Generation of Hydrogen Gas as a Result of Drilling Within the Saturated Zone

Hydrogen gas was discovered within the steel casing above standing water in a percussion-drilled borehole on the Hanlord Site in south-central Washington state. In situ measurements of the borehole fluids indicated anoxic, low-Eh (<-400 mV) conditions. Ground water sampled from adjacent wells in the same formation indicated that the ground water was oxygenated. H₂ was generated during percussion drilling, due to the decomposition of borehole waters as a result of aqueous reactions with drilled sediment and steel from the drilling tools or casing. The generation of H₂ within percussion-drilled boreholes that extend below the water table may be more common than previously realized. The ambient concentration of H₂ produced during drilling was limited by microbial activity within the casing-resident fluids. H₂ was generated abiotically in the laboratory, whereby sterilized borehole slurry samples produced 100 times more H₂ than unsterilizcd samples. It appears that H₂ is metabolized by microorganisms and concentrations might be significantly greater if not for microbial metabolism.     

A Single Packer Method for Characterizing Water Contributing Fractures in Crystalline Bedrock Wells

Water levels and water quality of open borehole wells in fractured bedrock are flow-weighted averages that are a function of the hydraulic heads and transmissivities of water contributing fractures, properties that are rarely known. Without such knowledge using water levels and water quality data from fractured bedrock wells to assess groundwater flow and contaminant conditions can be highly misleading. This study demonstrates a cost-effective single packer method to determine the hydraulic heads and transmissivities of water contributing fracture zones in crystalline bedrock wells. The method entails inflating a pipe plug to isolate sections of an open borehole at different depths and monitoring changes in the water level with time. At each depth, the change in water level with time was used to determine the sum of fracture transmissivities above the packer and then to solve for individual fracture transmissivity. Steady-state wellbore heads along with the transmissivities were used to determine individual fracture heads using the weighted average head equation. The method was tested in five wells in crystalline bedrock located at the University of Connecticut in Storrs. The single packer head and transmissivity results were found to agree closely with those determined using conventional logging methods and the dissolved oxygen alteration method. The method appears to be a simple and cost-effective alternative in obtaining important information on flow conditions in fractured crystalline bedrock wells.     

Cautions and Suggestions for Geochemical Sampling in Fractured Rock

Collecting water samples for geochemical analyses in open bedrock boreholes or in discrete intervals of boreholes intersected by multiple fractures is likely to yield ambiguous results for ground water chemistry because of the variability in the transmissivity, storativity, and hydraulic head of fractures intersecting the borehole. Interpreting chemical analyses of water samples collected in bedrock boreholes requires an understanding of the hydraulic conditions in the borehole under the ambient flow regime in the aquifer as well as during sampling. Pumping in open boreholes, regardless of the pumping rate and the location of the pump intake, first draws water from the borehole and then from fractures intersecting the borehole. The time at which the volumetric rate of water entering the borehole from fractures is approximately equal to the pumping rate can be identified by monitoring the logarithm of drawdown in the borehole as a function of the logarithm of time. Mixing of water entering the borehole from fractures with water in the borehole must be considered in estimating the time at which the pump discharge is representative of aquifer water. In boreholes intersected by multiple fractures, after the contribution from the borehole volume has diminished, the contribution of fractures to the pump discharge will be weighted according to their transmissivity, regardless of the location of the pump intake. This results in a flux-averaged concentration in the pump discharge that is biased by the chemical signature of those fractures with the highest transmissivity. Under conditions where the hydraulic head of fractures varies over the length of the borehole, open boreholes will be subject to ambient flow in the water column in the borehole. In some instances, the magnitude of the ambient flow may be similar to the designated pumping rate for collecting water samples for geochemical analyses. Under such conditions, the contributions to the pump discharge from individual fractures will be a function not only of the transmissivity of the fractures, but also of the distribution of hydraulic head in fractures intersecting the borehole. To reduce or eliminate the deleterious effects of conducting geochemical sampling in open boreholes, a straddle-packer apparatus that isolates a single fracture or a series of closely spaced fractures is recommended. It is also recommended that open boreholes be permanently outfitted with borehole packers or borehole liners in instances where maintaining the hydraulic and chemical stratification in the aquifer is of importance. In a field example, a comparison of results from sampling in an open borehole and in discrete intervals of the same borehole showed dramatic differences in the concentrations of chemical constituents in the water samples, even though chemical field parameters stabilized prior to both open borehole and discrete interval sampling.     

