INVESTIGATION OF RELATIONSHIPS BETWEEN GEOELECTRIC AND HYDRAULIC PARAMETERS IN A QUATERNARY ALLUVIAL AQUIFER IN YENAGOA, SOUTHERN NIGERIA

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1 Ife Jounal of Science vol. 17, no. 1 (015) INVESTIGATION OF RELATIONSHIPS BETWEEN GEOELECTRIC AND HYDRAULIC PARAMETERS IN A QUATERNARY ALLUVIAL AQUIFER IN YENAGOA, SOUTHERN NIGERIA Okiongbo, K. S. and Oboie, E. 1 Geophysics Unit, Depatment of Physics, Nige Delta Univesity, Wilbefoce Island, Bayelsa State, Nigeia Depatment of Geology, Nige Delta Univesity, Wilbefoce Island, Bayelsa State, Nigeia (Coesponding Autho: okenlani@yahoo.com) th th (Received: 5 Dec., 014: Accepted: 10 Mach, 015) ABSTRACT In an attempt to establish empiical electic-hydaulic elationships fo the pupose of analyzing suface esistivity soundings, geoelectical soundings using the Schlumbege aay wee caied out in Yenagoa and envions. Fouteen (14) VES stations wee occupied acoss the study aea. The field data wee intepeted using Intepex IX1D compute softwae and the aquife esistivity (ρ) at each location was estimated. The hydaulic conductivity (K) detemined fom a efeence boehole was combined with the nomalized electical conductivity (σ) to estimate a constant Kσ. This constant was integated with the Da Zaouk paametes and used to estimate the hydaulic conductivity and tansmissivity values at othe VES locations whee K values wee unknown. The esults showed that the hydaulic conductivity vaied fom m/day while the tansmissivity vaied fom m /day. Coelation of geoelectic and hydaulic paametes of the aquife showed that the hydaulic conductivity (K) exhibited bette coelation with the appaent fomation facto (F a) than tansmissivity (T). Tansmissivity was linealy elated to nomalized tansvese esistance (T R) via the equation T = 0.018T R while the hydaulic conductivity was elated to the aquife esistivity () though the equation K = These empiical equations could be used to pedict the hydaulic paametes in goundwate studies in the aea. Keywods: Hydaulic Conductivity, Tansmissivity, Aquife, Tansvese Resistance, Appaent Fomation Facto INTRODUCTION Coelations between hydaulic and geoelectic paametes have been studied by many authos (Kelly, 1977; Niwas and Singhal, 1981; Onuoha and Mbazi, 1988; Mbonu et al., 1981). These c o e l a t i o n s a e i m p o t a n t b e c a u s e empiical/semi-empical elations deived fom such elationships could be used to extapolate aquife paametes using suface esistivity measuements. Physical chaacteistics of aquifes such as hydaulic conductivity, tansmissivity and stoativity that contol goundwate flow and tanspot ae vey impotant popeties and ae usually estimated fo goundwate flow model calibation. These paametes ae also impotant popeties fo the assessment of contaminated land, and fo safe constuction of civil engineeing stuctues. Conventional methods fo the estimation of these aquife popeties equie the application of field hydogeological methods such as pump tests which involve measuement of the ise and fall of wate level with espect to time. The wate-level fluctuations with time ae then intepeted to aive at aquife paametes. Sometimes, laboatoy expeiments such as pemeamete measuements ae conducted to obtain small-scale estimates of poosity, hydaulic conductivity and totuosity. These measuements, howeve, ae time-consuming and costly. Pumping test and pemeamete measuements in the laboatoy ae based on the Physics of fluid flow in poous media (de Lima and Niwas, 000). In the electical geophysical method, the flow of electical cuent though the ock is used to detemine the esistivities and thicknesses of diffeent geological fomations which have a esistivity contast. The two flows, goundwate flow and electical cuent, ae though diffeent in pinciple, and ae govened by diffeent physical laws, have an obvious analogy. This is because the physical conditions (totuosity and poosity) that contol the electic cuent flow (and electical esistivity) also contol the lateal flow of the wate (hydaulic conductivity) in poous media (de Lima and Niwas, 000). Exploiting this similaity, attempts have been made by many

