Desalination, 12 (1989) 275-292 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

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Electrical Conductivity and Total Dissolved Solids-What is Their Precise Relationship?

N.R.G. WALTON

Hydrogeochemical Engineer & R.O. Consultant, 25, Eric Lock Road, Shrewsbury SY3 OHQ (U.K.), Tel.: 0743-723771

(Received July 25,1988)

SUMMARY

The ability of RO plants to consistently produce water within the usual 500 mg/l WHO guidelines is a major factor in determining the longer term success of the plant, and is a principal criterion for guarantee and contractural obli- gations. However, since total dissolved solids (TDS) is not easily measured, except under controlled conditions in reputable laboratories, a common alter- native method is to utilise the simple permeate electrical conductivity (EC) reading and multiply by a standard correction factor (typically 0.7) to obtain the required TDS result. This paper demonstrates the considerable problems, both theoretical and practical, associated (but generally not appreciated) with these apparently simple measurements and shows that just one simple linear conversion factor cannot be suitable throughout the range of waters encoun- tered in the desalination industry, but that several different K factors ranging from 0.50 to 0.75 need to be used for increasingly saline waters. The apparent simplicity of the TDS and EC measurements are shown to be illusory and much care is needed before taking contractural actions based upon these results.

Keywords: desalination, reverse osmosis, distillate, permeate, water quality, quality measurement, electrical conductivity, total dissolved solids, water chemistry.

INTRODUCTION

Much confusion exists throughout the water industry over this very simple but important question. It may come as a surprise to some workers in the de- salination industry to find that there is unfortunately no simple precise rela- tionship between these two parameters although workers in every field of water studies from physical chemistry through electrochemistry, hydrochemistry, soil and irrigation science, hydrology, geochemistry to marine chemistry each claim to have the best approximation.

What they are actually using is a tolerable empirical approximation which appears to hold good within the range of ion concentrations and salinities that

OOll-9164/89/$03.50 0 1989 Elsevier Science Publishers B.V.

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their particular subject deals with. Thus the theoretical chemists continue to build on the pioneering works of the early physical chemists, Arrhenius, Ost- wald, Debye and Hiickel, Onsager, Kohlrausche et al. from early in this century using ideal solutions and infinite dilutions to formulate absolute definitions for individual ion behaviors, whilst soil and irrigation scientists get more in- volved with ionic strength effects due to their interest in the balance between monovalent and divalent ions, and engineers - preferring a simple on-site rule of thumb - often simply take the factor of 0.7 so often found on the fixed scales of commercial electrical conductivity-total dissolved solids (EC-TDS) meters and think little more about it.

This factor of 0.7 is typically used as the fixed K factor in the well-known expression

TDS=K.EC

where TDS is in mg/l and EC is in @/cm at 25 ’ C. However there is no fixed factor and no linear relationship of the above type which is applicable through- out the water industry for the reasons which will be demonstrated in this paper. Nevertheless, what can be usefully and practically employed are a few well- chosen linear K factors to represent distilled waters, natural waters, brackish waters and seawaters accordingly. A range of K factors is especially required in the desalination industry because, by definition, the complete range of water types is dealt with from distilled and fresh natural waters through natural brackish waters to seawaters and reject brines. The consistent use of just one K factor (typically 0.7)) even though this is the average value between possible extremes of 0.5 to 0.9, can lead to errors of up to 30% in TDS estimation from just this one theoretical simplification alone. This paper goes on to discuss the many problems and sources of both random and systematic errors associated with the theory and measurement of both EC and TDS values, which will dem- onstrate that the simplicity generally associated with these two parameters in the desalination industry is merely a facade covering a multitude of simplifi- cations, assumptions, and approximations which have been conveniently over- looked in the search for the simple K factor.

WHY LIFT THE LID FROM THIS PARTICULAR CAN OF WORMS?

The need for greater accuracy in estimating TDS from EC results rather than using one simple factor to cover all cases is becoming increasingly impor- tant due to:

(i) Tighter new plant design criteria and specifications. (ii ) Plant operation efficiency calculations. (iii ) Contractural specification and guarantee requirements. (iv) WHO and local health requirements for potable quality water. The increasing use of RO and ED desalination systems makes this review of

the EC-TDS relationship more pertinent due to the reliance of both plant design and membrane performance and guarantees upon good product EC- TDS results - especially when dealing with brackish water desalination. Fur- thermore, the almost universal reliance on a current WHO limit of 500 mg/l TDS for potable water, brings the manufacturers of one-pass seawater RO desalination plants close to the limits, since at typically 99% membrane salt rejection rates, standard seawater RO permeate will contain around 330 mg/l TDS and Arabian Gulf seawater around 450 mg/l TDS. Reliance upon EC- TDS conversion factors then becomes critically important for performance guarantee evaluation, since the direct measurement of TDS is not easily and accurately carried out without controlled laboratory conditions and skilled technicians.

