UNITED STATES DEPARTMENT OF THE INTERIOR Harold L. Ickes, Secretary GEOLOGICAL SURVEY W. C. Mendenhall, Director Water-Supply Paper 887 METHODS FOR DETERMINING PERMEABILITY OF WATER-BEARING MATERIALS WITH SPECIAL REFERENCE TO DISCHARGING-WELL METHQDS 3 BY * L. K. WENZEL WITH A SECTION ON " v DIRECT LABORATORY METHOD^ AND BIBLIOGRAPHY ON PERMEABILITY AND BY V. C. FISHEL UNITED STATES GOVERNMENT PRINTING OFFICE WASHINGTON : 1942 For sale by the Superintendent of Documents, Washington, D. C. ..-.--- Price 60 cents CONTENTS Page Abstract- _ _ ______-________-______-_--_------_-_-_-_-------_-____ 1 Introduction._____________________-----_--__----_---_---_---______ 2 Acknowledgments. _____-_____________-_-_-___---_--______---______ 2 The Darcy law and its relation to permeability _____________________ 3 Statement of Darcy's law.__________-_____---_-_-_-_-_-________ 3 Laboratory investigations on flow of fluids________________________ 4 Coefficient of permeability____________________________________ 7 Permeabilities of natural earth materials.__ __________________________ 11 Organizations making permeability tests in the United States.________ 19 Bibliography ou permeability and laminar flow, by V. C. Fishel_________ 20 Methods for determining permeability.______________________________ 50 Laboratory methods.__________________________________________ 50 Indirect methods-...______________________________________ 50 Hazen formula_________-___-_-___-_-_-___-___-________ 50 Slichter formula.______________________________________ 52 Terzaghi formula._____________________________________ 54 Hulbert and Feben formula_____________________________ 54 Fair and Hatch formula______________________________ 55 Direct methods__________________________________________ 55 Discharging apparatus, by V. C. Fishel ________________ 56 Constant-head apparatus.__________________________ 56 Variable-head apparatus _________________________ 59 Nondischarging apparatus, by V. C. Fishel.______________ 66 Comparison of methods.___________________________________ 68" Field methods._________________-----_-_-__----_-_-_-_-_-______ 71 Ground-water velocity methods_____________________________ 71 Dye methods..___--_-__------_-_--_-__----___--_____- 72 Salt methods_--______--__--_---_-_-_--_--------_______ 73 Chemical method___-_-_-_________-________________ 73 Electrolytic method _____________________________ 74 Discharging-well methods_________________________________ . 75 Draw-down methods.__________________________________ 76 Equilibrium methods._ ____________________________ 76 Fundamental principle of equilibrium formula. ____ 76 Simple development of general equilibrium formula. 77 Equilibrium formulas._________________________ 79 Slichter formula.__________________________ 79 Turneaure and Kussell formula.____________ 80 Thiem formula.___________________________ 81 Israelsen formula._________________________ 82 Wyckoff, Botset, and Muskat formula.______ 82 Limiting formula._________________________ 83 Gradient formula._________________________ 85 Non-equilibrium method.__________________________ 87 Relation between equilibrium and non-equilibrium fo"- mulas __________________________________________ 90 Methods based on change in rate of discharge frcrrx wells_______________________________________ 91 Application of equilibrium method...____________ 91 Application of non-equilibrium method___________ 92 ra IV CONTENTS Methods for determining permeability Continued. Field methods Continued. Discharging-well methods Continued. Page Recovery methods.____________________________________ 94 Slichter formula for determining specific capacities of wells.__________________________________________ 94 Theis formula_____________________________________ 95 Muskat formula-__________________________________ 96 Advantages and disadvantages of discharging-well methods. " 97 Behavior of the water level in the vicinity of a discharging welL________ 98 Behavior of the water level in the vicinity of a well after its dircharge has stopped ________________________________________________________ 101 Effect of differences between theoretical assumptions and field conditions on permeability methods.________________________________________ 102 Initial sloping water table or piezometric surface._________________ 102 Heterogeneity of water-bearing material._________________________ 104 Extent of cone of depression.___________________________________ 107 Partial well penetration._______________________________________ 109 Slow draining of water from water-bearing material._______________ 110 Vertical percolation_______________________________-____________ 111 Miscellaneous differences _______________________________________ 111 Procedure for determining permeability by discharging-well methods ___, 112 Collection of field data..