Abstract:
A method for measuring hydraulic conductivity of geological samples using a closed volume pumping system that ensures constant volume of test liquid within the sample and a shaped tube of mercury to provide a constant pressure difference across the sample to eliminate second order influences on the hydraulic conductivity measurement and to speed measurement.

Description:
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
     This invention was made with United States government support awarded by the following agencies: NSF Grant No. 9800255. The United States has certain rights in this invention. 
    
    
     CROSS-REFERENCE TO RELATED APPLICATIONS 
     BACKGROUND OF THE INVENTION 
     The invention relates generally to geological test instruments, and, in particular, to instruments for detecting how well fluids are conducted through geological materials such as clays, rocks, and soil. 
     The hydraulic conductivity of geological materials is important for determining their drainage capacity and the mobility of liquids such as oil or water in subsurface strata. The hydraulic conductivity of less permeable geological media may be less than 10 −4  cm/sec. 
     Measurement of such hydraulic conductivities presently entails placing the sample in a test cell so that liquid flow may occur only between an inlet and outlet opening in the cell. Tubing connects the openings to burettes containing the test fluid, typically water. The burettes have adjustable heights and graduation lines so that the column heights of the contained fluid may be easily measured. 
     In the “fallinghead risinghead” method of measuring hydraulic conductivity, the water level in one burette is placed above the water level in the other to establish a pressure differential across the sample and the rate of flow measured by comparing, at periodic intervals, the changing heights of the liquid columns in the burette. 
     In the “fallinghead” method, only one burette is used and the remaining opening in the test cell drains into a graduated cylinder or similar device. 
     In both methods, the burettes are typically open to the air. However, they may be closed and pressurized, for example with compressed air, to achieve a greater pressure difference. This pressurization addresses the problem that steady state hydraulic flow necessary to establish conductivity can take many hours or weeks to occur. 
     In a “constant volume” method originally described by Bjerrum, L. and Huder, J., in their publication  Measurement of Permeability of Compact Clays , Proc. 4 th  Intl. Conf. on Soil Mech. and Foundation Eng., 1957, a closed loop is established between the inlet and outlet to and from the test sample so that the test sample always has a constant volume of test fluid. A falling column of mercury incorporated into this closed loop provides the pressure difference across the test sample. While this method has decreased measurement times (by decreasing the time to steady state hydraulic conductivity where inflow equals outflow), the test results can still take many hours or days to stabilize. 
     All of these methods have produced erratic results if insufficient time is allowed for stabilization to occur. 
     BRIEF SUMMARY OF THE INVENTION 
     The present invention provides a test of hydraulic conductivity suitable for geological materials, but where test results are obtained in minutes rather than hours and where variations in the measurements are much reduced. 
     In the invention, a closed loop of test fluid is maintained with constant pressure differential. A “constant head mercury column” is used to provide constant differential pressure in a closed loop environment ensuring a constant fluid volume in the sample. 
     Specifically, the present invention provides a method for testing geological materials for hydraulic conductivity including the steps of enclosing the sample material in a cell having fluid impermeable walls and a first and second opposed port separated by the sample. The geological sample is saturated with a test fluid and placed under a constant pressure difference across the first and second ports while fluid flow of the test fluid through the ports is matched so that a constant volume of test fluid is within the sample. 
     It is thus a principal object of the invention to eliminate variations of pressure difference in a closed loop system such as may affect the stability of the measurement of geological materials of complex characteristics. Although the inventors do not wish to be bound to a particular theory, it is believed that the changing pressure difference inherent in prior art constant volume devices may unpredictably influence the measurement by changing, the hydraulic gradient in the sample, the pore water pressure and the stress on the sample. By providing a constant pressure difference, as well as a constant volume of test fluid in the sample, these and other second order effects on the measurement of hydraulic conductivity are eliminated. 
     The greater stability in the measurement further shortens the necessary measurement time. 
     The constant pressure difference across the first and second ports may be ensured by the use of a tube, a portion of which is filled with a material of greater specific gravity than the test fluid. A vertically oriented portion of this tube is completely filled with the material of greater specific gravity and connects at its upper end with horizontal tube at partially filled with the material of greater specific gravity. An interface exists separating the material of greater specific gravity from the test fluid. The free ends of the tube are attached one to each of the first and second ports. 
     It is thus another object of the invention to provide a means for producing a constant pressure difference across the sample that may be used in a closed loop and that is compatible with the goal of a constant volume of fluid flow. The vertically oriented flexible tube may be part of a constant volume connection between the first and second ports that ensures the same fluid flow into the first port as out of the second port. The horizontal tube, which adds no hydraulic head to the hydraulic head already applied by vertically oriented flexible tube, is used to measure the volume of fluid flow 
     The connections between the vertically oriented tube and the horizontal tube and the first and second orifices may provide interfaces between the material of greater specific gravity and the test fluid and these interfaces may have an identical cross- sectional area. 
     Thus, it is another object of the invention to eliminate the effect of pressure drop caused by meniscus capillary pressure of the various fluids. 
     One interface between the material of greater specific gravity and the test fluid may be an upwardly extending tube terminating in an orifice of a predetermined cross-section and surrounded by a well. 
     Thus, it is another object of the invention to provide a connection between the material of greater specific gravity and the test fluid that is both fixed in height and of a predetermined and constant cross-sectional area. 
     The foregoing and other objects and advantages of the invention will appear from the following description. In the description, reference is made to the accompanying drawings which form a part hereof and in which there is shown by way of illustration a preferred embodiment of the invention. Such embodiment does not necessarily represent the full scope of the invention, however, and reference must be made to the claims herein for interpreting the scope of the invention. 
    
