Assessment of Unconfined Aquifer Hydraulic Characteristics Using Self-Potential Method: Case Study in Laylan Sub-Basin, Kirkuk, Iraq

Abstract


Introduction
The study area is located in the Kirkuk governorate, northeastern part of Iraq (Fig. 1), it is about 26 km to the southeast of Kirkuk city with coordinates 35° 28' 41 '' -35° 11' 58'' latitudes, and 44° 38' 00'' -44° 23' 10'' longitudes, and it is about 210 km² area.many geological formations are outcrops within the study area.The exposed geological units in the study area are Fatha, Injana, Muqdadiyia, and Bai Hassan formations and Quaternary sediments.All these units belong to the Tertiary and Quaternary period.
Generally, the oldest sediments are exposed on the external borders of the studied basin, while the recent sediments covered the mid of the basin (Abo-Khumra, et al., 2021).During the last years of the last period and the years that followed.The use of geophysical techniques in the environmental application of shallow depth targets has rapidly increased lately; (Oliveti, & Cardarelli, 2019).The technique of self-potential (SP) widely used in environmental applications (Reynolds, 1997).There are a lot of global and local studies in this field, such as Ali ( 2018) carried out Self-potential investigations in farming land nearby Quldara Village, Northeast Kikruk town to determine Near surface and subsurface soil texture, organic materials percentage, pH, electrical conductivity Ec and electric resistivity in the laboratory.Study chemical analyses and redox potential are there available for comparison with the SP measurements, the hydroelectric problem of porous rocks: inversion of the position of the water table from self-potential data.The self-potential (SP) method is a fast and cheap reconnaissance tool sensitive to groundwater flow in unconfined aquifers.Jinadasa and De Silva (2009), resistivity imaging and selfpotential applications in groundwater investigations in hard crystalline rocks.the study obtained show areas of low resistivities and negative self-potential anomalies, which correlate well with the possibly areas with groundwater accumulations.Four wells were selected in this study in order to collect data that will be analyzed later for the purpose of identifying the hydrogeological characteristics in the study area, Fig. 2 shows the distribution of the selected wells in the study area and Table 2 shows the coordinates of each of these wells where the values of the ground water static levels of these wells were monitored relative to surface and the change in their levels during pumping operations, where the hydraulic properties will be evaluated through data yielded from pumping test operations for the selected wells.In order to delineate relationships between the self-potential measurements and the wells hydrological properties, the SP device is setup nearby the tested well that readings where recording during the draw down operation .The flow of groundwater during a pumping test experiment is responsible for a measurable electrical field at the ground surface owing to the electro kinetic coupling between the Darcy velocity and the electrical current density.This electrical field can be measured passively with a network of non-polarizable electrodes connected to a digital multichannel multimeter with a high internal impedance (>10 Mohm).the electrical response is analyzed in terms of piezometric head distribution.This new methodology, which we call ''electrography'' allows visualization of preferential fluid flow pathways and the distribution of heads during pumping test experiments.Wher the aims of this tudy was Obtaining mathematical equations that are used to calculate draw down values by using the self-potential value, by which the characteristics of the basin are evaluated at a high level of accuracy.

Materials and Methods
The self-potentials survey was carried out using the field techniques electrode configurations, Potential Self-potentials measurement was carried out using two non polarizable porous pot electrodes connected to precision voltmeters capable of measuring to at least 1 mV.Each electrode is made up of a copper electrode dipped in a saturated solution of copper sulphate which can percolate through the porous base to the pot (Reynolds, 1997); (Ali, 2018).Where the readings of four wells were taken in the study area, as the Table1 shows the values of their coordinates, the Fig. 2 shows the distribution of wells over the area, and the Fig. 3 shows the lithology of the area surrounding those wells  3. Results