2 164 Okiongbo and Oboie: Investigation of Relationships between Geoelectic and Hydaulic Paametes eseaches to obtain estimates of hydaulic paametes using esistivity data (Bussian, 1983; Kuma et al., 001; Singh, 005). Studies fom diffeent geological settings evealed contasting empiical models fo the estimation of hydaulic conductivity (K) fom esistivity data. Diect and invese elationship between the log of esistivity (ρ) and the log of K have been epoted, depending on the subsuface mateial (Huntley, 1986). In the case of elatively clay-fee sand and silt, an invese elation between the log of esistivity (ρ) and the log of K was epoted due to the mutual dependence of ρ and K on poosity (Heigold et al., 1979). Hydaulic conductivity inceases with poosity ( f) but ρ deceases (Achie, 194). In the case of clay-containing mateial, a diect elationship between the log of esistivity (ρ) and the log of K is epoted due to the mutual dependence of ρ and K on clay content (Kosinski and Kelly, 1981). Hydaulic conductivity deceases with clay content, as does ρ due to suface conduction in clays. Although valuable in a paticula setting, it is appaent that a geneal model between K and ρ does not exist (Puvance and Andicevic, 000). Though empiically established electical-hydaulic elationships often wok easonably well, howeve, they ae usually only applicable to the specific study site o to sites with simila chaacteistics (Huntley, 1986; Puvance and Andicevic, 000). The objective of this study was to detemine the elationship between aquife hydaulic popeties and Vetical Electical Sounding (VES) deived esistivity in the unconsolidated alluvial sediments of Yenagoa and envions. Study Aea o The study aea lies between latitudes and o Noth of the equato and longitudes o o and East of the pime meidian within the coastal aea of the Nige Delta (Fig. 1). LEGEND Yenagoa VES Stations MWS (Meade belt wooded black swamps-sand, Gavel, fesh wate swamps) MS (Mangove swamps-sand, clay and mangove swamps) AB (Abandoned beach idgessand and pebbles) Fig.1. Map of Bayelsa State Showing the Study Aea and the VES Stations

3 Okiongbo and Oboie: Investigation of Relationships between Geoelectic and Hydaulic Paametes The aea is a peneplain, intesected by numeous ceeks, ives and lakes (e.g Epie Ceek, Ikoli Rive, Oxbow lake). The study aea has suface elevation anging between 40 and 50 m above mean sea level and coves an aea of about 100 km. It is located within the topical equatoial climate egion with a o tempeatue ange of 3 38 C. The geomophology of the aea is monotonously flat and the egional slope is towads the south. Aveage annual ainfall is about 3000 mm and this seves as the majo souce of goundwate echage. The study aea is undelain by the deposits of the Quatenay Coastal Plain Sands, which esult fom the sediment laden dischages of the Rive Nige that is spead on the delta by its vaious tibutaies. These sediments ae geneally an admixtue of medium to coase-gained sands, sandy clays, silts and clays. The deposits constitute the shallow unconfined aquife that is exploited by shallow (< 30m) boeholes and hand dug wells that seve as the pimay wate supply souce fo many semiuban and uban communities in the aea and in the Nige Delta egion in geneal (Amajo 1991). Wate table in lage sections of the Nige Delta is close to the suface but subject to spatial and seasonal vaiations. In the study aea, the wate table is about 3 4 m duing the dy season (Ekine and Osobonye, 1996). Duing the wet season, the wate table ises consideably, in some cases, to the gound suface. Based on the esults of hydogeochemical analysis, the electical conductivity (EC) of the goundwate vaies between µs/cm. Total dissolved solids (TDS) vaies between 51 and 1410 mg/l. Okiongbo and Douglas (013) epoted that the concentation of majo ions in the goundwate is within acceptable limits except in some few cases. MATERIALS AND METHOD Fouteen (14) geoelectical soundings using the Schlumbege aay with a maximum cuent electode half-spacings (AB/) anging between 100 and 00 m wee caied out acoss the study aea (Fig 1) with the ABEM SAS 3000 Teamete Resistivity Mete. The positions and suface elevations of the VES locations wee also ecoded duing the suvey with a GPS eceive. The calculated appaent esistivity data wee inveted using the Intepex, 1-D invesion 165 softwae. All depths wee constained with the lithological log fom the neaest boehole. The model paametes fo each VES station ae pesented in Table 1. All the VES stations wee located close to pe-existing wate boeholes. Goundwate samples wee collected fom the boeholes. These goundwate samples wee analysed fo the Electical Conductivity (EC). The electical conductivity of the goundwate and the VES intepetation esults, wee used to detemine the appaent fomation factos using Achie (194) equation. Pump test was caied out on the existing boehole at Okaka close to VES station 8 to detemine the hydaulic conductivity. The pumping test data wee intepeted using Jacobs staight line method (Fette, 1994) following the fomula:.3q T T =, K = 4 p Ds H (1) Whee T is the tansmissivity in m /s, Q is the ate 3 of dischage in m /s, s is the slope in m, K is the hydaulic conductivity in m/s, and H is the satuated thickness in mete obtained fom the boehole data. The tansmissivity and hydaulic conductivity values obtained wee m /day and 8.0 m/day espectively. Achies law (Achie, 194) elates the bulb esistivity of a fully satuated ganula medium to its poosity and the esistivity of the fluid within the poes accoding to equation: () whee ρ b is the bulk esistivity, ρ w is the esistivity of the satuating wate, f is the poosity of the medium, and the dimensionless coefficients aand m (cementation facto and coefficient of satuation) depend on the ock type. The atio b b = a f w -m w is called the Fomation Facto, F. This is the tue Fomation Facto when the fomation is a clay-fee, clean sand. If the aquife is a clayey o shaly sand, then the Fomation Facto becomes appaent (F a). The tansvese unit esistance (T R) and the longitudinal conductance (L C) (both ae Da- Zaouk paametes) ae defined as follows:

