Groundwater Geophysics Phần 8 docx

13 Vertical flows in groundwater monitoring wells 381 Altogether, it is important to distinguish between the diverse types of vertical density driven transport processes, so to differentiate between processes that enhance gradients (double-diffusion) and processes that flat- ten gradients (overturning convection). 13.2.2 Field equipments and procedures Free convective flow in the water column of groundwater monitoring wells can be detected by means of high-resolved geophysical temperature and fluid conductivity logs. Borehole logging systems and their advantages over simple hydrogeological probes operated via a hand-driven cable reel were previously described in Sect. 13.1.2. For investigating density driven vertical flows, a combined probe for detection of temperature and water conductivity is used. Measurements have to be taken during the downward movement of the logging tool (probe) and it is crucial that the water column is undisturbed and has achieved thermal equilibrium with the surrounding formation. For a reliable interpretation, simultaneously acquired temperature and fluid conductivity logs with high resolution in depth and measured value are required along with hydraulic pressure which is either measured directly or calculated from depth to water table. To detect even the smallest signatures in the measured parameters the probe should be lowered with a slow velocity (e.g 1-2 m/min) and operated with a high sampling rate (e.g. hundred samples per meter). 13.2.3. Data processing and interpretation For detecting and differentiating vertical density driven transport processes in groundwater monitoring wells or shallow boreholes up to several hundred meters depth, two interpretation algorithms have been recently devel- oped (Berthold and Börner 2007). From the geophysical borehole logs the fulfillment of the necessary condition for the onset of free convection, a destabilizing inhomogeneity in density, can be evaluated. Identifying an instable density layering, however, is not sufficient to decide about the actual presence of a free convective flow. The water column can absorb a certain level of instability without leaving its initial stable state. A density instability that exceeds this critical threshold is the required sufficient condition whereby convection or double-diffusion, respectively, sets in with the smallest disturbance of the density field. The two computational algorithms approach the problem of detecting vertical density driven transport processes from a cause orientated (driving 382 Frank Börner, Susann Berthold forces) and an effect orientated (e.g. convection cells) perspective, respectively. Cause orientated interpretation The cause orientated interpretation is based on the fact that density driven vertical transport processes can be distinguished according to the prevail- ing temperature and saline concentration gradients and its directions in the water column. Necessary conditions for the occurrence of a certain density driven transport processes are shown in Fig. 13.9. Sufficient conditions for free overturning convection to start are determined through a stability analysis based on Rayleigh's theory (Rayleigh 1916), relating a so-called Rayleigh number to a critical Rayleigh number. The dimensionless Rayleigh number Ra describes the ratio of the dissipa- tive forces (viscosity and heat/mass diffusion) to the impelling forces (buoyancy). For thermal convection it is defined as: z T D lg Ra T t Δ Δ ν α 4 = (13.2) Input values are gravity acceleration g, thermal expansion coefficient α , temperature gradient T Δ / z Δ , thermal diffusivity D t , kinematic viscosity ν , and a characteristic length l that depends on geometry. For water columns, i.e. vertical channels with circular cross section, the characteristic length corresponds to the radius. The critical Rayleigh number is the decisive threshold that describes the state when convection starts. The thermal critical Rayleigh number (first critical mode) for water columns in monitoring wells can be calculated from the following equation (Gershuni and Zhukhovitskii 1976): [] ) ~ 26927 ~ 147942567(3) ~ 10333(3 ) ~ 71(5 96 2 λλλ λ ++−+ + = columnc Ra (13.3) where λ ~ is the ratio of the thermal conductivities of fluid and surrounding