Hydrogeophysical Parameters Estimation for Aquifer Characterisation in Hard Rock Environment: A Case Study from Yaounde, Cameroon ()
1. Introduction
In the past decade, the importance of groundwater resource in Yaounde areas has increased considerably and interest in exploration for potential sources has grown. Exploitation of the resources must be carried out with extreme care in order not to deplete them, and to ensure a long-lasting use of water. Efficient management of groundwater resources, therefore, depends on accurate groundwater modelling to predict aquifer behaviour during exploitation. Several methods are available in groundwater hydrology for the evaluation and estimation of the hydraulic characteristics of aquifers, like transmissivity, hydraulic conductivity, and storability [1]. The most commonly used methods involve conducting pumping tests on existing or newly drilled wells followed by analysis and interpretation of pumping test data. However, it should be appreciated that such tests are capital and labour intensive, requiring several boreholes, many operatives, and a considerable amount of equipment [2]. Furthermore, the estimation of hydraulic conductivity is crucial for the reliable simulation of the groundwater flow of one aquifer. Geophysical methods, particularly those involving resistivity, can contribute considerably to increase accuracy of the groundwater model, not only by delineating the aquifer extension and marking structural features, but also by establishing a relation between geoelectrical and hydrogeological parameters. [3] has characterized and derived the transmissivity and hydraulic conductivity of the Neogene aquifer in Al-Salamyeh region in Syria through the application of vertical electrical sounding technique (VES). [4] used electrical soundings to estimate transmissivity in Italy. [5] established an empirical relation between aquifer electrical resistivity and aquifer hydraulic conductivity and a semi-empirical relation between the aquifer formation factor and hydraulic conductivity. [6] reported that the relation between transmissivity and transverse resistance is more meaningful. [7] noted that it is better to use a modified transverse resistivity instead of transverse resistance. This modification is used to consider variations in the groundwater quality. [8] analysed the correlation between aquifer and geoelectrical parameters in both the saturated and unsaturated zones of aquifers. [9] used geoelectric resistivity soundings for groundwater evaluation in two different areas, namely the city of New Qena and the El-Khatatba area in Egypt. The main objectives of this paper, therefore are:
• Establishing and verifying a field scale theoretical relationship between geoelectrical resistivity data and hydrogeological data (hydraulic conductivity, and transmissivity) in order to improve the characterization of aquifer parameters.
• Establishing the corresponding maps of the variations of hydraulic and electrical properties of the aquifer across the study area.
2. Description of the Study Area
The city of Yaounde is located on the western edge of the plateau of Southern Cameroon between longitudes 11˚E and 13˚E and latitudes 3˚N and 5˚N (Figure 1). Semiarid climatic conditions prevail in the area, with minimum and maximum temperature of 23˚C and 26˚C, respectively.
2.1. Geology
Yaounde city belongs to the Pan-African Chain of Central Africa [10]. The soil is made up of thin layer of topsoil, a clay sand horizon furniture, clay with occasional blocks of weathered rock underlying [11] and finally bedrock which forms the base. Its basement is made up (Figure 1) of migmatites and gneisses [12].
In Yaoundé, the bedrock is neither porous nor soluble, but it is discontinuities (faults, diaclases) the formation; this last being anisotropic and heterogeneous.
2.2. Hydrogeology
The study area is characterized by continuous alterites aquifers, approximately exploitable overlying water bearing fissures or fracture aquifers in the bedrock [13]. These types of aquifers are superimposed or isolated. In a crystalline medium, capacitive and conductive functions both exist within each aquifer. Generally, the weathered medium is capacitive while the basement is conductive [14].
3. Geoelectrical Measurements and Interpretation
The geoelectrical data was obtained using the Schlumberger electrode configuration. The method is based on measuring the potentials between a pair of electrodes, while transmitting direct current (DC) between another
Figure 1. Geological map of Yaoundé area (modified [19]).
electrode pair. The depth of penetration is proportional to the separation between the current electrodes. By varying the electrical electrode separation, information about stratification of the ground is provided. The soundings were carried with maximum current electrode spacing ranging to 80 m. The electrical resistivity (ρ) of the medium is determined from the measurement of potential difference (ΔV) and injected current (I) as:
(1)
K is the geometric coefficient or array constant. The VES curves were obtained by plotting the apparent resistivity against electrode spacing, a computer program Genres [15], was used to reduce the geo-electrical sounding curves into values of thickness and resistivity of individual[11] layers. A total of seventeen (17) VES stations were sampled and the interpretation of sounding curves is summarized in [13]. The accuracy in estimating the thickness and electrical resistivity of the aquifer were maintained while interpreting the VES data at RMS error < 6%. A typical resistivity curve is shown in Figure 2.
