METHOD FOR DETERMINING THE REMAINING WATER VOLUME IN A WATER SOFTENING SYSTEM USING H+/(NA+ AND/OR K+)-ION EXCHANGE RESINS

Abstract

A method of determining the remaining water volume (RLV) which can still be softened prior to the exhaustion of an ion exchange resin contained in a filter device. A water softening system, a computer program and a computer readable medium having stored thereon the computer program.

Claims

1. A method of determining the remaining water volume (RLV) which can still be softened prior to the exhaustion of an ion exchange resin contained in a filter device, the determination comprising the steps of: i) sequentially measuring a water characteristic w, wherein w is selected from one or more of pH and electrical conductivity LF, and wherein w is determined by a sensor in softened water obtained from the filter device, at increments of softened volume (V.sub.S) to acquire measured data points (V.sub.Si, w.sub.i) with i=1, 2, 3, . . . , N and N ; ii) after each measuring of a sequential data point (V.sub.Si, w.sub.i) in step i) which data point is defined as new data point, a polynomial is approximated between all previously measured data points (V.sub.Sp, w.sub.p) with p=1, 2, . . . i-1, and the new data point (V.sub.Si, w.sub.i); iii) after each polynomial approximation in step ii), the polynomial is analyzed for an inflection point IP (V.sub.IP, w.sub.IP) which corresponds to a point: ) (V.sub.Si, w.sub.app_i) of the polynomial being a point approximated for (V.sub.Si, w.sub.i) in step ii), wherein at point (V.sub.Si, w.sub.app_i), a difference w between w.sub.app_1 of point (V.sub.S1, w.sub.app_S1) of the polynomial being a point approximated for (V.sub.S1, w.sub.1) in step ii) and w.sub.app_i of point (V.sub.Si, w.sub.app_i) of the polynomial is 50 S/cm for w being electrical conductivity LF or is 1.5 for w being pH; or ) where the second derivative of the polynomial is 0 or where there is a change of sign of the second derivative from positive to negative or from negative to positive; iv) repeating steps iii) and iii) with the next higher i, and when an inflection point is determined in step iii), RLV is calculated based on V.sub.IP of the inflection point IP.

2. The method according to claim 1, wherein the method comprises at least one of the following features: In step iii)), said difference w is 55 S/cm for w being electrical conductivity LF or is 1.65 for w being pH, most preferably said difference w is 60 S/cm for w being electrical conductivity LF or is 1.8 for w being pH; and/or the ion exchange resin has a (Na.sup.+ and/or K.sup.+)/H.sup.+ loading ratio between 3:1 to 1:3, more preferably between 2:1 to 1:2, even more preferably between 1.5:1 to 1:1.5, and most preferably between 1.2:1 to 1:1.2; and/or V.sub.S1 is within a range of 0.22% to 5% of the maximum volume capacity V.sub.cmax of the ion exchange resin, preferably within a range of 0.3% to 3% of the maximum volume capacity V.sub.cmax of the ion exchange resin, more preferably within a range of 0.35% to 2% of the maximum volume capacity V.sub.cmax of the ion exchange resin, and most preferably within a range of 0.4% to 1.5% of the maximum volume capacity V.sub.cmax of the ion exchange resin; and/or an increment of softened volume (V.sub.S) is within a range of 0.01% to 0.5% of the maximum volume capacity V.sub.cmax of the ion exchange resin, preferably within a range of 0.02% to 0.25% of the maximum volume capacity V.sub.cmax of the ion exchange resin, more preferably within a range of 0.025% to 0.15% of the maximum volume capacity V.sub.cmax of the ion exchange resin, and most preferably within a range of 0.03% to 0.1% of the maximum volume capacity V.sub.cmax of the ion exchange resin.

3. The method according to claim 1, wherein in step ii), prior to approximating a polynomial between all previously measured data points (V.sub.Sp, w.sub.p) and the new data point (V.sub.Si, w.sub.i), a straight line L.sub.1 having a slope sl.sub.1 is fitted between the first measured data points within a range V.sub.Si=0 up to a threshold Volume V.sub.T.

4. The method according to claim 3, wherein V.sub.T is within a range of up to 5% of the maximum volume capacity V.sub.cmax of the ion exchange resin, preferably up to 4%, more preferably up to 2%, and most preferably 1.5%.

5. The method according to claim 1, wherein a remaining filter life time (RLZ) is calculated by dividing RLV by an average water consumption dV.sub.average of a water volume per hour.

6. The method according to claim 1, wherein for the inflection point IP (V.sub.IP, w.sub.IP) according to step iii)), the polynomial is a 1.sup.st to 4.sup.th degree polynomial, preferably 1.sup.st or 3.sup.rd degree polynomial, most preferably a 1.sup.st degree polynomial.

7. The method according to claim 1, wherein for the inflection point IP (V.sub.IP, w.sub.IP) according to step iii)), the degree of the polynomial is 4 to 8, more preferred 5 or 6 and most preferred the degree is 5.

8. The method according to claim 1, wherein for the inflection point IP (V.sub.IP, w.sub.IP) according to step iii)), a local maximum LM (V.sub.LM, w.sub.LM) adjacent to inflection point IP (V.sub.IP, w.sub.IP) is determined, wherein the difference between w.sub.IP and w.sub.LM is in a predetermined range w.sub., preferably the predetermined range w.sub. is 4 to 1000 S/cm, more preferably 6 to 800 S/cm, and most preferably 10 to 300 S/cm for the water characteristic w being electrical conductivity LF.

9. The method according to claim 8, wherein the local maximum LM (V.sub.LM, w.sub.LM) is a first derivative of the polynomial where there is a change of sign from positive to negative, or the first derivative of the polynomial is 0 and the second derivate is smaller than 0.

10. The method according to claim 1, wherein for the inflection point IP (V.sub.IP, w.sub.IP) according to step iii)), for the water characteristic w being electrical conductivity LF, a drop above the preferred predetermined range, preferably >300 S/cm between local maximum LM(V.sub.Lm, w.sub.Lm) adjacent to inflection point IP (V.sub.IP, w.sub.IP) and the infection point IP(V.sub.IP, w.sub.IP), is attributed to a change in raw water quality and is no IP.

11. A water softening system, comprising: I. An inlet for influent raw water and II. an outlet for effluent softened water, III. a filter device containing an ion exchange resin, IV. an electronic device capable of receiving signals emitted a. by a sensor for measuring the water characteristic w, arranged in the softened water outlet which signal is selected from one or more of the electrical conductivity (LF) and the pH, b. by a volume meter for measuring the volume flow of softened water likewise arranged in the softened water outlet which signal is the flowed softened water volume (V.sub.S), which volume meter is optionally coupled with an hour and/or minute meter, V. an interface for transmitting the signals received under IVa) and IVb) to an electronic control unit, and VI. an electronic control unit, , wherein the electronic control unit has a memory to: I. store the repeatedly/sequentially measured water characteristic w, which is selected from one or more of the electrical conductivity LF and the pH of the filtered (i.e. softened) water at increments of softened water volume (V.sub.S), received from the interface to acquire measured data points (V.sub.Si, w.sub.i) with i=1, 2, 3, . . . , N and N ; and II. store an executable computer program which is capable of executing the following method steps: a. after each storing of a sequential data point (V.sub.Si, w.sub.i) in step I) which data point is defined as new data point, approximating a polynomial between all previously measured data points (V.sub.Sp, w.sub.p) with p=1, 2, . . . i-1, and the new data point (V.sub.Si, w.sub.i); b. after each polynomial approximation in step IIa), analyzing the polynomial for an inflection point IP (V.sub.IP, w.sub.IP) which corresponds to a point: ) (V.sub.Si, w.sub.app_i) of the polynomial being a point approximated for (V.sub.Si, w.sub.i) in step ii), wherein at point (V.sub.Si, w.sub.app_i), a difference w between w.sub.app_1 of point (V.sub.S1, w.sub.app_S1) of the polynomial being a point approximated for (V.sub.S1, w.sub.1) in step ii) and w.sub.app_i of point (V.sub.Si, w.sub.app_i) of the polynomial is 50 S/cm for w being electrical conductivity LF or is 1.5 for w being pH; ) where the second derivative of the polynomial is 0 or where there is a change of sign of the second derivative from positive to negative or from negative to positive; c. repeating steps Ila) and IIb) with the next higher i, and when an inflection point is determined in step lib), RLV is calculated based on V.sub.IP of the inflection point IP.