4 166 h L C = T R = h (3) (4) whee h is the thickness of the aquife and ρ is the esistivity of the aquife. The goundwate flow though an aquife is govened by the tansmissivity T, which is expessed as: T = Kh (5) whee K is the hydaulic conductivity. Niwas and Singhal (1981) detemined analytically the elationship between tansmissivity and tansvese esistance on one hand and the tansmissivity and longitudinal conductance on the othe. Niwas and Singhal (1985) modified these elationships by using a modified aquife esistivity (ρʹ), known as nomalized aquife esistivity (Kosinski and Kelly, 1981) to incopoate vaiations in the quality of goundwate. Howeve, the modification facto is the atio of the aveage poe wate esistivity and ( - w)the poe wate esistivity (ρ w) at the measuing point. The nomalized aquife esistivity (ρ) is defined as = (6) Thus, the hydaulic and electic paametes wee combined to give a elationship between tansmissivity (T) and nomalized tansvese esistance (T R) as follows: Divide equation 5 by equation 4 T Kh K = = TR h KTR T = KsT (7) R = Fo nomalized Tansvese esistance (T R) ʹ R T = ρh (8) Theefoe, ʹ ʹ T = =KσT R (9) ʹ ʹ whee ρ and σ ae nomalized esistivity and conductivity espectively. ʹ If o α = Kσ (10) Then - w w KT R K = a Okiongbo and Oboie: Investigation of Relationships between Geoelectic and Hydaulic Paametes T = α T R (11) The elationship between tansmissivity (T) and ʹ nomalized longitudinal conductance (L ) can be established thus: Divide equation 5 by equation 3 T LC Kh =, h hence T = K L C Fo nomalized longitudinal conductance T = K = L C KLC C (1) h whee L C = whee T = Aquife tansmissivity (m /s) K = Hydaulic conductivity (m/s) T R= Tansvese esistance of the aquife (Ohm- m ) -1 L C = Longitudinal conductance (Ohm ) Ρ= nomalized aquife esistivity (Ohm-m) The poduct KLC was assumed to be constant at a efeence point of the aquife and theefoe known. Thus, we define b = KLC (13) Pio to the investigation of tansmissivity vaiations thoughout the aquife, the appopiate Kσ constant was calculated. The Kσ poduct was expessed in tems of both tansvese esistance (T R) and longitudinal conductance (L C). Mazac et al. (1985) obseved that conditions whee the tansvese esistance is dominant occu when the aquife ests on a thickness of less pemeable mateial athe than diectly on bedock. Since the aquife ests on less pemeable clayey mateials as shown in the sounding cuves at all stations in the study aea, it was moe appopiate to estimate the tansmissivity vaiations in this aquife by means of the tansvese esistance (Eq. 11) athe than the longitudinal conductance (Eq. 1). The α = Kσ constant was calculated by using the K value fom the pumping test (K = 8.0 m/day) and the modified electic conductance (σ) fom each VES station. This constant has been combined with the nomalized tansvese esistance (T R) at the emaining stations to