The need for a quick and simple conversion from EC to TDS arises from the dichotomy between design standards and operational utility. All standard val- ues for the degree of mineralisation of waters are expressed in the absolute terms of TDS, which is not a parameter which is readily measurable. The re- lated value of EC is however simply and conveniently measured by on-line variable resistance devices which can be coupled to recorders and alarms etc. for continuous monitoring of plant performance. The difficulty is to find a simple relationship between these two related measurements without gross oversimplification making the chosen factor or expression too erroneous.

This paper will demonstrate that the true precise relationship between these two parameters throughout the range of natural water salinities is almost im- possibly complicated, whilst at the other extreme the use of just one simple K factor is a gross oversimplification which leads to potentially large errors. It is however possible to compromise by defining several K factors which can be applied in the correct circumstances to give a very good approximation of TDS from an EC result, thereby maintaining the operational simplicity and utility of EC readings.

TOTAL DISSOLVED SOLIDS (TDS) -DEFINITION AND MEASUREMENT

What is TDS?

Superficially this question appears to be self evident, but this hides a number of important points both theoretical and practical. The question of what is “dissolved” and what is not has long been a difficult question in the water industry, since particles, ions and molecules exist throughout an entire size spectrum both individually and in larger polymeric agglomerations, through colloidal suspensions to visible particulate matter. The dividing line between what is truly dissolved and what is in colloidal suspension or agglomeration can only be drawn by reference to a specific filter mesh size.

Since micron-sized colloidal particles are evident under a simple microscope,

the line had to be drawn at the sub-micron size and the figure of 0.45 pm has tended to become the internationally accepted standard in the water industry for deciding what is in true solution or “dissolved” matter and what is “partic- ulate” matter. This dividing line came about largely arbitrarily as a matter of practical necessity since 0.45 pm was the smallest pore-size filter paper com- mercially available in the 1960s and early 1970s when these matters were being deliberated internationally.

Sampling problems

Having defined “dissolved”, what about the practical difficulties associated with collecting a 0.45 pm filtered water sample?

It is very often not practicable to filter the sample on site, so any filtration (if carried out at all) generally takes place in the laboratory after many hours or days later. In this time interval, a whole range of physical, chemical and biological activities can take place in the sample bottle, e.g.

(i) Oxygenation of sample can lead to precipitation of previously dissolved species like iron and sulphide.

(ii) Degassing of CO, can give a raised pH which will upset the carbonate equilibria and may precipitate CaCO,.

(iii) Biological decay of dissolved NO; ions which may subsequently degas as volatile NH3 or N2 gases.

(iv) Biological utilisation of COz, dissolved organic matter and PO:- ion uptake.

(v) Agglomeration of micro-colloids originally smaller than 0.45 pm. Many of these biological changes can be slowed down to relative insignific-

ance by storing the sample in the cold and dark immediately after collection and prior to analysis. However, the overall error potential is such that samples should ideally be filtered in situ at the time of collection, then kept in a refrig- erator prior to analysis, which should ideally be within 24 h of sample collection and filtration.

Analytical problems

The standard TDS measurement is normally carried out by evaporating an accurately weighed water sample in a platinum crucible to dryness at lBO”C, followed by cooling in a dessicator and weighing the residue to constant weight. Theoretical problems associated with this are:

(i) The bicarbonate equilibrium is upset by the rise in temperature, and 50% of the original bicarbonate ion dissolved in the water is lost as CO, gas when CaCO, scale precipitates viz.

2HCO,-CO;- +CO,+H,O

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Since bicarbonate is often a dominant ion in most fresh natural waters, this can be the source of very large errors unless corrected for.

(ii) Upon precipitation of the dissolved salts during evaporation, some water of crystallisation can be incorporated into the crystal structure, which will then be weighed as “solid” material. Using a temperature of 180’ C rather than the originally lower temperature of 110°C helps to minimise this problem, but when significant quantities of sulphate salts are present, as in brackish waters and seawater, the calcium and magnesium sulphates tend to retain some water of crystallisation, even at 180 ’ C.