12. The water softening system according to claim 11, wherein in the executable computer program, the method steps according to claim 2 are applied.

13. The water softening system according to claim 11, wherein the water softening system comprises at least one of the following features: the electronic control unit has means for communicating RLV and/or RLZ to a user or by transmitting RLV to a remote location, optionally RLV and/or RLZ can also be stored in a cloud and downloaded at the request of a user and then be displayed via a portal; and/or the memory includes a sl.sub.1 ft register.

14. The computer program comprising instructions to cause the water softening system according to claim 11 to execute the steps of the method of determining the remaining water volume (RLV) which can still be softened prior to the exhaustion of an ion exchange resin contained in a filter device, the determination comprising the steps of: i) sequentially measuring a water characteristic w, wherein w is selected from one or more of pH and electrical conductivity LF, and wherein w is determined by a sensor in softened water obtained from the filter device, at increments of softened volume (V.sub.S) to acquire measured data points (V.sub.Si, w.sub.i) with i=1, 2, 3, . . . , N and N ; ii) after each measuring of a sequential data point (V.sub.Si, w.sub.i) in step i which data point is defined as new data point, a polynomial is approximated between all previously measured data points (V.sub.Sp, w.sub.p) with p=1, 2, . . . i-1, and the new data point (V.sub.Si, w.sub.i); iii) after each polynomial approximation in step ii), the polynomial is analyzed for an inflection point IP (V.sub.IP, w.sub.IP) which corresponds to a point: ) (V.sub.Si, w.sub.app_i) of the polynomial being a point approximated for (V.sub.Si, w.sub.i) in step ii), wherein at point (V.sub.Si, w.sub.app_i), a difference w between w.sub.app_1 of point (V.sub.S1, w.sub.app_S1) of the polynomial being a point approximated for (V.sub.S1, w.sub.1) in step ii) and w.sub.app_i of point (V.sub.Si, w.sub.app_i) of the polynomial is 50 S/cm for w being electrical conductivity LF or is 1.5 for w being pH; or ) where the second derivative of the polynomial is 0 or where there is a change of sign of the second derivative from positive to negative or from negative to positive; iv) repeating steps ii) and iii) with the next higher i, and when an inflection point is determined in step iii), RLV is calculated based on V.sub.IP of the inflection point IP.

15. A computer readable medium having stored thereon the computer program according to claim 14.

16. The method according to claim 2, wherein in step ii), prior to approximating data point (V.sub.Si, w.sub.i), a straight line L.sub.1 having a slope sl.sub.1 is fitted between the first measured data points within a range V.sub.Si=0 up to a threshold Volume V.sub.T., and wherein V.sub.T is within a range of up to 5% of the maximum volume capacity V.sub.cmax of the ion exchange resin, preferably up to 4%, more preferably up to 2%, and most preferably 1.5%.

17. The method according to claim 16, wherein a remaining filter life time (RLZ) is calculated by dividing RLV by an average water consumption dV.sub.average of a water volume per hour, and wherein for the inflection point IP (V.sub.IP, w.sub.IP) according to step iii)), the polynomial is a 1.sup.st to 4.sup.th degree polynomial, preferably 1.sup.st or 3.sup.rd degree polynomial, most preferably a 1.sup.st degree polynomial.

18. The method according to claim 17, wherein for the inflection point IP (V.sub.IP, w.sub.IP) according to step iii)), the degree of the polynomial is 4 to 8, more preferred 5 or 6 and most preferred the degree 5, wherein for the inflection point IP (V.sub.IP, w.sub.IP) according to step iii)), a local maximum LM (V.sub.LM, w.sub.LM) adjacent to inflection point IP (V.sub.IP, w.sub.IP) is determined, and wherein the difference between w.sub.IP and w.sub.LM is in a predetermined range w.sub., preferably the predetermined range w.sub. is 4 to 1000 S/cm, more preferably 6 to 800 S/cm, and most preferably 10 to 300 S/cm for the water characteristic w being electrical conductivity LF.

19. The method according to claim 18, wherein the local maximum LM (V.sub.LM, w.sub.LM) is a first derivative of the polynomial where there is a change of sign from positive to negative, or the first derivative of the polynomial is 0 and the second derivate is smaller than 0, and wherein for the inflection point IP (V.sub.IP, w.sub.IP) according to step iii)), for the water characteristic w being electrical conductivity LF, a drop above the preferred predetermined range, preferably >300 S/cm between local maximum LM(V.sub.Lm, w.sub.Lm) adjacent to inflection point IP (V.sub.IP, w.sub.IP) and the infection point IP(V.sub.IP, w.sub.IP), is attributed to a change in raw water quality and is no IP.

20. The water softening system according to claim 12, wherein the water softening system comprises at least one of the following features: the electronic control unit has means for communicating RLV and/or RLZ to a user or by transmitting RLV to a remote location, optionally RLV and/or RLZ can also be stored in a cloud and downloaded at the request of a user and then be displayed via a portal; and/or the memory includes a shift register.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0060] FIG. 1 is a graph of GH vs. conductivity for Na.sup.+/H.sup.+ exchange resins;

[0061] FIG. 2 illustrates a LF vs. softened water volume curve;

[0062] FIG. 3 is a graph plotting filtrate conductivity vs. filtrate volume;

[0063] FIG. 4 is a further graph illustrating filtrate conductivity vs. filtrate volume;

[0064] FIG. 5 is a further graph illustrating filtrate conductivity vs. filtrate volume;

[0065] FIG. 6 depicts a flowchart of a particularly preferred determination of the inflection point IP.

[0066] FIG. 7 is a further graph illustrating filtrate conductivity vs. filtrate volume;

[0067] FIG. 8 is a further graph illustrating filtrate conductivity vs. filtrate volume; and

[0068] FIG. 9 depicts a flowchart of an alternative determination for the inflection point IP.

DETAILED DESCRIPTION OF THE INVENTION

[0069] The invention relates to a method for operating a water softening system with a softening device comprising an ion exchange material, specifically a (Na.sup.+ and/or K.sup.+)/H.sup.+-exchange resin. In the softening process the hardness-forming ions, calcium and magnesium ions, are replaced with sodium and/or potassium ions, and/or protons. This ion exchange is performed by means of a resin (ion exchange resin) loaded with sodium and/or potassium ions and protons. In the following, sometimes only the terms Na.sup.+/H.sup.+-exchange resin and Na.sup.+/H.sup.+ loading ratio are exemplary used, because Na.sup.+/H.sup.+-exchange resin and Na.sup.+/H.sup.+ loading ratio are preferred. However, it is noted that generally, also (Na.sup.+ and/or K.sup.+)/H.sup.+-exchange resin and (Na.sup.+ and/or K.sup.+)/H.sup.+ loading ratio may be applied, since in the present method, potassium ions (K.sup.+) provide for similar conductivity values in water like sodium ions (Na.sup.+).

[0070] The point in time when the ion exchange resin has matured to exhaustion depends on the nominal capacity of the ion exchange resin, on the water quality (i.e., the GH and/or KH of the raw water), and on the water consumption. Under the framework of the present invention LF measurements with Na.sup.+/H.sup.+ exchange resins have been performed. It was found that there is no direct correlation between conductivity and total hardness (see FIG. 1; GH vs. LF). If one would use a linear regression of the plotted data (total hardness vs. conductivity) this would result in a miscalculation of the exhaustion time by a factor of about .sup.rd for about .sup.rd of the total number of measurements (see FIG. 1). The ion exchange processes and the impact of these processes on the electrical conductivity (LF) of water which has passed an ion exchange resin with Na.sup.+ as well as H.sup.+ donor ions are complex.