Figure 2. Sounding curves and relevant lithological sections in the study area.
3.1. Pumping Tests Data Collection and Interpretation
In carrying out a pumping test, groundwater was pumped from the borehole and the response of the aquifer was measured in the same or nearby observation boreholes. A model was then used to estimate transmissivity values from the aquifer response. The heterogeneity of the hard rock system has been modeled as an equivalent porous medium. Thus, the primary and secondary porosity and the transmissivity distribution are replaced with a continuous porous medium having equivalent hydraulic properties. The Jacob’s method has been used in conjunction with the [16] method for interpretation of the pumping tests. Aquifer bulk resistivity at pumping sites has been obtained from krigged estimates of aquifer resistivity data from VES stations (Figure 3). Aquifer layers have been taken as those overlying the basement layer. The tests consisted of two phases: the productive phase which lasted 1 h followed by a recovery phase, which was maintained until the water level in the borehole recovered or until three readings in succession were identical.
During the aquifer test, records of water levels before and after pumping, well discharge rate and the duration of the pumping test were made. The measurement of water levels was carried out in the pumped wells using an electric sounder, which is triggered when the tape is in contact with water surface.
3.2. Model Parameters
A unit square cross-section area cut out of a group of n layers of infinite lateral extent is taken into consideration in order to derive the model parameters.
The total transverse unit resistance R is given by
(2)
where hi and ρi are respectively the layer thickness and the resistivity of i layer in the section.
The total longitudinal conductance S is
(3)
Figure 3. Iso-resistivity of the aquifer map.
The longitudinal layer conductance Si can also be represented by
(4)
where σi the layer conductivity. Conductivity in this case is analogous to the layer transmissivity Ti used in groundwater hydrology, given by
(5)
where Ki is the hydraulic conductivity of the i layer of thickness hi.
R and S in Equations (2) and (3) are called the DarZarrouk parameters, which have been shown to be a powerful tool during the interpretation of groundwater survey data [17]. The relationship between the transmissivity T and transverse resistance R can be explained as follows:
(6)
A similar relationship can also be derived between the transmissivity T and aquifer longitudinal conductance S, such as
(7)
In areas where the geological setting and water quality do not vary greatly, the product Kσ remains fairly constant [6]. Thus, knowing the values of K from the existing boreholes, and σ from the sounding interpretation around the boreholes, one can evaluate the transmissivity and its variation from one place to another through the determination of R or S related to the aquifer, according to Equations (5) and (6) [3]. The calculated values of the hydraulic parameters correspond to the mean values, as deduced from all the aforementioned methods. The values of field transmissivity from pumping tests of the alluvial aquifer were used for comparison with the computed transmissivity. The transmissivity values from pumping tests are shown in Table 1.
4. Results and Discussion
The application and interpretation of VES measurements carried out in the Yaounde area allow both thickness and resistivity of the aquifer to be obtained. Figure 3 shows the variation of the resistivity in the study area. Here the southern part of the study area has higher concentration of contour lines than the northern part.
The minimum resistivity of 4 ohm·m is observed in point VES 10, and a maximum resistivity of 196 ohm·m is obtained in point VES 8, with an average of 59.76 ohm·m and a standard deviation of 63.69 ohm·m.
This resistivity map indicates the presence of a lowresistivity zone, reflecting the direction of groundwater from east to west, and from southeast to northwest,
Table 1. Aquifer parameters from field test method.
where the recharge area is concentrated in the middle of the study area.
Figure 4 shows the distribution of the thickness in the Yaoundé zone, where a minimum thickness of 11.3 m is observed in point VES 7, and a maximum thickness of 63.3 m is obtained in point VES 2, with an average of 37.6 m and a standard deviation of 16.7 m. However, the resistivity of the layer depends more on the saturation of the layers and not necessarily on the thickness of the aquifer, hence higher resistivity may not correlate with areas of thicker aquifer.[12]