(iii) Heating to 180’ C can partially decompose organic matter and will drive off any volatile material present, although these effects are likely to be small.

Practical problems associated with the TDS measurement include: (i) The common substitution of a porcelain or other dish/crucible due to the

expense of platinum. This can result in errors due to precipitation of salts within the pores of the porcelain which become difficult to remove, and the hydration-dehydration cycle of the porcelain itself gives weighing errors at different temperatures.

(ii) The common substitution of loo-105 ’ C instead of 180’ C as the final evaporating temperature due to the general availability of water-baths but not such ready availability of controlled heating mantles for the higher tempera- tures. The increased presence of water of crystallisation, especially in sulphate salts, will cause errors in TDS weighings.

(iii) Sputtering of water sample during heating allows carry-over of salts with the water and into aerosols.

(iv) For low TDS samples, the accuracy in weighing, even with a good elec- tronic balance will lead to significant errors, e.g. a lo-mg/l TDS water sample will involve the weighing of just 1 mg of dried residue from the standard 100 ml sample; an error of up to 30% is quite conceivable here, just in the weighing alone. Of course larger samples can be evaporated, but time can then become a difficult problem for the laboratory.

(v) The availability of good laboratory facilities and skilled analysts will have an important effect on the final TDS result, with error potentials up to 40% not uncommon on the lower TDS waters. Even finger-marks on the dish can add a significant sweat-film at the sub-mg level and the inclusion of dust particles is always a constant problem unless the greatest care is taken.

(vi) Actual TDS evaporation measurements are not always carried out, es- pecially if a full chemical analysis is required at the same time; the TDS is then often calculated by adding together all the major cations: Na++K++Ca2++Mg2+, and major anions: HCO; + SO:- + Cl- + NO, in mg/l. Minor ions like Sr’+, F-, Br-, I-, Fe2+ are rarely included but, except for Br- in seawater, their omission is usually insignificant. However, neutral dissolved solids like Si02 and organic material can be a significant source of error in low TDS waters if they are not analysed for and included in the total analysed ions.

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Sometimes a TDS evaporation measurement is included alongside a full water analysis. In such cases it is interesting to compare the measured value with the calculated value of TDS. Differences of the order of 50% are not uncommon in potable waters. This gives some idea of the error magnitude that can be asso- ciated with individual TDS results due to a combination of some or all of the three theoretical and six practical problems listed above, and possibly others not listed here.

Thus using an actual TDS measurement as an absolute standard against which to judge an EC reading, is not always superior or beneficial. There are often times when the use of a good EC reading multiplied by the appropriate K factor is a better way of obtaining the TDS than by analysing for it. The important thing here is to use the correct K factor, since using the common 0.7 factor will generally not give a better result than the TDS evaporation method.

ELECTRICAL CONDUCTIVITY (EC) - DEFINITION, THEORY AND

MEASUREMENT

Background and definition

Theories of electrical conductivity of ions in solution were developed to- wards the end of the last century, building upon the pioneering works of Ohm and Faraday to formulate expressions for the electrical conductance of solu- tions, analogous to those developed in the electrical industry for electrical re- sistivity of solid matter. Hence the term specific conductance (or conductiv- ity) of a solution was developed as the simple reciprocal of specific electrical resistance (or resistivity ) . This involves an expression relating the resistance or conductance of a specific item within fixed dimensions.

Specific electrical conductance (SEC) was the originally accepted term, but often became shortened to electrical conductance, which implies an incorrect inverse connection with electrical resistance, rather than resistivity. Thus con- ductivity or electrical conductivity (EC) is now the generally accepted term for this measurement, although specific conductance is still used by the more academic workers.

Electrical conductivity (EC), as its name implies, is a measure of the ability of a conductor to carry an electric current. The EC of an electrolyte or aqueous solution is a summation of the current-carrying ability of every ion present and is dependent upon the number of ions per unit volume of solution and the mobilities with which each ion is able to move under the influence of the ap- plied electrical potential. Since the temperature dependence of EC is critical (about 2% per 1 “C), either the exact temperature of measurement or, more commonly, the EC result corrected to the standard thermodynamic reference temperature of 25 o C must be quoted. This is conveniently written as EC,,.

