. l o (11". .‘p /‘. 4...! o‘- ‘ .y‘ "l .3. '3 'SUV 1. ,: ,a..- “ -8 ". i ‘x‘ In. '. 4 ‘ 1 1 ‘\ . O ‘ at g I‘.. 'd' \ .a Q" "' ..\ ..\ x “:4: . .\;¢"'9.. . . \J . . . ..; ..- . .;\; .c K‘ . .. ‘v.-v ,n ~ I ' I .: .- Q-_ ,_q : - - oo- ‘ c‘ - s.‘ 1.. .. ‘3 ‘ g _. ..- ‘ . u . _ .‘ §~ \ _ q a r ‘ .-’-'- . . . i" . .‘n; _ - a A. , Z .. ”\‘QL‘S noéoi-ok‘o a d“..\oo’ .\~\.‘ \? ‘-\.— o\~$" ~- k'.\ . u.‘.;a .l . .3 l ' .4. .- ‘ . .' ‘: .. . , ‘ - .1- g " “, 7 . x T . 2‘ \ ' ‘ ’ : ‘5 " o‘~ '~ ‘ - .z ‘ .- \2. s. ,-» x .-~\ ~..~. .u ,. l ..'. ¢\-o Ca‘l-"Il L7 . A) I O x o C . \ \J . 5‘? \. -a. a. o o o .o-udv .. '; K _ I-. I. r“ ‘ . , 2 ' ,v -. \ \l rib-7 h... -~—A— \ . s 0". ‘ g _ 0 '. fl. ‘ ‘ .‘ ‘ 'q’; x .. g.“ or ‘, ‘4'. ‘ I'LQU'JJ ”p ,'\ 9! x! .\ Ooikotc: .3. .08“ ~‘5—-;. ‘w ‘6. 0'5"! ~~ ‘ ' ' (k. ' ' f; I ’.B'. ’ Li'u’- .T§‘.'.~ ' o"‘,:. ‘p 4. f' .5. t ‘ ' E. J: o _‘ ‘ I: g ‘ a“.th Ot\3s“\o\ ‘ 4 0" s ‘5 \JV Lid;\.’. ..' ‘ fl ‘ {2‘ ‘I .~ g s . I ' D r c ' ,a 3 ~ x w \ - 9 - I ”N: , ‘ q. . ‘ - .1, I 1 “\c RE- I - o\o - 0%:- \g u“... u \. n O a .' - , . a . 5' ’n of? 4' ..‘I t 2 Q: I ‘ - - ”issue 9 .' mmmmmmnnnrmlmu ; , 309994 0960 ‘ -y. _ 'l-x This is to certify that the thesis entitled "An investigation of the effects of Sphericity and roundness on the permeability of unconsolidated sediments." presented by Raymond Clair Perry has been accepted towards fulfillment of the requirements for Master of Science degree mm and Geography Major professor Date November 30. 3351 ’I"‘- . I c I.. . . ’ . , J. 3.. .. a .;. z maxed}: 2.9.1‘ 2 « ....:J.fi$.....« 44.: ., f. 1. . .1..., .~ .h: -3..‘._.‘ . 3. 9.». .u wt»... r 3‘... , . o. , AN INVESTIGATION OF THE EFFECTS OF SPHERICITY AND ROUNDNESS ON THE PERPEABEITY 0F UNCONSOLIDATED SEDIMENTS By Raymond Clair Perry, Jr. A IEIESIS Submitted to the School of Graduate Studies of Michigan State College of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Departnent of Geology and Geography 1951 fit: ACKNCNLEIXSEMENTS Ihe writer wishes to express his appreciation to the staff where of the Department of Geology and Geography at Michigan State College for their critical review of the manuscript. Dr. B. 1'. Sandefiar, under whose direction the report was prepared, especially is thanked for his consultations and advice. Mr. Arnold 1. Johnson, Hydraulic Engineer of the Lincoln, Nebraska office of the U. 8. Geological Survey, consented to the use of much valuable information which was the result of his original research. Mr. John G. Ferris and Mr. George H. Taylor of the U. 5. Geological Survey as well as the Ottawa Silica Company of Ottawa, Illinois are thanked for their cooperation. ..af**”f‘f'sf‘nr‘$ ’2 ‘4 .‘W i ..' ' ‘ .3}. QQJ...) '«f-v'nw. L}, 3.» ii Table 8 O O O O O O O O O Illustrations . . . . . AbatrBCteeeeeeee Introduction . . . . . . Method of Investigation Sphericity and Roundness Permeability...... Results........ Conclusions ...... Recommended Future Study Apperflix........ References....... CONTENTS iii Page iv 12 25 28 3O 31 39 Table II III VIII TABLES Sphencity and Roundness of varying counts of the sieved St. Peter . . . . . . Sphericity and Roundness values of the sieved portion of each sample. . . . . Factors for converting a Permeability coefficient at a given water temper- ature to a permeability coefficient at a water temperature of 60°F. . . . . . . . Order of decreasing Sphericity, Round- ness, and Permeability of the various sawleseeeeeeeeeeeeeeeeee 'lhe recorded data from which the St. Peter fine-Permeability curve was constnicted................ ‘Ihe recorded data from which the Eagle Harbor lime-Permeability Curve was constructed................ 'lhe recorded data from which the Grand Marais Time-Pemeability curve was constmcted................ ‘Ihe recorded data fran which the Sleeping Bear lime-Penmability curve was conSthtedOOOOOOOOOOOOOOOO The recorded data fran which the Mason Esker fine-Permeability curve was consthtedeeeeeeeeeeeeeeee ‘me recorded data fran which the Case- ville True-Permeability curve was con-StruCtedOOOOOOOOOOOOOOOO 'lhe recorded data from which the Detroit Beach Tims-Perme ability curve was constructed. 0 0 O O O O O O O O O O O O O 'Jhe recorded data from which the Copper Harbor lime-Permeability curve was CODStrUCtedeeeeeeeeeeeeeeee iv Page 10 19 27 31 32 33 35 37 38 Plate II III IILUSTRATI ONS Map of Michigan and adjacent areas showing the locations from which the sampleswere Obtained. e e e e e e e e e e e A photograph of the apparatus used in the permeability measurements . . . . . . . . She lime-Permeability curves of the St. Peter, Eagle Harbor, Grand Marais, Page 5 16 “fleepingBearsampleS............23 The Time-Permeability curves of the Mason Esker, Caseville, Detroit Beach, andCopperHarborsamples. ........... 2h ABSTRACT lhe effect the gemetric appearance of the constituent particles of a material has on its permeability has been the subject of emperical conjecture, but never the object of a detailed study. 'Lhis report describes the methods used and results obtained in determining the influence of sphericity and roundness upon the permeability of eight selected sand samples. Of the six variables most frequently mentioned as having an effect on permeability namely; size, sorting, shape, arrangement or packing, cementation or lithification, and sedi- mentary fabric, five are believed to have been eliminated by using unconsolidated, sieved samples and a uniform procedure for determining permeability. 