Streaming Potential Collection and Data Processing Techniques

Journal of Colloid and Interface Science233,348–355 (2001)doi:10.1006/jcis.2000.7296, available online at http://www.idealibrary.com on

Streaming Potential Collection and Data Processing Techniques

Philip M. Reppert1 and F. Dale Morgan

Earth Resources Laboratory, Department of Earth Atmospheric and Planetary Sciences, Massachusetts Institute of Technology,42 Carleton Street, Cambridge, Massachusetts 02142

Received July 7, 2000; accepted October 16, 2000

To date, no comprehensive comparison of streaming potentialcoupling coefficient collection or processing techniques has beenmade. Here, time-varying streaming potential and dc streamingpotential data collection and processing techniques are presentedand compared. The time-varying streaming potential data includesinusoidal and transient data. The collection techniques includeacquiring dc streaming potentials at various pressures, acquiringtime-varying streaming potentials at varying pressure, acquiringstreaming potentials as a function of frequency, and collecting time-varying raw data. The processing techniques include dc filtering,rms processing, cross-correlation, spectral analysis, and plotting ofraw time-varying streaming potential versus raw pressure data. Theresults show that all processing methods yield the same couplingcoefficient within 3%. The analysis also shows that if there is a goodsignal-to-noise ratio, all processing methods perform satisfactorily.If the signal-to-noise ratio is poor, then the spectral analysis outper-forms the other processing methods. The data collection methodsare all adequate, but individual applications may make one methodsuperior to another. C© 2001 Academic Press

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INTRODUCTION

When preparing to make measurements of streaming potial coupling coefficients, it is important to know which mesurement technique and data processing scheme is best sua specific application. In recent years, there have been advain acquiring and processing streaming potential data, but thas not been any comprehensive comparison of the diffemethods.

In 1952, Packard (1) presented a method for measurinstreaming potentials and the associated coupling coefficas a function of frequency and also as a function of pressPackard processed his ac data using the rms methodolog1973, Somasundaran and Kulkarni (2) presented a new aptus for measuring dc streaming potentials which automatedcollection and allowed measurements to be made at elevtemperatures. They analyzed the data to determine couplinefficients using the traditional method, which is to determ

1 To whom correspondence should be addressed at Department of Geocal Sciences, Clemson University, Clemson, SC 29634. Fax: (864) 656-1E-mail: [email protected].

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the slope of the data in the streaming potential versus presplots. In 1971, Korpi and DeBruyn (3) analyzed the effectselectrode polarization on measurements of dc streaming potial and determined that silver/silver chloride electrodes havevantages over platinum electrodes. In 1975 and 1978, SearsGroves (4, 5) presented modifications to Packard’s experimeapparatus for collecting streaming potential measurementsfunction of frequency and pressure. They used the rms meto analyze their data. Alekhinet al. (6) and Jayaweeraet al. (7)in 1985 and 1994, respectively, presented an approach for msuring high-temperature dc streaming potentials up to 200◦C. In1995, Jouniaux and Pozzi (8) used transient and dc methodmeasuring streaming potentials under triaxial stress. Theynot describe how they processed their transient data. Theyreported discrepancies between their transient results anddc results. In 1995, Pengraet al.(9) developed an apparatus andata acquisition technique for measuring low-frequency streing potentials. They used a phase lock loop amplifier and digsignal analyzer to process the signals. In 1998 and 2000 Repet al. (10) and Reppert (11), respectively, developed a newparatus for measuring wide-bandwidth ac streaming potentThis methodology made use of spectral analysis to determinereal and imaginary parts of the signal. Also in 2000, ReppertMorgan (12) presented a new method for acquiring streampotential data while simulating earthin situ conditions of ele-vated temperatures and pressures. This work showed that uthe ac technique or transient allowed the pore fluids to remaithe sample during the testing until equilibrium conditions wereached.

As can be seen from the recent literature, most advancestreaming potential measurements have been to the experimapparatus. There is little information in the literature concernthe collection and processing techniques associated with streing potentials. Consequently, it is not always apparent which dcollection or data processing technique is best suited for oexperiment. There are three basic methods for collecting streing potential data: dc, ac, and transient. There are also five bmethods presented for processing and analyzing the data: fiing dc data, rms processing, cross-correlation, spectral analand using the raw data. It is the intent of this study to makcomparison of the different collection methods and processtechniques of streaming potential coupling coefficient data. T

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STREAMING POTENTIAL COLLECT

dc case is presented first, followed by the ac case and thetransient data processing and collection techniques.

