowledge is necessary to determine what size pump will be required, where to set the bowls, and what to expect in the way of longtime yield from the water-producing formation. A pumping test is usually conducted to secure data to help answer these questions. A pump is temporarily set in place. Preferably, pumping is continued at a constant rate for several hours, possibly even three or four days, depending on the case. The discharge from the well is maintained at a constant rate, usually by a valve-orifice arrangement, and the distance to water is recorded at known times throughout the test. The difference between the non-pumping level and the pumping level is called the drawdown. Notice in Figure 1 that a simple bubbler system is being used to measure the water level in the pumped well. The hand pump forces air down through the airline. The air under pressure displaces water that would normally fill the airline. As water is displaced, the pressure . increases until air bubbles out of the bottom of the airline. -A gage with a scale of pressure values marked off in “ft of water” may be used to measure airline pressure. The maximum reading on the pressure gage indicates to a first approximation the “head of water” over the bottom of the airline. If the length of the airline is known, the distance from the top of the casing to the water level may be determined by subtraction. This type FIG. 1- TYPICAL FIELD SETUP FOR WELL PRODUCTION TEST USING MANUAL BUBBLER SYSTEM IN PUMPED WELL.

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4 BUBBLER SYSTEM Introduction and Description of Basic Components Although industrial concerns may use direct or electrical methods for measuring liquid levels, they have found bubbler system (or air-purge) instrumentation advantageous when liquid level measurements must be taken from many scattered storage tanks. An industrial application of the bubbler system method is shown in Figure 2. FIG. 2-INDUSTRIAL APPLICATION OF BUBBLER SYSTEM INSTRU-MENTATION TO MEASURE TANK LEVELS. As may be noted from Figure 2, three components are necessary for a bubbler system setup: (1) a flow control device, (2) an instrument to measure pressure, and (3) an airline and instrument tubing. The flow control device is merely a metering device which can maintain a known rate of gas flow down the airline. When the bottom of the airline can be observed, the rate of flow is usually adjusted so that ten to fifteen bubbles form per minute. A pressure-sensing instrument is required to indicate the airline pressure. Air is commonly used to purge the liquid out of the airline. Obviously, the gage pressure at the airline nozzle is due to the hydrostatic head of liquid above this elevation. If the pressure difference between the nozzle elevation and the recorder is negligible, the pressure recorder or gage reading is a measure of the water level above the bottom of the airline. The pressure recorder may be located on the control panel of the instrument room along with other similar instruments and the operator can tell at a glance what is going on in his section of the plant. This method may also be used to determine the density or specific gravity of liquid chemicals during their manufacture. In this case, as shown in Figure 3, two airlines are used. The pressure recorder actually registers the difference in pressure between two levels but may also record the specific gravity of the fluid if the scale is graduated properly. The Peoria Laboratory Subdivision of the Survey is now using a modified bubbler system to measure liquid levels in two head tanks connected to a venturi meter that meters silt-laden raw river water. Besides these applications, the system has also been used to measure liquid levels in tanks, sewer lines, rivers, etc. The above description of a basic bubbler system application is rather simplified. This simplification is justified when small changes of level are to be measured. If large ranges are to be measured the factors causing the discrepancy between observed and true values should be investigated to correct the pressure recorder reading so that a reasonable linear value of error is realized. The figures and diagrams used in the remainder of this report, as well as the examples cited, will be concerned with the immediate problem of measuring water levels in wells. The subject matter is general however, and can be applied to any situation desired. Discussion of General Principle of Operation In order to clarify some of the factors, not readily apparent, which affect the accuracy of the bubbler system, a field setup using carbon dioxide as the purge gas is illustrated in Figure 4. Two parts of the equipment shown are not commonly used and are described in detail later: the electromagnet to hold the bubbler nozzle against the steel casing at a given elevation, and the carbon dioxide bottled gas cylinder and pressure reducer. However, these modifications do not affect the general principle of operation. FIG. 3-INDUSTRIAL APPLICATION OF BUBBLER SYSTEM INSTRUMENTATION TO MEASURE SPECIFIC GRAVITY. Assuming static conditions of water level, a manometer type equation of pressures may be devised involving the known and unknown parameters: Where: Pa = atmospheric pressure, A, B, and C are distances measured in feet, A and (B + C) are known, (used in conjunction with F igure 4 and the analysis of field data), (wair) = specific weight of air in lbs/ft3 at known atmospheric pressure and temperature conditions, (wH2O) = actual specific weight of water at a known temperature in lb/ft,3