雄安新区现今地温场特征及成因机制

雄安新区位于渤海湾盆地冀中坳陷内,区内主要包含有牛驼镇凸起、容城凸起、高阳低凸起等次级构造单元.通过分析该区最近实测的8口钻井测温曲线和108块岩石热导率实测数据并结合前人的研究成果,对雄安新区内部地温梯度、大地热流分布规律等进行了分析.结果表明雄安新区内部不同构造单元地层的地温梯度在垂向上可划分为两段：上部沉积盖层段,地温梯度值在25.2~58.9℃·km^-1之间;下部白云岩段地温梯度较低,主要在5℃·km^-1附近.同时地温梯度在平面上具有明显的区域性特征,牛驼镇凸起地温梯度值最高,范围为46.5~58.9℃·km^-1;容城凸起区地温梯度次之,范围在32.0~40.9℃·km^-1之间;凹陷及低凸起区地温梯度较低,唯一的实测值显示为25.2℃·km^-1.通过搜集的热流值绘制的热流图也显示出凸起区热流值高,凹陷区热流值相对较低的特点.雄安新区较高的现今地温场特征与其处于弧后拉张的构造背景相关.同时,基岩地层凹凸相间的格局、砂泥质盖层直接覆盖在碳酸盐地层之上的地层组合、热储层段内的地下水对流作用、断裂的发育等共同造成了雄安新区较高的现今地温场特征.     

Strain and tilt changes measured during a water injection experiment at the Nojima Fault zone, Japan

Abstract In order to make geophysical and geological investigations of the Nojima Fault on Awaji Island, Japan, three boreholes measuring 1800 m, 800 m and 500 m deep were drilled into the fault zone. The fault is one of the seismic source faults of the 1995 Hyogo-ken Nanbu earthquake of M 7.2. A new multicomponent borehole instrument was installed at the bottom of the 800 m borehole and continuous observations of crustal strain and tilt have been made using this instrument since May 1996. A high-pressure water injection experiment within the 1800 m borehole was done in February and March 1997 to study the geophysical response, behavior, permeability, and other aspects of the fault zone. The injection site was located approximately 140 m horizontally and 800 m vertically from the instrument. Associated with the water injection, contraction of approximately 0.7 × 10⁻⁷ str (almost parallel to the fault) and tilt of approximately 1 × 10^-7 rad in the sense of upheaval toward the injection site were observed. In addition to these controlled experiments, the strainmeter and tiltmeter also recorded daily variations. We interpret strain and tilt changes to be related to groundwater discharge and increased ultra-micro seismicity induced by the injected water.     

A tracer dilution method for fracture characterization in bedrock wells

This investigation was undertaken to develop an integrated method of downhole fracture characterization using a tracer. The method presented can be used to locate water-bearing fractures that intersect the well, to determine the ambient fracture flow rate and hydraulic head, and to calculate fracture transmissivity. The method was tested in two fractured crystalline bedrock wells located at the University of Connecticut in Storrs. The method entails injecting a tracer (uranine dye) into the well, while at the same time water is pumped out of the well. After steady-state conditions are reached, a borehole tracer concentration profile is developed. The dilution of the tracer is used to locate the inflowing fractures and to determine their flow rate. The fracture flow rate, plus the drawdown in the well, is then used to determine the fracture hydraulic head, transmissivity, and ambient flow rate.     

Origin and Extent of Fresh Paleowaters on the Atlantic Continental Shelf, USA

While the existence of relatively fresh groundwater sequestered within permeable, porous sediments beneath the Atlantic continental shelf of North and South America has been known for some time, these waters have never been assessed as a potential resource. This fresh water was likely emplaced during Pleistocene sea-level low stands when the shelf was exposed to meteoric recharge and by elevated recharge in areas overrun by the Laurentide ice sheet at high latitudes. To test this hypothesis, we present results from a high-resolution paleohydrologic model of groundwater flow, heat and solute transport, ice sheet loading, and sea level fluctuations for the continental shelf from New Jersey to Maine over the last 2 million years. Our analysis suggests that the presence of fresh to brackish water within shallow Miocene sands more than 100 km offshore of New Jersey was facilitated by discharge of submarine springs along Baltimore and Hudson Canyons where these shallow aquifers crop out. Recharge rates four times modern levels were computed for portions of New England's continental shelf that were overrun by the Laurentide ice sheet during the last glacial maximum. We estimate the volume of emplaced Pleistocene continental shelf fresh water (less than 1 ppt) to be 1300 km³ in New England. We also present estimates of continental shelf fresh water resources for the U.S. Atlantic eastern seaboard (10⁴ km³) and passive margins globally (3 × 10⁵ km³). The simulation results support the hypothesis that offshore fresh water is a potentially valuable, albeit nonrenewable resource for coastal megacities faced with growing water shortages.     