DC STREAMING POTENTIALS

Dc streaming potentials have been extensively studiedover 100 years, with numerous treatments of the subjectvariety of journals. It is not the intent of this section to gia detailed treatment of streaming potentials but rather toa brief review for the reader who is not acquainted withsubject. For a detailed treatment of the subject, the readreferred to texts in colloid science such as those by Hunterand Lyklema (14).

Streaming potentials occur in a fluid when there is relatmotion between the fluid and a charged surface. At the interbetween the fluid and the charged surface, an electrical dolayer forms. This double layer has a charge density that deexponentially away from the surface. The distance at whichcharge density decays by 1/e is called the Debye length. ThDebye length can extend from a few nanometers for a contrated electrolyte solution to a few hundred nanometers fodilute electrolyte solution. As the fluid moves tangentially to tdouble layer, it pulls the ions of the double layer along. Thmoving ions near the surface give rise to a convection curre

Iconv=∫v(r )ρc(r ) dr, [1]

wherev(r ) is the fluid velocity andρ(r ) is the charge densityEvaluating the integral and applying the appropriate boundconditions gives

Iconv= πεa2ζ1P

ηl, [2]

whereη is the viscosity of the fluid,ε is the permittivity ofthe fluid,a is the radius of the capillary or pore, andζ is thezeta potential, which is the potential at the slipping plane. Tslipping plane is the plane where the fluid velocity goes to zeFrom equilibrium considerations, a conduction current formthe bulk of the fluid to balance the convection current nearsurface. The conduction current,

Icond= πσa2

l1V, [3]

flows through the resistive bulk fluid to generate a potencalled the streaming potential.1V is the voltage measureacross the sample, andσ is the conductivity of the fluid. Settingthe convection current equal to the conduction current givesto the Helmholtz–Smoluchowski equation,

1V = εζ

ησ1P, [4]

where1V/1P is referred to as the coupling coefficient.

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DC COLLECTION AND PROCESSING TECHNIQUES

Flow-through streaming potentials are created when a cstant differential pressure is applied across the sample, indua constant flow through the sample. The differential pressand voltage across the sample are measured and are repeaseveral different pressures, with a plot of the raw data showFig. 1. The resulting voltages are then plotted versus the diential pressures, as shown in Fig. 2. The slope of the best-fitthrough the data is the coupling coefficient, V/Pa. It shouldnoted that there are several different methods for generaticonstant pressure across the sample. They can range froma pump (4) to elevating the fluid reservoir (15).

There are several limitations to the dc method, such asnoise, drift, and concerns about electrode stability and polartion (3). Somasundaran and Kulkarni (2) claim to have mmeasurements for signals as small as 0.1 mV using themethod. However, with high-impedance samples, it is difficulmake measurements as small as 0.1 mV because of low sito-noise ratios. With rocks, it is not uncommon to have streaing potential signals smaller than 0.1 mV. This is in the ranwhere signal-to-noise issues in dc measurements start tocome important. Another potential drawback of dc streampotential measurements is the quantity of liquid required forexperiment. This can be a hindrance when working with limiamounts of liquid or liquids that are hazardous.

An advantage of the dc streaming potential measurementhe simplicity of the experiment. If small signals are not bemeasured, equipment needs are minimal. The equipment caas simple as a good-quality voltmeter and a ruler to meathe pressure head. Consequently, no special pressure-drdevice is required to create a differential pressure acrosssample.

FIG. 1. Typical dc streaming potential response. These data were collectedon a glass filter with 70- to 90-µm pore diameters using 10−3 M KCl.

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FIG. 2. Dc streaming potential data of Fig. 1 versus the differential pressacross the sample. The straight line through the data is the least-squaresthe data, which gives a coupling coefficient of−1.32µV/Pa.