The absolute units for EC are mhos/cm, although for practical purposes pmhos/cm are commonly used. However, the mho (or reciprocal ohm) has now

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TABLE I

Typical EC,, values of natural waters

Water type Approximate EC @S/cm) at 25°C

Ultra-pure water 0.05-0.5 Distilled waters l-10 Rain waters 5-50 Potable waters 50-1000 Brackish waters 2000-20,000 Saline waters 20,000-40,000 Seawaters 40,000-60,000 Brines 60,000+

been directly replaced by the Siemens, thus @/cm are now the usual units for the expression of EC, with natural waters having the typical values as illus- trated in Table I.

Theoretical background

The measurement of EC,, always involves the combined measurement of two or more ions. To express conductivity as an absolute property of individual ions, use is made of a parameter called the equivalent (or molar) conductance (A) of each ion, which is defined as

A= 1000% in S cm’/equiv. (or mol)

where EC,, is expressed in its absolute units of S/cm at 25” C and C is the concentration of the ion in chemical equivalents per litre or mol per litre.

Since chemical normalities and equivalents are now being phased-out in the current mood for international standardisation of units, the concentration nowadays is expressed by mol/l.

Thus, the A value becomes molar conductance rather than equivalent con- ductance as in the past. Molar conductivities approach a limiting upper value with increasing dilution, so that a parameter A, -the molar conductance at infinite dilution - can be defined for each individual ion. In practice, infinite dilution is approached at around 10m4 M for many simple salt solutions, with corresponding EC& values around 10 ,&/cm.

Tables of A, values can be found in any high school physical chemistry text book, but a few relevant examples are listed in Table II. From such tables of A, values, theoretical results for the conductivity of dilute solutions can be directly calculated as follows:

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TABLE II

Examples of typical molar conductances of common ions

Ion Molar conductance (S cm*/mol) at 25°C (/i,)

K+ 73.5 Na+ 50.1 H+ 349.8 Cl- 76.3 OH- 198.0 HCO, 45.4

TABLE III

Calculated and measured values for ECzs of a range of concentrations of standard KC1 solutions, illustrating the change in K value for more concentrated solutions

KC1 solution concentration

mdl Molarity

Electrical conductivity

Calculated Measured

W/cm) W/cm)

TDS/EC

(K)

7.455 1O-4 14.98 16.8 0.503 74.55 10-3 149.8 146.9 0.507 745.5 10-2 1498.0 1408.9 0.529 7455 10-l 14,980 12,856 0.580

74,550 1.0 149,800 111,342 0.670

For example, the approximate EC of a 10 A3 A4 standard KC1 solution can be calculated from the data in Table II, as follows:

EC& = (73.5+76.3)~106~1/1000~10-3=149.8 @S/cm

Similarly a 10m4 M KC1 solution would have EC,, = 14.98 @/cm, and so on. Actually measured standard values for these solutions are however slightly different as illustrated in Table III.

Theoretical relationship with TDS

Table III clearly shows the non-linearity of the TDS-EC relationship even for a series of standard single salt KC1 solutions, where concentrations greater than 10m3 M show increasingly large deviations reaching 26% at 1 M concen- tration. Similar results are ‘obtained using other single salt electrolyte solu- tions. However, natural waters contain a mixture of various different salts and the depression of EC& with increasing total salt concentration then becomes

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even greater due to both physical and electrical ionic interactions. The bicar- bonate ion in particular has a rather low molar conductance, and since it is often a dominant ion in natural (fresh) water systems, it often exerts a marked depressive effect on the conductivity of fresh water, so that the TDS/EC re- lationship (K value) increases dramatically.

For example, to take an extreme case, a 10V3 M solution of NaHC03 will have an approximate EC,, calculated from the data in Table II of

(50.1+45.4)~106~1/1000~10-3=95.5$3/cm

and since the TDS of such a solution is 84 mg/l, the TDS/EC relationship or K value = 0.88, which is the upper extreme value for any natural water system.

Thus, it can be clearly seen that both increasing concentration and different ionic composition, even in single salt solutions, can have a marked effect on the TDS-EC relationship. Consequently, the relationship or K value cannot be considered to be either fixed or linear, although the natural mix of ions in natural water systems allows the extreme values of single-salt solutions to be neglected.

Temperature effects

The main physical effect of temperature is to increase ionic mobility at higher temperatures through decreasing the viscosity of the solution.

