SDI normalization and alternatives

Desalination 279 (2011) 390–403

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Desalination

j ourna l homepage: www.e lsev ie r.com/ locate /desa l

SDI normalization and alternatives

A. Alhadidi a, A.J.B. Kemperman a,⁎, J.C. Schippers b, B. Blankert c, M. Wessling a, W.G.J. van der Meer a

a Membrane Technology Group, IMPACT Institute of Mechanics, Processes and Control Twente, Faculty of Science and Technology, University of Twente, P.O. Box 217,7500 AE Enschede, The Netherlandsb UNESCO-IHE Delft, Westvest 7, P.O. Box 3015, 2601DA Delft, The Netherlandsc Norit X-flow, P.O. Box 741, 7500 AS, Enschede, The Netherlands

⁎ Corresponding author. Tel.: +31 53 4892956; fax:E-mail address: [email protected] (A.J.B.

0011-9164/$ – see front matter © 2011 Elsevier B.V. Adoi:10.1016/j.desal.2011.06.042

a b s t r a c t
a r t i c l e i n f o
Article history:Received 20 February 2011Received in revised form 19 June 2011Accepted 21 June 2011Available online 29 July 2011

Keywords:Silt Density IndexVolume-based Silt Density IndexTesting conditionsMathematical modelsNormalization

Estimating the fouling potential is a prerequisite for controlling membrane fouling in reverse osmosissystems. Two different tests are routinely used to that end: the Silt Density Index (SDI) and the ModifiedFouling Index (MFI0.45). SDI test, however, has disadvantages which make it unreliable. One disadvantage isthat no linear relationship exists between SDI and the colloidal concentration in the water. Besides that, theSDI is not based on a filtrationmodel. Finally, the SDI is not corrected for the testing condition parameters suchas temperature, pressure and membrane properties.The SDI test is simple and does not require advanced professional skills, but the above mentioneddisadvantages make it unreliable. This work offers practical tools to resolve these disadvantages, such as aslide tool to calculate the SDI from the measured collection times. It also proposes a normalized SDI (SDI+),and offers a line chart and slide wheel charts for this conversion, thus correcting for different test conditionsand membrane resistance.Finally, this paper introduces a new fouling index. This volume-based SDI, SDI_v, compares the initial flow ratewith the flow rate after filtering the standard volume. It has a linear relationship to the particle concentrationif complete blocking is the dominant fouling mechanism during the test, and is independent of testingconditions and membrane resistance. The mathematical model and experimental results show that SDI_veliminates most of the disadvantages of the traditional SDI. The SDI_v is the second fouling index developed atthe University of Twente, 30 years after the MFI0.45.

+31 53 4894611.Kemperman).

ll rights reserved.

© 2011 Elsevier B.V. All rights reserved.

1. Introduction

Reverse osmosis (RO) membrane systems are used to desalinateseawater, among other things. However, flux decline due to foulingphenomena in the ROunit remains a challenge.Membrane fouling leadsto increased resistance to transport across the membrane and thespacers, and hence to a decline in permeability. Significant foulingoccurs even when several pretreatment steps are applied. Several typesof fouling may take place in RO membrane systems, e.g. inorganicfouling or scaling, particulate and colloidal fouling, organic fouling, andbiological fouling or biofouling. To minimize RO fouling and its impact,monitoring the fouling potential of the RO feed water is important. TheAmerican Society for Testing and Materials (ASTM) introduced the SiltDensity Index (SDI) as a standard test for RO fouling potential due toparticles. It compares the initialflow ratewith theflow rate after 15 minoffiltration usingmicrofiltration (MF)membraneswith anaverage poresize of 0.45 μm. MF membrane properties such as pore size, porosity,hydrophilicity, zeta potential and surface roughness affect the fouling

rate during the SDI test [2–9], as do nature of the colloids and waterproperties [2,10–12]. Consequently, there are growing doubts about thepredictive value of the SDI [12]. Several other deficiencies affect theaccuracy and reproducibility of the SDI, such as [13]:

— Lack of a correction factor for temperature;— Lack of correction for variations in membrane resistance;— Lack of linear correlation with the concentration of colloidal/

suspended particles.

Nevertheless, the SDI test has been applied for decades [1] and isused worldwide for various purposes such as comparing differentpretreatment methods [14,15], design of new desalination plants[16,17] and performance monitoring [18].

2. Theory and background

This section describes the two fouling indexes SDI and MFI0.45. Italso briefly summarizes the mathematical relation between SDI andMFIwhichwas developed in previouswork. Finally, fourmathematicalmodels describing the influence of different fouling mechanisms onthe SDI are presented.

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Table 1Definition of the four fouling mechanisms. The parameters m and C relate to the foulingmechanisms and particle concentration. Total resistance is a function of filtration state w[21].

Details Definitions m C

Cake filtration 0wR

RM

Intermediate blocking 1

wA

1

Standardblocking

1.5 2

391A. Alhadidi et al. / Desalination 279 (2011) 390–403

2.1. Definition of SDI

To determine the SDI, the rate of plugging of a membrane filterwith pores of 0.45 μm and a diameter of 47 mm is measured at207 kPa, in the following three steps:

1) The time t1 it takes to filter the first 500 mL is determined.2) Usually after 15 min (tf), the time t2 required to filter another

500 mL is determined.3) The index is then calculated with the following formula.

SDI =100%tf

1− t1t2

� �=

%Ptf

: ð1Þ

If the plugging ratio (%P) exceeds 75%, a shorter period tf must betaken, e.g. 10, 5 or 2 min.