    
     BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
     FIG. 1 is a cross-sectional view of an apparatus suitable for use with the present invention showing a test cell incorporating a geologic material connected to an interface chamber in turn driven by a bent column pressure source; 
     FIG. 2 is a detailed view of the material interface of FIG. 1; and 
     FIG. 3 is a flow chart showing the steps of operation of the device of FIG.  1 . 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Components of the Control System 
     Referring now to FIG. 1, test apparatus  10  suitable for use with the present invention includes a test cell  32  holding a sample  14  of geological material of generally cylindrical dimensions with parallel upper and lower ends. 
     The ends of the sample may be covered with a diffuser  15 , such as a layer of geofabric, which acts to allow free fluid flow and distributes the flow along the ends of the sample and thus pressure equalization at the ends. 
     Abutting the diffusers  15  are parallel, rigid upper and lower end caps  16  and  18 . Upper end cap  16  includes an inlet port  20  and a first saturation port  22  whereas lower end cap includes an outlet port  24  and a second saturation port  22 . Each of the inlet port  20 , the outlet port  24 , and the saturation port  22  have separate valves  26  which may be opened to allow passage of test fluid through the various ports or closed to block that passage. 
     The upper and lower end caps  16  and  18  are commensurate with the bases of the sample  14 , extending only to the edge thereof, where they join to and are joined by a cylindrical flexible membrane  28  enclosing the sample  14  on its sides with the upper and lower end caps  16  and  18  covering the sample&#39;s top and bottom. 
     The membrane  28  is fluid impermeable and is compressed against the sides of the sample  14  by the pressure of a fluid bath  30  contained in a closed cell  32  surrounding the sample, membrane, and end caps. Pressurization of the cell  32  may be accomplished by cell pressurization line  34 . When the membrane  28  is thus compressed, fluid flow between the inlet port  20  and the outlet port  24  must be through the sample  14  and not along its outer edges. 
     The inlet port  20  is connected to a mercury separator  36  consisting of a vertical tubular column capped at its upper and lower ends by plugs  38  and  40 , respectively, and partially filled with the working fluid of the test, typically water  41 . The inlet port  20  connects through valve  26  to a passage in the upper plug  38  providing a Tconnection, one branch of which connects to the top of a water column  42  and the other branch of which connects through a bleed valve  44  to the atmosphere. The bleed valve  44  is used to remove any air from the system, such as will naturally migrate to the top of the water column  42  during set-up. 
     Referring now to FIGS. 1 and 2, the lower plug  40  supports an orifice tube  46  extending upward into the water column  42 , the outer walls of which provide about the orifice tube  46  a well  48 . The orifice tube  46  connects through lower plug  40  to an internal Tvalve  50 , which may alternatively connect separator inlet  52  to the orifice tube  46  or to a well drain  54  at the bottom of the well  48 . 
     During operation of the test, when the valve  50  is in a first position shown in FIG. 2, water will be forced from the water column  42  through the sample  14  by the introduction of mercury through separator inlet  52  into orifice tube  46 . The mercury so introduced forms beads  56  which promptly fall into the well  48 , thus displacing water  41  but preserving a constant cross-sectional area of interface  58  between the water and mercury. As will be described below, this cross-sectional area is matched to a second interface between mercury and water in a capillary tube so as to provide a balancing between meniscus forces at this interface such as might upset an accurate measurement of pressure difference between the inlet orifice  20  and the outlet orifice  24 . It will be understood that other materials than mercury and water may be employed., However, the high specific gravity of mercury with respect to water provides an extremely compact instrument. 
     When the valve  50  is in the second position, not shown in FIG. 2 but shown in FIG. 1, mercury may be drawn from the well  48  through the well drain  54  back out of separator inlet  52  for a resetting of the test apparatus  10 . 
     Referring now again to FIG. 1, separator inlet  52  may be connected by a vertically oriented flexible tube  60  to the horizontal tube  66 , which is a capillary tube. The flexible tube  60  is such as to provide constant internal volume during testing and thus may be, for example, a malleable metal tube of small internal diameter that may be flexed for bending yet that will maintain a constant volume during operation of the test. The vertical separation distance between the end of the orifice tube  46  and the horizontal tube  66  is the vertical height Z. The height Z and the specific gravity of the mercury within the orifice tube  46  and vertically oriented flexible tube  60  determines the pressure difference across the sample  14 . The flexure of flexible tube  60  allows adjustment of the height of the horizontal tube  66  such as will determine a pressure difference across sample  14 . Note, generally flexible tube  60  is flexible yet not expansive or compressible, and which thus may facilitate easy hook up of tube  66  and the separator  36 . 
     The upper end of the flexible tube  60  connects with a horizontal tube  66  partially filled with mercury to provide a second mercury water interface at end  68 . The horizontal tube  66  may be a capillary tube of small diameter to accentuate movement of the end  68  of the column of mercury as may be measured against a scale  70  extending along horizontal tube  66  with flow through the flexible tube  60  into the inlet port  20 . The rate of flow may be determined by a measurement of a distance x whereas the volume of flow will be Δx times the cross-sectional area ol the capillary of horizontal tube  66 . At the far end of the horizontal tube  66  with respect to its connection with vertical tube  60  is a bleed valve  72  whose operation will be explained shortly and a connection with a return tube  74  which connects through valve  26  to the inlet port  20 . 
     Referring now to FIGS. 1 and 3, at a first step  80  in a test procedure using this apparatus  10 , the sample  14  is placed within the test cell  32  and the cell is pressurized through the introduction of pressure into cell  32  thus pressing the flexible membrane  28  tightly against the sample  14 . 
     Next, at process block  82 , the sample is saturated by an opening of valves  26  associated with the saturation ports  22  to saturate the sample  14  with the working fluid, typically water. At this time, valves  26  associated with the inlet and outlet ports  20  and  24  are closed. The fluid entering through the saturation ports  22  infuses the sample and dissolves small amounts of gas within the sample. 
     After a suitable period of time, valves  26  associated with the inlet ports  20  may be opened followed by an opening of valve  44  to bleed out any gas within the separator  36 . As indicated by process block  84 , valve  44  is then closed and bleed valve  72  is opened with valve  50  (shown in FIG. 2) connected to the well drain  54  causing mercury to flow backward out of separator inlet  52  up vertical flexible tube  60  and along horizontal tube  66 . When the mercury-test fluid interface  68  reaches the end of the scale near bleed valve  72 , bleed valve  72  is closed. Sufficient mercury is placed in well  48  so that no water is introduced into flexible tube  60 . At this time, valves  26  associated with the saturation orifices  22  are closed and valves  26  associated with the inlet and outlet ports are opened. Valve  50  is set to connect separator inlet  52  with orifice tube  46  (as shown in FIG. 2) as indicated by process block  86  and the test may begin. 
     At the start of the test, the water  42  from the separator  36  is forced through inlet ports  20  by the weight of the mercury in the column of flexible tube  60  with the weight of mercury in horizontal tube  66  having no effect, but the end  68  of the tube indicating a volume flow through the sample. Hydraulic conductivity is computed from the readings on the capillary of horizontal tube  66  using a modified form of the constant head equation. If head loss within the tubing is negligible, then fluid mechanics shows that the difference between the water pressure at the inlet port  20  and outlet port  24  is: 
     