SINUSOIDAL (AC) STREAMING POTENTIALS

Sinusoidal streaming potential signals (Fig. 3) can also bealyzed to determine zeta potentials, since the surface chemaspects of ac streaming potentials are the same as in the dcThe main difference between the two methods is how the psure is applied across the sample. In the dc case, the pressconstant whereas in the ac case, the pressure varies withThe following analysis of the sinusoidal data is based on lookat streaming potentials in the frequency domain. ConsequeEq. [1] now becomes

Iconv(ω) =∫v(r, ω)ρc(r ) dr. [5]

FIG. 3. Typical ac streaming potential response. These data were colleon a glass filter with 70- to 90-µm pore diameters using 10−3 M KCl.

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Integrating Eq. [5] for a capillary model, we find the frequencdependent convection current to be

Iconv(ω) = −2πεaζ1P(ω)

ηlk

J1(ka)

J0(ka), [6]

whereJ0 is a Bessel function of the first kind with order zerJ1 is a Bessel function of the first kind with order one, and

k =√−iωρ

η. [7]

The conduction current moving through the bulk fluid is afrequency dependent, since it must balance the conveccurrent,

Icond(ω) = 1V(ω)πa2σ

l. [8]

Setting the convection current equal to the conduction curgives

C(ω) = 1V(ω)

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ka

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whereC(ω) is the frequency-dependent coupling coefficieEquation [9] is the ac Helmholtz–Smoluchowski equation. Tfrequency at which inertial terms start to dominate over viscterms is often called the transition frequency and for a capillmodel is given by

ωt ≡ a2

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η

ρ. [10]

A thorough treatment of ac streaming potentials is givenReppertet al. (16) and Pride (17).

SINUSOIDAL SIGNAL PROCESSING TECHNIQUES

There are several methods for processing and collectingnusoidal streaming potentials. We first present the procestechniques, followed by the collection methodologies. The fimethod of processing involves measuring the rms signal for bthe streaming potential and the differential pressure (1, 4, 5,The ratio of the rms streaming potential signal to the rms psure signal determines the streaming potential coupling cocient. This method has the advantage of being computationfast and not needing extensive data acquisition equipmentit has the disadvantage of having signal-to-noise problems.method works well only when the measured signal is grethan any background noise. The main disadvantage of themethod is that any dc offset, such as from the electrodes, i

ctedcluded into the measurement. When the rms processing methodis used, the phase of the pressure and voltage must be monitored

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to determine whether the coupling coefficient is negative or pitive. If the signals are in phase, the coupling coefficient is pitive, and if they are out of phase, the coupling coefficientnegative.

The second method of processing involves calculatingcross-correlation of both the streaming potential signal anddifferential pressure signal and calculating the ratio of the crocorrelated signals. Cross-correlation is a means of extracinformation about a signal in a noisy environment by usinknown reference signal, where the reference signal has thefrequency as the signal in the noisy environment. The crocorrelation function looks for similarities between the two snals and allows the noisy signal to be evaluated based onsimilarities or correlation with the reference signal. In streampotential applications, cross-correlation can be accomplisheusing either a reference signal or a noise-free differential psure signal as the reference signal. This method has the adtages of having very good signal-to-noise characteristicsof removing any dc offset from the measurement. If the msuring signals are in the microvolt range, however, backgronoise can vary from frequency to frequency. This backgronoise can exceed or be a significant part of the measurednal. Because of the nature of cross-correlation measuremthere is no direct way of monitoring the noise at the measufrequencies.

The third method of processing the data uses spectral ansis. It involves calculating the amplitude spectrum of bothstreaming potential and differential pressure signals. The crcoupling response is obtained by taking the ratio of the streampotential response to the differential pressure response (FigThis method has the advantage of allowing the background nto be determined at the measured frequency. After the bground noise at the frequency of interest is determined, arection can be made or a different frequency can be chosenecessary. Consequently, streaming potential measuremenbe made in the microvolt or submicrovolt range, dependingthe quality of the electronics. Spectral analysis also allowsreal and imaginary components of the coupling coefficient todetermined (10, 11, 16). Another advantage is that dc offsetbe completely removed from the data. This method is comtationally intensive compared to the other methods, which ismain disadvantage.