2.2. Modified Fouling Index

The Modified Fouling Index (MFI0.45) was derived by Schippersand Verdouw in 1980 [13]. To determine the MFI0.45, the flowthrough the membrane filter is measured as a function of time.

tV

=μ·RM

dP·A+

μ·I2·ΔP·A2

M

·V ð2Þ

V accumulated filtrate volume (L or m3)t time (s)AM membrane area (m2)ΔP applied pressure (Pa)μ water viscosity (Pa.s)RM clean membrane resistance (m−1)I fouling potential index (m−2)

The MFI0.45 (in s/m6) is derived from the slope in the relation t/Vvs. V, tgα, at a temperature of 20 °C, a pressure of 207 kPa, and amembrane surface area of 13.8×10−4 m2 (47 mm diameter). It iscorrected for temperature and pressure and is therefore independentof temperature and pressure.

The water viscosity at a temperature T (in °C) is calculated usingthe following empirical equation [19].

μ = 0:497 × T + 42:5ð Þ−1:5 ð3Þ

2.3. Relationship between SDI and MFI

We developed a mathematical model describing the relationshipbetween SDI and MFI. It can be used to calculate SDI as a function ofMFI and the testing condition parameters [19]:

SDI =100

tf minð Þ 1− μ·RM + MFI·Vc·ΔP·AM

MFI·Vc·dP·AM +ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiμ2·R2

M + 4·MFI·dP2·A2M·tf

q0B@

1CA

ð4Þ

MFI measured MFI (s/m6)Vc volume of the first and second sample Vc=V1=V2 (m3)AM membrane area (m2)tf elapsed filtration time, usually 15 min (900 s)ΔP applied pressure (Pa)μ water viscosity (Pa.s)

1.5wV RM

Complete blocking 2

wA RM

1

2.4. Fouling model

Hermia [20] described four empiricalmodels that correspond to fourbasic types of fouling: cake filtration, intermediate blocking, standard

blocking, and complete blocking. The parameters considered by thesemodels have a physical meaning and contribute to the comprehensionof themechanisms ofmembrane fouling. Thesemodelswere developedfor dead-end filtration and are based on constant-pressure filtrationlaws. They are summarized in Table 1, where:

wR represents the specific cake resistance and is defined as thevolume of feed water per unit area for which the cakeresistance is equal to the membrane resistance;

wA represents the pore blocking potential and is defined as thevolume of feed water per unit area that contains enoughparticles to block the pores completely; and

wV represents the pore filling potential and is defined as theamount of feed water per unit area that contains enoughparticles to fill the pores completely.

We developed a mathematical model to determine the filtratedvolume V as a function of the filtration time t [22]:

V tð Þð Þ =

AM·R1−mM

C· 1−mð Þ 1 +2−m·C·ΔP·Rm−2

m t� �

μ

0@

1A1−m2−m

−1

0BBB@

1CCCA; m≠1;2

AM·wAln 1 +ΔP·t

wA·μ·RM

� �; m = 1

AMwA 1−e−

ΔP·twA·μ·RM

0B@

1CA; m = 2

8>>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>>:

ð5Þ

The time t to collect filtration volume V can be calculated byinverting Eq. (5):

t Vð Þ =

μ2−mð Þ·C·ΔP·Rm−2

M

V·C· 1−mð ÞR1−mM ·AM

+ 1

!2−m1−m−1

0BB@

1CCA; m≠1;2

e

V

wR·AM−1

0BB@

1CCA·

RM·wR·μΔP

; m = 1

lnAM·wA

AM·wA−v

� �·RM·wA·μ

ΔP; m = 2

8>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>:

ð6Þ

392 A. Alhadidi et al. / Desalination 279 (2011) 390–403

Eqs. (5) and (6) can then be combined to give an analyticalexpression for the SDI [22], which is not shown here as the equationsare rather large.

3. Material and methods

Three different 0.45 μmmembranes were used to perform SDI andMFI0.45 tests in the Evides seawater UF/RO desalination plant atJacobahaven, the Netherlands. Reference testing conditions (TO, ΔPO,RMO and SDIO) were as defined hereafter.

3.1. SDI setup

Fig. 1 shows a scheme of the apparatus used for the SDI tests. Theapplied pressure was maintained by the feed pump in the auto-matic setup. The feed tank was isolated, so as to keep the watertemperature constant (±1 °C) throughout the test. The flow rate,pressure and temperature were measured. Before installing themembrane filter, the water to be tested was flushed through theapparatus in order to remove any entrained contaminants. A 0.45 μmMF membrane filter (25 mm in diameter) was placed on the supportplate of the holder. The membrane filter was touched only withtweezers to avoid puncturing or contamination. It was checkedwhether the O-ring was in a good condition and properly placed. Thetrapped air was bled out through a relief air valve in the filter holder.The times to collect the first sample (141 mL, to correct for thedifferent membrane diameter of 25 mm) and the second sampleafter 15 min of total elapsed flow were calculated from the collectedfiltration data.

From the raw data from the SDI setup, the resistance and filteredvolume were calculated. Then C, m and RM were determined by least-squares curve fitting [23], which minimizes an error criterion:

min ∑n

i=0R vi;RM ;C;mð Þ−Rið Þ2 ð7Þ

Here n is the number of data points,wi is the accumulated filtratedvolume per unit area and Ri is the total resistance at data point i.