       
           u   i   −u   o   =Z ( G   Hg −1)γ w+L   (1)  
       
     
     Where u i  is the inlet water pressure at inlet port  20 , u o  is the outlet water pressure at outlet port  24 , Z is the elevation difference between the tip of orifice tube  46  and the center of the horizontal tube  66 , G Hg  is the specific gravity of mercury (13.54 at 23° C.) and L is the thickness of the sample  14  measured between the end caps  16  and  18 . Equation (1) ignores the net capillary pressure drop caused by the water mercury menisci as may be done because the orifice size of the tube  46  equals the capillary size of horizontal leg  66 . 
     Inspection shows that the drop in elevation across the sample  14  cancels when the drop in total head is calculated, thus by applying Darcy&#39;s Law, the hydraulic conductivity is computed as follows:              K   =           a   c        L       A                   Z        (       G   Hg     -   1     )                (       Δ                 x       Δ                 t       )               (   2   )                                
     Where Δx is the horizontal displacement of end  68  during a time At and ac is the cross-sectional area of the capillary tube. Equation (2) is simpler than that required using other techniques. 
     The above description has been that of a preferred embodiment of the present invention. It will occur to those that practice the art that many modifications may be made without departing from the spirit and scope of the invention. In order to apprise the public of the various embodiments that may fall within the scope of the invention, the following claims are made.