'Jhe sphericity and roundness of each sample was measured and correlated with the laboratory determination of its relative permeability. me results indi- cate the more spherical the particles the higher the relative permeability; at least within the limits dictated by the range in sphericity and roundness of the samples which were used. Additionally, either extremity ‘in so far as sphericity is con- cerned, apparently can be modified by abnormal roundness in the opposite direction. ‘Ihus a material composed of grains having a "high" sphericity will have a "high" relative permeability only if the roundness of the particles also is correspondingly high. war? aim/owe— / ////30/ :57 LI) AN INVESTIGATION OF THE EFFECTS OF SPI-IERICITY AND ROUNDNESS ON THE PERMEABILITY OF UNCONSOLIDATED SEDIMENTS By Raymond Clair Perry, Jr. INTRODUCTION 'Ihe most important physical properties of sediments are those related to their pore spaces or ”interstices". 'Ihe ability of a rock to contain fluids within its mass (porosity), and more impor- tant the ability to allow fluid movement (permeability), either natural or artificially induced, is of the utmost importance in the accumulation, migration, geological and geographical distributation, as well as in the extraction of oil, gas, and ground water. Moreover, both porosity and permeability vary within wide limits and are subject to constant revision as the normal geologic processes, from sedimentation through lithification and possibly metamorphism, occur. It may be said that any problems concerning porosity and permeability become more couple: with the progression of these geologc processes. It would seem apparent than that am attempt to understand thoroughly either porosity or permeability must start with a study of natural, unconsolidated, clastics and not with drill core or even well samples. In this respect the ‘writer is in.agreementwwith Graton and Fraser (1935) who studied the problem.extensively from.the theoretical viewpoint and‘whose ‘well known.papers were publidhed.in.the Journal of Geology. ‘Various authors list different factors as contributing to the sometimes puzzling behavior of sediments insofar as their fluid relationdhips are concerned. There is general agreement however, that six particle characteristics are among those factors present. Fraser (1935 ), Pettijohn (191.9), Krmnbein and 81.088 (1951) and LeRoy (1950) indicate the following: 1. Size 2. Shape 3. Sortins h. Arrangement or*packing 5. Cementation or lithification 6. Sedimentary fabric In addition surface texture, mineralogical composition, (LeRoy 1950), and.nethod of deposition (Fraser 1935) have been mentioned. An effect due to fabric appears only recently in the literature and apparently has received.litt1e, if any, investigation. Pettijohn.(l9h9) has recognized the effect fabric may have as evidenced by the following statements from.his book: "In actual stratified sediments the permeability has been fmmd greater parallel to the bedding than perpendicular to it. lubrication and other anisotropic fabric patterns are in some way responsible for the vectorial character of the permeability." Obviously the easiest way to study the effect of am one of these characteristics upon permeability is to conduct research in such manner as to control the effect of the others. 'lhe presence of too many variables, in the judgement of the writer, has sub- tracted from the value and usefulness of may otherwise scholarly achievements. It is the purpose of this study to determine the effect that one of these particle characteristics, namely shape, may have upon permeability. The method used is believed to offer the best pos- sibility of obtaining objective results. MEflIOD OF INVESTIGATION Eight sands, representing at least three different environ- ments, were used in this study. 'lhe names by which they will be referred in this report and the environment and origin of each are as follows: St. Peter Marine (Lamar 1928) Sleeping Bear Lake Michigan dune Grand Morals Lake Superior dune Mason Esker Central Michigan glacial Caseville Lake Huron-Saginaw Bay beach Copper Harbor Lake Superior beach Detroit Beach Lake Erie beach Eagle Harbor Lake Superior beach Plate I is a generalized map of Michigan and adjacent areas showing the locations fran which the saxmnles were obtained. is all the sands were unconsolidated any effect on permeability ch10 to cementing material was nullified. lite other variables, size and sorting, were essentially eliminated by sieving. Each sample was placed in the Ro-tap for 10 minutes and only that fraction passing through Tyler sieve 28 (.589 mm.) but retained on sieve 35 (.h17 m.) was used in the final analysis. A small part of each was mounted on slides and retained for the "shape analysis. Of the remaining factors generally accepted as affecting permeability sedimentary fabric is important in laboratory permea- MICHIGAN DEPARTMENT OF CONSERVATION GEOLOGICAL SURVEY DIVISION SCALE N ‘1! m PLATE I Map of Michigan and adjacent NV“ #3 / 67 areas showing locations Eng” "0'” cow" mm' m “'0'! “N W” B ‘ .. were obtained at“ O M ~I I s” a" R ‘L‘KE f LAKE SUPER/0 DOMINION OF , Grand Marais . CANADA . ONTONAGON / gt? «5 . ooocaIc 1, LUCE § \ , d W',}...\. ALGER g\ c O &\ ”*0” SCHOOLCRAFT CH'PPEWA V- s I ~\ . K‘ ”0”,. DICKINSON “Km“ ~ ' \u H Chum/[L ° ~ ~ ”‘0 - I . bfi’f “Wcm " o O I o ‘ .. '7 § - -" ' l ‘0 A0 ‘f \ b / j 9; msouc ISLE <"‘ / P 00 OTSEGO I JALPENA " ANTRIH uoumonzucv g leapinfibsar e / V 0 .' GRAND KALKASKA CRAWFORD OSCODA ALCONA I g, TRAVERSE I .' \ c .I 't ISTEE wzerRD HISSAUKEEROSCOHMON OGEMAW IOSCO =0 './ b . ! \ 95m LAKE OSCEOLA CLARE snow I I OCEANA utcosn ISABELLA MIDLAND I : NEWAYGO I ‘ I I '\ IIOIIICALJOIIAIIOT S‘G'NA‘" “4'. ’ 5<\ KENT I '. OITAIIA IONIA CLINTON m: | ‘ I \ V -' r . AKLAND I .ALLEGAII BARRY EATOTFNGKAM LIVNGSTON o I V“ BUR" IIALAIIAZOO CALHOUN JACKSON WASHTENAVI wAvIIL . .' 51 / scams CASS BRANCH HILLSDALI’. LENAVIEE MONROE 'LLI'O'. ...... "_-- _. —.._..Jo—SEP.H-[..