The well known approximation of the effect of temperature upon EC of about 2% per 1 o C is a very general average which is reasonable enough when used on a mixed-ion natural water at approx. Ifr 15 ’ C from the international stan- dard of 25’ C. However, each individual ion has its own often very different temperature coefficient, which varies with both concentration and absolute temperature, with especially large departures (up to ten times) from the 2% approximation evident in very cold and very hot water, where viscosity changes and dissolved CO, ionisation rates change rapidly.

Many workers have attempted to fit empirical cubic and quartic equations to describe the observed variations in EC with temperatures. However, in prac- tice, general agreement suggests that the simple linear equation:

EC,, =EC,[1+0.022(25-t)]

i.e., a 2.2% per 1 “C temperature change is the most useful practical application for temperature correction within ambient natural temperatures for most mixed-ion natural waters.

It should be noted that most commercially available EC meters make use of this simple relationship to electronically correct for temperature deviations from the standard 25’ C by applying an automatic 2% per 1 “C correction. How- ever, one should beware of older meters which may temperature-correct to the previous 20” C standard temperature which will give an immediate 10% error

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to the EC reading if this fact is not noticed. The writer came across an inter- esting example in one Middle-Eastern country where alarm was occasioned by the latest annual country-wide wellwater salinity (EC) survey which indicated a 10% rise in virtually all water well EC readings. It was sometime before this universal EC rise was attributed to the change from an old 20” C standard temperature meter to a new 25 ‘C standard meter.

pH effects

Pure water itself is not a conductor of electricity, since it exists in a molec- ular rather than ionic structure. However, there is always a very slight ioni- sation tendency in water as given by the ionic product of water K,= lo-l4 at 25°C. i.e.,

H,O=H++OH-: K _ [H+ I [OH+ I = lo-14 mol/]

,+.- FL01

This gives an EC of about 0.05 @/cm, an exceptionally low value. However, at especially high ( >9) or low ( < 5) pH values, the EC of water becomes significant. e.g., at pH 5, H+ = 10m5 M. Now since An+ = 349.8 mho cm’/mol (Table III), which is about five times higher than the molar conductance of other cations, due to its very small size and high mobility, its EC contribution would be

Similarly at high pH values, say pH 9, ( [H+ ] = lo-’ M), since K, = 10-14, [H+] [OH-] =10-14, therefore [OH-] =10-14/10-g=10-5 M and non- is similarly several times larger than other anions at 198.0 mho cm2/mol (see Table III), then the EC of pH 9 water at 25’ C can be calculated as

198.0. 106/103. 10m5M = 1.98 @/cm

However, since virtually all waters used and produced within the desalination industry normally lie within the natural water pH range of 5-9, the contribu- tion to EC measurements of non-neutral, ionised water molecules is evidently very small and generally negligible.

Undesirable electrical effects

Polarisation The inevitable polarisation problems associated with passing electric cur-

rents through aqueous solutions of electrolytes are largely overcome by the use of alternating currents (AC) of moderate frequency, typically 1000 Hz.

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AC frequency The typical moderate AC frequencies (1000 Hz) used in many ordinary com-

mercial EC meters is necessarily a compromise between the need to minimise polarisation in high EC waters and reduce the capacitance effects which be- come increasingly significant in low EC waters. Higher AC frequencies (2000- 4000 Hz) are often used in salinometers for oceanographic work to minimise polarisation potential, whilst EC meters especially designed for use with dis- tilled, de-ionised and high purity waters typically operate at 60-100 Hz to min- imise capacitance errors. At very high frequencies (co. 10,000 Hz) however, the inter-ionic forces break down and conductivity again approaches the high assymptotal values reached at infinite dilution.

Capacitance The capacitance effect is directly related to the frequency of measurement

and the length of cable between measuring cell and meter. Thus for broad- spectrum EC meters with a fixed frequency of around 1000 Hz, it is advisable to keep cable lengths to less than about 20-30 m to minimise capacitance prob- lems. More sophisticated broad ranging instruments include a variable null- balancing capacitor to allow for increased accuracy especially at low ( < 100 @/cm) conductivities, where capacitance errors can reduce the measured con- ductance by up to 10%.

Impedance Boundary layer impedance is set up on the surface of the measuring elec-

trodes due to polarisation effects. This can either be reduced by using an ap- propriate measuring frequency for the salinity of the water to be measured or more practicably, by changing the size and material of the cell electrodes. De- positing platinum-black on the surface of platinum electrodes or using spe- cially prepared graphite-carbon electrodes with a cell of the appropriate size, can significantly reduce impedance and reactance effects on conductivity measurements.