Seismicity changes related to a water injection experiment in the Nojima Fault Zone

Abstract A water injection experiment was carried out by the scientific drilling program named the 'Nojima Fault Zone Probe' during the two periods 9–13 February and 16–25 March 1997. The pumping pressure at the surface was approximately 4 MPa. The total amount of injected water was 258 m³. The injection was made between depths of 1480 m and 1670 m in the Disaster Prevention Research Institute, Kyoto University (DPRI) 1800 m borehole drilled into the Nojima Fault zone. A seismic observation network was deployed to monitor seismic activity related to the water injections. Seismicity suddenly increased in the region not far from the injection hole 4 or 5 days after the beginning of each water injection. These earthquakes were likely to be induced by the water injections. Most of the earthquakes had magnitudes ranging from −2 to +1. Numerous earthquakes occurred during the first injection, but only one could be reliably located and it was approximately 2 km north of the injection site. Between the two injection periods, earthquakes concentrated in the region approximately 1 km northwest of the injection site. During and after the second injection experiment, earthquakes were located approximately 1.5 km west of the injection site. Those earthquakes were located approximately 3 km or 4 km from the injection point and between 2 km and 4 km in depth. Values of intrinsic permeability of 10⁻¹⁴–10⁻¹⁵ m² were estimated from the time lapse of the induced seismic activity. The coefficient of friction in the area where the induced earthquakes occurred was estimated to be less than 0.3.     

An Unsteady State Tracer Method for Characterizing Fractures in Bedrock Wells

Evaluating contaminants impacting wells in fractured crystalline rock requires knowledge of the individual fractures contributing water. This typically involves using a sequence of tools including downhole geophysics, flow meters, and straddle packers. In conjunction with each other these methods are expensive, time consuming, and can be logistically difficult to implement. This study demonstrates an unsteady state tracer method as a cost‐effective alternative for gathering fracture information in wells. The method entails introducing tracer dye throughout the well, inducing fracture flow into the well by conducting a slug test and then profiling the tracer concentration in the well to locate water contributing fractures where the dye has been diluted. By monitoring the development of the dilution zones within the wellbore with time, the transmissivity and the hydraulic head of the water contributing fractures can be determined. Ambient flow conditions and the contaminant concentration within the fractures can also be determined from the tracer dilution. This method was tested on a large physical model well and a bedrock well. The model well was used to test the theory underlying the method and to refine method logistics. The approach located the fracture and generated transmissivity values that were in excellent agreement with those calculated by slug testing. For the bedrock well tested, two major active fractures were located. Fracture location and ambient well conditions matched results from conventional methods. Estimates of transmissivity values by the tracer method were within an order of magnitude of those calculated using heat‐pulse flow meter data.     

Comparison of formation and fluid-column logs in a heterogeneous basalt aquifer

Deep observation boreholes in the vicinity of active production wells in Honolulu, Hawaii, exhibit the anomalous condition that fluid-column electrical conductivity logs and apparent profiles of pore-water electrical conductivity derived from induction conductivity logs are nearly identical if a formation factor of 12.5 is assumed. This condition is documented in three boreholes where fluid-column logs clearly indicate the presence of strong borehole flow induced by withdrawal from partially penetrating water-supply wells. This result appears to contradict the basic principles of conductivity-log interpretation. Flow conditions in one of these boreholes was investigated in detail by obtaining flow profiles under two water production conditions using the electromagnetic flowmeter. The flow-log interpretation demonstrates that the fluid-column log resembles the induction log because the amount of inflow to the borehole increases systematically upward through the transition zone between deeper salt water and shallower fresh water. This condition allows the properties of the fluid column to approximate the properties of water entering the borehole as soon as the upflow stream encounters that producing zone. Because this condition occurs in all three boreholes investigated, the similarity of induction and fluid-column logs is probably not a coincidence, and may relate to aquifer response under the influence of pumping from production wells.     