—.- D; at . INDIANA r'—" d'fi'o ER/E 0 St. Pete! ' I k bility measurements under certain conditions. A certain amount of ”zoning" often takes place in a poorly sorted sediment during a permeability deter-runation; generally in the form of the heavy, coarse material settling while the finer material tends to rise. According to Johnson (1951) this fine particle migration may result in “pore plugging.” Toe result is the formation of several zones, each with different permeability characteristics. The problems involved would be much like those encountered with soil samples, only less obvious. Although it is impossible, by mechanical means at least, to isolate a single grain size, the size range obtainable fran sieving is believed so small as to render any effect on permea- bility due to fabric as negligible. ‘Ihe two remaining variables; shape and particle arrangement or packing, are not to be discounted. 'nie sands were selected from such locations as might reasonably be expected to give a wide range in shape. 'lhe St. Peter sample, particularly sieve size 35, is very "round” (Lunar 1928), while the Copper Harbor sand, locally at least, is generally considered "angular." One might reasonably expect the beach, dune, and esker sands to be intermediate between these two extremes insofar as shape characteristics are concerned. ‘Ihe variable effect due to pain arrangement or packing, if not controlled, was minimized by adopting a standard procedure as recmended by Johnson (1951). It is explained fully in the section under permeability. SPHERICITI AND ROUNDNESS Sphericity and roundness are two components, which combine to produce the geometric aspect of a particle. While perhaps related, they are not synommous, a fact made clear by Wadell (1932). He recognized a relationship betwaen the surface area and the volume of a particle and realized a sphere has the least surface area of am shaped particle of a given volume. For arv particle the ratio s/S may be expressed, where S is the surface area of the particle and s is the surface area of a sphere having the same volume as the particle. For a Sphere this ratio will be unity, but for aw other shaped particle its value will be less than 1.000. ‘Ihis relation- ship was given the name sphericity by Uadell (l932 ). As it is difficult to measure ,the surface area of am particle, sphericity is often expressed as the ratio between the so-called nominal diameter of a particle and the diameter of the circumscribing sphere. The nominal diameter is the diameter of a sphere having the same volume as the particle while the diameter of the circum- scribing sphere usually is the greatest diameter of the particle. To translate this last relationship into planer units for use in measuring projected grains Wadell (1935) has suggested the fallen- ing formula for determining sphericity: (1 II g c (1) Dc where dc is the diameter of a circle equal in area to the area of -3- the projected grain (nominal diameter) and Dc is the diameter of the smallest cirole which would circumscribe the projected grain. Wadell's method of sphericity measurement is very time can-- suming as it is necessary to trace the projected image of the grain before any measurements may be made. Riley (191d) has proposed a rapid method for determining sphericity, which he has found especially adaptable to particles of sand size. It is called the inscribed circle sphericity and involves the square root of the ratio of the inscribed circle 1, and the circumscribed circle Dc as: III-V235: Measurements are made with the aid of a concentric circle protractor made to fit the microscope occular. Drawings of the individual grains are not necessary. Schmitt (19h9) combined the best points of both methods and arrived at a scheme, which is both rapid and accurate. After removing the occular and lower nicol of a polarizing microscope the grains were projecwd with the aid of a camera lucids attached to the barrel of the microscope. ‘Ihe projections were made di- rectly on to a concentric circle protractor, made with black lines on heavy white paper, with which the diameter of the inscribed and circumscribed circles of each grain were easily measured. The roundness of a particle involves the sharpness or round- ness of its corners. According to Wadell (1935) roundness is essentially a planimetric conception, referring to the smooth curv- ature of the outline of a plane area, projected area, or cross section. It usually is expressed as the ratio between the average roundness of the corners and the radius of the maximum inscribed circle according to the formula: fl 24,3 (3) where r is the radius of a corner, R is the radius of the inscribed circle, and N equals the number of corners measured. The value obtained from measuring a particle of perfect roundness using this formula is 1.000. This method is readily adapted to a camera lucida projection directly onto a heavy paper concentric circle protractor. Using Riley's method of sphericity, as modified by Schmitt, and Wadell's method of roundness, measurements were made of the particles found in the sieved fraction (.Im m. diameter - .589mm. diameter) of each sample. The medium used in the preparation of the glass slides has the trade name ”molar." Because of its high index of refraction (n a 1.66) it has been found more satisfactory than Canada Balsam for projection methods. It imparts a high re- lief to quartz, the most frequent mineral in sands. With the aid of a mechanical stage it was easy to devise a system whereby the same grain was not measured twice. A sufficiently large sample -10.. was mounted so that only those grains in the center of the field a and in sharp focus were considered. Measurements were