material. The critical thermal Rayleigh number calculated from this equation deviates from the exact value by only a fraction of one percent (Ger- shuni and Zhukhovitskii 1976). Free convection in water columns depends strongly on their diameter and thermal properties of the surrounding material. The smaller the diameter of a water column the larger the friction forces along the wall around the water column (e.g. casing or borehole) and the larger the stabilizing 13 Vertical flows in groundwater monitoring wells 383 effect. Free convection can start at considerably lower temperature gradients in large diameter wells or boreholes as in small diameter wells (Fig. 13.10). 0.001 0.01 0.1 Temperature gradient in K/m 1 10 100 1000 10000 The r mal Rayleigh numbe r Depth below water table ( ∅ 50 mm) 10 m 100 m critical Rayleigh number for a water column in bedrock with thermal conductivity of 2.1 W/(Km) ∅ 125 mm ∅ 100 mm ∅ 75 mm ∅ 50 mm Fig. 13.11. Thermal Rayleigh numbers for four casing diameters as function of thermal gradient. Results are based on water with a temperature of 10°C and a fluid conductivity of 0.3 mS/cm. The shaded zone above the critical thermal Rayleigh number indicates the zone of thermal convection For a quick estimate, a critical thermal Rayleigh number of 148 can be used resulting from a mean thermal conductivity of 2.1 W/(mK) for rock and a value of 0.6 W/(mK) for water. The value can be adjusted according to the actual thermal conductivity of the surrounding formation, in case a high-precision analysis is required. For solutal convection a solutal Rayleigh number Ra s is defined in anal- ogy to the thermal Rayleigh number as: z S D lg Ra S s Δ Δ− = ν β 4 (13.4) with haline contraction coefficient β , solutal gradient zS ΔΔ / , and solutal diffusivity S D . In this equation the solutal gradient carries a negative sign as it has an inverse effect on density ρ compared to the temperature gradient (Eq. 13.5). 384 Frank Börner, Susann Berthold () ST β α ρ ρ +−= 1 0 (13.5) For solutal convection, the critical Rayleigh number for a shallow vertical layer is Pi 4 ≈ 97.4. As Gershuni and Zhukhovitskii (1976) expect that this number is also representative for a more general case, this value is used as a first approximation for water columns. The chance of pure solutal convection in a groundwater monitoring well (i.e. only salinity but not temperature varies with depth), however, is low. The critical thresholds for density driven flows caused by both temperature and solutal gradient are based on the so-called local stability. It describes the ratio of the stabilizing to the destabilizing component (Turner 1973): 1± ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂∂ ∂∂ −= z/S z/T R β α ρ (13.6) The exponent +1 is applied if temperature decreases with depth and the exponent -1 otherwise. In case ρ R >> 1, the water column is stable. If R ρ tends towards one, double-diffusion may occur even if the water column is globally stable. If the local stability is smaller than one, but positive (0 < ρ R < 1), instability and possibly convective mixing occurs. As critical thresholds are used: ρ R < 1 for thermosolutal convection, 1 < ρ R ≤ 2 for saltfingers (Saiki et al. 2000), and 1 < ρ R ≥ 10 for diffusive convection (Kelley et al. 2003). Necessary parameters for the cause orientated algorithm are calculated from geophysical borehole measurements of temperature-conductivity- (pressure) probes and compared to the above mentioned critical thresholds. By doing so, each section of the water column can be rated according to its stability or instability. Not only is it possible to differentiate between stable and unstable sections, also the kind of density driven vertical transport process can be identified based on the conditions comprised in Fig. 13.9. Effect orientated interpretation The effect orientated interpretation is based on the idea that free convection phenomena like convection cells and thermohaline staircase are virtu- ally directly observable in primary measurement logs like temperature and fluid conductivity. A thermohaline staircase - a phenomenon of double-diffusion - is a very distinct feature and easily recognizable in high-resolved temperature and 13 Vertical flows in groundwater monitoring wells 385 fluid conductivity logs without any further