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(wCO2) = specific weight of carbon dioxide gas under known temperature andpressure conditions expressed in lb/ft,3 Pb = the effective pressure required to make a bubble form and break away at the nozzle elevation (expressed in ft of water), hL = frictional head loss in the airline expressed in ft of water, and Pr = pressure recorder reading in ft of water. Equation 1 may be derived from well-known principles of hydrostatics. It is necessary to assume an arbitrary sign convention such as: (+) when the pressure is increased in the direction of travel around the bubbler system circuit and (-) when the pressure is decreasing in the direction of travel. The pressure at the datum is atmospheric (Pa). The pressure at the water surface inside the well is [Pa + B(wair)]. The pressure in the water at the bubbler nozzle is [Pa + B(wair) + C(wH2O) ]. The remaining terms in Equation (1) may be written in a similar manner by moving up the airline to the pressure recorder and finally back to the datum. By canceling Pa and assuming A = 0 (the pressure recorder 5 FIG. 4-SCHEMATIC OF FIELD SETUP USING ADAPTED BUBBLER SYSTEM.

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6 is usually situated at the datum), it is possible to solve for C(wH2O) directly: From equation (2) it is possible to solve for the submergence of the nozzle (C) by either multiplying the entire equation by 1/(wH2O) or by originally expressing all pressures in “ft of water.” Therefore, if C can be calculated, the distance from the datum to the water level may be found by subtracting C from the known (B + C) measurement. Since the elevation of the top of the casing is known, the elevation of the water in the well can be determined directly by subtraction. The problem then reduces to the evaluation of unknowns in Equation (2). As a first approximation, the unknown C (in ft) may be assumed to equal the pressure recorder reading expressed in ft of water if the magnitude of the other corrections is small percentage-wise. This assumption gives us a means of calculating the unknown terms in Equation (2) to their first approximation. For convenience all values in Equation (2) except the pressure recorder reading Pr and C(WH2O) have been termed corrections. The B(wair) correction may be calculated from procedures outline in Appendix I and the Pb, correction will be explained in detail later (Page 9). However, the hL, and (B + C) (wCO2) corrections need further consideration at this time. According to Kemler,1 the latter corrections are interrelated if the airline flow is considered from a theoretical standpoint. If we consider flow down the airline starting at the pressure recorder junction and assume isothermal flow and negligible kinetic energy: where dL is an increment of length measured down the airline, dh = total head loss over this increment, V = velocity through increment or velocity of flow in ft/sec, f = Darcy-Weisbach friction factor for increment, and d = airline diameter in ft. This differential equation cannot be integrated directly since V, the velocity, is also a variable. However, it is possible1 to separate it and by suitable substitution and integration obtain: 1Kemler, E. A., “A Study of the Data on the Flow of Fluids in Pipes,” Trans. A.S.M.E., Hydraulics Division, Vol. 55, No. 10, August 31, 1933, p. 20. e = base of natural logarithms, 2.718 , a = airline cross-sectional area, in ft2, P1 = pressure at top of airline, in lb/ft2, P2 = pressure at nozzle, in lb/ft2, w1 = specific weight of the gas at the top of the airline in lb/ft3, W = flow rate of gas in lbs/sec, g = local acceleration of gravity in English units, L = length of the airline in ft, and µ= absolute or dynamic viscosity of the purge gas at a known temperature. As shown in its simplest form, Equation (4) is difficult to solve for P2 and is only as correct as the assumptions used in its derivation. Neglecting kinetic energy is a reasonable assumption. For example, the maximum airline velocity head encountered in this study (CO2 gas at a maximum flow rate of 6.45 x 10-6 lbs/sec, atmospheric airline pressure and airline diameter of 0.01077 ft) equalled about 1.1 x 10-6 ft of water. Equation (4) was derived for a straight vertical airline and its accuracy is also almost entirely dependent upon the constancy of both C1 and C2. These conditions are usually not found in the field. In an attempt to obtain a workable correction formula, it was decided to assume that the velocity term in Equation (3) was, for all practical purposes, a constant. Then it would be possible to integrate directly. Laboratory tests, which are described later, established that highly satisfactory results could be obtained by calculating hL and (B + C) (wCO2), separately, instead of using Equation (4). Methods for the calculation of these corrections are presented in Appendix I. One more correction must be evaluated before Equation (2) can be solved for C(WH2O)- This correction is Pb, the effective bubble pressure. Laboratory tests (described below) were conducted to evaluate this unknown, empirically, for the particular nozzle shape used. Laboratory Studies for Development of Adapted Bubbler System Flow Control To evaluate the hL correction, the flow rate must be known. Three different types of commercial flow-control devices were secured and tested. In addition, two glass capillary tubes were constructed and tested.