Vertical seismic profiling using distributed acoustic sensing with scatter-enhanced fibre-optic cable at the Cu–Au New Afton porphyry deposit,British Columbia,Canada

Wireline logs and vertical seismic profile data were acquired in two boreholes intersecting the main mineralized zone at the Cu–Au New Afton porphyry deposit, Canada, with the objectives of imaging lithological contacts, fault zones that may have acted as conduits that channelled the mineralization, and alteration zones. Log data provide physical rock properties for the main lithologies and alteration zones. Calliper logs reveal many faults and caved-in zones generally indicating rocks with low integrity at the borehole wall. The preponderance of these zones, as indicated by the logs, suggests that their response may dominate the seismic-reflection wavefield. Outside fault zones, compressional and shear-wave velocities exhibit significant variability due to porosity, the heterogeneity of volcanic fragmental rocks and alteration. Distributed acoustic sensing was used to acquire vertical seismic profiling data in the two boreholes surveyed with wireline logs. Straight and helically wound fibre-optic cables housed standard fibres and a fibre engineered to increase the intensity of backscattering at the distributed acoustic sensing interrogator. Standard and engineered optical fibres placed in the two boreholes were daisy-chained together to form two 5-km-long continuous fibres that were interrogated at once with two interrogators. A new generation of interrogator connected to the engineered fibres provided field data with lower noise level and higher signal-to-noise ratio. These data with higher signal-to-noise ratio from straight fibre-optic cable were processed and used for depth imaging. Depth images benefitted from new migration weights that account for the directional sensitivity of the straight fibre-optic cable and limit the extent of migration artefacts. Migration results show several reflectors with shallow dips to the northwest, some explained by faults intersecting the surveyed boreholes. The main sub-vertical lithological and alteration contacts at New Afton generated downgoing reflections that were not considered in the migration.     

A New Rapid Method for Measuring the Vertical Head Profile

This study describes a new technique for measuring the head profile in a geologic formation. The technique provides rapid, low cost information on the depth of water‐producing zones and aquitards in heterogeneous aquifers, yielding estimates of hydraulic heads in each zone while identifying any potential for cross contamination between zones. The measurements can be performed in a typical borehole in just a few hours. The procedure uses both the continuous transmissivity profile obtained by the installation (eversion) of a flexible borehole liner into an open borehole and the subsequent removal (inversion) of the same liner from the borehole. The method is possible because of the continuous transmissivity profile (T profile described by Keller et al. 2014) obtained by measuring the rate of liner eversion under a constant driving head. The hydraulic heads of producing zones are measured using the reverse head profile (RHP) method (patent no. 9,008,971) based on a stepwise inversion of the borehole liner. As each interval of the borehole is uncovered by inversion of the liner, the head beneath the liner is allowed to equilibrate to a steady‐state value. The individual hydraulic heads contributing to each measurement are calculated using the measured transmissivity for each zone. Application of the RHP method to a sedimentary bedrock borehole in New Jersey verified that it reproduced the head distribution obtained the same day in the same borehole instrumented with a multilevel sampling system.     

New Method for Continuous Transmissivity Profiling in Fractured Rock

A new method is presented to search for hydraulically transmissive features in open boreholes in bedrock. A flexible borehole liner made of a watertight, nylon fabric is filled with water to create a constant driving head to evert (reverse of invert) the liner down the hole so that the liner pushes the borehole water out into transmissive fractures or other permeable features. The descent rate is governed by the bulk transmissivity of the remaining permeable features below the liner. Initially, the liner descent rate or velocity is a measure of transmissivity (T) of the entire hole. As the everting liner passes and seals each permeable feature, changes in the liner velocity indicate the position of each feature and an estimate of T using the Thiem equation for steady radial flow. This method has been performed in boreholes with diameters ranging from 96 to 330 mm. Profiling commonly takes a few hours in holes 200‐ to 300‐m long. After arrival of the liner at the bottom of the hole, the liner acts as a seal preventing borehole cross connection between transmissive features at different depths. Liner removal allows the hole to be used for other purposes. The T values determined using this method in a dolostone aquifer were found to be similar to the values from injection tests using conventional straddle packers. This method is not a replacement for straddle‐packer hydraulic testing of specific zones where greater accuracy is desired; however, it is effective and efficient for scanning entire holes for transmissive features.     