[0071] Na.sup.+/H.sup.+ ion exchange resinsfor example those of the polyacrylic typeare weakly acidic ion exchangers (due to the pending COOH groups). In these weakly acidic ion exchangers the H.sup.+ ion is energetically favored (because smaller) over the Na.sup.+ ion (because larger). These types of ion exchange resins therefore prefer the exchange of Na.sup.+ for Ca.sup.2+ or Mg.sup.2+, and only very reluctantly release H.sup.+. Thus total hardness (GH), e.g. CaSO.sub.4 in the water is exchanged to yield Na.sub.2SO.sub.4, and carbonate hardness (KH), e.g. Ca(HCO.sub.3).sub.2.fwdarw.2 NaHCO.sub.3, are exchanged. Yet, these exchange processes do not lead to a sufficiently significant change in conductivity (LF), since the limiting conductivities of Ca.sup.2+, Mg.sup.2+ and Na.sup.+ are about the same.

[0072] In order to be able to draw any conclusions about the state of a weakly acidic ion exchange resin from the LF, exchange reactions need to be taken into account that affect LF. The first reaction of this kind is the exchange of H.sup.+ for Ca.sup.2+ and Mg.sup.2+. As stated above, this rarely happens unless another element in the water has a higher affinity to H.sup.+ than the exchange resin itself. This applies to KH. The exchange of e.g. Ca.sup.2+ (Ca(HCO.sub.3).sub.2.fwdarw.2 H.sub.2CO.sub.3) takes place because HCO.sub.3.sup. has a higher affinity to H.sup.+ than the exchange resin. Thus KH is capable of reducing LF, since carbonic acid is formed which is only weakly dissociated. Ions that contribute to LF (e.g. Ca.sup.2+, Mg.sup.2+) are thus removed from the water and neutral molecules (H.sub.2CO.sub.3) that do not contribute to the LF are formed. However, as long as the exchange resin can release Na.sup.+ and/or K.sup.+ in abundance, i.e. as long as the resin is still loaded with Na.sup.+ and/or K.sup.+, the exchange remains neutral from the LF point of view. Only towards the end of the service life of the weakly acidic ion exchange resin, when the Na.sup.+ and/or K.sup.+ loading decreases, the H.sup.+ exchange increases, resulting in a decrease of LF and pH, which decrease allows the determination of the inflection point (IP). It is thus evident that the (Na.sup.+ and/or K.sup.+)/H.sup.+ loading ratio of a weakly acidic ion exchange resin plays a decisive role in the course of the LF over the service lifetime of the resin. The higher the H.sup.+ loading, the stronger the LF decrease in the filtrate will be compared to the LF in the raw water. Preferably, the (Na.sup.+ and/or K.sup.+)/H.sup.+ loading ratio is between 3:1 to 1:3, more preferably between 2:1 to 1:2, even more preferably between 1.5:1 to 1:1.5, and most preferably between 1.2:1 to 1:1.2. For the aforementioned loading ratios, a Na.sup.+/H.sup.+ loading is particularly preferred. The loading ratio is a ratio of moles of (Na.sup.+ and/or K.sup.+) to moles of H.sup.+. Another reaction that needs to be taken into account when interpreting the LF of filtered water of a weakly acidic ion exchange resin is the decomposition of the water (autoprotolysis), which specifically occurs at the beginning of the service life of an exchange resin. The exchange resin itself decomposes water into H.sup.+ and OH.sup. and then replaces the H.sup.+ with Na.sup.+. Thus, the LF from water changes to a higher LF due to an increase of the LF contributing ions Na.sup.+ and OH.

[0073] In summary, at the beginning of the service life of a fresh Na.sup.+/H.sup.+ ion exchange resin the following processes essentially take place: [0074] Exchange of 2Na.sup.+/Ea.sup.2+; this exchange is almost LF neutral. [0075] Hydrolysis; i.e. the splitting of water into H.sup.+ and OH.sup. leading to an exchange of Na.sup.+ for H.sup.+ by the ion exchange resin; the resulting formation of Na.sup.+ and OH.sup. slightly increases the total LF value. [0076] Also the exchange of H.sup.+ for Ca.sup.2+ may occur to a minor extent (at the beginning of the service life), which then also slightly reduces the LF again by the formation of H.sub.2CO.sub.3.

[0077] As a result, as illustrated in FIG. 3, the LF of the filtrate at the beginning of the resins life is either slightly higher or slightly lower than the LF of the raw water, depending on the H.sup.+-loading of the resin and the contribution of autoprotolysis.

[0078] As illustrated in FIG. 4, depending on the GH and KH proportions in the water, the conductivity (LF) in the filtrate will then decrease with increasing lifetime (volume of softened water) due to the increasing proportion of the H.sup.+/Ca.sup.2+ exchange of the KH until only this H.sup.+/Ca.sup.2+ exchange takes place at the end of the service life. This is because the Na.sup.+ exchange is preferred over the H.sup.+ exchange, so that the latter remains after the Na.sup.+ is exhausted. Once also the H.sup.+ resin is close to be exhausted, the exchange resin is close to be exhausted and the conductivity (LF) rises again due to the ions of GH and KH of the raw water.

[0079] Thus, in the exemplary diagrams of FIGS. 3 and 4, which show the conductivity (LF) of the softened water vs. the volume of softened water, the conductivity (LF) in the beginning decreases at a low to moderate slope which reflects the ongoing 2Na+/Ea.sup.2+ exchange. The diagram of FIG. 3 was obtained by carrying out the present method with a BRITA PURITY C 150 Finest ion exchange resin cartridge, wherein the tap water which was filtered with said ion exchange resin cartridge had a total hardness (GH) of 27 dH and a temporary hardness (KH) of 5 dH. The diagram of FIG. 4 was obtained by carrying out the present method with a BRITA PURITY C 150 Finest ion exchange resin cartridge, wherein the tap water which was filtered with said ion exchange resin cartridge had a total hardness (GH) of 20 dH and a temporary hardness (KH) of 10 dH. By carrying out a multitude of experiments with commercial ion exchange filter cartridges of BRITA of the so-called PURITY C Finest series and by applying steps i) and ii) according to the present method and analyzing the resulting measured data points and polynomials approximated between these experimental data points, it was surprisingly found that the inflection point IP can be determined either by step iii)) or step iii)), wherein IP obtained therewith allows to calculate RLV in step iv). The alternative steps iii)) or iii)) both allow a reliable IP determination.

Determination of Inflection Point IP (V.sub.IP, w.sub.IP) by Means of Step iii))

[0080] In step iii)), after each polynomial approximation in step ii), the polynomial is analyzed for an inflection point IP (V.sub.IP, w.sub.IP) which corresponds to a point (V.sub.Si, w.sub.app_i) of the polynomial being a point approximated for (V.sub.Si, w.sub.i) in step ii), wherein at point (V.sub.Si, w.sub.app_i), a difference w between w.sub.app_1 of point (V.sub.Si, w.sub.app_S1) of the polynomial being a point approximated for (V.sub.Si, w.sub.i) in step ii) and w.sub.app_i of point (V.sub.Si, w.sub.app_i) of the polynomial is 50 S/cm for w being electrical conductivity LF or is 1.5 for w being pH.

[0081] Preferably, in step iii)), said difference w is 55 S/cm for w being electrical conductivity LF or is 1.65 for w being pH, most preferably said difference w is 60 S/cm for w being electrical conductivity LF or is 1.8 for w being pH.

[0082] Even though different threshold values may be selected for difference w, namely for w being electrical conductivity 50 S/cm, preferably 55 S/cm and most preferably 60 S/cm, and for w being pH1.5, preferably 1.65, most preferably 1.8, with all different threshold values, an inflection point IP can be reliably obtained. This is because already the smallest threshold values for difference w, namely 50 S/cm for w being electrical conductivity and 1.5 for w being pH, indicate a significant change of conductivity and pH respectively, which change indicates that the Na.sup.+ resin is close to its exhaustion point and the H.sup.+ exchange starts to dominate. When inserting V.sub.IP obtained by means of step iii)) in below described formula (IV), filter exhaustion factor FA can be determined. The aforementioned smaller thresholds for difference w are obtained at lower volume values for V.sub.IP. With said lower values obtained for V.sub.IP, in turn, lower filter exhaustion factors FA are obtained. It was experimentally found that surprisingly, even with the aforementioned smallest threshold values for difference w, namely 50 S/cm for w being electrical conductivity and 1.5 for w being pH, reliable RLV values can be obtained.