filtering or data processing due to its characteristic steps and jumps (Fig. 13.12). Similar signatures in temperature and fluid conductivity logs were, so far, interpreted as hydraulic leakages if occurring in the cased section or forced vertical convection if occurring in the screened section of the well (Fig. 13.12). Consequently, a technical control of the well casing, as often demanded in hydrological monitoring, requires an additional determination of the causes for steps or jumps in temperature and fluid conductivity logs. 14.2 14.5 14.8 15.1 15.4 15.7 Temperature [°C] 80 70 60 50 40 30 Depth [m] 03691215 Conductivity [mS/cm] 13 14 15 16 17 Temperature [°C] 180 170 160 150 140 130 120 Depth [m] 036912 Conductivity [mS/cm] 9 1011121314 Temperature [°C] 200 180 160 140 120 100 80 Depth [m] 1.25 1.3 1.35 1.4 1.45 1.5 Conductivity [mS/cm] PVC casing screen clogged screen steel casing forced convection free convection Fig. 13.12. Characteristic temperature and fluid conductivity logs in groundwater monitoring wells with forced convective flow (left) and double-diffusive free convective flow (middle and right), indicating their similarities (Berthold and Börner 2007) Convection cells are leading to small temperature perturbations in the otherwise linear temperature gradient. Owing to their small amplitude, a series of convection cells - a phenomenon of overturning convection - is less easy recognizable in high-resolved temperature and fluid conductivity logs and the corresponding oscillations are often dismissed as noise and thus disregarded. In a so called synthetic convection log, this oscillations can be sepa- rated, and thus emphasized, by determining the difference of a smoothed input log and a weighted moving average filtered log (Fig. 13.13). Owing to the fact that temperature and fluid conductivity typically change simultaneously and that both affect density, a decision concerning stability or vertical flow requires knowledge about the combined effect, i.e. the density profile in the water column. The synthetic convection log is, hence, calculated from a synthetic density log, which is derived from temperature, fluid conductivity, and hydraulic pressure logs using the equation of state for freshwater (Chen and Millero 1986). Thereby it is assumed, that sodium chloride is the key contributor to water conductivity and that density is insignificantly affected by dissolved gases. If other salt ions or a 386 Frank Börner, Susann Berthold significant amount of density-influencing dissolved gases exist in the in- vestigated water column, additional correction terms have to be imple- mented. Pressure or depth Temperature Hydrostatic pressure Conductivity Smoothing and high-pass filtering to eliminate global trend Synthetic convection log Synthetic water density log Fig. 13.13. Flow chart of the effect orientated interpretation algorithm Strong oscillations in the synthetic convection log indicate convection cells and small or no oscillations indicate the absence of convection cells (Fig. 13.15). In that way, the water column can be divided into sections without or with measurable vertical free convective flow. 13.2.4 Examples Measurement examples indicating thermohaline staircases due to double- diffusion in the water column are shown in Figs. 13.12 and 13.14. 0.40.450.50.550.6 Conductivity [mS/cm] 20 15 10 Depth [m] 11.3 11.4 11.5 11.6 11.7 Temperature [°C] 0.36 0.38 0.4 0.42 0.44 Conductivity [mS/cm] 30 25 20 15 10 Depth [m] 9.8 9.9 10 10.1 10.2 Temperature [°C] Double-diffusion saltfinger type Double-diffusion diffusive convection type Fig. 13.14. Thermohaline staircases due to double-diffusion in the water column of two open boreholes 13 Vertical flows in groundwater monitoring wells 387 A measurement example, including temperature and fluid conductivity borehole logs and the corresponding outputs from the cause and effect orientated algorithm is shown in Fig. 13.15. With the cause orientated algorithm it can be decided whether sufficient conditions for a density driven flow are reached and what type of density driven flow is present. The effect orientated algorithm indicates sections with measurable free convective flow. Results from the cause and effect orientated interpretation algorithm compare well. Both computational algorithms, however, have