An additional impedance (and capacitance) effect is associated with long cable lengths, especially in highly conductive waters where the cable resistance then becomes of a similar magnitude to the electrolyte resistance being mea- sured. In this instance an increase in measuring cell dimensions (see below) is required to increase the measured electrolyte resistance and thereby de- crease the significance of the cable resistance.

Overall electrical effects There are inevitably interactive effects between the electrical factors of fre-

quency, capacitance, impedance and reactance, although it is only really nec- essary to take account of these factors at very low or very high conductivities, where the compromise electronics built into the standard broad-spectrum EC

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meter designed to give good results at economic prices, start to give increasing error potential. For accurate measurement of EC at < 50 @/cm or > 50,000 @/cm it is advisable to use measuring systems dedicated to these extreme values since they will incorporate the different frequencies, capacitance cor- rection, change in cell size, etc., which is necessary to maintain accuracy at these extremes. For instance, marine chemists and oceanographers often use specially designed EC measuring systems called salinometers. Apart from reading directly in resistance (ohms) and salinity (ppm NaCl) these operate at higher frequencies, utilise larger measuring cells and contain a more accu- rate non-linear temperature correction facility to enable more accurate con- ductivity readings to be obtained in seawater.

Measuring cell dimensions

The usual measuring (1.0 cm) cell contains electrodes of a fixed size and arrangement, so that the electric current is passing through exactly 1.0 cm3 of water. Any slight deviations from this rigidly fixed volume are compensated for by a factor known as the “cell constant”, which for a 1.0 cm3 cell, normally has a factor of between 0.85 and 1.15 depending upon manufacturing toler- ances. This factor is usually marked onto the measuring cell itself, for manual correction or on some meters it can be corrected for by an internal compen- sation resistor which, when set to the value of the cell constant, will automat- ically correct the EC reading.

Each new cell will have its own individual cell constant, as determined by the manufacturer from its EC& readings in a series of standard solutions.

This cell constant correction facility present on some EC meters can be used as a standardisation control for recalibration when fouling or abrasion may have altered the effective cell constant, although great care is needed during any restandardisation procedure due to the possibility of contamination of the standardising solutions, even with distilled water.

The use of a l.O-cm measuring cell, although common, is not universal. Once again it is an operational compromise. The measurement of low EC ( < 100 @/cm) waters is more accurately obtainedusing a O.l-cm cell, whilst the mea- surement of high EC water ( > 20,000 @/cm) requires the use of a 10.0 cm cell for greater precision and accuracy. This is due to the fact that an error in the typical Wheatstone bridge resistance measurement is set up if the measured resistance strays too far from any standard value, since the added resistance of very dilute solutions effectively occurs as the reciprocal effect of parallel resistors rather than the additive effect of series resistors. Changing the size of the measuring cell can help to maintain a similar resistance over very large changes in salinity, with a consequent reduction in measurement error.

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Other practical problems with EC measurements

(i) The simple trapping of an air-bubble between the measuring electrodes is a surprisingly common cause of erroneously low EC results, since the air bubble occupies a portion of the fixed volume of the EC cell, thereby reducing the measured conductivity.

(ii) Fouling of the electrode surface - particularly in on-line measurement cells - also commonly leads to decreasing EC values with time. Small amounts of filmy organic substances like oils or surfactants are often the cause of sim- ple, cleanable fouling incidents. Longer term damage can be done by erosion and corrosion of the electrode surfaces, or even poisoning as when sulphides contact platinum electrodes and lead to serious electrode malfunctions with time.

(iii) Range-switching innacuracies are particularly frustrating in most av- eragely-priced EC meters, with over- or under-reading of typically up to 10% when switching from one decade-range resistor to another. The answer to this is to recalibrate with the appropriate KC1 standard solution each time the dec- ade range is changed, although this is often impractical. However, process con- trol instrumentation rarely requires range-switching once correctly set, so this problem afflicts mainly the laboratory and other multi-purpose and portable meters.

(iv) Some meters are fitted with very loose calibration or cell-constant switches which are too easily knocked or moved during use and necessitate recalibration, which may be very difficult if in isolated field locations.

(v) The presence (or absence) of the important temperature compensation facility is often incorrectly understood. It is sometimes thought that one must set the dial to the temperature at which one wishes to report the result, i.e. 25 ‘C, instead of the actual water temperature. This obviously can lead to very large errors at the rate of about 2% per lo C.