[0083] It was surprisingly found by a multitude of experiments that when determining inflection point IP (V.sub.IP, w.sub.IP) by means of step iii)), that in case the above defined difference w is 60 S/cm for w being electrical conductivity LF or is 1.8 for w being pH, the determination of inflection point IP and in turn of RLV is particularly reliable.

[0084] FIG. 5 exemplary shows the determination of inflection point IP (V.sub.IP, w.sub.IP) by means of step iii)) according to the present method. In the diagram of FIG. 5, a polynomial of first order (see black straight line) is approximated between the data points measures in step ii), which data points are indicated in grey. The first measured volume V.sub.S1 is 4 l, wherein w.sub.app_1 of point (V.sub.Si, w.sub.app_1) of the polynomial is 745, 19 S/cm, and at a filtrate volume V.sub.S1 of 342 l, w.sub.app_i of point (V.sub.Si, w.sub.app_i) of the polynomial is 685, 13 S/cm. Hence, the difference w is 60.06 S/cm here. Thus, at (V.sub.Si, w.sub.app_i), the difference w is 60 S/cm for w being electrical conductivity LF, which is the particularly preferred difference w, for the first time during carrying out steps i) to iv), and hence, the IP is reached at (V.sub.Si, w.sub.app_i). It is noted that after IP is determined in step iii)), RLV can be calculated according to step iv), and thus, the method can be ended/stopped when inflection point IP is reached. However, in FIG. 5, for analysis purposes, measurement of datapoints according to step i) was carried out further after the IP was reached. For the IP determination depicted in FIG. 5, a BRITA PURITY C150 Finest ion exchange filter cartridge was used, which has a maximum volume capacity V.sub.cmax of 1833 l. The tap water which was filtered with said ion exchange resin cartridge had a total hardness (GH) of 18 dH and a temporary hardness (KH) of 13 dH.

[0085] FIG. 6 depicts a flow chart of a particularly preferred determination of the inflection point IP according the present method applying step iii)), in which a difference w between w.sub.app_1 and w.sub.app_i being e.g. 60 S/cm, which is the particularly preferred difference w, is determined for w being electrical conductivity LF for the first time during carrying out of steps i) to iv), and thus, the IP is reached. This determination of IP by means of difference w is also applicable when in the present method, pH is measured as water characteristic w, wherein in this case, e.g. the particularly preferred difference w being 1.8 for the first time during carrying out of steps i) to iv) may indicate inflection point IP.

Determination of Inflection Point IP (V.sub.IP, w.sub.IP) by Means of Step iii))

[0086] Alternatively to step iiia), step iii)) may be applied for determination of the inflection point IP. In step iii)), after each polynomial approximation in step ii), the polynomial is analyzed for an inflection point IP (V.sub.IP, w.sub.IP) which corresponds to a point where the second derivative of the polynomial is 0 or where there is a change of sign of the second derivative from positive to negative or from negative to positive. That is, the inflection point determined according to step iii)) represents an inflection point in the mathematical sense, i.e. a point at which the curvature of a polynomial changes.

[0087] The second derivative is a derivative in the mathematical sense of differential calculus.

[0088] FIG. 7 exemplary shows the determination of inflection point IP (V.sub.IP, w.sub.IP) by means of step iii)) according to the present method. In the diagram of FIG. 7, a polynomial of 5th order (see black dotted line) is approximated between the data points measures in step ii), which data points are indicated in grey. The diagram of FIG. 7 was obtained by carrying out the present method with a BRITA PURITY C 150 Finest ion exchange resin cartridge, wherein the tap water which was filtered with said ion exchange resin cartridge had a total hardness (GH) of 27 dH and a temporary hardness (KH) of 5 dH. As can be gathered from FIG. 7, once the Na.sup.+ capacity of the Na.sup.+/H.sup.+ exchange resin comes closer to its exhaustion point the LF starts to decrease with further increasing volume until a sharp decrease in the conductivity with further increasing volume of water which has passed through the exchange resin can be observed. This decrease stops when most of the H.sup.+ capacity is saturated, too. Then, the conductivity increases due to more and more raw water which can be seen in the filtrate. As exemplarily shown in FIG. 7, when calculating a polynomial fit into the measured curve, an inflection point (IP) can be seen near the water volume of 300 l. This inflection point can be derived according to step iii)) by making a second derivative of the fitted curve formula. Because due to the discontinuous measurement curve it is not likely that the second derivative of the polynomial is exactly 0 at the IP. Therefore, preferably, a change of sign of the second derivative from negative to positive is used as an indication of the IP. In case the aforementioned conditions for said second derivative are obtained for the first time during carrying out of steps i) to iv), the inflection point IP is reached. It is noted that after IP is determined in step iii)), RLV can be calculated according to step iv), and thus, the method can be ended/stopped when inflection point IP is reached. However, in FIG. 7, for analysis purposes, measurement of datapoints according to step i) was carried out further after the IP was reached-e.g., at V=407 l where w=1405 m, the exhaustion point of the ion exchange resin was reached.

[0089] The IP indicates, as described above, that the Na+ resin is close to its exhaustion point and the H+ exchange starts to dominate. From that point it can be experimentally derived how much capacity is left until the filter cartridge reaches its exhaustion point. Depending on the ratio between Na.sup.+/H.sup.+, the remaining capacity can vary in a wide range.

[0090] It can be seen, that the inflection point already can be detected, even when only a few additional data points to higher volumes are known. Consequently, the IP can be detected, either by means of step iii)) or step iii)), even if the filter still is in use, and in step iv), a remaining volume (RLV) may be calculated based on V.sub.IP of the inflection point.

[0091] Thus, in the method of the present invention, the RLV can be determined from an analysis of the measured LF vs. softened water volume. It is to be understood that instead of the electrical conductivity other water characteristics which are also based on the measurements of electrical conductivity, e.g. the pH value, can be used instead. An example for pH is shown in FIG. 8.

[0092] FIG. 8 exemplarily shows that in step i), as a water characteristic w, besides of the electrical conductivity LF (indicated in dark grey), likewise, pH (indicated in light grey) may be measured. The diagram of FIG. 8 was obtained by carrying out the present method with a BRITA PURITY C 500 Finest ion exchange resin cartridge, wherein the tap water which was filtered with said ion exchange resin cartridge had a total hardness (GH) of 20 dH and a temporary hardness (KH) of 5 dH. In FIG. 8, for the same experimental example, the curves obtained from measurement of LF and pH are very similar at the beginning starting from V being 0 l and at the end when the filter is exhausted. Although the curve's shape differs in the middle part, the decreasing parts between around 1250-1300 l for measured pH and around 1200-1350 l for measured conductivity can clearly be seen. Since the decreasing parts overlap within similar value ranges, IP can be determined in step iii) for both w being electrical conductivity LF and w being pH. That is, the method works with measurement in step i) of both electrical conductivity and pH. This is no surprise, since it is known in the art of water chemistry that the pH value affects the water's conductivity. Therefore, IP determination by means of step iii)) and step iii)) is also possible when measuring pH as water characteristic w, wherein it was experimentally found that for the IP determination according to step iii)), the difference w being 1.8 for w being pH is particularly preferred.