5 Okiongbo and Oboie: Investigation of Relationships between Geoelectic and Hydaulic Paametes investigate the tansmissivity vaiations thoughout the study aea. Hydaulic conductivity was computed using equation (10). Table gives a summay of the intepeted esults showing the aquife thicknesses, esistivities, hydaulic conductivities, and tansmissivities. RESULTS AND DISCUSSION The VES cuves in the studied aea ae lagely dominated by fou laye KH and HK type (Figs. & 3) with the occuence of a limited numbe of thee laye K type and five laye KHK and HKH types. Based on the coelation between the VES esults and the lithological infomation fom the 167 boehole, thee majo subsuface layes ae ecognised. The topmost laye, consisting of calcaeous loam mixed with oganic matte (Amajo, 1991), is epesented in the geoelectical column by the uppe two layes of which the uppe one has a thickness of about 0.6 m and a esistivity of 189 Ωm. The undelying laye has a thickness of about 1.7 m with a esistivity of 349 Ωm and consists of silty sand (Fig. ). The incease in the esistivity value fom the suface downwads is attibuted to the incease in gain size. (a) (b) 1000 VES 3 ) -m m h (O y it iv s ist e R t n e a 100 p A VES 3 Depth m (Akenfa) (Ohm -m) Top soil Silty sand Fine-medium sand Sandy clay Electode Spacing AB/ [m] 30 Top soil Fine-medium sand Sandy clay Fig. (a) VES (VES 3) Cuve and (b) Coelation of the VES Intepetation Results with the Lithology of the neaest Boehole The thid laye esistivity is 560 Ωm and the laye is intepeted to be the fesh wate satuated alluvial sand aquife. The boehole lithology log shows that the aquife is composed of fine-medium gained sand. The fouth geoelectic laye extends fom the base of the ovelying alluvial aquife to a depth of 7.7 m. This laye which has a elatively low esistivity (7 Ωm) is egaded as wate satuated sandy clay. The fifth laye has a esistivity of 710 Ωm which is typical of sand.

6 168 Okiongbo and Oboie: Investigation of Relationships between Geoelectic and Hydaulic Paametes (a) (b) Depth Lithology VES 1 Desciption (m) (Ohm-m) Top soil Clay Fine medium sand Top soil Clay Figue 3 shows the esults obtained fom VES-1 location. The fist geoelectic laye extends fom the gound suface to a depth of 0.4 m with laye esistivity of 65 Ωm. The second geoelectic laye extends to a depth of m, with esistivity value of 10 Ωm. This laye coesponds to clay. The thid geoelectic laye extends to a depth of about 33 m and has a laye esistivity of 06 Ωm. This laye coesponds to fine-medium gained sand. The estimated hydaulic conductivity and tansmissivity values using equations 10 and 11 espectively ae pesented in Table 1. The obtained esults indicate that the tansmissivity values ae high ove the entie aea and vay fom m /day. This is consistent with the findings of Fine-medium Sand Fig. 3 (a) VES (VES 1) Cuve and (b) Coelation of the VES (VES 1) Intepetation Results with the Lithology of the neaest Boehole. Amajo (1991) in the study aea using pump test data. The hydaulic conductivity values ange fom m/day. These esults ae ealistic in view of the fact that the aquife is composed of unconsolidated fine-medium-coase sand (Mbonu et al., 1991). Figues 4 and 5 show plots of hydaulic conductivity and tansmissivity vesus the appaent fomation facto. The plots indicate an incease in hydaulic conductivity and tansmissivity with incease in appaent fomation facto. Howeve, the estimated hydaulic conductivity (K) values exhibit bette coelation with the appaent Fomation Facto (F a) than tansmissivity (T) with appaent Fomation Facto (F a).

7 (Ωm) Okiongbo and Oboie: Investigation of Relationships between Geoelectic and Hydaulic Paametes 169 Fig. 4. Relation Between Hydaulic Conductivity and Appaent Fomation Facto Table 1. Geoelectical Laye Paametes (Resistivity and Thickness) Obtained fom the Intepetation of Geoelectical Soundings Thicknesses (m) Resistivity VES No VES Location h 1 h h 3 h 4 ρ 1 ρ ρ 3 ρ 4 ρ 5 RMS Eo (%) 1 Tombia H/C Azikoo Akenfa III Emeyal- Otueke Rd D Wessey- Igbogene D Egiani-Emeyal II Tombia WateBoad Otueke EJARS Fam-Elebele Agbobii Ongolo Ogbia Sec Sch Otueke Table. Aquife Electical and Hydaulic Paametes Estimated fom Vetical Electical Sounding Data VES VES h ρ ρw σ ρ K o TR TR α=kσ α=kσ K c=αρ T No Location (m) (Ohm-m) (Ohm-m) (m/day) ( Ohm-m ) ( Ohm-m ) (m/day) (m /day) 1.0 Tombia H/C Aziko Akenfa III Emeyal - Otueke D Wessey Pe Emey D Egiani Tombia WateBoad Otueke Ejas Fam Elebele Agbobii Ongolo-Okaka Ogbia Sec Sch Otueke h=aquife thickness (m), ρ= aquife esistivity (Ohm-m), ρ = nomalized aquife esistivity (Ohm-m), ρ w= poe wate esistivity (Ohm-m), K o= hydaulic conductivity fom pump test data (m/day), T R = tansvese esistance (Ohm-m ), T R = nomalized tansvese esistance (Ohm-m ), K c = Computed hydaulic conductivity (m/day), T = tansmissivity (m /day)