not con- fined to quartz particles although it was the most common mineral of each sample. After measuring 200 grains of the St. Peter sand the average sphericity and roundness were computed for the first 75 grains, the first 150 grains, and the total 200 grains. his results are summarized in the follaving table. TABLE I Sphericity and Roundness of Varying Counts of fileved St. Peter M @hericitz Roundness 7S .8688 {761:9 150 .8632 .7617 200 .8677 .7681 It is apparent that little, if any, accuracy is to be gained by counting 200 grains rather than 75. It was decided therefore, that the measurement of 100 grains from each sample would result in representative figures for the sample as a whole. Table II, on the following page, gives the results obtained by measuring the sphericity and roundness of 100 grains from each sample. TABLE II Sphericity and Roundness Values of the Sieved Portion of Each Sample M2. fihericitz Roundness St. Peter .868 .768 Eagle Harbor .8h9 .501 Grand Marais .832 .620 Sleeping Bear .828 .532 Mason Esker .820 .IIO‘? Copper Harbor .819 .307 Detroit Beach .812 .396 Caseville .806 .II20 PERMEABILITY The permeability of a material is a measure of its ability to allow fluid movement into and through its mass. Clearly it is related tOIporosity, especially to the size and arrangement of the interstices. A.rock material may be highly porous and either permeable or impermeable, but in.no case can.it be both nonfiparous and permeable. Clays actually may be very porous and contain a large volume of f1uid.for their mass, but the pore spaces and connecting passages are so small that most of the liquid is held by'mmlecular attraction, thus making them essentially impermeable. Such materials as coarse sands, gravels, and certain.types of lavas may’be less porous than.clay, but due to the size and arrangement of the pores be able to transmit large volumes of”water. These rocks are said to be highly permeable. A wide range in the permea- bility of different rock types has been observed. Generally, fine materials such as fine sand, are less permeable than coarse gravels. Coefficients of permeability, expressed in Heinzer's units, ranging from .0002 for a clayey silt to 90,000 for a gravel have been de- termined in the hydrdlogic laboratory'of the U. S. Gedlogical Survey; Thus the gravel has a capacity for carrying water at a rate about h50,000,000 times that of the clayey silt (Wenzel l9h2). A.Meinzer unit is defined as the flow in gallons per day through a cross-sectional area of 1 square foot under a hydraulic gradient of 100 per cent at a water temperature of 60°F. It is a unit used in this report and is designated as Pm. -12- .13- Hagen.(1839) and Poiseville (18h6) have been given credit for first studying the flow of water through capillary tubes. They found that the rate of flow through capillaries varied directly as the hydraulic gradient of the system. Hagen also investigated the effect of temperature on the viscosity of water, (Tolman 1937 ). Later Darcy (1856) conducted experiments on sand and.verified.the results of Hagen and Poiseville, applying the principles to the study of water movement through water bearing materials. He .formmlated his conclusions into what is known.as Darcy‘s law. For permeability measurement it may be expressed as Q : PIAt, in which Q is the volume of flow, P is the permeability coef- ficient of the material, I is the hydraulic gradient of the system, 1 is the cross-sectional area of the material, and t is the length of the period of flow. Subsequent investigation.has been carried out to determine the validity of the law under the extremely low hydraulic gradients which occur in nature. The results obtained from the study of the flow of”water through sand samples indicate the law applies for heads as low as 2 or 3 inches per mile. Tolnan (1937) states that normal ground water gradients seldcm.exceed.l per cent, or 53 feet per mile. It is evident that the basis for permeability measure- ments is well founded. There are two methods by which the permeability of a water bearing material may be determined with am degree of accuracy. One is a field method, which involves pumping tests and the other is a laboratory method involving determinations, according to the principles of Darcy's law, on undisturbed samples. It is diffi- cult, if not impossible, to secure completely undisturbed samples of rock, particularly unconsolidated rock. Ihe problem is inten- sified when dealing with subsurface formations. Even the collec- ' tion of volumetric samples is undesirable as it is doubtful if the original particle arrangement can be reproduced though the original volume may be attained. Furthermore, the lithologic characteristics of many rocks, particularly sediments, change so rapidly within short distances that the permeability of any one sample probably would not approach the permeability of the formation. Reduced to practicality and economics, laboratory permeability measurements may be of doubtful value. he field methods, whereby the canbined formational characteristics contribute to the results, are more reliable. For the collection of basic data, hatever, laboratory methods are more than adequate; if their limitations are recognized. In this research it was not necessary to arrive at absolute values for the permeability of the various sand samples. Relative values are Just as desirable and, as will be shown later, actually involve less chance of error. Consequently, the permeability values in this report are not to be taken as the true permeability of amr sample or type of sand; but rather as a value relative to that of the other samples and it is believed, in the correct order of magnitude. 