3.2. Membrane

In accordance with the 2007 ASTM standard regarding the MFmembrane material to be used in the SDI test, commercialnitrocellulose (M4) and cellulose acetate (M7) membranes were

pHTΚ

Clean water tank

Isolated feed tank

Clean waterpump

Feedpump

Fig. 1. Flow sheet of the SDI setup (automated, using feed gear pump). Feed tank is shown. pHrate (F) and temperature (T) are measured in the feed line.

chosen. For comparison, a nylon 6,6 membrane (M5) was also tested.Table 2 lists the properties of these membranes.

3.3. Defined reference testing conditions

Membrane resistance, feed temperature, applied pressure andmembrane area are themain testing parameters in this study. In orderto study the effect of each parameter independently, the referencetesting conditions (see Table 3) were defined as follows.

In the updated 2007 version of the ASTM standard, the membranefilter was better specified than previously. The pure water flow timeshould be 25–50 s for 500 mL under an applied pressure of 91.4–94.7 kPa; the calculated membrane resistance RM consequentlyranges from 0.39×1010 to 2.65×1010 m−1. The average value of1.29×1010 m−1 was defined as the reference membrane resistancefor RM.

The reference temperature of the feed was set to 20 °C and thestandard ASTM pressure of 207 kPa was taken as the referencepressure for the applied pressure ΔP. A membrane with a diameter of47 mm was chosen as standard membrane size, implying that thereference membrane area AMO is equal to 13.8×10−4 m2. The ROlimitation for the feed water, SDIO=3, was defined as the target valuefor the SDI.

3.4. Measured and normalized SDI

During the SDI test, the tandV filtration data were automaticallyrecorded and the testing conditions (T, ΔP, and RM) were measured.Themeasured SDI was calculatedwith Eq. (1). The fouling parameter Iwas estimated from the curve of t/V vs. V. The normalized SDI (‘SDI+’)was determined by using the fouling model or the charts describedhereafter. Fig. 2 schematically describes these methods.

4. Results and discussion

We developed new tools for calculating and for correcting the SDI.A small circular chart can be used to determine the required samplevolume for different membrane diameters (25, 47 and 90 mm). Wealso created a tool to be used in calculating the SDI with the aid of themeasured t1 and t2 values. We devised line and wheel slide charts tonormalize the measured SDI for the testing conditions (T, ΔP, and RM)based on the SDI/MFI0.45 relationship while assuming cake filtrationas well as 100% particle retention. For each different foulingmechanism, we created a chart to eliminate the influence of thetesting parameters on the SDI.

T

PF

0.45µm membrane

Flushing outlet

Air-Relief valve

, temperature (T) and conductivity (K) aremeasured in the feed tank. Pressure (P), flow

Table 2Microfiltration membrane used in this work. Pore size as given by the manufacturer.

Code Material Nominal Pore size (μm) Average RM (m−1)

M4 Nitrocellulosea 0.45 0.64×1010

M5 Nylon 6,6 0.45 2.65×1010

M7 Cellulose acetatea 0.45 0.85×1010

a ASTM standard material.

1833.4 mL

500 mL

141.5 mL

SDImeasured

Experimental data

t & V

Model

Estimated Fouling parameter

t1, t

2, t

f

SDInormalized

RM

Reference: TP

Fig. 2. Diagram showing the determination of SDImeasured and SDInormalized.


4.1. Determining the sample volume

In the ASTM standard, the volumes to be collected are 500 mLwhich is based on amembrane diameter of 47 mm. The ASTM includestwo other standard membrane diameters, namely 25 and 90 mm. Thesample volumes for those two diameters are 141.5 and 1833.4 mL, ascalculated by Eq. (8). For other membrane sizes, the sample volumeneeds to be adjusted, in direct proportion to the membrane area:

V1;2 = Vo ×AM

AM0ð8Þ

Here,

V1, 2 sample volumes 1 and 2 [L]Vo reference standard sample volume [500 mL]AMO reference membrane area [13.8×10−4 m2]AM membrane area [m2]

Fig. 3 is a tool that shows the sample volumes V1 and V2 for themembrane diameters 25, 47 and 90 mm.

Fig. 3 is a useful tool for operators in the field and should beproduced as a chart in the actual dimensions of the membranes. Theoperator can place the membrane on the chart, and then read thecorrect sample volume for that membrane.

4.2. Calculating SDI when tf equals 15 min

In the field, errors can easily occur when calculating the SDI withthe aid of a calculator. Fig. 4 presents a new tool (slide chart) forcalculating the SDI based on the measured t1, t2, and tf=15 min. Thistool was designed for t1and t2 between 10 s and 100 s and calculatesthe SDI on the basis of Eq. (1).

The top and central rulers indicate t1 and t2 in seconds, while thebottom ruler indicates the calculated SDI value for tf equaling 15 min.The chart in Fig. 4 is used as follows. After determining t1 and t2, thecentral ruler moves to the left until the value of t1 in the top ruler isplaced on top of the value of t2 on the central ruler. The value locateddirectly below the arrow on the central ruler then indicates the SDIvalue for tf=15 min. Fig. 5 shows an example of how to use this slidechart. In this particular case, the slide rule indicates the SDI value fort1=20 s and t2=30 s at tf=15 min as SDI=2.22.

4.3. Normalized SDI for a cake filtration mechanism (SDI+)

By assuming only cake filtration and 100% particle rejection duringthe SDI test, the SDI/MFI0.45 relationship was used to normalize theSDI (SDI+) to the reference testing conditions as defined in Table 3.

Table 3Reference conditions.