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7 Equipment ancPProcedure: The liquid displacement method is almost universally accepted as a standard of gas flow measurement.2 This method was employed in the calibration of the flow control devices tested. The construction and setup in the laboratory is shown in Figure 5. Using this device, the rates of flow under various differential pressure conditions, were measured. FIG. 5 – LABORATORY SETUP OF GAS FLOW MEASUREMENT UNIT. A schematic sketch of the essential components of this gas measurement calibration unit is shown in Figure 6. FIG. 6-SCHEMATIC OF POSITIVE DISPLACEMENT METHOD OF GAS FLOW MEASUREMENT. 2Westmoreland, J. C., “Metering Gas Flow”, Instrumentation, Vol. 6, No. 4, First Quarter 1953, p. 27. To insure saturation, gas was allowed to bubble through the displacement liquid (water) for several hours prior to starting the tests. At the start of each test, valve A was opened and the storage tank was elevated, forcing the water level in the glass cylinder to rise above the top etch mark. Valve A was then closed, forcing gas to flow into the glass measurement cylinder. As the gas depressed the water level in the glass cylinder, the storage tank was lowered manually so that level 1 was maintained at the same elevation as level 2. The time required for level 2 to travel between the two etch marks on the glass cylinder was recorded. (This amounted to catching 0.031610 ft3 of the gas at atmospheric pressure in a known time.) Both gas temperature and barometric pressure were recorded during the calibration. The specific weight of the gas was computed from the ideal gas law, pv = nRT, and the calibration results were reported graphically. Three types of commercial flow-regulating instruments and two glass capillaries were calibrated using the above method of gas measurement as the primary standard. The commercial instruments were individually mounted and levelled in position as shown in Figure 5. The discharge line from each of these instruments was connected to the intake of the gas measurement unit. The intake line pressure for the flow control instrument was maintained at a known pressure by a welding pressure regulator. Both air and carbon dioxide were used in the calibration of the commercial instruments. Figure 7 shows a capillary tube constructed by “flame pulling” of one-quarter inch thick-walled glass tubing. A considerable amount of care was exercised in handling the capillary to avoid breakage during coiling. A brace between the two end sections was provided to add to the structural soundness. The capillary was then mounted inside a protective housing constructed of two-inch pipe fittings. The ends of the capillary were fitted with drilled-out plastic pipe bulkhead unions packed with string and non-hardening gasket material. A metal to glass joint was obtained which could stand 300 psi at a temperature of 120°F without leakage. FIG. 7-TYPICAL GLASS CAPILLARY TUBE. The setup for calibration of these capillary tubes is shown in Figure 8. To the right of the box containing the carbon dioxide cylinder and regulators is a constant-temperature water bath. A mercury manometer is located directly in front of the bath. The gas flow liquid displacement meter is located in the background. Figure 9, a sketch of the equipment, will aid in understanding its operation.

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