11113 has been accomplished by following a uniform pro- -15- cedure designed to eliminate human error as much as possible. he apparatus used is pictured on page 16. It is a constant- head, discharging type permeameter designed.by Meinzer in.l923. It 'was devised specifically to measure the rate of flow of water through cdlumns of’unconsdlidated.materials under low heads, such as are found in nature (Wenzel l9h2). The glass cylinder is about 20 centimeters high and.has an inside diameter of 7 centimeters. A.coiumn.of sample about 10 centimeters in.length is placed within the cylinder and is supported on a perforated disk covered with cheesecloth about midway‘between the inlet a, and the outlet for the upper pressure gage b. ‘Water from the glass reservoir c is introduced below the sample, under a.head which remains essentially' constant. It percdlates upward through the sample and discharges at d. he difference in head at the top and bottan of the sample is measured by the two pressure gages, e and 6'. They indicate respectively, the elevation at which the water is being discharged after passing through the sample and the elevation of the head under which the water is being introduced into the sample from below. Tap water enters the reservoir through a rubber’hose f in a volume great enough to maintain an overflow at 3, thus insuring a constant head at that point. As stated in the section under permeability, Darcy‘s law, when given.area and time dimensions and applied to permeability, may be written Q 3 PIAt where Q is the volume of flow, P the permeav bility coefficient, I the hydraulic gradient, A.the cross-sectional 3.658385 £38th 2: 5 to»: 33630 2: .0 $2029... < __ Bani .17- area of the material, and t the length of the period of flow. - Transposing, the equation may be written as: P = _L (h) IAt he hydraulic gradient I, is actually the difference in head at the bottom and top of the sample, as measured by the two pressure gages, divided by the length of the column of material or: I = h (5) P=_%_£_ (6) he cross-sectional area of the sample using this apparatus is 38.50 square centimeters. he values for Q, l, h, and A are measured in centimeters, and the value t in seconds. hen formula (6) becomes: P g 3%?6111; ' (7) in which P is the coefficient of permeability in cubic centimeters per second through a cross-sectional area of 1 square centimeter under a hydraulic gradient of 100 per cent at a water temperature of 60°F. By multiplying equation (7) by the factor 21,200 (wenzel 191:2) the coefficient is expressed in Meinzer units where Pm equals the flow in gallons per day through a cross-sectional area of 1 square foot under a hydraulic gradient of 100 per cent at a water .18.. temperature of 60°F. as: P - (8) m ‘ £355 ht Equations (7) and (8), multiplied by the appropriate temperature conversion factor in Table III, are the ones used in this report. It was necessary to control as closely as possible the effect packing or particle arrangement would have on the permeability values of the various samples. An attempt was made to do this by using a uniform system of "wet packing" the samples in the percol- ation cylinder. Four or five millimeters of water was allowed to rise above the cheesecloth covered disk before two or three centi- meters of sample was inserted. With the aid of a handle on a rubber stopper this increment was rammed and packed until no further volumetric decrease occurred. Additional fractions of sample were added and packed in the same manner, being kept wet by the capil- lary action of the water, until the sand column measured ten centi- meters in length. Following the procedure described in the preceding paragraph a sample of the St. Peter was prepared for a trial test. Discharge readings and associated data necessary to calculate the permeability were taken at regular intervals for a period of twenty dws. Par- ticular attention was directed to the "megascopic peculiarities" which appeared to influence the test. Within five hours from the beginning of the ezqaeriment the water in the reservoir was notice- ably contaminated with air, exhibiting a milky color and containing TABLE III Factors for converting a.permeability coefficient at a given water temperature to a.permeability coefficient at a ‘water temperature of 60°F. :rature Factor Temggfature Factor 55 ' 1.08 66 .92 56 1.06 67 .91 57 1.01; 68 .89 58 1.03 69 .88 59 1.01 70 .87 60 1.00 71 .86 61 .99 72 .85 62 .97 73 .8h 63 .96 7h .83 6h .95 75 .82 65 h .93 76 .81 -19- -20- hundreds of minute air bubbles. his entrapped air caused an occasional bubble to boil through the sample leaving behind a cavity from five to fifteen millimeters in length. he erratic repetition of this "boiling" resulted not only in the rearrange- ment of the particles, but contributed to a general volumetric increase of the sample. Within eight hours a slight coloration of the white St. Peter sand, near the lower end of the sample, was noted. It was brownish-yellow and may have been iron stain. Since the particular sample of St. Peter used was over 95 per cent quartz, the source of the coloration was due probably to dissolved minerals in the tap water. In about seven days this staining had effected the entire sample and apparently its color was increasing in intensity. hroughout the test the permeability of the sanlple decreased. mnor recoveries, as well as short periods of apparent stabiliz- ation, occurred within the overall trend. However, no pattern recognizable to the author was observed. hen no new peculiar- ities seemed to be forthcoming the test was discontinued and a sample of the Copper Harbor sand was placed in the permeameter. he same method of "wet packing" was employed and similar observ- ations