Parameter Reference value

RMO 1.29×1010 m−1

TO 20 °CΔPO 207 kPaAMO 13.4×10−4 m2

SDIO 3

For practical use in the field, we developed a line chart and slide wheelcharts for normalizing SDI this way.

t0 is defined as the required time in seconds for the 0.45 μmmembrane used in the SDI test to collect a sample volume V0 of an ROpermeate at a constant applied pressure of 207 kPa (2.07 bar) at 20 °C.The sample volume V0 should be adjusted in direct proportion to themembrane area using Eq. (8) or with the aid of our new tool (Fig. 3).The time t0 is a measure for the membrane resistance RM. At least onemeasurement of t0 for each membrane batch is recommended. Therelation between RMand t0 is described by Darcy's law in Eq. (9) [24]:

RM =ΔPμ × J

=ΔP

μ ×V0

AM × t0

= const × t0 ð9Þ

Here, J is the flux [m3/m2 s], μ is the water viscosity=0.001 Pa.s,ΔP=207 kPa, AM=13.8×10−4 m2 and V0=500 mL. Therefore, themembrane resistance RM[m−1] can be converted to t0[s] with Eq. (10).

RM = 0:57 × 109 × t0 ð10Þ

Fig. 3. Selecting the sample volume V1,2 for different membrane diameters 25, 47 and90 mm.

100010010 20 30 40 50 80 200 500

100010020 30 40 50 80 200 500

5 4

2.22 0.03.33

4.44

4.76

5.33

6

t1[S]

SDI

t2[S]

Fig. 4. Tool for calculating SDI for t1 and t2 and tf=15 min.


Based on Darcy's law and Eq. (3), t0 should be normalized fortemperature:

t0 at 20 ∘C =T + 42:5TO + 42:5

� �−1:5× t0 ð11Þ

where T is the measured temperature in °C.The resulting chart tools can be presented either as one line chart

or as a set of slide wheel charts. The following two examples showhow they can be used to normalize the measured SDI.

Example 1. Line charts to correct for T, ΔP and RM

Fig. 6 contains three charts (T,ΔP and RM) within one framework.Based on the model in Eq. (4) and the reference conditions of Table 3,each chart is calculated one by one by varying the target parameterwithin a range of T(10–60 °C), ΔP (1–3 bar) and t0(4.51–72.26 s) fordifferent fouling potential indexes I, corresponding to the SDI rangeof 0–6.66. The suggested range of t0 corresponds to the 0.45 μm MFresistance range of commercially available membranes (0.39×1010–

2.65×1010 m−1) [25]. The fouling potential index I=1.056×109 m−2

corresponds to the reference conditions in Table 3.Fig. 6 is the line chart, used as follows, for correcting the SDI for T,

ΔP and RM. The line chart contains three sub-charts: temperature,pressure andmembrane resistance (as t0). Startingwith themeasuredSDI value on the x-axis in the left corner, the target line extendsvertically until it reaches the actual temperature. The target line thenmoves to the right in the direction of the pressure lines until it reachesthe actual applied pressure. The next step for the target line is to movedown in the resistance chart represented by t0(the time needed to

10010 20 30 40 50 80

10020 30 40 50 80

6

Fig. 5. Example indicating SDI=2.22 whe

collect the sample volume of RO production under a pressure of207 kPa). After reaching the actual membrane resistance (that is, themeasured t0), the target line then moves horizontally to the left sideand the normalized SDI value can then be read on the Y-axis.

Example 2. Slide wheel charts for T, ΔP and RM

Three slide wheel charts for normalizing the SDI for T, ΔP and RMare presented in Figs. 7, 8 and 9, respectively. Similar to the line chart,the slide wheel charts were calculated with the model in Eq. (4). Eachchart for each parameter was calculated for different fouling potentialindexes I corresponding to an SDI range of 0–6.66 and for a proposedrange of T (6–58 °C), ΔP (1.5–2.8 bar) and t0(1–43 s).

Fig. 10 shows an example of the slide wheel chart's implementa-tion if a membrane resistance is assumed that is different from thereference value. t0=22.6 s corresponds to the reference testingconditions in Table 3 (T0, ΔP0, RM0 and AM0)

The wheel chart contains two wheels: an external fixed wheel andinternal slide wheel. Fig. 9 shows a potential starting situation of thewheel. The fixed external wheel indicates t0=22.6 s, while theinternal slide wheel indicates the SDI values for different foulingpotentials (SDI=5, 4, and 3). Let's assume that we perform an SDI testwith a membrane that has a lower resistance than the referencemembrane, that we collect 500 mL of clean water in 18 s instead of22.6 s, and that we measure an SDI value of 5. To correct thismeasured SDI for membrane resistance, the internal slide wheel canthen be turned in the direction of themeasured t0(counter-clockwise)until the measured SDI faces t0=18 s as shown in Fig. 10. Thenormalized SDI value (SDI+) then can be read in the internal slidewheel as the SDI value which faces t0=22.6 s and on the same slide asSDI=5, hence SDI+=5.25 (indicated in Fig. 10 by the red lines).

1000200 500

1000200 500

5 4

2.22 0.0

3.33

4.44

4.76

5.33

t1[S]

SDI

t2[S]

n t1=20 s, t2=30 s and tf=15 min.

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7

Temperature [oC] Applied pressure [bar]

SDI Measured

SD

I Nor

mal

ised

0

1

2

3

4

5

6

7

0 1 2 3 4 5 6 7

20

10

30405060

t0 [s]

5.6 s

90.5 s

0

1

2

3

4

5

6

7

2

11.5

2.53

3.0 bar1.0 bar

10 oC

60 oC

90.545.222.611.35.6

Fig. 6. Line chart to normalize the SDI value to the reference testing conditions: T [°C], ΔP [bar], t0 [s] while assuming cake filtration and 100% particle rejection.