their little weaknesses. The cause orientated algorithm reaches its limit at thermohaline staircases with very high parameter contrasts, as it will identify the convective well mixed layers as stable regions. Nonetheless, the thermohaline staircase can be read off directly from the primary borehole logs, as indicated above. The effect orientated algorithm reaches its limit if temperature gradients and so oscillations become very small, especially in data with a comparatively high noise level. It is then difficult to distinguish between actual oscillations and oscillations induced by instrumental noise. In that case, a precise filtering of the noise frequencies is needed, requiring exact knowledge of the noise level. 9.65 9.75 9.85 Temperature [°C] 20 19 18 17 16 15 14 13 12 11 10 9 Depths [m] 0.27 0.28 0.29 0.3 Conductivity [mS/cm] -0.001 0 0.001 Synthetic convection log [kg/m 3 ] TC SC TSC SF DC Type of density-driven flow 10 Sufficient conditions for density-driven flow yes no TC - Thermal convection SC - Solutal convection TSC - Thermosolutal convection SF - Saltfingers DC - Diffusive convection Fig. 13.15. Temperature and fluid conductivity borehole logs shown alongside with results from effect and cause orientated interpretation Combining cause and effect orientated interpretation algorithm helps diminishing theses difficulties and significantly improves the reliability of the interpretation as causes and effects of free convection are examined at the same time. 388 Frank Börner, Susann Berthold Barczewski B, Grimm-Strele J, Bisch G (1993) Überprüfung der Eignung von Grundwasserbeschaffenheitsmeßstellen. Wasserwirtschaft 83:72-78 Berthold S, Börner F (2006) Untersuchung der verfälschenden Wirkung vertikaler Konvektion in Grundwassermessstellen auf in-situ-Messungen oder entnommene Grundwasserproben. Gemeinsame Mitteilungen des DGFZ e.V. und seiner Partner 3:175-191, ISSN: 1611–5627 Berthold S, Börner F (2007) Detection of free vertical convection and double- diffusion in groundwater monitoring wells with geophysical borehole measurements. Environmental Geology (Online First). DOI: 10.1007/s00254-007- 0936-y Chen C, Millero FJ (1986) Precise thermodynamic properties for natural waters covering only the limnological range. Limnology and Oceanography 31:657- 662 Church EP, Granato EG (1996) Bias in Ground-Water Data Caused by Well-Bore Flow in Long-Screen Wells. Ground Water 34:262 - 273 Drury MJ (1984) Borehole temperature logging for the detection of water flow. Geoexploration 22:231-243 Ferson LM (1983) Standards and Practices for Instrumentation. Instrument Soci- ety of America, Research Triangle Parc, North Carolina Flach GP, Elci A, Molz JF (2003) Detrimental Effects of Natural Vertical Head Gradients on Chemical and Water Level Measurements in Observation Wells: Identification and Control. Journal of Hydrology 281:70-81 Fricke S, Schön J (1999) Praktische Bohrlochgeophysik. Enke im Thieme Verlag, Stuttgart Gershuni G, Zhukhovitskii E (1976) Convective stability of incompressible fluids. Keter Publishing House Jerusalem Ltd. Hayashi M (2004) Temperature-electrical conductivity relation of water for environmental monitoring and geophysical data inversion. Environmental Moni- toring and Assessment 96:119-128 Hutchins SR, Acree SD (2000) Ground Water Sampling Bias Observed in Shal- low, Conventional Wells. Ground Water Monitoring and Remediation 20:86 - 93 Jessop AM (1990) Thermal Geophysics. Developments in Solid Earth Geophysics 17:38 – 257 Kelley DE, Fernando H, Gargett A, Tanny J, Özsoy E (2003) The diffusive regime of double-diffusive convection. Progress in Oceanography 56:461-481 Kelly WE, Mareš S (1993) Applied geophysics in hydrogeological and engineer- ing practice. Elsevier, Amsterdam, ISBN: 0444889361 9780444889362 Keys WS (1997) A Practical Guide to Borehole Geophysics in Environmental In- vestigations. CRC Press Inc, Lewis Publishers Liptak BG, Venzel L (1982) Instrument Engineers’ Handbook. Chilton Book Company, Radnor, Pennsylvania Martin-Hayden JM, Robbins GA (1997) Plume distortion and apparent attenuation due to concentration averaging in monitoring wells. Ground Water 35:339 - 346 13.3 References 13 Vertical flows in groundwater monitoring wells 389 Michalski, A (1989) Application of temperature and electrical-conductivity