made throughout a twentyéeven day test. he Copper Harbor sand resembles coffee in appearance, nevertheless iron colored stains were soon evident throughout the sample. Although uniform in chemical canposition the Copper Harbor sample contains a great- er variety of minerals than the St. Peter sand. It is composed -21- chiefly of‘basaltic material and.the commonly associated basic minerals. The prospect of micro-chemical changes between.the dissolved chemicals of the water and the mineral constituents of the sample should not be discounted. Cavities, resulting from released air bubbles, occurred at irregular intervals as in‘ the previous test. he permeability generally decreased throughout the test. Canpared with the St. Peter, it dropped faster to a lower level and when plotted against time its curve tended to be flatter in its later extremity. Minor fluctuations as well as short inter- vals of stabilization were observed, but like those of the St. Peter, they did not occur in a definite pattern. Qwviously the method of "wet packing" was unsatisfactory. he recessional curves had nopoints in common thus making re- lative permeability determination hazardous. he effect of en- trapped air, although undetermined in magnitude, apparently effects the results considerably. Johnson (1951) described the method of packing he employs in the Hydrologic Laboratory of the U. 3. Geological Survey at the University of Nebraska. He has designed the "Johnson Caupaction Table", which is motor driven and consists essentially of a table on which the percolation cylinder containing the dry sample is clamped. he table is raised one-half inch by means of a cam and allowed to drop once each second, thus packing the sample. he results of considerable research on his part indicate twenty-five drops will give a packing -22- "very similar to natural packing for many materials.” He warns against simple jarring, rodding, tamping, or tapping methods of packing due to the presence of the human factor which precludes arw possibility of consistency. Although the "Johnson Canpaction Table" was not available a method identical in principle was devised. he percolation cylinder, with ten centimeters of dry sample in place, was raised one and one- half inches and allowed to drop on a book. Twenty-five drops in this manner were given each sample and usually resulted in a ten to twenty per cent reduction in its volume. he uniformity of the operation is believed to have nullified the variable effect packing can have on permeability. 0f the six variables listed on page 2 which can effect permeability to an undetermined degree, all have been eliminated except shape. his factor can be measured and in this study will be held responsible for any differences encountered in the permeability of the various samples. After packing a sample in the permeameter as described the ap- paratus was started and the exact time of the initial discharge re- corded. At each succeeding fifteen minute interval the discharge, water temperature, difference in head at the 13m ends of the column, and the length of the column were measured and the permeability cal- culated. he discharge was measured for a five minute period. Read- ings were contirmed in this manner for 2 hours and 1:5 minutes and the results plotted in the form of a time-permeability curve. he curve for each sample is shown on page 23 or 21:. he recorded data fran which they were drawn is contained in Tables V-XII in the Appendix. «30:36 BEE Est oEE. _ a... m up. .2 _ [/Wr/J {/fi )7 ¢ CON 00¢ teem 9.335 means. 265 Shae: seem 3.6.". .5] of a0 «2:3 Ezfieosaoasosz oak .: whdui g7 K /{ sneeze»; .23.: Eat 25... I]. .E m .E N .2 _ / .33: .8300 ll: / :88 28.8 ll. / 2:3er I aoxnu .332 III: of so noise 3:33.52. .66: 2: >_ m._.<.._i 00m 00¢ 000 000 000. 00w. RESULTS Johnson (1951) describes the behavior of a sample when.its permeability is being determined in the following words: "If nary closely spaced readings are taken, it isusually found that the permeability, using tap water, will have a period of slight increase during the first few days, followed by a short period of relative stabilization. his is then followed by a period of continuously decreasing permeability until finally attaining a minimum value. In addition to this general tendency, it will usually be observed that the permeability is subject to fluctuations during the courseof each day." flthough the permeability measurements in this study trans- gressed a period of hours rather than days a similar sequence in behavior was obvious. All of the samples decreased steadily from an original high value to a distinct point of inflection. Within this initial downward trend a short period of slight increase was noted for five of the eight samples. An increase in permeability may actually have occurred in the other three samples but due to the time unit employed not be evident. At the inflection point all of the curves flattened sharply and became essentially straight lines for the remaining period of record. he irregularity of the initial phase of the curves apparently is due to inherent air and gases escaping through the sample. he conclusion of this is marked by the period of slight increase after which decline continued to the inflection point. he second phase of the curves, that from the -25- -26.. inflection point on, represents a period of relative stability. 