Due to the proportional relation between t0and RM, the internalwheel in Fig. 10 has to be turned counter-clockwise if the measuredmembrane resistance RM is smaller than the reference membraneresistance RMO(1.29×1010 m−1) and clockwise if the measured RM isgreater than RMO.

4.4. Normalizing SDI for different fouling mechanisms (SDI+)

The filtration laws for constant pressure and the parameters Candm are shown in Table 1 [20]. The constant C is proportional to theparticle concentration, whereas the exponent m is defined by thefouling mechanism resulting in m values of 0, 1, 1.5 and 2, but can infact be any other real value. By using Eqs. (5) and (6) for the assumedm and C values, the SDI can then be calculated. The relationshipbetween the constant C and membrane resistance can be generalizedas follows:

C ≈ R1−mM

w R;A;Vð Þð12Þ

For the mvalues of 0, 1, 1.5 and 2, their associated log (C) valueranges (2 to 12, −4 to 2, −10 to −4 and −15 to −10) and thereference testing conditions of Table 3, Fig. 11 shows the normalizedSDI (SDI+) values, as calculated by using Eqs. (5) and (6).

When an SDI test is performed, the filtration data t and V can beused to determine the parameters C and m by using Eq. (7). For themain four mvalues (corresponding to the four fouling mechanisms),the normalized SDI value (SDI+) for T, ΔP and RM can be obtained byintersecting the C value with the dotted line in Fig. 11.

Fig. 11 can be used for correcting the SDI for the testing conditionsand the membrane resistance when only one type of fouling occursduring the SDI test, (i.e. the m value is exactly 0, 1, 1.5 or 2) andparticle rejection is 100%.

4.5. Alternatives for SDI

We suggest a new volume-based SDI, indicated as SDI_v.

4.6. Definition of the volume-based SDI_v

In the SDI test, the time between the two measurements tf is fixed(5, 10 or 15 min) and the total volume that is filtered in that timedepends on the flow rate. Thus, any effect that increases the flowthrough the membrane will increase the fouling load of themembrane and consequently, the measured SDI will be higher. Thisexplains our observation that the SDI increases with increasingtemperature (decreasing viscosity implies increased flow), increasingpressure and decreasing membrane resistance [22]. To assure that themembranes are subjected to the same fouling load in any testingcondition, it is much more logical to collect the second sample after afixed filtrated volume VfO instead of a fixed time tf. Such a volume-based SDI test would overcome the effects the testing conditions mayhave and would diminish the effect of the membrane resistance onthe test outcome.

4.6.1. Definition 1To determine the SDI_v [%/m], the volume-based plugging ratio

per specific unit volume [m3/m2] of a membrane filter with pores of

Fig. 7. Slide wheel chart to normalize the SDI value to the reference testing conditions T [°C] assuming cake filtration and 100% particle rejection.


0.45 μmand a diameter of 47 mm at 30 psi (207 kPa) is measured. Themeasurement is done as follows:

1) The time t1 is defined as the time required to filter the firststandard volume V1 of 500 mL.

2) t2 is defined as the time it takes to filter another 500 mL (V2), afterthe first standard volume VfO has been filtered.

3) The index is calculated using the following formula.

SDI v =100%VfO

AMO

1− t1t2

� �=

%P vVfO

AMO

ð13Þ

where t1 [s] is the time to collect the first sample V1, t2[s] is the time tocollect the second sample V2 after filtrating the standard volume VfO,AMO is the reference membrane area [m2] and %P _v is the volume-based plugging ratio [%].

4.6.2. Definition 2SDI_v [%m] also can be defined as the plugging ratio after a fixed

filtrated volume VfO divided by 15, for a membrane filter with pores of

0.45 μm and diameter of 47 mm at 30 psi (207 kPa). Here, 15 is adimensionless factor to scale SDI_v down to the standard (time-based) SDI values between 0 and 6.66.

SDI v =100%15

1− t1t2

� �=

%Pv15

ð14Þ

Here, t1 [s] is the time to collect the first sample V2, and t2 [s] is thetime to collect the second sample V2 after filtering the standardvolume VfO.

Both definitions can be used as the new fouling index. The volumeof the first sample V2 (500 mL), the second sample V2 (500 mL) andthe standard volume VfO should be adjusted in direct proportion to themembrane area. In this study, Definition 1 is used unless otherwisementioned.

4.7. Calculation of SDI_v

Eqs. (5) and (6) can be combined to yield analytical expressionsfor the SDI_v for different fouling mechanisms based on C and m.The reference filtrated volume VfO is arbitrarily defined as theaverage accumulated volume collected in 15 min (V15) for the four

Fig. 8. Slide wheel chart to normalize the SDI value to the reference testing conditions ΔP [bar] while assuming cake filtration and 100% particle rejection.


fouling mechanisms, at reference testing parameters as defined inTable 3:

VfO =VfO Cakeð Þ + VfO Interð Þ + VfO Stanð Þ + VfO Compð Þ

4= 14:58 L:

Here, (Cake) stands for cake filtration (14.1 L), (Inter) forintermediate blocking (14.5 L), (Stan) for standard blocking (14.7 L)and (Comp) for complete blocking (15.0 L). The sample volumes V1

and V2 (500 mL) are based on a 47-mm filter diameter. When adifferent filter diameter is used, the sample volumes V1 and V2 mustbe adjusted in direct proportion to the filter diameter, as described inEq. (8).