PW1
The well elevation was 331 m. the pumping test was conducted in two cases of pumping and recovery, The total depth of the well is 120 m .Because of the inability to identify the true lithology of this well, it was relied on the lithology of nearby wells, as shown in Fig. 3 to identify the lithology of the layers that the well penetrates, and then identify the saturated thickness that was calculated and was (b) = 50m.The depth of the groundwater was measured by groundwater depth detector.static water level was (52.5 m).The pumping rate of the well is (8 liters / sec).The water draw down with time and self-potential reading recording indicated in Table 2 .In order to find the type of relationship between each of the draw down and time with the values of (SP) on the other hand (Fig. 5) was drawn where the values were represented.For the purpose of calculating Hydraulic properties of aquifer, three methods Jacob ,Theis and Hantush were applied (Fig. 4) (Theis et al., 1940;Cooper & Jacob, 1946;Hantush et al.,1960), and the average was taken for all Methods.Transmissivity value was = (12.32m 2 / day), with hydraulic conductivity value = (0.23 m/day).The relation between the time of drawdown of ground water level and self-potential value and its recovery, Fig. 5 shows decreasing of Sp value on with increasing the drawdown time other hand the (Sp) values and vice-versa in upward or recovery part, one could deduced that Sp reading is sensitive with the water movement or it can be affected by the proximity and distance of water from the ground surface drawn the self-potential value with drawdown of ground water level hows an inverse linear relation between them r = 0.91 (1) Where : = draw down.Sp= self-potential Equation 1 has strong correlation coefficient between the ground water draw down and selfpotential measured values, so it could be applied in case of absence of one of the parameters , i.e draw down values to calculate the well hydrological properties.

PW2
the well is located at the intersection of longitude (44° 31' 44''.94) and latitude (35° 18' 24''.20) (Fig. 2) a depth of 130 m, a diameter of 20 cm, and elevatioof 340 m the depth of the static water (63.5 m), the well penetrates the quaternary deposits (Al-Ahmed, 2017), the experimental pumping test duration was 90 minutes with a constant discharge of (4 L/Sec), the data of draw down was recorded versus time.The water Transmissivity was calculated from the average of the three methods Jacob, Theis and Hantush it was T=(17.22 m2 / day) (Fig. 6).Table 3 shows the data of the pumping test, draw down Self-potential values versus time.The hydraulic conductivity (K)was =( 0.21 m/day) was calculated for a saturated thickness of 80 m obtained from the lithology of the surrounding wells (Fig. 3) .In Fig. 7 which represents the relation between the time of drawdown of water table and selfpotential value and its shows increasing of water table depth with decreasing of Sp value on other hand, the Sp value increasing with upward or recovery part which indicates that Sp reading is sensitive with the water movement or it can be affected by the proximity and distance of water from the earth surface, the self-potential value with drawdown of water table shows a liner inverse relation between them R2 = 0.703.draw down(m) b

PW3
This well locates in the study area with cross of coordinates longitude (44° 34' 35''.49) and latitude (35° 15' 42''.70), its depth equal to 120 m, a diameter of 25 cm, and at elevation 331m.a.s.l, the static water level is 44m and as it is illustrated in Fig. 2, and the well penetrates the quaternary sediments, and the productivity of the well depends mainly on the sandy gravel layers which equal to10 L/Sec, the data of the draw down was recorded versus time, then the pumping was stopped after the level was reached the steady state.The water conductivity (T) was calculated, from the average of the three methods Jacob, Theis and Hantush it was T=(78.29 m2 / d) (Fig. 8).Table 4 shows the data of the pumping test, selfpotential values .the hydraulic conductivity (K) was calculated for a saturated thickness of 45 m, which was 1.739 m/day respectively, and that the value of the storage coefficient (4.32 ).