[0093] In the present method of determining the remaining water volume (RLV) which can still be softened prior to the exhaustion of an ion exchange resin contained in a filter device, the determination comprises: [0094] i) sequentially measuring a water characteristic w, wherein w is selected from one or more of pH and electrical conductivity LF, and wherein w is determined by a sensor in softened water obtained from the filter device, at increments of softened water volume (V.sub.S) to acquire measured data points (V.sub.Si, w.sub.i) with i=1, 2, 3, . . . , N and N ; [0095] ii) after each measuring of a sequential data point (V.sub.Si, w.sub.i) in step i) which data point is defined as new data point, a polynomial is approximated between all previously measured data points (V.sub.Sp, w.sub.p) with p=1, 2, . . . i-1, and the new data point (V.sub.Si, w.sub.i); [0096] iii) after each polynomial approximation in step ii), the polynomial is analyzed for an inflection point IP (V.sub.IP, w.sub.IP) which corresponds to a point: [0097] ) ) (V.sub.Si, w.sub.app_i) of the polynomial being a point approximated for (V.sub.Si, w.sub.i) in step ii), wherein at point (V.sub.Si, w.sub.app_i), a difference w between w.sub.app_1 of point (V.sub.Si, w.sub.app_S1) of the polynomial being a point approximated for (V.sub.Si, w.sub.i) in step ii) and w.sub.app_i of point (V.sub.Si, w.sub.app_i) of the polynomial is 50 S/cm for w being electrical conductivity LF or is 1.5 for w being pH; or [0098] ) where the second derivative of the polynomial is 0 or where there is a change of sign of the second derivative from positive to negative or from negative to positive; [0099] iv) repeating steps ii) and iii) with the next higher i, and when an inflection point is determined in step iii), RLV is calculated based on V.sub.IP of the inflection point IP.

[0100] In the method according to the invention, approximating a polynomial means polynomial interpolation of the given data point set (V.sub.Si, w.sub.i) with i=1, 2, 3, . . . , N by a polynomial of a degree (also called order) that passes through the points of the dataset (see e.g. https://en.wikipedia.org/wiki/Polynomial_interpolation). The degree of the polynomial selected for approximation according to step ii) may be as low as suitable for step iii) as long as said degree still provides a reliable determination of the inflection point IP. It was found that for steps iii)) and iii)), different degrees of polynomial are preferable.

[0101] For the inflection point determined by means of step iii)), it is preferred that the polynomial is a 1.sup.st to 4.sup.th degree polynomial, more preferably 1.sup.st or 3.sup.rd degree polynomial, most preferably a 1.sup.st degree polynomial.

[0102] For the inflection point determined by means of step iii)), it is preferred that the degree of the polynomial is 4 to 8, more preferred 5 or 6 and most preferred the degree is 5.

[0103] In step iii), determination of the inflection point IP is performed: [0104] ) By observing when at point (V.sub.Si, w.sub.app_i) of the polynomial being a point approximated for (V.sub.Si, w.sub.i) in step ii), a difference w between w.sub.app_1 of point (V.sub.Si, w.sub.app_S1) of the polynomial being a point approximated for (V.sub.Si, w.sub.i) in step ii) and w.sub.app_i of point (V.sub.Si, w.sub.app_i) of the polynomial is 50 S/cm for w being electrical conductivity LF or is 1.5 for w being pH; or ) by forming the second derivative of the polynomial; the point where this second derivative is 0 or where there is a change of sign of the second derivative from positive to negative or from negative to positive constitutes an inflection point IP.

[0105] According to step iv), when an inflection point is determined in step iii), RLV is calculated based on V.sub.IP of the inflection point IP. RLV may be calculated based on the water volume V.sub.IP measured at the inflection point IP according to the aforementioned formula (I):

[00001]$\begin{array}{cc}\mathrm{RLV}=V_{\mathrm{IP}}*f,& \left(I\right)\end{array}$

wherein f is the remaining capacity factor. The remaining capacity factor f depends on the ion exchange resin's Na.sup.+/H.sup.+ loading ratio, as well as on which kind of step is applied for determination of V.sub.IP the inflection point IP, namely whether step iii)) or iii)) is applied.

[0106] For example, formula (I) can be derived using filter parameters FA and . FA is the filter exhaustion factor indicating which proportion of the filter's ion exchange resins capacity is exhausted, wherein FA is a value within the following range: 0.0<FA<1.0. By carrying out a multitude of experiments with commercial ion exchange filter cartridges of BRITA of the so-called PURITY C Finest series by applying steps i), ii) and iii) according to the present method, inflection points IP were obtained with step iii)) or step iii)). V.sub.IP of the experimentally obtained inflection points IP were divided by the volume capacity V.sub.c_@total hardness of the ion exchange resin for the water applied, as shown in formula (IV):

[00002]$\begin{array}{cc}\mathrm{FA}=V_{\mathrm{IP}}/V_{\mathrm{c\_}@\mathrm{total}\mathrm{hardness}}& \left(\mathrm{IV}\right)\end{array}$

[0107] It is noted that V.sub.c_@total hardness is the volume capacity of the ion exchange resin obtained for water having a certain water total hardness applied to the ion exchange resin until the ion exchange resin reaches its exhaustion point. V.sub.c_@total hardness of the ion exchange resin depends on the (Na.sup.+ and/or K.sup.+)/H.sup.+ loading ratio of the ion exchange resin as well as on the amount of ion exchange resin contained in the filter device. For example, for BRITA's commercial PURITY C Finest filter cartridges, V.sub.c_@total hardness is indicated in the example. After calculating a multitude of FA values for V.sub.IP obtained by means of the present method's step iii)) and iii)) respectively, it was surprisingly found that independent from the size/capacity of ion exchange resin applied, e.g. irrespective whether a small PURITY C Finest filter cartridges of type C150 or a big one of type C1100 was applied, for all experimentally tested PURITY C Finest filter cartridges, to which water having different total water hardness was applied, an averaged FA was obtained for V.sub.IP obtained by means of step iii)) and for V.sub.IP of the inflection point IP obtained by means of step iii)), respectively. Namely, for V.sub.IP obtained by means of step iii)) with the particularly preferred difference w being 60 S/cm for w being electrical conductivity LF a FA=0.60 was empirically found, and for V.sub.IP obtained by means of step iii)) a FA=0.76 was empirically found, wherein a multitude of experimentally measured Vie values divided by V.sub.c_@total hardness according to formula (IV) were averaged in order to obtain the averaged FAs. is the molar capacity of the filter (sum of Na.sup.+ (and/or K.sup.+) and H.sup.+ ion exchange resin) in [mmol].

RLV can then be calculated according to the formula (II)

[00003]$\begin{array}{cc}\mathrm{RLV}\left[l\right]=\frac{\mathrm{.down-triangle-solid.}}{\mathrm{GH}\left[\mathrm{dH}\right]/5.6}-V_{\mathrm{IP}}& \left(\mathrm{II}\right)\end{array}$

wherein GH can be calculated with the formula (III)

[00004]$\begin{array}{cc}\mathrm{GH}\left[\mathrm{dH}\right]=\frac{5.6*\mathrm{.down-triangle-solid.}*\mathrm{FA}}{V_{\mathrm{IP}}}& \left(\mathrm{III}\right)\end{array}$

[0108] It is to be understood that in formulae (II) and (III) other conversion factors than 5.6 can be used if other total hardness units, e.g. fH or [mmol] Ea.sup.2+ ions etc. are desired.

[0109] When inserting formula (III) into formula (II), formula (IIa) is obtained:

[00005]$\begin{array}{cc}\mathrm{RLV}\left[l\right]=\frac{V_{\mathrm{IP}}}{\mathrm{FA}}-V_{\mathrm{IP}}=V_{\mathrm{IP}}*\left(\frac{1}{\mathrm{FA}}-1\right)& \left(\mathrm{IIa}\right)\end{array}$

[0110] From formula (IIa) it can be seen that it is not necessary to know the total hardness (GH) of the water applied to the ion exchange resin, and it is also not necessary to know the molar capacity of the filter, since both GH and are truncated. Hence, with formula (IIa), RLV can be easily calculated based only on V.sub.IP of the inflection point and FA.