t1 and t2 are required to calculate the SDI_v in Eq. (10). Theseparameters are derived from Eqs. (5) and (6) by using the followingseven steps:

1. t1 follows from Eq. (6);2. t2 cannot be determined directly and, as a consequence, a couple of

steps are needed;3. By substituting VfO for V in Eq. (6) one obtains tf;4. Vtotal=VfO+V2 (Vtotal, VfO and V2 are the volumes filtered in ttotal, tf

and t2 respectively);

5. Substitution of Vtot for Vin Eq. (6) gives ttotal;6. t2 follows from t2= ttotal− tf;7. The SDI_v finally is calculated by substitution of t1 and t2 in

Eq. (13).

The filtrated volume V can be plotted as a function of time t in atypical fouling curve as schematically presented in Fig. 12, illustratingthe steps to determine SDI_v from a time–volume curve.

4.8. SDI_v sensitivity to particle concentration and fouling mechanism

The sensitivity of SDI_v to the particle concentration was studiedby using the SDI_v model described in Section 4.6.2. The relativeparticle concentration was varied, where a relative concentration of 1corresponds to SDI_v=4.36. Fig. 13 shows SDI_v values plotted vs. theparticle concentration. The reference testing conditions of Table 3were assumed, and a standard filtrated volume VfO of 14.58 L wasused.

Fig. 13 shows that the SDI_v sensitivity to the particle concentra-tion is different for the four fouling mechanisms. The SDI_v has alinear relationship with particle concentration if complete blocking isthe dominant fouling mechanism during testing. We have previouslystudied the sensitivity of the standard (time-based) SDI to the particle

image of Fig.�8

Fig. 9. Slide wheel chart to normalize the SDI value to the reference testing conditions as t0 while assuming cake filtration and 100% particle rejection.


concentration and different testing condition parameters [25]. Fromcomparing the sensitivity of SDI_v in Fig. 13 (a) and the sensitivity ofthe time-based SDI Fig. 13(b), we conclude that SDI_v has a morelinear relationship with particle concentration than the time-basedSDI.

4.9. SDI_v sensitivity to testing parameters and fouling mechanism

The sensitivity of SDI_v to variations in the testing conditionparameters was studied as well. The fouling indexeswA,V were assumedto be independent of the membrane resistance RM; the relationshipbetween wR and RMwas described before [21,22]. Assuming the threefouling mechanisms of standard, intermediate and complete poreblocking, SDI_v was plotted as a function of RM (0.5×1010 m−1b

RMb3.0×1010 m−1) in Fig. 14. SDI_v was also plotted as a functionof ΔP (0.5 bar b ΔP b 2.75 bar) and T (10°C b T b 50°C) for the fourdifferent mechanisms (cake filtration and the three types of poreblocking).

Fig. 14 shows that the SDI_v is independent of the variation in thetesting condition parametersΔP and T for all four foulingmechanisms.For intermediate, standard and complete blocking, SDI_v is alsoindependent of the membrane resistance RM.

For cake filtration as the only fouling mechanism Fig. 15presents the effect of the membrane resistance RM on the SDI_vresults. For this graph, the SDI_v index was calculated based on thetwo definitions given in Section 4.6.1. The specific cake resistanceRC was assumed to be equal to 1.056×109 m−2, corresponding tothe reference testing conditions and a time-based SDI equal to 3.The membrane resistance RM was varied between 0.3 and2.7×1010 m−1.

The SDI_v2 and SDI in Fig. 15 are on the same scale and can becompared. We can conclude that the new fouling index SDI_v2 is lesssensitive to a variation in the membrane resistance than the time-based standard SDI. From Figs. 13, 14, and 15, we conclude that theintroduction of the SDI_v solves most of the problems of the time-based SDI and is closer to an ideal fouling index.

4.10. Experimental validation

The standard SDI and MFI0.45 indexes were measured in theEvides RO/UF desalination plant in Jacobahaven, the Netherlands,described before [26]. UF feed was diluted with RO permeate withdifferent dilution ratios to investigate the influence of the foulantconcentration on the SDI; 50 mL, 100 mL, 200 mL, 300 mL and

image of Fig.�9

Fig. 10. An example of using the slide wheel chart to normalize the SDI value to the reference testing conditions: RM [m−1] while assuming cake filtration and 100% particle rejection.


500 mL of UF feed were diluted in 25 L of RO feed. Three differentmembranes with different membrane resistances (M4, M5 and M7)were used to carry out the SDI tests. Table 2 shows the averagemembrane resistances of these membranes. SDI results werenormalized for membrane resistance and temperature (SDI+).

The filtration data (V versus t) that were used to calculate the(time-based) SDI can be also used to calculate the SDI_v. However,filtration data for the time-based SDI were limited to a total filtrationtime of 20 min. Based on SDI_v definition 1, an accumulated filtratedvolume VfO of 3.65 Lwas suggested for the 25-mmdiameter cell. In thecase of a high membrane resistance (M5), VfO would need more than20 min collection time. In order to compare the three membraneswith the available data, a standard VfO of 1.25 L instead of 3.65 L wasassumed. To obtain a comparable fouling load for the time-based SDIand SDI_v, tf was decreased to 5 min and the SDI5 was calculated. Thetime-based SDI5, normalized SDI+ and SDI_ v results were plottedversus the fouling potential index I as shown in Fig. 16.

