Experimental Measurements of Specific Storativity by the Determination of Rock Elastic Parameters
KV 184/07
May 2007
Executive Summary

As groundwater becomes ever more important as a viable source of fresh water in arid and/or remote areas where surface water supplies are insufficient to sustain life, agriculture and industry, it has become important to accurately estimate, manage and monitor this valuable resource. Much has been done to improve the management of this valuable resource by the development of numerical models that give a realistic estimate on how groundwater reserves will react to changing circumstances in groundwater conditions. The accuracy of these predictions is limited to the effective accuracy of the predictive model, which in turn rely on accurate data on all the variables which will affect the flow of groundwater.

This paper presents a method developed by the authors to determine storativity by determining actual specific storativity values of the rock that make up an aquifer. Storativity is one of the hydrological parameters which affect the flow of groundwater as well as the outcome of predictive models. Storativity is an ambiguous parameter in that it is dependent on two unknown variables, namely aquifer thickness and rock elastic parameters. At present, storativity is estimated using borehole pump test data and inverse modelling, which is not always an accurate measure of the parameter.

Specific storativity is the parameter which specifies the amount of water released by a rock sample when exposed to a change in pressure head, as is the case when a confined aquifer is mined. Specific storativity is determined by experimentally measuring the elastic parameters of a rock sample, in this case, a core sample. These measurements are done in two ways. The first is to measure the compressive and shear wave velocities of the rock by inducing an ultrasonic pulse into one side of the core sample and measuring the time it takes the pulse to travel through the sample. The travel times are then converted into compressive and shear velocities which in turn are used to determine the bulk modulus and shear modulus of the sample. The second method involves using resonant ultrasound spectrography (RUS), which measures the natural resonance frequencies of a rock sample induced by an ultrasonic frequency sweep in the sample. These resonance frequencies are then numerically modelled to determine the bulk modulus and shear modulus of the rock sample.

Both of these methods use apparatus, developed by the authors, which clamp a cylindrical rock core sample between two sets of ultrasonic transducers. One set of transducer produces compressive ultrasonic waves, and the other produce shear ultrasonic waves. An analog-to-digital converter is used to read the changing voltage levels in the transducers, induced by the ultrasonic pulse travelling through the sample or the resonant vibrations of the sample induced by the ultrasonic frequency sweep in the sample.

Once the elastic parameters are known, they are applied to equations which relate specific storativity to the sample’s elastic parameters. The storativity values can then be calculated. The results obtained for the different core samples are shown in Tables E1 to E4.

Table E1 - Time-of-Flight results
Rock Type Specific Storativity Shear Velocity Compressional Velocity
1/L   m/s  m/s
TMG Sandstone 1.295E-06 1936 4879
Schist 6.459E-06 1617 2163
Quartzite 1.318E-06  2331 4806
Gneiss 1.048E-06 2590 7445
Shale (Campus site) 1.244E-05 1090 1559
Granite 1.786E-06 2409 4107
Dolerite 1.408E-06 2631  4773
Dolomite  1.148E-06 2881  6262
Sandstone (Campus site)  2.009E-05 1643 2011

  
Table E2 - Resonant ultrasound spectography results
Rock Type Calculated Resonance Frequency Recorded Resonance Frequency
Hz Hz
TMG Sandstone 94 95
Schist 194 190
Quartzite 205 202
Gneiss 135 130
Shale (Campus site) 117 120
Granite 426 430
Dolerite 197 200
Dolomite 236 237
Sandstone (Campus site) 246 250


Table E3 - Elastic parameter results
Rock Type Shear Modulus Bulk Modulus Compressibility Lamé Variable µ
Kg/s²m Kg/s²m  Pa
TMG Sandstone 4.952E+09 2.485E+10 4.025E-11  4.952E+09
Schist 3.862E+09 1.761E+09 5.678E-10 3.862E+09
Quartzite 8.034E+09 2.344E+10 4.266E-11 8.034E+09
Gneiss 9.573E+09 6.633E+10 1.508E-11 9.573E+09
Shale (Campus site) 1.480E+09 1.054E+09 9.488E-10 1.480E+09
Granite 7.027E+09 1.106E+10 9.046E-11 7.027E+09
Dolerite  9.858E+09 1.930E+10 5.181E-11 9.858E+09
Dolomite 1.167E+10 3.958E+10 2.527E-11 1.167E+10
Sandstone (Campus site) 3.248E+09  5.352E+08 1.868E-09 3.248E+09



Table E 4 - Additional parameter results
Rock Type Lamé Variable λ Young's Modulus Poisson's Ratio Acoustic Impedance
Pa
TMG Sandstone  2.155E+10 1.393E+10 4.485E-01 3.283E+13
Schist  8.136E+08  6.694E+09 3.640E-01 2.602E+12
Quartzite 1.808E+10 2.163E+10 4.091E-01 3.465E+13
Gneiss 5.995E+10 2.740E+10 4.630E-01 9.466E+13
Shale (Campus site) 6.759E+07 3.024E+09 4.186E-02 1.312E+12
Granite 6.370E+09 1.740E+10 3.223E-01 1.339E+13
Dolerite 1.273E+10 2.527E+10 3.604E-01 2.749E+13
Dolomite 3.179E+10 3.188E+10 4.225E-01 5.565E+13
Sandstone (Campus site) 1.630E+09 3.223E+09 1.341E+02 6.439E+11

Although the study shows that specific storativity can be accurately determined by this system, it is important to realise that this system is also dependant on a number of things. The first is that the samples used in the testing process must be prepared very carefully. Attention to the cutting edge is essential, the flatter the cut, the better the result. The samples must also be selected to be as homogeneous as possible to avoid discrepancies between the time-of-flight and RUS results. The length of the sample must also be kept as long as possible to improve the sampling error induced. Although the system gives very good results due to the dual checking of time-of-flight and RUS methods results, it is always a good idea to check to results against average known specific storativity values for the rock type under test to determine a final result. This will give the user an idea of whether the results obtained are realistic or not, and may necessitate the need to test the sample again or use a different sample to compare the obtained values. Testing should be carried out in a noise-free environment to ensure that the results are not false and that all results should be checked at least twice to verify consistency.

Copies of this report are available from the Foundation price £15.00, less 20% for FWR members.