The last method of data processing really requires no sigprocessing. In fact, the time-varying streaming potential sigis plotted versus the time-varying differential pressure signand then the slope is calculated (Fig. 5). When the slope isculated by a least-squares method, the large number ofpoints gives an accurate result. This method has the advanof being simple and fast but has the disadvantage of requirigood signal-to-noise ratio. This method must be used at aquency lower than where inertial effects become evident influid. Inertial effects become evident in the signals when a ph
shift starts to occur between the streaming potential and presssignals.

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FIG. 4. (a) Amplitude spectra of the streaming potential and differenpressure across a porous glass filter with 70- to 90-µm pore diameters filledwith 10−3 M KCl. The spectra show a sinusoidal driving frequency of 26 H(b) The coupling coefficient is found by dividing the SP amplitude spectrby the pressure amplitude spectrum and reading the coupling coefficient adriving frequency. At the driving frequency of 26 Hz, the coupling coefficien−1.3µV/Pa. At frequencies other than the driving frequency, there is no sigconsequently, the readings at frequencies other than the driving frequencnoise.

FIG. 5. Raw streaming potential data versus raw differential pressureplotted for the same sample and chemistry as used in Fig. 2. The straigh
shows the least-squares fit of the data. The slope of the straight line gives acoupling coefficient of−1.29µV/Pa.

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SINUSOIDAL COLLECTION TECHNIQUES

There are three basic ways of collecting sinusoidal streampotential data. One method of collecting the data is to keepfrequency stationary and vary the amplitude of the differenpressure across the sample. The amplitude of the driving preis then plotted versus the amplitude of the streaming poteresponse. This gives a plot of streaming potential versus pre(Fig. 6), the slope of which is the coupling coefficient. It shobe noted that all experiments described in this section wereducted on the same 70- to 90-µm sample using 10−3 M KCl.The result in Fig. 6 is identical to that obtained in dc experime(Fig. 2), also demonstrated by others (4, 5). Consequently,method of data acquisition is well suited for determining zpotentials. This method has the advantage of giving a stacally accurate result whose accuracy increases with additimeasurements. The only disadvantage is that the measuremust be made well below the transition frequency if the dc liof the coupling coefficient is desired. This method can be uwith all ac data processing techniques.

Another collection method is to collect both streaming pottial data and differential pressure data versus frequency (10, 11, 16, 18). The measured voltage is divided by its cosponding pressure at each frequency to obtain the couplingefficient at that frequency. The coupling coefficient can thenextrapolated to the dc limit to obtain the dc response (5, 1016). The theory for frequency-dependent streaming poten(1, 11, 16, 17) shows that the frequency-dependent streapotential coupling coefficient remains constant at its dc liuntil the critical frequency is approached, where the coupcoefficient then starts to decrease with increasing frequeFigure 7 shows an example of frequency-dependent cr

FIG. 6. These data were collected at a single frequency while varyingpressure on the same sample and chemistry as in Fig. 2. The straight line th
the data is the least-squares fit to the data, whose slope gives a coupling ccient of−1.31µV/Pa.
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FIG. 7. With the same sample and chemistry as in Fig. 2, the couplingefficient versus frequency is shown using the ac method, with the coupcoefficient theory also plotted. The dc limit gives a coupling coefficient−1.31µV/Pa.

coupling data extrapolated back to the dc limit to obtain tdc coupling coefficient. In practice, if the measurement isan order of magnitude less than the critical frequency, it isnecessary to extrapolate to the dc limit. One can simplythe single-frequency measurement and achieve the same reIt has also been demonstrated that capillary or pore radiibe obtained from frequency-dependent streaming potential(10, 11, 16). Therefore frequency-dependent streaming potial data can be used to determine zeta potentials as well asradii. As with the previous method, the greater the numberdata points collected, the more accurate the results. This apto multiple-frequency or single-frequency measurements. Trms, cross-correlation, and spectral analysis techniques all wwith this collection method.