Fracture-frequency prediction from borehole wireline logs using artificial neural networks

Borehole-wall imaging is currently the most reliable means of mapping discontinuities within boreholes. As these imaging techniques are expensive and thus not always included in a logging run, a method of predicting fracture frequency directly from traditional logging tool responses would be very useful and cost effective. Artificial neural networks (ANNs) show great potential in this area. ANNs are computational systems that attempt to mimic natural biological neural networks. They have the ability to recognize patterns and develop their own generalizations about a given data set. Neural networks are trained on data sets for which the solution is known and tested on data not previously seen in order to validate the network result. We show that artificial neural networks, due to their pattern recognition capabilities, are able to assess the signal strength of fracture-related heterogeneity in a borehole log and thus fracture frequency within a borehole. A combination of wireline logs (neutron porosity, bulk density, P-sonic, S-sonic, deep resistivity and shallow resistivity) were used as input parameters to the ANN. Fracture frequency calculated from borehole televiewer data was used as the single output parameter. The ANN was trained using a back-propagation algorithm with a momentum learning function. In addition to fracture frequency within a single borehole, an ANN trained on a subset of boreholes in an area could be used for prediction over the entire set of boreholes, thus allowing the lateral correlation of fracture zones.     

Urban Ground Water Pollution: A Case Study in Cuttack City, India

A large number of ground water samples (360) was collected from 60 stations over six consecutive seasons to study the influence of the main sewerage drain on shallow ground water table beneath the municipal area of Cuttack, India. A majority of the samples collected from stations close to the drain exceeded the maximum permissible limits set by the World Health Organization (WHO). Almost all the samples near the drain exceeded the WHO limit for NO₃^- and Na⁺. However, the concentrations decreased as the distance from the drain increased. The winter season registered the maximum concentrations of NH₄⁺, NO₃^-, and SO₄^2- ions whereas the minimum values always coincided with the rainy season. R-mode factor analysis was conducted to find relationships amongst the 16 chemical parameters studied. Fluoride showed a negative correlation with Cl^-, Na⁺, NO₃^-, SO₄^2-, and PO₄^3-. The concentration of F^- may be lower in raw waste water than naturally occurs in the ground water. Therefore, a decrease in the concentration of F^- near the drain may be attributed to dilution by contributions of waste water to the ground water. The rest of the parameters were found to be directly related to the distance of collection points to the sewerage. The distribution of nutrients is strongly affected by leaching of waste water into the ground water.     

Estimating the permeability of the Nojima Fault Zone by a hydrophone vertical seismic profiling experiment

Abstract A multi-offset hydrophone vertical seismic profiling (VSP) experiment was done in a 747 m deep borehole at Nojima Hirabayashi, Hyogo prefecture, Japan. The borehole was drilled to penetrate the Nojima Fault, which was active in the 1995 Hyogo-ken Nanbu earthquake. The purpose of the hydrophone VSP is to detect subsurface permeable fractures and permeable zones and, in the present case, to estimate the permeability of the Nojima Fault. The analysis was based on a model by which tube waves are generated when incident P-waves compress the permeable fractures (or permeable zones) intersecting the borehole and a fluid in the fracture is injected into the borehole. Permeable fractures (or permeable zones) are detected at the depths of tube wave generation, and fracture permeability is calculated from the amplitude ratio of tube wave to incident P-wave. Several generations of tube waves were detected from the VSP sections. Distinct tube waves were generated at depths of the fault zone that are characterized by altered and deformed granodiorite with a fault gouge, suggesting that permeable fractures and permeable zones exist in the fault zone. Tube wave analysis shows that the permeability of the fault gouge from 624 m to 625 m is estimated to be approximately 2 × 10⁻¹² m².     