(vi) The use of older meters which have their internal temperature compen- sation fixed on the old British standard water temperature of 2O”C, leads to an immediate 10% error on all readings reported or understood to be standar- dised at the international standard of 25’ C.

SUMMARY OF EC AND TDS MEASUREMENT PROBLEMS

Having read the article so far, the reader may never feel quite the same about the once ever-so-simple “dip and read” EC result and may look a little more closely at any given TDS result. However, the writer intends only to point out the degree of potential errors due to both theory and practice inherent in any given EC or TDS result, so that a little operational tolerance and flexibility is obtained between clients, consultants and contractors over their sometimes

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fixed attitudes towards stated limits for plant operational guarantees and per- formance certification.

For example, the writer has been involved in several instances when reverse osmosis product waters appeared to lie outside the almost universal WHO limit of 500 mg/l TDS within the guaranteed lifetime of the membranes. In each case, the plants were relatively small < 500 m3/d and so had no on-site labo- ratory. On-line EC meters, corroborated with hand-held portable EC meters, gave readings of around 800-900 (us/cm which was reading 560-630 mg/l on the lower TDS scale of the same meters.

These meters had a fixed scale conversion of TDS = 0.7 x EC which is a fairly common, but terribly misleading, facet of many commercial EC meters.

Arguments ensued between clients, consultants and contractors over guar- anteed performance etc., etc., and even external analysis for TDS did not ini- tially resolve the matter due to conflicting results obtained from different laboratories.

If the EC meters are all correctly standardised, and can all agree on an EC reading -t 5%, then by using the correct conversion K factor of 0.55 for RO permeate waters, the “correct” TDS results of 440-495 could then be realised and hopefully agreed upon by all concerned.

RELATIONSHIP OF EC WITH TDS FOR THE DESALINATION INDUSTRY

Having now carefully defined both EC and TDS and outlined the many the- oretical and practical problems associated with their measurement, the need to define a good simple working relationship between EC and TDS is still re- quired to be able to reconcile the plant TDS design and international standard requirements with the EC operational readings obtained.

Since there is definitely no simple relationship between these parameters across the range of waters encountered in the desalination industry, and since complicated mathematical predictions which suit academics, theoreticians and computers are of little use to the majority of workers in the industry, the best alternative is to produce a series of K values for different ranges of salinities.

The correct way to do this is to take a series of samples of the water in question to a reputable laboratory and measure the EC and TDS a number of times until good precision and accuracy are statistically achieved, and then to take the ratio of the average values to obtain a “best possible” K factor. Of course, all the precautions such as filtration and bicarbonate correction for TDS measurements, and calibration and standarisation of EC measurements as listed in this paper need to be adhered to, to be sure of getting good, accurate results. Only then can the actual K factor for that particular ionic-mix water be relied upon.

However, since most desalination plants utilise fairly predictable water types, the K factors can be approximated in advance as shown in Table IV.

TABLE IV

Suggested K factors for use with different desalination water types

Water type Typical EC& (@J/cm )

K factor

Distillate l-10 0.50 RO permeate 300-800 0.55 Seawater 45,000-60,000 0.70 Reject brines 65,000-85,000 0.75

The reason for the predictability of the TDS-EC relationship for these water types is due to the overwhelming predominance (cu. 90% ) of just two ions in all these waters, namely Na+ and Cl-, and the increasingK factor with salinity reflects the hindrance of ionic mobility by the crowding effect of these ions at higher concentrations.

The major variability of EC with TDS comes with fresh, potable and brack- ish waters which contain a variety of dissolved salts, sometimes with Mg (HCO, )2 or Ca (HCO, )z predominant and sometimes CaS04, NaHCO, or NaCl as the dominant salt present. The complex ion-pairing and physical (size ) and electrical (charge) interactions which take place in solutions of these salts make any simple TDS-EC relationship impossible. However, many natural waters do contain a fairly well-balanced blend of the eight major ions, and so extremes of interaction due to large size or high charge effects are often bal- anced down so that most natural waters have K values which vary between 0.55 and 0.85. This of course is where the much used value of 0.70 comes in as simply the average between these two extremes.

However, from the desalination point of view, it is generally brackish waters with EC ranging from 2000-20,000 @/ cm which are of interest and these waters rarely have a K factor below 0.60 or above 0.67 due to the chemical evolutionary sequence of most brackish ground waters. Consequently, a good average K value of 0.63 has been found to satisfy most brackish Middle East groundwaters with salinities in the range of 2000-20,000 mg/l as TDS.