1 longer period of record probably would indicate the continuance of the curve as a straight line until the sample particles were completely saturated, after which it would drop sharply to a mini- nmm value of absolute permeability. By this time, however, several tangibles quite possibly could be affecting the results and will be discussed in the section under conclusions. In order to determine which samples were relatively most perme- able the readings from the point of inflection on were averaged. Except for two samples this average resulted in an order identical with the graphic position of the flat portion of the curves as well as the order of decreasing sphericity. A less exact correlation with roundness was probably due to the close relationship which often exists beWeen sphericity and roundness. Table IV indicates the order of decreasing sphericity, round- ness, and permeability, expressed in Heinser units, for each sample. It will be noted that the samples which are ideally “out of position“ are the Copper Harbor and the Caseville. heir positions are re- versed from that which would give a perfect direct sphericity-perme- ability correlation. his may be the result of the extremely low relative value of roundness of the Copper Harbor and the relative high roundness vane of the Caseville sands. he Copper Harbor, Caseville, and Eagle Harbor are the only samples which do not have a roundness value corresponding in position to their Sphericity value. he apparently important secondary effect of roundness on -27- permeability is shown also in the case of the Eagle Harbor sand. If its roundness value was in a.position similar to its sphericity the permeability might be expected to be higher in value and more nearly approach the St. Peter in this reapect. TABLE IV Order of Decreasing Sphericity, Roundness, and Permeability for each of the Samples. §phericitz Permeabiligz Roundness St. Peter .868 St. Peter 281 St. Peter .768 Eagle Harbor .819 Eagle Harbor 2141 Grand Harais .620 Grand Harais .832 Grand Harais 213 Sleeping Bear .532 Sleeping Bear .828 Sleeping Bear 212 Eagle Harbor .501 Mason Baker .820 Mason Baker 182 Caseville .h20 Copper Harbor .819 Caseville 175 Mason Esker .ho'r Detroit Beach .812 Detroit Beach 173 Detroit Beach .396 Caseville .806 Copper Harbor 167 Copper Harbor .30? C ON CLUSI ONS Although an apparently close correlation‘between.sphericity and permeability was found, this study should not be considered conclusive. At best it indicates a.possible relationship which may exist and which should be substantiated by further study before being fully accepted as fact. However, the results ob- tained in this research are believed to be an adequate basis for further study. If possible, even.more rigid control should be maintained in any additional work. Although offering no substantiating data, the author feels that the effect of mineral composition and re- sultant absorptive qualities of the particles may greatly affect permeability. Only'distilled‘water should.be used in laboratory measurements of’permeability. The total solid content of tap water may be great enough to plug pores, if megascopic in size, or capable of chemical action with the mineral constituents of the sample if in a dissolved state. As pointed out by Johnson (1951) either may contribute to decreasing permeability. A source of filtered water, whereby it has become de-aerated, Should be used in.any future study. Johnson.(l9§1) listed the effect of entrapped air as a.major source of error in.1aboratory measurements of permeability. A.mechanical device such as the "Johnson Comps, ction Table“ mentioned in.a.previous section should be used for packing the sample, thus eliminating the effect of human error on -28.. -29- the results. The author, surprised to discover'the sphericity values of the various samples ranged only from .806 to .868, found the significance of any sphericity difference in the second digit. The fact that all the values were so close in.magnitude may be a function of the nearly perfect sorting, which‘was obtained.by sieving. Thus a.re-evaluation of the basis for these measure- ments may be in order perhaps with the idea of determining a standard size grain as the basis for all computations. RECOI‘MENDED FUTURE STUDY If permeability is to be completely understood the writer believes the following problems must be made the subject of future study 3 l. ‘Ihe influence of all the variables known to affect permeability must be evaluated individually. This will involve such problems as devising a system whereby lab- oratory samples may be artificially cemented in order to study the effect of lithification on permeability under controlled conditions. 2. The information gained from studying all the factors known to affect permeability should then be used in m attempt to predict the permeability of laboratory samples. 3. Laboratory discoveries should be applied, whenever possible, to permeability problems encountered in the field. the ultimate aim of basic permeability research should be the derivation of methods whereby the extraction of our expendable fluid resources will become more efficient. APPENDIX APPENDIX TABLE V me Recorded Data Used to Canpute the Permeability and Construct the fine-Permeability Curve of the St. Peter Sample. Minutes Q ml h on t °r of P Pm 15 710 8.h 6h° .95 .0626 1325 30 600 8.h 65° .93 .0517 1100 1:5 51:0 8.h 65° .93 .0h66 988 1111‘. 165 8.h 66° .92 .0397 8&2 1.5 1:75 8.11 66° .92 .01106 860 30 1115 8.1; 6h° .95 .0366 777 1:5 335 8.5 611° .95 .0292 620 2hr. 190 8.6 65° .93 .0160 3110 15 180 8.6 66° .92 .0150 318 30 17h 8.6 67° .91 .01hh 30h h5 166 8.6 67° .91 .0137 290 3111‘. 1118 8.6 67° .91 .0122 258 15 11.2. 8.6 6h° .95 .0121; 263 30 138 8.6 65° .93 .0116 2146 I45 130 8.6 66° .92 .0108 230 -31- Minutes 15 30 h5 30 hS 15 30 hS 15 hS APPENDIX TABLEVI The Recorded Data Used to Compute the Permeability and Construct the fine-Penmability Curve le h20 360 390 Loo hoS too 375 160 150 130 130 120 100 of the Eagle Harbor Sample. hcm 8.6 8.6 8.7 8.7 8.7 8.7 8.7 8.8 8.8 8.8 8.8 8.8 8.8 8.8 8.5 t °F 6&0 6&0 660 660 660 660 660 660 -32- Pt .95 .95 .92 .92 .92 .92 .92 .92 .93 .95 .95 .95 .93 .92 .89 .0380 .0326 .0338 .o3h7 .0351 .03h7 .0325 .0137 .0130 .alzh .0115 .010h .00986 .0085? 