Influence of fracture anisotropy on ground water ages and chemistry,Valley and Ridge province,Pennsylvania

Model ground water ages based on chlorofluorocarbons (CFCs) and tritium/helium-3 (³H/³He) data were obtained from two arrays of nested piezometers located on the north limb of an anticline in fractured sedimentary rocks in the Valley and Ridge geologic province of Pennsylvania. The fracture geometry of the gently east plunging fold is very regular and consists predominately of south dipping to subhorizontal to north dipping bedding-plane parting and east striking, steeply dipping axial-plane spaced cleavage. In the area of the piezometer arrays, which trend north-south on the north limb of the fold, north dipping bedding-plane parting is a more dominant fracture set than is steeply south dipping axial-plane cleavage. The dating of ground water from the piezometer arrays reveals that ground water traveling along paths parallel to the dip direction of bedding-plane parting has younger ³H/³He and CFC model ages, or a greater component of young water, than does ground water traveling along paths opposite to the dip direction. In predominantly unmixed samples there is a strong positive correlation between age of the young fraction of water and dissolved sodium concentration. The travel times inferred from the model ages are significantly longer than those previously calculated by a ground water flow model, which assumed isotropically fractured layers parallel to topography. A revised model factors in the directional anisotropy to produce longer travel times. Ground water travel times in the watershed therefore appear to be more influenced by anisotropic fracture geometry than previously realized. This could have significant implications for ground water models in other areas underlain by similarly tilted or folded sedimentary rock, such as elsewhere in the Valley and Ridge or the early Mesozoic basins.     

Hydraulic properties of groundwater systems in the saprolite and sediments of the wheatbelt, Western Australia

Hydraulic properties of deeply weathered basement rocks and variably weathered sedimentary materials were measured by pumping and slug-test methods. Results from over 200 bores in 13 catchments, and eight pumping-test sites across the eastern and central wheatbelt of Western Australia were analysed. Measurements were made in each of the major lithological units, and emphasis placed on a ubiquitous basal saprolite aquifer. Comparisons were made between alternative drilling and analytical procedures to determine the most appropriate methods of investigation.

Aquifers with an average hydraulic conductivity of 0.55 m day⁻¹ occur in variably weathered Cainozoic sediments and poorly weathered saprolite grits (0.57 m day⁻¹). These aquifers are separated by an aquitard (0.065 m day⁻¹) comprising the mottled and pallid zones of the deeply weathered profile. Locally higher values of hydraulic conductivity occur in the saprolite aquifer, although after prolonged periods of pumping the values decrease until they are similar to those obtained from the slug-test methods. Hydraulic conductivities measured in bores drilled with rotary auger rigs were approximately an order of magnitude lower than those measured in the same material with bores drilled by the rotary air-blast method.

Wheatbelt aquifers range from predominantly unconfined (Cainozoic sediments), to confined (saprolite grit aquifer). The poorly weathered saprolite grit aquifer has moderate to high transmissivities (4–50 m² day⁻¹) and is capable of producing from less than 5 to over 230 kl day⁻¹ of ground water, which is often of a quality suitable for livestock. Yields are influenced by the variability in the permeability of isovolumetrically weathered materials from which the aquifer is derived.

The overlying aquitard has a low transmissivity (< 1 m² day⁻¹), especially when deeply weathered, indurated and silicified. The transmissivity of the variably weathered sedimentary materials ranges from less than 0.5 m² day⁻¹ to over 10 m² day⁻¹, depending on the texture of the materials and their position within the landscape. Higher transmissivity zones may occur as discrete layers of coarser textured materials. The salinity of the saprolite and sedimentary aquifers ranges from less than 2000 mgl⁻¹ to greater than 250000 mgl⁻¹ (total dissolved solids; TDS), depending on position within the landscape. Secondary soil salinization develops when groundwater discharge occurs from either saprolite or sedimentary aquifers.     

Electrokinetic phenomena associated with a water injection experiment at the Nojima fault on Awaji Island, Japan

Abstract Self-potential variations were measured to estimate the magnitude of electrokinetic and hydrological parameters (zeta potential and permeability) of the Nojima Fault zone in Awaji, Japan. The study observed self-potential variations that seemed to be associated with water flow from the injection well to the fracture zone, which were induced by turning the injection on and off. Amplitudes of the variations were a few to 0.03 V across 320–450 m dipoles. These variations can be explained well with an electrokinetic model. The quantity k/ζ (permeability/zeta potential) is in the range 1.6 × 10⁻¹³− 5.4 × 10⁻¹³ m²/V. Permeability of the Nojima fault zone can be estimated as approximately 10⁻¹⁶–10⁻¹⁵ m² on the assumption that the zeta potential is in the range –0.01 to –0.001 V.