[0111] When comparing formula (IIa) with formula (I), formula (Ia) can be derived:

[00006]$\begin{array}{cc}f=\frac{1}{FA}-1& \left(\mathrm{Ia}\right)\end{array}$

[0112] Factor f is the remaining capacity factor indicating which proportion of the filter's ion exchange resins capacity remains for softening the water at the inflection point IP. By inserting the aforementioned empirically found FA values into formula (Ia), namely FA=0.60 for V.sub.IP obtained by means of step iii)), and FA=0.76 for V.sub.IP obtained by means of step iii)), the respective factor f can be obtained. That is, f=0.67 for FA=0.60, and f=0.32 for FA=0.76.

[0113] In conclusion: In step iv), RLV may be calculated based on V.sub.IP of the inflection point IP and filter exhaustion factor FA by means of formula (IIa)

[00007]$\begin{array}{cc}\mathrm{RLV}=V_{\mathrm{IP}}*\left(\frac{1}{\mathrm{FA}}-1\right),& \left(\mathrm{IIa}\right)\end{array}$

wherein filter exhaustion factor FA is a value within the following range: 0.0<FA<1.0; preferably FA is a value between 0.30 to 0.90, more preferably 0.50 to 0.85, even more preferably FA is a value between 0.50 to 0.70 for V.sub.IP obtained by means of step iii) and between 0.65 to 0.85 for V.sub.IP obtained by means of step iii)), yet even more preferably FA is between 0.55 to 0.65 for V.sub.IP obtained by means of step iii) and between 0.70 to 0.80 for V.sub.IP obtained by means of step iii)), and most preferably FA is 0.60 for V.sub.IP obtained by means of step iii) and FA is 0.76 for V.sub.IP obtained by means of step iii)). Filter exhaustion factor FA may be calculated with formula (IV):

[00008]$\begin{array}{cc}\mathrm{FA}=V_{\mathrm{IP}}/V_{\mathrm{c\_}@\mathrm{total}\mathrm{hardness}},& \left(\mathrm{IV}\right)\end{array}$

wherein V.sub.c_@total hardness is the volume capacity of the ion exchange resin obtained for water having a certain water total hardness applied to the ion exchange resin until the ion exchange resin reaches its exhaustion point. Preferably, filter exhaustion factor FA is digitally stored in a memory, e.g. of an electronic control unit. The digitally stored FA is preferably provided by measuring an inflection point (IP) and dividing Vie of said inflection point by V.sub.c_@total hardness according to formula (IV), wherein V.sub.c_@total hardness is selected for the certain water total hardness applied to the ion exchange resin from a lookup table, e.g. a lookup table as shown in the present example, which lookup table may be digitally stored in a memory, e.g. of an electronic control unit, wherein a FA for V.sub.IP obtained by means of step iii)) is provided, and a FA for V.sub.IP obtained by means of step iii)) is provided. More preferably, FA is provided by measuring a plurality of inflection points (IP) and averaging the plurality of FAs calculated according to formula (IV), wherein an averaged FA for V.sub.IP obtained by means of step iii)) is provided, and an averaged FA for V.sub.IP obtained by means of step iii)) is provided.

[0114] Alternatively, in step iv), RLV may be calculated based on Vie of the inflection point IP and remaining capacity factor f by means of formula (I)

[00009]$\begin{array}{cc}\mathrm{RLV}=V_{\mathrm{IP}}*f,& \left(I\right)\end{array}$

wherein remaining capacity factor f is a value between 0.01 and 99.0; preferably f is a value between 0.11 to 2.33, more preferably 0.18 to 1.0, even more preferably f is between 0.43 to 1.0 for V.sub.IP obtained by means of step iii) and between 0.18 to 0.54 for f obtained by means of step iii)), yet even more preferably f is between 0.54 to 0.82 for V.sub.IP obtained by means of step iii) and between 0.25 to 0.43 for f obtained by means of step iii)), and most preferably f is 0.67 for V.sub.IP obtained by means of step iii)) and f is 0.32 for V.sub.IP obtained by means of step iii)).

[0115] Although by the present experiments, for V.sub.IP obtained by means of step iii)), an FA=0.60 was empirically found, and for V.sub.IP obtained by means of step iii)), an FA=0.76 was empirically found, wherein the resulting factor f is 0.67 for V.sub.IP obtained by means of step iii)) and f is 0.32 for V.sub.IP obtained by means of step iii)), it is understood that e.g. due to possible error deviations and/or deviations in the ion exchange resin (Na.sup.+ and/or K.sup.+)/H.sup.+ loading ratio, FA and f may not be the exact aforementioned values, and thus may vary within a certain (error) margin. Such error margins may be reflected by the above indicated (yet) even more preferred value ranges. Alternatively, (error) deviations of FA and f may be expressed by a percentual deviation: The aforementioned, most preferred FA and f single values may vary within a margin of preferably 10% of the FA or f value, and more preferably 5% of the FA or f value: FA being 0.6010% for V.sub.IP obtained by means of step iii) and FA being 0.7610% for V.sub.IP obtained by means of step iii)), and f being 0.6710% for V.sub.IP obtained by means of step iii)) and f being 0.3210% for V.sub.IP obtained by means of step iii)); or yet most preferred FA being 0.605% for V.sub.IP obtained by means of step iii) and FA being 0.765% for V.sub.IP obtained by means of step iii)), and f being 0.675% for V.sub.IP obtained by means of step iii)) and f being 0.325% for V.sub.IP obtained by means of step iii)). E.g., FA being 0.6010% means that FA is in a value range between 0.54 to 0.66.

[0116] The above described determinations of the inflection point IP and factors FA and f where experimentally obtained by carrying out the present method with BRITA's commercial PURITY C Finest filter cartridges, which preferably have a ion exchange resin Na.sup.+/H.sup.+ loading ratio between 1.5:1 to 1:1.5, and most preferably a ion exchange resin having a Na.sup.+/H.sup.+ loading ratio between 1.2:1 to 1:1.2. Therefore, in a particularly preferred embodiment of the present method, preferably a ion exchange resin Na.sup.+/H.sup.+ having a loading ratio between 1.5:1 to 1:1.5, and most preferably a ion exchange resin having a Na.sup.+/H.sup.+ loading ratio between 1.2:1 to 1:1.2, is applied.

[0117] If desired, also RLZ can be calculated. This requires the recording of time, e.g. the recording of V.sub.S [I] at increasing increments of time e.g. [minute], [hour], [days] or [weeks] depending on the desired level of accuracy. An average water consumption dV.sub.average[I/hour] can then be calculated, e.g. as arithmetic mean at any desired point in time during the use of the exchange resin, e.g. at the inflection point IP (dV.sub.average@IP). RLZ can then be calculated according to the formula RLZ=RLV/dV.sub.average@IP. It may even be desirable to take into account averages of 2, 3 or more weeks in order to smooth fluctuations which are due to single events like office/plant closures, company parties etc.

[0118] When applying step iii)) for determining the IP, after a moderate positive or negative slope the polynomial reaches a first local maximum LM (V.sub.LM, w.sub.LM) and then typically proceeds with a negative slope until it reaches the characteristic sharp inflection point IP (V.sub.IP, w.sub.IP) with further increasing volume of water which has passed through the exchange resin (see FIG. 7, inflection point at water volume 300 l). Thus, the first local maximum LM (V.sub.LM, w.sub.LM) is located where the first derivative of the polynomial changes its sign from positive to negative, or the first derivative of the polynomial is zero (0) and the second derivate is smaller than 0. The first derivative is a derivative in the mathematical sense of differential calculus. Typically, the difference in conductivity LF (LFs) between the local maximum LM and the inflection point IP is within a range of preferably 4 to 1000 S/cm, more preferably 6 to 800 S/cm, and most preferably 10 to 300 S/cm when using a typical Na+/H+ ratio as mentioned above.

[0119] FIG. 9 depicts a flow chart of the alternative determination of the inflection point IP according to step iii)) of the present method, in which a change of sign from positive to negative for the second derivative indicates inflection point IP. Then, optionally in addition, a local maximum near/adjacent to said IP may be determined, and the above difference in conductivity LF (LF.sub.) between the local maximum LM and IP being preferably within a range of 4 to 1000 S/cm, more preferably 6 to 800 S/cm, and most preferably 10 to 300 S/cm is determined. As explained above, a drop of LF to >1000, preferably >800 and most preferred >300 S/cm is attributed to a change in raw water quality and is no IP.

