The study describes the effect of calculating a generalised mean transmissivity or hydraulic conductivity value for a region or aquifer system as it pertains to South Africa. Resource determination of an area is usually driven by the determination of the bulk flow parameters, such as hydraulic conductivity and storativity values. At this stage a decision is usually made on the basis of either maintaining the area under natural conditions (no pumping), or an abstraction (pumping) scenario is envisaged. In both instances water levels, hydraulic testing and distribution of the water resources (aquifer) are required. Since it is not possible to evaluate the total area for these parameters certain assumptions have to be made such as that an average bulk flow parameter for an area can be determined. In wide-ranging situations a simple average of observation points is assumed to be sufficient.
A systematic research approach was followed in which a three-step process was used to evaluate methods of calculating these mean values.
In the first instance a conceptual model approach was used, and all bulk flow parameters were generated by means of matrices to represent the natural system. Three typically employed mean values (arithmetic, geometric and harmonic) were calculated for two different dimensional matrices, i.e., N x N (N = 100 and 1000) with different hydraulic conductivity zones. In addition the relative difference between these hydraulic conductivity zones were steadily increased to mimic observed parameters in the field, i.e. typical hydraulic conductivity of shale (K = 0.01 m/d) versus a fracture zone (K = 100 m/d). In all instances the harmonic mean performed the best and as the number of sample sets were increased, a reduction in mean values were observed. As part of the conceptual model approach, two typically encountered scenarios were investigated, i.e. natural flow and forced gradient conditions. Under these two scenario conditions the harmonic mean performed the best to estimate the actual observed hydraulic conductivity value.
Secondly, case studies were presented which highlighted the influence of sample size on observed parameters. Additionally, the effect of the differences between the low and high hydraulic conductivity zones on the calculated mean value as a function of sample size, was also reported. In all of these case studies the harmonic mean was the closest in approximating the observed hydraulic conductivity. It is evident from this section that the number of host rock (formation) hydraulic conductivity values plays a critical part in the mean value calculation since it is general practice in South Africa not to report low yielding borehole hydraulic test values.
In the third step, the results were discussed in the context of a more general approach to the problem of calculating a regional mean hydraulic conductivity of transmissivity value. The estimation of representa-tive transmissivity values were discussed as seen from a stochastic modelling perspective as well as from the deterministic point of view. A comparison between main stream groundwater and oil industry specialists were noted in which both groups share the fundamental training but differ on the methodology of determining the observed transmissivity values. The impact of horizontal heterogeneities and different fracture networks was discussed and the influence these features have on the actual transmissivity value obtained, i.e. the influence of internal boundaries on hydraulic test data. Scale effects were also addressed from a regional perspective, with a focus on apparent scaling and the actual regional transmissivity value which should be obtained.
The findings of this study are that in essence using geostatistical methods are not advised if regional transmissivity values are required from a South African perspective. The reason behind this statement is that the distribution of transmissivity values in an area does not follow the basic precepts that are required for these methods to work. In general the values are discontinuous in distribution and statistically skewed. Furthermore, the presence of transmissivity areas or points that differ significantly in magnitude, i.e. transmissivity values which differ by more than two orders, can be located within one meter from each other. The explanation of this phenomenon is the presence of dolerite dykes, which create baked-fractured zones with exceptionally large transmissivity values compared to the extremely low transmissivity ranges of the surrounding country rock (shales, mudstone and siltstone). In addition, the lack of data concerning low-yielding or âdryâ boreholes is a major source of concern since it influences the calculated mean value to a high degree.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:ufs/oai:etd.uovs.ac.za:etd-08192014-160953 |
| Date | 19 August 2014 |
| Creators | Steyl, Gideon |
| Contributors | Prof GJ van Tonder |
| Publisher | University of the Free State |
| Source Sets | South African National ETD Portal |
| Language | en-uk |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.uovs.ac.za//theses/available/etd-08192014-160953/restricted/ |
| Rights | unrestricted, I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to University Free State or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. |
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