4. PW4
This well is located in the study area with the intersection of the coordinates (44° 32' 22''.27)-( 35° 18' 33''.82) and as shown in Table 1 and its depth is equal to 130 m, and its diameter is 25 cm, and at elevation of 355m.above sea level the static water level is 72m and the well penetrates the quaternary sediments, and the productivity of the well mainly depends on the gravel layers as well as some clay layers, saturated thickness (B=40m) .Herein here is problem concerns the well designation which could not get down the groundwater depth detector in pumping test operation to measures the water draw down , the test constrain to measure the self-potential values accordingly with the water draw down elapse times (Table 5).

90
The constructed mathematical relation between the time of drawdown of and self-potential value (Which is directly proportional to the increase in water depth ) with decreasing of (SP) could deduced that (SP) reading , indicating sensitivity between the SP reading with the water movement or draw down of water table of this well (Fig. 10).After conducting a field survey of the wells referred to previously using the test pumping method and recording the decrease in the groundwater level in the selected wells during the unit time, readings were also taken simultaneously for the self-potential difference device and recording the values obtained during the passage of time and continuous pumping, as the data were collected and which were installed in each of the tables listed above , the empirical yields results were as follows: 1-In the well (PW1), the value of the correlation coefficient (r) between self-potential and draw down was (-0.95) and this value indicates that the correlation is of a very strong inverse type 2-In the well (PW2), the value of the correlation coefficient (r) between self-potential and draw down was (-0.8), and this value indicates that the correlation is of a strong inverse type.3-In the well (PW3), the value of the correlation coefficient (r) of self-potential and draw down was (-0.86), which is a value that indicates that the type of correlation 4-As for the observation well (PW4), the value of the coefficient (r) between the correlation between time and ) SP (in the cases of decline (-0.91).it is strong inverse type .Statistically.SP values: (y) Draw down:(x) time: (t)

Calculate some Hydraulic Characteristic of Aquifer by Using Equations
Through the statistical processes in which the values taken from the field by the pumping test process for well(pw4), in which the values of the self-potential are measured from the field , the draw -0.95 -0.84 -0.86 -0.91 r down were calculated using equation 1 and the results were was listed in the Tables 5 and 7 then transmissivity and subsequently the conductivity with the storage coefficients are calculated.T (c) =(10 m 2 / d) , the hydraulic conductivity ( K=0.25 m/day)

Conclusions
• The geophysical self-potential value is very sensitive to the ground water level changes, the coefficient between draw down and Sp it was strong inverse type in the all pumping well.• The two linear equations have been constructed from the statistical relationship between self-potential and draw down can be applied to determine the hydrological characteristic of another well if the well was in the seam basin condition.• Transmissivity value for the wells (PW1, PW2, PW3 ,PW4) were (12.32 m 2 /day), (17.22 m 2 /day), (78.29 m 2 /d), (10 m 2 /d) respectively.Therefore, the (SP) device can be considered a successful alternative to traditional measurement methods.• It was found from the study that the average values of hydraulic conductivity for the wells (PW1, PW2, PW3 ,PW4) were (0.113 m/day, 0.21 m/day, 1.74 m/day, 0.25 m/day) respectively.This convergence of values can indicate the sensitivity of the used (SP) device.• The geophysical method using the SP device was effective and highly sensitive to changes in the groundwater level in the wells during the pumping process.Thus, we can learn about the characteristics of the hydraulic reservoir by using the SP device, as it became possible to replace the value of the drawdown by the equation that was derived by Correlation coefficient.

Fig . 1 .
Fig .1.Location map of the study area

Fig. 2 .Fig. 3 .
Fig. 2. Distribution of the pumping well test over the study area

Fig. 7 .
Fig. 7. Relationship in PW2 (a) between time and sp ; (b) between draw down and SP

Fig. 9 .
Fig. 9. Relationship in PW3 (a) between time and SP; (b) between draw down and SP

Table 2 .
Drawdown and SP versus time for (PW1)

Table 3 .
Drawdown and sp versus time for PW2

Table 4 .
Drawdown and sp versus time for PW2

Table 5 .
Time and sp value for (PW4)

Table 6 .
Type of correlation between the sp and each of the time and draw down