When streaming potential data are collected with a sinusodriving source, some precautions should be taken to ensure hquality data. One precaution is to electrically shield the samand data acquisition equipment from any electromagnetic fiegiven off by the pressure-driving device. This also has thevantage of minimizing 60-Hz noise, which gives better signto-noise ratios for the processing methods. Another precauis to hold the sample securely to prevent any vibration fromoving the sample or electrodes. If these precautions are tastreaming potential measurements can routinely be made inmicrovolt range if cross-correlation or spectral analysis teniques are used. It should be pointed out that stacking of theis required to achieve measurements in the microvolt range.cross-correlation and spectral analysis techniques also havadvantage of removing electrode effects from the measuremeThe authors have made measurements and achieved equivresults with stainless steel and silver/silver chloride electro

oeffi-using AC collection techniques in conjunction with spectralanalysis.

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TRANSIENT STREAMING POTENTIALS

Lastly, data can be collected using the transient method19), as shown in Fig. 8. Chandler (19) first used this methomonitor the Biot slow wave in porous media by monitoring tstreaming potential response, but he did not determine coupcoefficients. Chandler developed Eq. [11], which relates the tsient pressure pulse to the transient streaming potential betthe center of a porous cylinder and the end of the cylinder:

Vs(t) = 1

2V0(t) exp(−t/T1) [11]

whereT1 is the characteristic time and

V0(t) = εζ

ησP0(t). [12]

The development of Eq. [11] is based on inertial termsbeing present in the solution. This occurs when the frequenconstituting the transient are an order of magnitude less thatransition frequency. The limitation of Eq. [11] is evident whraw transient streaming potential data are plotted versustransient pressure data (Fig. 9). The data in Fig. 9 show a cupart, which is related to the inertial part of Fig. 10, in whithe coupling coefficient spectral response data collected onsame sample are displayed. The straight-line part of Fig.related to the noninertial region in Fig. 10. Calculating the slof the noninertial region of Fig. 9 gives a coupling coefficieof 2.0µV/Pa. The frequency-domain analysis gives a coupcoefficient of 1.26µV/Pa. The frequency-domain analysis isagreement with the coupling coefficient analysis done usingother methods on the Porous Filter B sample.

FIG. 8. Typical transient streaming potential response. These data wcollected on a glass filter with 70- to 90-µm pore diameters using 10−3 M KCl.

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FIG. 9. With the same sample and chemistry as in Fig. 8, the raw data otransient method are plotted with a least-squares fit to the straight-line poof the curve. The best-fit line through the nonturbulent data gives a coupcoefficient of−2.0µV/Pa.

When calculating the slope of the curve of the streamingtential versus pressure, it appears that the data do not accfor the phase difference that can occur between the streampotential signal and the pressure signal. The phase differencPorous Filter B starts to occur at frequencies much lower tthe transition frequency, as can be seen in a plot of the PoFilter B theoretical phase (Fig. 11). Comparison of the theretical plots in Figs. 7 and 11 reveal that the phase shows

FIG. 10. With the same sample and chemistry as in Fig. 8, the transmethod coupling coefficient versus frequency is shown using spectral anaThe best-fit line through the noninertial region of the data gives a coup
coefficient of−1.26µV/Pa.

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FIG. 11. Theoretical plot of phase versus frequency for the Porous FilteComparison of this figure to Fig. 7 shows that inertial effects are present msooner in the phase data than the magnitude data. The transition frequenftof 710 Hz is shown in the figure. The transition frequency is the frequencwhich inertial effects start to dominate over viscous effects.

inertial effects much earlier than the magnitude data of Fig. 7the transient has no inertial effects, a plot of streaming potenversus pressure similar to the plot in Fig. 12 can be achievFigure 12 shows the plot of streaming potential versus pressfor a transient on Berea Sandstone. The same coupling cficient is obtained when using the frequency-domain analyon the same Berea Sandstone sample. It should be noted

FIG. 12. Transient streaming potential data plotted versus transient difential data for Berea Sandstone. The chemistry was initially di-ionized wathat was allowed to come to equilibrium with the rock over time. The slopethe least-squares fit line gives a coupling coefficient of−4.3 mV/bar, which is
in agreement with the other measurements on the same sample, obtainedthe sinusoidal spectral analysis method.
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the long-time part of the transient (low-frequency part) usuahas a very poor signal-to-noise ratio and should be avoidethe processing. Possible uses of the transient method whestreaming potential data are plotted versus pressure data aobtain coupling coefficients and zeta potentials where dc antechniques are not feasible.