805 690 715 735 7h5 735 690 290 275 262 220 210 185 Minutes 15 30 85 15 3o 85 2hr.- 30 85 3hr. 15 30 85 APPENDIX TABLEVII The Recorded Data Used to Compute the Permeability and Construct the Time-Permeability Curve le 520 810 370 335 310 300 305 180 135 128 116 106 105 92 of the Grand Harais Sample. hcm 8.6 8.6 8.5 8.5 8.5 8.5 8.5 8.5 8.6 8.6 8.6 8.6 8.5 8.5 8.5 t °F at 70° .87 65° .93 68° .95 65° .93 65° .93 66° .92 65° .93 65° .93 68° .95 68° .95 68° .95 68° .95 65° .93 66° .92 66° .92 .0810 .0386 .0322 .0286 .0268 .m53 .0260 .0209 .0121 .0089 .0078 870 733 685 560 536 552 883 256 287 235 212 192 188 168 lfinmtes 15 30 85 15 30 85 15 30 85 15 30 85 APPENDIX TABLE VIII and Construct the Time-Permeability Curve Q.ml 625 580 530 885 865 820 208 185 180 135 120 110 105 95 of the Sleeping Bear Sample. h cm t °F 88.5 69° 8.5 65° 8.5 63° 8.5 68° 8.5 63° 8.5 66° 8.5 66° 8.6 66° 8.6 67° 8.7 67° 8.7 66° 8.7 68° 8.9 68° 8.9 63° 8.9 63° 8: .88 .93 .96 .95 .96 .92 .92 .92 .91 .91 .92 .95 .95 .96 .96 .0086 .0080 The Recorded Data Deed to Compute the Permeability 1070 976 990 896 870 750 372 256 233 210 208 193 188 170 APPENDIX TABLEIX The Recorded Data Used to Compute the Permeability and Construct the Time-Penneability Curve of the Mason Esker Sample. mantee 0 ml h cm t °F t: P Pm 15 805 8.6 66° .92 .0338 716 30 385 8.5 66° .92 .0325 657 85 820 8.5 66° .92 .0358 750 1hr. 395 8.5 66° .92 .0333 705 15 365 8.6 66° .92 .0308 685 30 300 8.6 66° .92 .0250 530 85 128 8.7 68° .95 .0105 228 2hr. 120 8.8 68° .95 .0101 218 15 110 8.8 68° .95 .0093 196 30 105 8.8 68° .95 .0089 187 85 98 8.8 65° .93 .0081 171 3hr. 100 8.8 68° .95 .0088 171 15 92 8.8 68° .95 .0078 168 30 90 8.8 68° .95 .0076 161 85 90 8.8 68° .95 .0076 161 Minutes APPENDIX TABLE X The Recorded Data Used to Compute the Permeability and Construct the Time-Permeability Curve Qiml 550 850 395 300 120 112 108 105 88 80 80 76 75 of the Caseville Sample. h on 8.3 8.3 8.3 8.8 8.8 8.8 8.8 8.8 8.8 8.8 8.8 8.5 8.5 8.5 8.5 67° 66° 6’40 611° 618° 65° she 68° -35.. .86 .92 .96 .95 .95 .93 .92 .91 .92 .95 .95 .95 .93 .95 .95 .0867 .0808 .0375 .0278 .0108 .00991 .00986 .00910 .00881 .00795 .00760 .00715 .00700 .00680 .00670 995 795 590 230 210 201 193 178 169 161 152 188 '182 Rdnutes 15 30 85 1hr. 30 85 15 30 85 15 30 85 APPENDIX TABLE II The Recorded Data USed to Compute the Permeability and Construct the Time-Permeability Curve of the Dbtroit Beach Sample. Q‘ml 570 890 835 355 160 135 118 105 100 90 85 81 77 h cm 8.5 8.5 8.5 8.5 8.6 8.6 8.6 8.6 8.7 8.7 8.7 8.7 8.7 8.7 8.7 t °F bf P 68° .89 .0865 68° .89 .0800 66° .92 .0367 67° .91 .0296 68° .89 .0129 68° .89 . .0109 68° .89 .00958 68° .89 .00850 68° .89 .00796 68° .89 .00718 68° .89 .00718 68° .89 .00686 68° .89 .00678 69° .88 .00680 69° .88 .00606 985 850 780 630 265 231 200 180 169 152 152 185 135 130 Minutes 15 85 1hr. 30 85 2hr. 15 30 85 3hr. 30 85 APPENDIX TABLE XII The Recorded Data Used to Compute the Permeability and Construct the Time-Permeability Curve 02n1 780 670 395 255 160 182 126 116 102 82 73 67 61 55 of the Copper Harbor Sample. h on t OF 8.3 73° 8.5 67° 8.6 66° 8.6 67° 8.6 67° 8.6 68° 8.6 68° 8.6 68° 8.7 68° 8.7 68° 8.7 68° 8.7 68° 8.7 68° 8.7 68° 8.7 68° -33- tr .0560 .0329 .0210 .0132 .moz .00936 .00818 .00735 .00655 .00583 .00535 .00886 .00850 1305 1185 700 886 280 215 198 173 155 139 123 103 95 REFERENCES Darcy, H. (1856 ), Les fontaines publiques de la ville de Dijon, Parise Eraser, H. J. (1935), mcperinental Study of the Porosity and Permeability of Clastic Sediments, Journal of Geolog, 7010 2‘3, NO. 8, PP. 93h'96‘40 waton, L. C. and Fraser, He J. (1935 ), Systematic Packing of Spheres with Particular Relation to Porosity and Permeability, Journal of Geolog, vol. 83, H0. 8, pp. 889-880. Hagen, G. (1839 ), Ueber die Bewegung des Wassers in engen cylindrischen Rohren, Poggendorff innalen, vol. 86, pp. hZB-MZO Johnson, A. I. (1951), Hydraulic Engineer, U. 8. Geological Survey, Personal Communication. Krumbein, W. C. and 81063, L. L. (1951 ), Stratigrghz and Sedimentation, San Francisco, W. H. Freeman and Ccmpany, pp. 82-92. Lamar, J. E. (1928), Geology and Econanic Resources of the St. Peter Sandstone of Illinois, Illinois Geological Survey Bulletin 53, p. M. LeRoy, L. W. (1950), Subsurface Geologic Methods (a symposimn), Colorado School of Mines, Department of Publications, PP. 685-6870 Pettij ohn, F. J. (19189) Sedimentary Rocks, New York, Harper and Brothers, pp. 86255. Poiseuille, J. (1886), Recherches experimentales sur le mouvement des liquides dans les tubes de tres petit diametre, Hem. Savants Etrangg, vol. 9. Riley, N. A. (1981), Projection sphericity, Journal of Sedimentary Petrolg, vol. 11, No. 2, p. 98. Schmitt, G. T. (1949 )5 A Petrographic Investigation of the Relationship of Deposition of Sediments in a Group of Eskers Related to the Charlotte Till Plain, Unpublished thesis for the degree of Master of Science at Michigan State College, pp. 85-187. ~80- Tolman, C. F. (1937 ), GroundHater, New York, McCray-Hill Bock 0mm, Inst, pp. 200-2014. waden, H. (1932), Volume, Slaps and Roundness of Rock Particles, Journal of Geolog, vol. 80, pp. 883-851. Wadell, H. (1935 ), Volume, Slape and Roundness of Quartz Particles, Journal of Geolpg, vol. 83, pp. 266-269. wenzel, L. K. (1982), Methods of Determining Permeability of Water-Bearing Materials, U. 8. Geological Survey, Water-Supply Paper 881, pp. 3-13 , 5&3. - u-‘ Ho 20 ‘53 HICHIGQN STQTE UNIV. LIBRQRIES I I‘ll" llHlllHl lllllllll HI "ll HHHII llll 31293009940960