[0120] In order to analyze the complete LF curve over the whole lifetime of the exchange resin, the conductivity preferably is measured at increments of softened water volume V.sub.S. It is preferred that the larger the filter capacity, the larger is the volume increment of softened water after which the next LF is measured. As an example: for a maximum volume capacity V.sub.cmax of less than 3750 liters, LF maybe measured every 0.5 l of softened water. For a filter capacity of between 3750 and 7850 liters, LF maybe measured every 1.0 l of softened water and for filter capacities larger than 7850 liters, LF maybe measured every 2.0 l of softened water. Preferably, increments of softened water volume V.sub.S, or in other words volume intervals between V.sub.S1 and V.sub.Si+1 are within a range of 0.2 l to 2.5 l, more preferably within a range of 0.4 to 2.2 l, most preferably within a range of 0.5 l to 2.0 l.

[0121] Instead of in terms of liters, the increments of softened water volume V.sub.S may alternatively be expressed in percentage of the maximum volume capacity V.sub.cmax of the ion exchange resin. Preferably, the measurement of w selected from pH and/or LF is carried out at increments of softened water volume V.sub.S, or in other words volume intervals between V.sub.S1 and V.sub.Si+1, within a range of 0.01% to 0.5% of the maximum volume capacity V.sub.cmax of the ion exchange resin, preferably within a range of 0.02% to 0.25% of the maximum volume capacity V.sub.cmax of the ion exchange resin, more preferably within a range of 0.025% to 0.15% of the maximum volume capacity V.sub.cmax of the ion exchange resin, and most preferably within a range of 0.03% to 0.1% of the maximum volume capacity V.sub.cmax of the ion exchange resin. With these increments of softened water volume V.sub.S (or in other words volume intervals between V.sub.S1 and V.sub.Si+1), it is safeguarded that a reliable polynomial approximation is obtained in step ii). Because, if the volume intervals are too big, only few data points (V.sub.Si, w.sub.i) are measured, which would result in an inaccurate polynomial approximation.

[0122] Furthermore, it is preferred that the first measured volume V.sub.S1 is within a range of 0.01% to 0.5% of the maximum volume capacity V.sub.cmax of the ion exchange resin, preferably within a range of 0.02% to 0.25% of the maximum volume capacity V.sub.cmax of the ion exchange resin, more preferably within a range of 0.025% to 0.15% of the maximum volume capacity V.sub.cmax of the ion exchange resin, and most preferably within a range of 0.03% to 0.1% of the maximum volume capacity V.sub.cmax of the ion exchange resin. Especially for the IP determination according to step iii)), it is important that V.sub.S1 is a volume relatively close to V=0 l to make it possible to accurately determine the IP by means of difference w, but on the other hand V.sub.S1 should not be too close to V=0 l, because too close to V=0 l, there might be disturbing factors which may be caused by different, unknown parameters, resulting in not plausible conductivity values in case V.sub.S1 is too close to V=0 l. If V.sub.S1 is too far from V=0 l, let's say e.g. 30% or 50% of the maximum volume capacity V.sub.cmax of the ion exchange resin, then an alleged IP would be indicated too late and erroneously.

[0123] The term maximum volume capacity V.sub.cmax of the ion exchange resin as used herein means the ion exchanges resin's maximal capacity for filtering water until the ion exchange resin reaches its exhaustion point, which maximal capacity is obtained when water of low total hardness, namely 4-6 dH, is applied to the ion exchange resin. The maximum volume capacity V.sub.cmax of the ion exchange resin depends on the (Na.sup.+ and/or K.sup.+)/H.sup.+ loading ratio of the ion exchange resin as well as on the amount of ion exchange resin contained in the filter device. For example, for BRITA's commercial PURITY C Finest filter cartridges, maximum volume capacity V.sub.cmax is indicated in the example.

[0124] The number of measurement points (V.sub.Si, w.sub.i), of course, depends on the memory capacity of the electronic control unit which is used in the water softening system. As an alternative to the storage of the complete LF curve over the whole lifetime of the exchange resin, e.g. in case of a more limited memory capacity, for example only the last 5 measurement points, preferably only the last 25 measurement points, more preferably only the last 50 points and most preferred only the last 250 measurement points of the LF curve can be stored in the memory of the electronic control unit. An alternative for working on the original measured data is using smoothed data sets. Only one method should be mentioned here. Shift registers with nominal capacities of 5 to 251 are preferably used.

[0125] Typically, a shift register is used as memory, where the measurement points are added to the register until the register has reached its nominal capacity. The next measurement point which is then to be stored either deletes the oldest measurement point from the register and adds itself as latest measurement point or causes all previous measurement points to be deleted from the register and starts a fresh register. When the shift register has reached the nominal capacity an arithmetic average or median of each shift register set of datapoints is calculated and stored together with the water volume value of the latest point. The first part of the conductivity/volume curve at the beginning of the filtration with a fresh ion exchange resin is hard to predict (as described above) and depends on a lot of parameters, which are typically not known when the filter cartridge is used. Nevertheless, it is known from experiments that the behavior of the conductivity/volume curve at the beginning of the filtration does not influence the RLV of the filter. However, different behavior at the beginning of filtration, which may be caused by different, unknown parameters, disturbs the polynomial fitting. To avoid this disturbing influence, a straight line L.sub.1 having a slope sl.sub.1 may be fitted between the first measured data points within a range V.sub.Si=0 up to a threshold Volume V.sub.T. The slope sl.sub.1 of this line L.sub.1 is about zero (0), i.e. it can vary within 10%, preferably 5%, more preferred 1%, wherein in this context, the percental values mean a slope expressed in percentage. That is, a slope sl.sub.1 varying within 10% is a slope between 1/10 and + 1/10, a slope sl.sub.1 varying within 5% is a slope between 1/20 and + 1/20, and a slope sl.sub.1 varying within 1% is a slope between 1/100 to + 1/100. The aforementioned numerical values expressed in terms of fractions, here 1/10, 1/20 and 1/100, express the ratio of the legs of a slope triangle of a line, here the straight line L.sub.1 having a slope sl.sub.1. A slope triangle is a right triangle that has its hypotenuse on the line that contains it, in this case the straight line L.sub.1. The slope triangle has two legs parallel to the axes of a coordinate system, one leg runs vertically, the other horizontally, wherein the slope is expressed by the ratio of the length of the leg running vertically to the length of the leg running horizontally. E.g., for a slope 1/10, the length of the leg running vertically is 1 wherein the length of the leg running horizontally is 10. A slope of a line is positive in case y value, which is indicated on ordinate of a coordinate system, always increase when x value, which is indicated on abscissa of the coordinate system, increases, while the slope is negative in case y value always decreases when x increases. It is preferred that the polynomial approximation according to step ii) is applied to straight line L.sub.1. This means that in step ii), for V.sub.S1>V.sub.T, the polynomial is approximated between all previously measured data points (V.sub.Sp, w.sub.p) with p=1, 2, . . . i-1 and the new data point (V.sub.Si, w.sub.i), and for V.sub.S1 s V.sub.T, the aforementioned polynomial is approximated through the straight line L.sub.1. Thereby, one approximated polynomial is obtained.

[0126] The threshold volume V.sub.T is typically within a range of up to 5% of the maximum volume capacity V.sub.cmax of the ion exchange resin, preferably up to 4%, more preferably up to 2%, and most preferably 1.5%. V.sub.cmax is the volume of the ion exchange resin which has been softened before the total hardness GH in the filtrate reaches a value of 6 dH half of the GH value in the raw water. Hence, preferably, first measured data points represent data points within the range of 0 l to V.sub.T as described above.

[0127] Thus, the electrical conductivity LF of the filtered (i.e. softened) water (V.sub.S) is measured at increasing increments of softened water volume (V.sub.S), and the LF values are then recorded as a function of the volume of softened water V.sub.S, resulting in a LF vs. softened water volume curve, as illustrated in FIG. 2.