8 170 Okiongbo and Oboie: Investigation of Relationships between Geoelectic and Hydaulic Paametes Pfannkuchs (1969) model povides the theoetical basis fo the obseved elationship between hydaulic conductivity and appaent fomation facto and suggested that in addition to poosity and totuosity, thee is a mutual dependence of appaent fomation facto and hydaulic conductivity on gain size. Fig.5. Relationship Between Tansmissivity and Appaent Fomation Facto Fohlich and Kelly (1985) obseved that if the aquife is chaacteised by a high esistivity in a typical K type cuve, the tansvese esistance is a unique paamete and can diectly be coelated with the hydaulic tansmissivity. Coelation between tansmissivity (T) and nomalized tansvese esistance (T R) is pesented in Figue 6. The egession line fitted to these data indicates the following elationship. The slope of the line is positive which indicates an incease in T with an incease in T R. This is in ageement with an ealie wok done by Fohlich and Kelly (1985). The obseved scatte is attibuted to hydaulic and electical anisotopies, as well as lithological and minealogical vaiations, gain size, and size and shape of the poes and poe channels (Salem, 1999). T=0.018T R (R =0.83) Fig. 6. Relation Between Tansmissivity and Modified Tansvese Resistance

9 Okiongbo and Oboie: Investigation of Relationships between Geoelectic and Hydaulic Paametes Figue 7 shows a linea elationship between hydaulic conductivity (K) and esistivity of the aquife mateials. This is consistent with the obsevation of Kelly, (1977) and Niwas and 171 Singhal, (1981) that in aquife mateials composed of gavel, coase sand and sand with clay, the hydaulic conductivity inceases with esistivity. Fig.7. Relation Between Hydaulic Conductivity and Resistivity The egession line fitted to these data is of the fom: K = (R =0.58) CONCLUSION The pupose of this study was to investigate elationships between hydaulic and geoelectic paametes in an alluvial aquife. The pactical applicability of the method lies in the fact that the hydaulic conductivity must be known fo any efeence point in the aea, then it can be possible to get a faily good idea of the hydaulic paametes of the aquife in othe locations fom geoelectical soundings. The obtained esults indicate that the tansmissivity values ae high ove the entie aea and vay fom m /day. The hydaulic conductivities ange fom m/day. Computed hydaulic conductivity (K) values exhibit bette coelation with the appaent fomation facto (F ) than tansmissivity a (T). This study also shows a diect elationship between tansmissivity and nomalized tansvese esistance. Hydaulic conductivity was found to be linealy elated with aquife esistivity. Because of the inhomogenity of the alluvial deposits, it would be uneasonable to expect unique esults fom geoelectics. Howeve, the empiical elations obtained in this study can be used to pedict the hydaulic paametes as peliminay infomation fo futhe management of goundwate supply in the aea. ACKNOWLEDGEMENTS The authos ae gateful to the Postgaduate Exploation Geophysics students in the Depatment of Physics who assisted with the VES data acquisition. We also thank the anonymous eviewes fo thei citical comments and suggestions that impoved the quality of the manuscipt. REFERENCES Amajo, L. C Aquifes in the Benin Fomation (Miocene Recent), Easten Nige Delta, Nigeia. Lithostatigaphy, H yd a u l i c s a n d wa t e q u a l i t y. Envionmental Geology & Wate Science, 17, Achie, G The electical esistivity log as an aid in detemining some esevoi chaacteistics. Petoleum Tansactions of the Ameican Institute of Minealogical and Metallugical Enginees, 146, Bussian, A. E Electical conductance in poous medium. Jounal of Geophysics, 48, de Lima, O. A. L., Niwas, S Estimation of hydaulic paametes of shaly sandstone

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