logging in ground water monitoring. Ground Water Monitoring and Remediation 9:112-118 Molz FJ, Young SC (1993) Development and application of borehole flowmeters for environmental assessment. Log Analyst 34:13–23 Newhouse MW, Izbicki JA, Smith GA (2005) Comparison of velocity-log data collected using impeller and electromagnetic flowmeters. Ground Water 43:434-438 Paillet FL (2000) A field technique for estimating aquifer parameters using flow log data. Ground Water 38:510–521 Rayleigh L (1916) On convection currents in a horizontal layer of fluid, when the higher temperature is on the under side. Philosophical Magazine 32:529-546 Ruddick B, Gargett AE (2003) Oceanic double-diffusion: introduction. Progress in Oceanography 56:381-393 Saiki EM, Kerr RM, Large W (2000) Three-dimensional initiation of thermohaline fingering. In: Proceedings of the IUTAM Symposium on Developments in Geophysical Turbulence, Bolder, USA Simmons CT, Fenstemaker TR, Sharp Jr JM (2001) Variable-density groundwater flow and solute transport in heterogeneousporous media: approaches, resolu- tions and future challenges. Journal of Contaminant Hydrology 52:245-275 Solodov IN, Malkovsky VI, Pek AA Benson SM (2002) New evidence for the combined influence of vapor condensation and thermal convection on groundwater monitoring wells. Environmental Geology 42:145-150 Turner JS (1973) Buoyancy Effects in Fluids. Cambridge University Press, Cam- bridge, UK Further readings Brandt A, Fernando HJS (1995) Double-diffusive convection. Geophysical Mono- graph 94 Johnson DE, Pile KE (2002) Well Logging in Nontechnical Language. 2nd Edi- tion, PennWell Publishing, Tulsa Luckner L, Schestakov WM (1991) Migration Processes in the Soil and Ground- water Zone. Lewis Publishers Inc. Molz FJ, Melville JG (1996) Discussion of combined use of flowmeter and time- drawdown data to estimate hydraulic conductivities in layered aquifer systems. Ground Water 34:770 Paillet FL (2000) A field technique for estimating aquifer parameters using flow log data. Ground Water 38:510-521 Paillet FL, Reese RS (2000) Integrating borehole logs and aquifer tests in aquifer characterization. Ground Water 38:713-725 Plawsky JL (2001) Transport Phenomena Fundamentals. Marcel Dekker, New York 14 Aquifer structures – pore aquifers For the water supply, pore aquifers are the most important kind of aquifers. After some general remarks on geophysical exploration of pore aquifers, case studies and field examples on pore aquifer surveys under different hydrogeological condition are presented. This includes buried Quaternary valleys in Northern Germany and Denmark (Helga Wiederhold), large TEM surveys for Quaternary aquifers on a Danish island (Flemming Jørgensen et al.), and a VES survey to map fractured limestone aquifers in Egypt (Mohamed Mabrouk et al.). 14.1 Pore aquifers – general Reinhard Kirsch 14.1.1 Definition Groundwater can be found in pore spaces of unconsolidated and consolidated sedimentary rocks and weathering layers, in joints and fissures of hard rock, in fault zones, and in karst caves. Aquifers with water reservoir stored in pore spaces are called pore aquifers or porous aquifers. Similar conditions for geophysical exploration are in aquifers connected to joints and fissures of rocks, e.g., originated by cooling of igneous rocks. So, also this type of aquifer will be treated as pore aquifer, while fault zones and karst caves, where the water reservoir is embedded in nearly impermeable material, are treated in Chap. 15 “fracture zones and caves”. 14.1.2 Porosity – a key parameter for hydrogeology The volume of open space (pore space) in rocks in relation to the total rock volume is called porosity Φ: total porespace V V =Φ (14.1) Porosity due to pore space between mineral grains or clastic rock frag- ments is called primary porosity; an additional porosity due to tectonic fractures or dissolution caves is called secondary porosity. Both porosities [...]