[0128] The above described calculations can be performed using conventional programmable electronic devices in combination with a memory device, e.g. a dynamic memory device, in which the data pairs of LF and water volume, and optionally the time areat least temporarilystored. The memory may, of course, also be an integral part of the programmable device; preferably a shift register is used as memory.

[0129] The method according to the present invention is broadly applicable even in situations of varying water qualities (varying KH, GH). As outlined above, the decrease in conductivity after the initial low to moderate decline is dependent on the KH. In cases of raw water with a low KH the corresponding conductivity decrease is lower than in cases with raw water of higher KH. Yet, it was found that even in case of a raw water with a KH of as low as 2 dH a decrease of about 70 S/cm is still detectable, so that a reliable indication of remaining volume (RLV) can be made with the method according to the invention. If the Na+/H+ ratio is in a above mentioned preferred ratio and a LF drop of >1000, preferably >800 and most preferred >300 S/cm is observed between the LF at the detected local maximum and the possible IP determined according to step iii)b), this drop is attributed to a change in raw water quality and is no IP. Yet, changes in the water quality are rare, and if they occur they extend over a range of one day up to several weeks after which the water quality typically returns to its initial quality over a period of several months. Thus, within the lifetime of a typical ion exchange resin used in the present invention in the worst case two changes in the water quality of the raw water can be expected. But even then at least the remaining volume (RLV) can always be reported.

[0130] In a further embodiment the invention relates to a water softening system. The water softening system may comprise: [0131] I. An inlet for influent raw water and [0132] II. an outlet for effluent softened water, [0133] III. an ion exchange device loaded with an ion exchange resin, [0134] IV. an electronic device capable of receiving signals emitted [0135] a) by a sensor for the water characteristic w, which is selected from one or more of the electrical conductivity (LF) and the pH, wherein the sensor is arranged in the softened water outlet and which signal is selected from one or more of the electrical conductivity (LF) and the pH and [0136] b) by a volume meter for measuring the volume flow of softened water, likewise arranged in the softened water outlet which signal is the flowed softened water volume (V.sub.S), which volume meter is optionally coupled with an hour or minute meter, and [0137] V. an interface for transmitting the signals received under IVa) and IVb) to an electronic control unit; and [0138] VI. an electronic control unit, [0139] wherein the electronic control unit has a memory to: [0140] I. store the repeatedly/sequentially measured water characteristic w, which is selected from one or more of the electrical conductivity LF and the pH of the filtered (i.e. softened) water at increments of softened water volume (V.sub.S), received from the interface to acquire measured data points (V.sub.Si, w.sub.i) with i=1, 2, 3, . . . , N and N ; and [0141] II. store an executable computer program which is capable of executing the following method steps: [0142] a. after each storing of a sequential data point (V.sub.Si, w.sub.i) in step I) which data point is defined as new data point, approximating a polynomial between all previously measured data points (V.sub.Sp, w.sub.p) with p=1, 2, . . . i-1, and the new data point (V.sub.Si, w.sub.i); [0143] b. after each polynomial approximation in step IIa), analyzing the polynomial for an inflection point IP (V.sub.IP, w.sub.IP) which corresponds to a point where: [0144] ) (V.sub.Si, w.sub.app_i) of the polynomial being a point approximated for (V.sub.Si, w.sub.i) in step ii), wherein at point (V.sub.Si, w.sub.app_i), a difference w between w.sub.app_1 of point (V.sub.S1, w.sub.app_S1) of the polynomial being a point approximated for (V.sub.S1, w.sub.i) in step ii) and w.sub.app_i of point (V.sub.Si, w.sub.app_i) of the polynomial is 50 S/cm for w being electrical conductivity LF or is 1.5 for w being pH; or [0145] ) where the second derivative of the polynomial is 0 or where there is a change of sign of the second derivative from positive to negative or from negative to positive; [0146] c. repeating steps Ila) and IIb) with the next higher i, and when an inflection point is determined in step IIb), RLV is calculated based on V.sub.IP of the inflection point IP.

[0147] In said water softening system, in the executable computer program, the method steps described above and/or defined in the subclaims relating to the present method may be applied. This means that features described for any one of steps ii), iii) and iv) of the method may likewise be applied in the computer program according to any one of steps Ila), IIb) and IIc), respectively.

[0148] RLV and optionally RLZ can be calculated as described above for the present method for determining the remaining water volume in a water softening systems using H.sup.+/(Na.sup.+ and/or K.sup.+)-exchange resins, preferably H.sup.+/Na.sup.+-exchange resins.

[0149] The electronic control unit may further have means for communicating RLV and optionally RLZ to a user, e.g. by way of an optical display or an acoustic signal or by transmitting RLV and optionally RLZ to a remote location e.g. via LAN/WLAN/Inter-net; optionally the data can also be stored in a cloud and downloaded at the request of a user and then be displayed via a portal.

[0150] In a further embodiment the invention relates to a computer program and a computer readable medium. The computer program according to the present invention comprises instructions to cause the water softening system according to the present invention to execute the steps of the method according to the present invention. The computer readable medium according to the present invention has stored thereon the computer program according to the invention.

Example

[0151] For the present method for determining the remaining water volume in a water softening systems using H.sup.+/Na.sup.+-exchange resins, commercial ion exchange filter cartridges of BRITA of the so-called PURITY C Finest series were applied. Different types of PURITY C Finest filter cartridges exist, namely e.g. types C150, C300, C500, C1100, which differ in their capacity for filtering water until the ion exchange resin is exhausted. The ion exchange resins of these filter cartridges are weakly acidic ion exchange resins having a Na.sup.+/H.sup.+ loading within the above described preferred Na.sup.+/H.sup.+ loading ratios, such that they provide a capacity as shown in the following table. It is noted that this table is disclosed in the instruction manual of the cartridge for the user's information, and the data of this table may be digitally stored in a memory of a filter head of the cartridge, such that the capacity information can be used for the present method.

[0152] It is noted that in the table below, the maximum volume capacity V.sub.cmax of the ion exchange resin is the filter capacity indicated for the total hardness 4-6 dH. That is, for PURITY C Finest C150 V.sub.cmax is 1833 l, for C300 it is 3000 l, for C500 it is 5690 l and for C1100 it is 10000 l.

[0153] Furthermore, in the table below, V.sub.c_@total hardness being the volume capacity of the ion exchange resin obtained for water having a certain water total hardness applied to the ion exchange resin until the ion exchange resin reaches its exhaustion point is listed. E.g., V.sub.c_@total hardness for a total water hardness of 20 dH is 1707 l for PURITY C Finest C500 or 550 l for PURITY C Finest C150.

TABLE-US-00001 dH PURITY C Finest - Filter capacity in liters (GH) C150 C300 C500 C1100 4 1833 3000 5690 10000 5 1833 3000 5690 10000 6 1833 3000 5690 10000 7 1571 2571 4877 8571 8 1375 2250 4268 7500 9 1222 2000 3793 6667 10 1100 1800 3414 6000 11 1000 1636 3104 5455 12 917 1500 2845 5000 13 846 1385 2626 4615 14 786 1286 2439 4286 15 733 1200 2276 4000 16 688 1125 2134 3750 17 647 1059 2008 3529 18 611 1000 1897 3333 19 579 947 1797 3158 20 550 900 1707 3000 21 524 857 1626 2857 22 500 818 1552 2727 23 478 783 1484 2609 24 458 750 1423 2500 25 440 720 1366 2400 26 423 692 1313 2308 27 407 667 1264 2222 28 393 643 1219 2143 29 379 621 1177 2069 30 367 600 1138 2000 31 355 581 1101 1935 32 344 563 1067 1875 33 333 545 1035 1818 34 324 529 1004 1765 35 314 514 975 1714

[0154] Besides of the aforementioned weakly acidic ion exchange resin providing the capacities indicated in this table, the filter cartridges of BRITA's PURITY C Finest series further comprise a charcoal filter providing for further filtration effects such as mechanical filtration of the water to be filtered as well as removal of undesired coloring and/or odors of the water to be filtered. However, the charcoal filter's characteristics are irrelevant for the present method.