In Fig. 16(a), membrane M4 with the lowest membrane resistanceshows the highest SDI at a certain fouling load. Contrarily, M5with thehighest membrane resistance reveals the lowest SDI. SDI_v resultsbased on Fig. 16(b) show a more linear relationship with the fouling

index I. In addition, there is less difference between the curves for thethree membranes. Thus, SDI_v is less sensitive to differences in themembrane resistance compared with the time-based SDI. Thestandard SDI results were normalized to SDI+ for the membraneresistance and temperature in Fig. 16(c). The curves of the threemembranes are almost identical, especially at higher fouling indexes.An ideal fouling index should not be affected by differences in themembrane resistance and should have a linear relationship with theparticle concentration. However, the membrane resistance affectsSDI_v, while SDI+ has no linear relation with the particleconcentration.

The fouling index SDI_v can be calculated through the SDI_v/MFI0.45 relation following the steps in Section 4.6.2 which resultsin Eq. (15).

SDI v=100VfO

AM

1−

μ⋅RM⋅VC

dP⋅AM+ MFI⋅V2

C

μ⋅RM⋅ VfO + VC

� �ΔP⋅AM

+ MFI⋅ðVfO + VCÞ2−μ⋅RM⋅VfO

ΔP⋅AM−MFI⋅V2

fO

0BBBBB@

1CCCCCA

ð15Þ

image of Fig.�10

-4

-2

0

Intermediate Blocking m=1

Log

(C)

2

4

6

8

10

12

Cake Filtration m=0

Log

(C)

-10

-9

-8

-7

-6

-5

Standard Blocking m=1.5

Log

(C)

0.01 0.1 1 10-15

-14

-13

-12

-11

Complete Blocking m=2

SDI normalized

Log

(C)

Fig. 11. The normalized SDI values for measured C and m values. By assuming thereference conditions (Table 3), C and m, Eqs. (5) and (6) were used to calculate SDI.

t1 t2

V1

V2

tf

VfO

ttotal

Vtotal

t

V

Fig. 12. Theoretical diagram showing the filtrated volume as function of time and thevariables used to determine SDI_v. VfO=14.58 L.

0.0 0.5 1.0 1.5 2.0 2.50

2

4

6

8

10

Idea

l Fou

ling

index

Cake Filtration m=0 Intermediate Blocking m=1 Standard Blocking m=1.5 Complete Blocking m=2

SD

I_v

[%/m

]

Relative particle concentration [-]

0 1 2 30

1

2

3

4

5

6

7 Cake Filtration m=0 Intermediate Blocking m=1 Standard Blocking m=1.5 Complete Blocking m=2

SD

I

Relative particle concentration [-]

Idea

l fou

ling

inde

x

a

b

Fig. 13. The sensitivity of (a) volume-based SDI_v and (b) time-based SDI for therelative particle concentration, where a relative concentration of 1 corresponds toSDI_v=4.36. The standard filtrated volume Vf is 14.58 L and the reference testingconditions as listed in Table 3 were assumed.


where VC is the sample volume VC=V1=V2 and MFI is the modifiedfouling index. Another option is to determine SDI_v by measuring thefouling potential index I:

SDIv =200·AM·I

2·AM·RM + 2·I·Vf + VC·I: ð16Þ

Normalizing SDI_v can be done by measuring the fouling potentialindex I and substituting it and the reference testing conditions fromTable 3 in Eq. (16).

image of Fig.�11

0 1 2 30

2

4

6

8

10

0 1 2 3 0 20 40 60

Intermediate Blocking m=1 Standard Blocking m=1.5 Complete Blocking m=2

SD

I_v

[%/m

]

RM[×1010m-1] P [bar]

Cake Filtration m=0 Intermediate Blocking m=1 Standard Blocking m=1.5 Complete Blocking m=2

T[oC]

Fig. 14. The sensitivity of SDI_v for membrane resistance, pressure difference andtemperature for the standard filtrated volume of Vf=14.58 L.

0.0 0.4 0.8 1.2 1.6 2.0 2.40

5

10

15

20

25

M4 M5 M7

SD

I 5 M

easu

red

Fouling index I [×1010 m-2]

0.0 0.4 0.8 1.2 1.6 2.0 2.40

5

10

15

20

25

M4 M7 M5


25

SD

I_v

[%/m

]

a

c

b


SDI_v can be normalized using Fig. 17 for target t0 (4.5–72.3 s).Starting with the measured SDI_v value on the x-axis, a target lineextends vertically toward the resistance lines represented by t0(thetime needed to collect the sample volume of RO production underpressure 207 kPa). After reaching the actual membrane resistance(measured t0), the target line then moves horizontally to the left andthe SDI_v normalized value can be read on the Y-axis.

4.11. Sensitivity of SDI_v to errors

By definition, the scale of the standard SDI is 0–6.66 (%P/15 min)while the scale of the SDI_v based on definition 1 is 0–9.5 (%P_v/VfO/AM).Due to this difference in scale, the comparison between the sensitivitiesof both indexes is presented as a percentage of the actual value.When we assumed the cake filtration mechanism, reference testingconditions (Table 3) and a fouling potentialwR of 12.22 (corresponding

0 1 2 3 4 50

2

4

6

8

SDI [%/min]

SDI_v 2 [%/m]

SDI_v 1 [%/m]

SD

I

RM[×1010 m-1]

Ideal fouling index

Fig. 15. The sensitivity of the standard SDI and SDI_v based on definitions 1 (SDI_v1)and 2 (SDI_v2) in Section 4.6.1 for the membrane resistance RM. The standard filtratedvolume Vf was 14.58 L, the cake resistance 1.055×109 m−1 with the assumed referencetesting conditions of Table 3.