The best processing method to obtain information on coupcoefficients when using the transient collection method is to tthe Fourier transform of the data and divide the streaming potial signal by the pressure signal (Fig. 10). This analysis is baon the frequency-domain analysis presented in the sinusosection. Errors associated with inertial effects can be avoiby using the frequency-domain analysis. To accomplish tthe coupling coefficient is read from the zero-slope part offrequency-domain coupling coefficient. As mentioned in the pvious paragraph, the signal-to-noise ratio in the low-frequepart of the data can be poor. Therefore, low frequencies shbe avoided in fitting the frequency-dependent coupling coecient theory, Eq. [9], to the transient data. It is also usefullook at the streaming potential and pressure spectra individuto see at what frequency the signal-to-noise ratio starts to sthe coupling coefficient data. Applications for the spectral anysis technique of analyzing transient data are to determinepotentials and the average pore size of the sample.

The data analysis methods available for looking at transdata are limited to spectral analysis and the plotting of the streing potential data versus the pressure data and then calculthe slope. These two techniques are applied in the same wadescribed in the sinusoidal signal processing techniques.

With the transient method of collecting data, the limitatiodue to inertial effects and poor signal-to-noise ratios can be mimized. To do this, sufficiently large streaming potential signmust be generated to get a better signal-to-noise ratio at thefrequencies. This requires an initial high-pressure pulse. Atend of the transient (low-frequency component), the signalnoise ratio will be poor. However, the initial high-pressure pumay have increased the signal-to-noise ratio enough to geable data for data processing. If the transient has high-frequecomponents, inertial effects may be seen in the data. Also, ifsample permeability is high, most of the data with good signto-noise ratios may include inertial effects. Consequently, wcalculating the slope of the curve of streaming potentials verpressure to determine the coupling coefficients, it is best to hthe sample permeability sufficiently low that inertial effects aabsent or at least minimized. Data of streaming potential vepressure have been successfully collected on Berea Sandswhich can have a porosity as high as 20% and permeabilithigh as 500 mDarcy. When transient data are analyzed byspectral analysis technique, the limitation is also the signalnoise ratio at low frequencies. If it is desired to see bothcritical frequency and the dc limit of the coupling coefficientwo separate transients (with different frequency compone

usingmay have to be used to get accurate data in the frequency rangeof interest. It should be noted that when the spectral analysis

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technique is used, spurious results may be obtained if thvalue at the beginning of the transient is not the same athe end of the transient. In other words, step function transishould be avoided.

When transient streaming potential data are collected,precautions should be taken to ensure quality data. First,sample and data acquisition equipment need to be electricshielded from any electromagnetic filed in the laboratory. Tincreases the signal-to-noise ratio in the long-time part oftransient. Second, the sample should be securely held to preany vibration of the sample or electrodes. If these precautare taken, streaming potential measurements can be mathe microvolt range. Stacking of the data is required to achimicrovolt-range measurements.

The transient method has the advantage of not requirinsinusoidal source to drive the pressure. However, significamore stacking of the data is usually required because of thesignal-to-noise ratio of the transient method.

SUMMARY

Data processing and collection techniques have beensented for DC, sinusoidal, and transient streaming potential dThe data shown in the figures were collected within 1 h usingthe same sample with identical chemistry for each techniqexcept the transient raw data technique (Fig. 12). The datacessing results agree within 1.8% for all processing methwhen using the sinusoidal collection technique. The couplingefficients measured using different collection techniques agwithin 3.1%, with the transient method having the worst stdard deviation. The advantages and disadvantages of eachnique have been discussed. Each collection technique andcessing method may lend its use to particular experimentthe measurements have good signal-to-noise ratios, any o
techniques will give adequate results. If the measurementson samples that give poor signal-to-noise ratios, the sinuso
ON AND PROCESSING TECHNIQUES 355

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collection technique using spectral analysis or cross-correlato process the data will give superior results. At the prestime, the transient technique has limited applications becaussignal-to-noise issues.

ACKNOWLEDGMENTS

We thank the DOE (Grant DE-FG02-00ER15041) and the NSF (Grant E9526710) for their support of this work. We also thank Dr. Dan Burns forreview and comments on this paper.

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