Fig. 1 gives a generalised view of the change in K factor with increasing salinities for different water types. The dominant HCO, ion concentration of many fresh waters gives the very steep rise in K value at low concentrations, whilst the increasing importance of SOi- in brackish waters maintains K val- ues well-above the single mono-valent KC1 standard line, whereas the fall-off in Kvalue between 1000 to 10,000 mg/l TDS is due to the dominance of inter- ion interference causing reduced EC values at higher TDS values. It is in this region where K factors can have the highest variability due to the opposing effects of increased physical resistance and ionic interactions at higher con- centrations, and the disproportionate ratio of divalent to monovalent ions.

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0.4 loo lb

I IO2

I IO’

I IO’

I IO5

TOS (mdl)

Fig. 1. Plot of TDS against K values showing fields of dominance for different water types.

Fig. 1 also shows that the waters important to the desalination industry occupy very limited fields on the diagram and generally follow the exponential trend of the NaCl line. Their limited positions on this field diagram clearly illustrate the progressive increase in K values for increasing salinity waters, but within very limited ranges, which indicates the proposed use of the four different K values for the four different desalination water types.

CONCLUSIONS

(i) The measurement of both TDS and EC has been shown to be neither theoretically as simple nor operationally as straightforward as is often assumed.

(ii) Both results contain a host of simplifications, assumptions and poten- tial errors that can easily give rise to total error factors in excess of 30% unless the most careful background investigations, calibrations and cross-checkings are carried out within reputable laboratories.

(iii) The relationship between EC and TDS has been shown to be neither simple nor linear although because of the actual complexity of the precise re- lationship a practical compromise has been suggested utilising four different K factors - one for each water type encountered in the desalination industry.

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(iv) The use of just one K factor for all water types cannot be justified since errors of up to 25% can be introduced from just this one approximation alone.

(v) The common use of a “standard” K factor of 0.7, which is chosen as an average between the possible extremes of 0.5 and 0.9, and is often to be found in the direct transformation of EC readings to TDS results on the face of many commercial EC meters, is very misleading and, particularly in the product water side of desalination plants where it is most important, will give immediate errors of some 25%.

(vi) The non-recognition of the large error inherent in this direct transfor- mation of EC to TDS, can be the cause of contractural arguments as specifi- cations and guarantees can appear to be broken when the normal (WHO) 500 mg/l product TDS limit is apparently breached at an EC& value of only 715 @/cm instead of the more realistic value of 910 $S/cm.

(vii) The many other factors involved in obtaining good EC and TDS re- sults, particularly electronic simplifications and compromises within commer- cial EC meters and analytical errors in TDS results, have been described to give an overall appreciation of the problems and errors inherent in each of these results, suggesting that a more cautious approach to result-interpreta- tion should be pursued.

(viii) The temperature effect on EC has been shown to be different for each individual ion present, although it is concluded that the use of the standard approximation of 2.2% per 1 ‘C is good enough for most mixed-ion waters within + 15’ C of the 25’ C standard reference temperature. However, the correct use of the temperature compensator and the awareness of older meters internally compensating to the old standard of 20’ C has been pointed out as an important source of often unnoticed error.

(ix) The theoretical basis for the recommended substitution of four individ- ual K factors for use in different stages of desalination plants has been pre- sented, and is considered to be the simplest and most practically useful method of obtaining a TDS estimation from an EC result. These factors can be pre- sented with some certainty in the desalination industry, because the water types involved are generally very predictable and are overwhelmingly com- posed of the two simple ions of Na+ and Cl- even in the distillate-permeate product waters.

(x) The recommended appropriate K factors are:

Distillates, with EC,, of l-10 @/cm, K=0.50

Permeates, with EC,, of 300-800 pS/cm, K= 0.55

Seawaters, with EC& of 45-60 mS/cm, K= 0.70

Brines, with ECz5 of 65-85 mS/cm, K~0.75

(xi) Thus the linear formula

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with TDS in mg/l and EC&, in @S/cm can still be used for estimating TDS from EC by substituting the appropriate K factor, and the result can then often be more accurate than the error-prone direct TDS measurement.

(xii) For the WHO limit of 500 mg/l TDS, the corresponding limiting EC& reading for permeate waters will be 500/0.55 =910 @/cm which is some 27% higher than the figure of 715 @/cm obtained by straightforward conversion using the standard K= 0.7 single factor.