____________-___-______-_--_-_-______ 112 Choice of site._____________________ _______'______--______ 112 Preliminary test_----_--__-_____-_____-_---_-_-_---_-_-___- 113 Location of line of observation wells________-_-_-_-___-_____- 113 Method of locating observation wells on a line________________ 114 Construction of observation wells____________-_-_-_-_-___-_- 114 Cleaning observation wells__________________________________ 114 Measuring points __-__--___-_______-____-_-__.__--____- 115 Making water-level measurements. __________________________ 115 Making preliminary water-level measurements ________________ 115 Determining the thickness of water-bearing material ___________ 116 Observations during test.__-________-_______-_____---.____- 116 Observations after test.____________________________________ 116 Interpretation of data_--___-_---___-_----__---__------- ________ 117 Draw-down curves _-___-____-_-_-_---____--_-_-__--_____ 117 Profiles-of the cone of depression____--------_------------__- 117 Computation of permeability__________________-_..__-_--_-_-- 117 Pumping tests in Nebraska and Kansas._______-______-___-__-_-___-- 117 Test near Grand Island._______________________________________ 117 Computations of permeability.._______________-!_____-_______ 122 Limiting formula._____________________________________ 122 Gradient formula..____________________________________ 123 Non-equilibrium formula.______________________________ 124 Recovery formula._______________-_-___--_-__ -_-_-___ 125 Test near Kearney___-_-_______________-__.___-__-__----____- 127 Computations of permeability_________-_________-____-_--__- 129 Limiting formula._____________________________________ 129 Gradient formula._____________________________________ 129 Non-equilibrium formula_______________________________ 130 CONTENTS V Pumping tests in Nebraska and Kansas Continued. Page Test near Gothenburg________________________________________ 131 Computations of permeability_______________________________ 133 Limiting formula.___---__----__-_-_-_-_-__-___-___-___ 133 Gradient formula___________________.__________________ 134 Non-equilibrium formula___---___-__________-______-___ 134 Test near Scottsbluff_________________________________________ 135 Computations of permeability...____________________________ 137 Limiting formula--------__--------_--__--------_-_---_ 137 Gradient formula______________u_________-__________-__ 138 Non-equilibrium formula____-__-___-_______-_-___-_-___ 138 Recovery formula-______-__--___-_-_____-____________- 141 Test near Wichita, Kans_______________________________________ 142 Computations of permeability____---__-__-_-_----_-___-_---_ _ 144 Limiting formula__--__---____----____-_----_-_____-___ 144 Gradient formula._____________________________________ 145 Non-equilibrium formula.______________________________ 146 Comparison of field coefficients of permeability determined by different methods from data collected in pumping tests in Nebraska and Kansas.__-__-__-_______--_----__----_________-__________-__ 146 Method for determining the effectiveness of wells.____________________ 147 Records of draw-down for pumping tests in Nebraska._________________ 151 Grand Island_______________________________'______________-___ 151 Kearney______________________________________________________ 180 Gothenburg_________________________________________________ 183 Scottsbluff _________-_-_-------_---_----_-_------------_-_----- 184 Index..--__-__---___________-___-____--_________-_---_____.___--- 191 ILLUSTRATIONS PLATE 1. Type curve for non-equilibrium formula______-___________ Ir pocket 2. Curve for Grand Island test obtained by plotting s against r2/<_----------------------------------------------- IE pocket 3. Curve for Kearney test obtained by plotting s against r2/2__ In pocket 4. Curve for Gothenburg test obtained by plotting s against r2/2_ In pocket 5. Curves for Scottsbluff test obtained by plotting s against r2/t. _______________________________________________ In pocket 6. Curve for Wichita test obtained by plotting s against r2/._ _ _ In pocket FIGURE 1. Diagram illustrating laboratory and field application of the coefficient of permeability, Pm, expressed in Meinzer's units _____---___---_-_-___--__-_____--____-_-________ 8 2. Diagram of constant-head type of discharging permeability apparatus. _ ______ J ___________________________________ 57 3. Diagram of variable-head type of discharging permeability apparatus- ___________________________________________ 60 4. Diagram of apparatus for collecting and making permeability tests of volumetric samples___________________________ 65 5. Diagram of nondischarging ty pe of permeability apparatus 66 VI CONTENTS