0.0 0.4 0.8 1.2 1.6 2.0 2.40

5

10

15

20

M4 M7 M5

SD

I 5 N

orm

aliz

ed


Fig. 16. (a) Standard time-based SDI for 5 min elapsed filtration time (b) SDI_v values(c) time-based SDI normalized for the membrane resistance and the testing conditionparameters (SDI+).

to a standard SDI value of 3), SDI_v was found to be equal to 4.36. Thesensitivity of the SDI and SDI_v to errors in t1, t2, V1and V2was examinedassuming variations of 1 s, 1 s, 50 mL and 50mL, respectively. Table 4

0

2

4

6

8

10

0 2 4 6 8 10

SDI_v Measured [%/m]

SD

I_v

Nor

mal

ized

[%/m

]

t0 [s]90.545.222.611.3

5.6

90.5 s

5.6 s

Fig. 17. Line chart to normalize the SDI_v value to the membrane resistance represented by t0 [s] assuming cake filtration and 100% particle rejection.


shows the errors in SDI_v for these assumed variations which werecalculated using the SDI_v definition in Eq. (13).

The results in Table 4 show that the SDI_v is not sensitive to ameasurement error in T, ΔP and RM. The SDI_v is more sensitive toerrors in t1 and t2 than the time-based SDI, and more specifically, it ismore sensitive to errors in measuring the time to collect the firstsample t1 than for the error in measuring the time to collect thesecond sample t2. From Table 4, we can conclude that the new foulingindex SDI_v in general is less sensitive to errors.

5. Conclusions

For use in SDI tests, we developed a tool to determine the requiredsample volumes V1, 2 according to membrane diameter. The SDI valuecan also be calculated using Eq. (1) along with a slide bar for ameasured t1 and t2 when tf=15 min. Based on the mathematicalmodel that we developed in previous work [19], the standard SDI canbe normalized into SDI+ for the test condition parameters T, ΔP andmembrane resistance RM by using a line chart or slide wheel chartsand assuming cake filtration and 100% particle retention. SDI can benormalized into SDI+ for T, ΔP and RM assuming different foulingmechanisms by using another line chart based on the measuredparameters C and m.

Table 4The effects of accuracy errors of the equipment on SDI=4.36.

Parameters Error InfluenceSDI_v=4.36±

% ofSDI_v=4.36

% ofSDI=3.00⁎

T 1 [°C] 0.00 0.00 1.00dP 7 [kPa] 0.00 0.00 1.67RM 0.1×1010

[m−1]0.17–0.19 3.90–4.36 6.67

AMO 2 mm 0.00 0.00 0.00t1 1 [s] 0.22 5.14 1.00t2 1 [s] 0.12 2.85 2.33t15 10 [s] 0.00 0.00 0.67V1 50

[mL/500 mL]0.52 11.95 12.33

V2 50[mL/500 mL]

+0.52, −0.58 11.95–13.20 12.33

Calculated from other work [27].

A new fouling index, SDI_v, is suggested, 30 years after theMFI0.45. The SDI_v compares the initial flow rate with the flow rateafter filtering a standard volume VfO and usingMFmembranes with anaverage pore size of 0.45 μm. The SDI_v has a linear relationship withthe particle concentration if complete blocking is the dominantfouling mechanism during testing. SDI_v shows a more linearrelationship to the particle concentration than the standard, time-based SDI. Furthermore, the mathematical model shows that SDI_vis independent of the testing parameters T and ΔP and less sensitiveto membrane resistance. In experiments, three membranes withdifferent resistances were used to determine the standard SDI andSDI_v at a UF/RO desalination plant. SDI/5 min values were normal-ized to SDI+ for the temperature and the membrane resistances. Bynormalizing the standard SDI values into SDI+, the effect oftemperature and membrane type is eliminated. Moreover, the SDI_vis less susceptible to measurement errors and has a better linearrelationship to the particle concentration comparedwith the standardSDI. In conclusion, the SDI_v is a better index for determining thefouling potential of an RO feed than the standard SDI.

Abbreviations

AM membrane area [m2]AM0 reference membrane area 13.4×10−4 [m2]ΔP0 reference applied pressure 207 [kPa]ΔP applied pressure [Pa]J flux [m3/m2 s]I fouling potential index (m−2)Mμ viscosity [Pa.s]%P plugging ratio [%]%P _v volume-based plugging ratio [%]R total resistance [m−1]RM membrane resistance [m−1]SDI Silt Density Index [%/min]SDIO reference Silt Density Index [%/min]SDI5 Silt Density Index for tf 5 min [%/min]SDI_v volume-based Silt Density Index [%/m]SDI+ normalized silt density index [%/min]t1,2 time to collect the first or second samples [s]tf elapsed filtration time [s]t0 time to collect V0 of RO product [s]


V filtered volume [m3]V1,2,C sample volume [m3]V0 sample volume for RO product [m3]VfO average standard filtrated volume [m3]wR, A, V fouling potential [m3]

Acknowledgments

The authors of this paper would like to acknowledge the scientificand financial support of Vitens, Evides and Norit X-Flow B.V. Part ofthis work was carried out within the framework of the InnoWATORsubsidy regulation of the Dutch Ministry of Economic Affairs (projectIWA08006 ‘Zero Chemical UF/RO System for Desalination’).

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SDI normalization and alternatives