... cross-section (Fig 14 .8) shows the characteristic geological structures for Northern Germany For the water supply the Neogene and Quaternary sand layers yield the important groundwater reservoirs Critical points for groundwater management and protection are areas where the normal layering is disturbed, e.g., by glacial valleys, by faults (not sketched in Fig 14 .8) or where the groundwater bearing layers... m- gS gS /s 2300 m Q Mg c fS 300 T c fS 0 Q Mg c fS 200 600 ms 400 300 T RR c fS 0 100 200 300 ms borehole borehole 387 5/2 387 5/1 SW CMP c) NE 20 40 60 80 100 120 elevation m.s.l 50 m 0m Ba se Q 0 LT borehole 387 5/2 0 S U fS 100 fS mS c fmS U U (LT) OGT 200 Q T ? OBKS HT 300 m borehole 387 5/1 UBKS fS gS c c U mS fS c mS fS VSP Vpave Vpint (m/s) 1000 2000 Cond_Log (mS/m) 3000 0 100 200 0 100 100 200 200... segments The interpretation of these signals is enabled or improved by logging and vertical seismic profiling (VSP) A groundwater observation well – 3 18 m deep - about 750 m south of the line in Fig 14.9 is used for this The seismic impulse source system Sissy (Wiederhold et al 19 98) is used as source, the receiver spacing is 4 m The VSP raw data (Fig 14.10a) show P wave signals of good quality The... methods turn out to be convincing for mapping buried valleys if a good conductive layer is embedded in less conductive material measured measured calculated calculated 1.95 2.0 2.0 1.95 2.1 2.1 1. 98 1. 98 2.0 1 .8 2.0 2.07 Q OGT OBKS HT UBKS UGT Fig 14.15 Gravity cross section Ellerbek Valley: left: simple model with a density contrast of 50 kg/cm3; right: more sophisticated model based on structural information... layers, the values for layers with resistivities exceeding 80 - 120 Ωm are not precisely determined; they just have a high resistivity Furthermore, for certain combinations of layer thicknesses and resistivities, equivalence problems make it impossible to determine either the exact thickness or exact resistivity of the layers (Fitterman et al 1 988 ) Like all electromagnetic diffusion methods, TEM has a... space partly filled with clay minerals, (e) porosity related to clay content (artificial sand – clay mixture, Marion et al 1992), (f) electrical resistivity related to clay content after Sen et al (1 988 ) The grey shaded area in Figs 14.1c and f denotes similar resistivities for clayey and clay-free material, this can lead to interpretation errors 394 Reinhard Kirsch Although pore aquifers are treated... Wiederhold et al 19 98) The quality of high resolution shallow reflection survey depends on the field parameters and selection of an appropriate seismic source With the technical developments of the last years a good choice of seismic sources and seismographs is available Examples from two surveys in Northern Germany are shown corresponding to the valley types sketched in Fig 14 .8 (Wiederhold et al... a 24 channel Geometrics seismograph with 10 m geophone spacing First arrivals of shot and reversed shot were interpreted by the GRM-method (Palmer 1 981 ) The steeply dipping basement (5935 m/s) in the depth range 20 – 60 m is overlain by an aquifer (17 48 m/s) and unsaturated sands (405 m/s) The aim of this survey was to find drill locations; a well drilled at the right side of this profile could use... m, and the length of the deeper valleys can be more than 100 km Buried valleys are of great hydraulical importance If they are filled with sandy material they are groundwater reservoirs of great yield, but often the valleys also incise deep groundwater reservoirs or cut through their covering layers The map of maximum glacial extent of the Quaternary glaciations shows that North America and Northern... HydroGeophysics Group of the University of Aarhus (Sørensen et al 2005) that provides rapid and dense lateral coverage and is used in hydrogeological surveys and especially in buried valley mapping in Denmark (Danielsen et al 2003) with the same geologic characteristic as the above reported survey after Poulsen and Christensen (1999) To cover even larger areas the newest development of the HydroGeophysics . S (1993) Applied geophysics in hydrogeological and engineer- ing practice. Elsevier, Amsterdam, ISBN: 044 488 9361 9 780 44 488 9362 Keys WS (1997) A Practical Guide to Borehole Geophysics in Environmental. same time. 388 Frank Börner, Susann Berthold Barczewski B, Grimm-Strele J, Bisch G (1993) Überprüfung der Eignung von Grundwasserbeschaffenheitsmeßstellen. Wasserwirtschaft 83 :72- 78 Berthold. conductivity logs. 14.2 14.5 14 .8 15.1 15.4 15.7 Temperature [°C] 80 70 60 50 40 30 Depth [m] 03691215 Conductivity [mS/cm] 13 14 15 16 17 Temperature [°C] 180 170 160 150 140 130 120 Depth