US20050165575A1

US20050165575A1 - Automated regression analysis and its applications such as water analysis

Info

Publication number: US20050165575A1
Application number: US11/083,410
Authority: US
Inventors: Jacob Mettes
Original assignee: Individual
Current assignee: Individual
Priority date: 2003-09-23
Filing date: 2005-03-18
Publication date: 2005-07-28
Also published as: US20100204926A1; US7906339B2

Abstract

Methods and instrumentation based on the concept of an “Absolute Principle” are relatively rare but, when applicable, offer some very unique advantages. This patent teaches how to automate the use of non-linear curve fitting to widen this concept enabling the determination of multiple properties instead of typically only a single entity as well as dealing systematically with more complex relationships between entities. As a possible application, the invention further deals with analyzing the composition of water regarding inorganic as well as organic species and the use hereto of conductivity measurements as a function of temperature or the mixing ratio with another fluid.

Description

CROSS-REFERENCES TO RELATED APPLICATIONS

This application is based on PCT/US2003/029961 filing date Sep. 23, 2003, priority date Sep. 23, 2002.

Background

1. Field of Invention
This invention relates to “Absolute Principle” based methods and instrumentation, mathematical model descriptions of phenomena, automation and the use of non-linear curve fitting algorithms. In its application it relates to water analysis, organic and inorganic components in aquaous solutions and conductivity measurements relevant to industries in the field of drink and waste water, semiconductor manufacturing, pharmaceutical manufacturing and power generation.
Apart from analysis, wider applications are typically in the field of monitoring chemical or mechanical processes and equipment, machines, engines or vehicles.
2. Description of Prior Art
Absolute Principle:
Analytical instruments based on an “absolute principle” translate the entity to be analyzed into one or more other entities that are directly, without any instrument dependent factors, related to the entity to be analyzed. The relationship between the entities is based on well-established literature values, laws of physics or chemistry, or the like. This means that, in principle, when the measurements of the related entities are correct, automatically the derived value of the entity to be analyzed will be correct.
The “chilled mirror” hygrometer is an example of an instrument based on an absolute principle. It translates the measurement of a concentration of moisture in a gas in the determination of the temperature of the onset of frost formation on the surface of a mirror in the process of being cooled down. Well-established curves from the National Institute of Standards and Technology (NIST) relate dewpoint temperatures to moisture concentrations. Such hygrometers cannot be calibrated by offering it calibrated moisture standards and certainly do not allow tweaking NIST curves making the instrument read the standard. Instead, the hygrometer's temperature sensor is calibrated with a traceable temperature standard. This last calibration is definitely easier to do than the first, specifically at very low concentrations were moisture standards are unavailable.
Calibrating an instrument typically means offering it a number of known calibrated standard concentrations, plotting these concentration values on the x-axis of a calibration curve and plotting the response of the instrument on the y-axis. Then, interpolating a line through the points creates the calibration curve. It is, commonly excepted, bad practice to extrapolate the curve into a concentration range where there are no more calibration points, leaving the instrument to be used only in the interpolated range. Unfortunately, in numerous cases it is very difficult to create standards with very low concentrations. Particularly in such cases, an absolute principle based method can be very valuable.
Non-Linear Curve Fitting:
Non-linear regression or curve fitting is known in the prior art and is one of the more sophisticated, difficult to use and to prepare for parts of the toolbox of a scientist. It enables in principle to mold measured data into a number of parameters used in a mathematical model that describes the phenomenon behind the measured data. It is typically applied as some form of the Levenberg-Marquardt algorithm on a case by case basis as part of a particular study. Its successful application heavily relies on the skills of the operator who needs understanding of the phenomenon as well as of the mathematical intricacies of the method. A number of pitfalls prohibit its use in an automated fashion such as:

- the difficulty to distinguish sometimes numerous local solutions from the, unique, global solution,
- the requirement to come up with a reasonably good initial value set,
- limited knowledge of the underlying physical or chemical properties and their dependencies,
- the temptation to try to solve more unknowns than the number of equations which is not so easy to recognize as in a linear case,
- the need to define an accurate often typically non-linear mathematical model that fully describes the observable features in terms of a complete set of parameters,
- the non existence of an analytical solution for the mathematical model making that there are no formulas to program into the computer.
- complex interactions making that there is no single mathematical model but many such models depending on the selection of the species under investigation.
- lengthy calculation in terms of the mathematical model can make the use of the curve fitter impractically slow these calculations are down over and over again with slightly variations in the parameters.
  Water Analysis:

Large quantities of water are used in industry with quality levels ranging from ultra pure in semiconductor & pharmaceutical manufacturing, to pure water in power generation, down to lesser purity levels in drink and waste water. All applications need some form of analysis capability where the large number of potential contaminants is a major complicating factor. First discussed, section (a), are laboratory type instruments capable of scanning such multitude of species with low detection limits followed by more on line style instruments that typically monitor one specific contaminant only, section (b). TOC analyzers are discussed in section (c) and address contamination by organic species. Section (d) discusses relatively inexpensive, robust, conductivity sensors that are used on line as a non-specific indicator for the overall water quality. Conductivity sensors feature fast response time and high sensitivity. Main disadvantages of conductivity sensors are the lack of information regarding the nature of the contamination and the dependency of the conductivity on the temperature. This last issue is addressed by the use of temperature compensated conductivity readouts. Such readouts however, are still troubled by the lack of knowledge of a sample's composition and the poor accuracy by which some of the chemical properties of the involved species are known, section (e).
(a) Laboratory Instruments:
Laboratory instruments typically rely on grab samples analyzed in a central laboratory. Where semiconductor fabs might have permanent lines going to sample points enabling to perform a number of measurements daily with little sampling contamination, drink and waste water are typically sampled at two week periods. The laboratory type instruments mentioned hereunder have the following common disadvantages of being very labor intensive, requiring high operating costs, high initial investment and frequent calibration.

- Ion Chromatogrphy: An ion chromatograph is a laboratory instrument. It separates the different ions by their species specific elution time measured after injection of a small amount of analyte into a column. The instruments normally have more columns and need frequent calibration for each species to be analyzed.
- ICP: A nebulizer injects analyte into an argon or helium stream. A plasma is created in this gas stream followed by the observation of the optical emission spectrum (ICP-OES). Alternatively, ions created in the plasma can be routed into a mass spectrometer (ICP-MS).

Not a feature of the instrumentation itself but of the practice of (grab) sampling is the associated long response time and the potential of sample contamination. Obviously, applying such technologies to scan continuously online would provide a better guarantee of the ongoing water quality but are normally cost prohibitive.
(b) Specific Species Detectors:
For relatively high impurity concentrations there are a number of colorimetric or luminescence based techniques that use specific chemicals to create color change or light emitting reactions. One typically needs one instrument per chemical species to be monitored. Apart from limitations in detection limits, these techniques are typically not rigorously specific for a single species and involve often-delicate controlled flows of costly consumable chemicals. However, these techniques feature fast response times associated with on line applications.
(c) TOC Measurements:
Monitoring water properties such as Total Organic Carbon, TOC, is highly relevant in a number of important industrial processes; in particular, the semiconductor and pharmaceutical industries both use ultrapure water in large quantities.
Most state of the art methodologies for measuring TOC involve oxidizing organic molecules in the analyte water by UV radiation (see U.S. Pat. No. 4,626,413).
The produced CO₂can be measured in situ, typically by measuring the change in conductivity of the analyte water sample itself. One method, the “stopped flow technique”, measures the change in conductivity of a trapped, static, water sample over time, i.e., by monitoring the conductivity as the oxidation reaction proceeds, to determine the end conductivity value at the completion of the reaction (U.S. Pat. Nos. 4,626,413 and 4,666,860). Another method measures the conductivity of a continuously flowing water stream before and after it is exposed to a UV lamp that oxidizes the organics in the stream (See, e.g., Egozy U.S. Pat. No. 5,272,091). Note that this last method is potentially faster than the first, but might suffer from incomplete oxidation giving too low TOC values. The stopped flow technique might suffer from a buildup of contamination in a stagnant analyte from leaching or diffusion of atmospheric carbon dioxide through O-rings, seals and insulators. The continuous flow technique does not have such buildup as it is flushed continuously. These two basic methods use a conversion algorithm to generate a value for the TOC content based on a conductivity value prior and after oxidation. This algorithm assumes that the sample prior to oxidation consists only of pure water and dissolved CO₂, referred to as TIC or total inorganic carbon. These methods further assume that after the oxidation only oxidized carbon is added, originating from organic carbon contamination. The algorithm will produce the TOC value strictly based on the conductivity measurements. This means that once the conductivity measurements are calibrated with traceable conductivity standards, no further calibration is required with TOC standards. This so-called “absolute principle” is a particular advantage when measuring very low concentrations for which it is difficult to generate TOC standards. Note that one has to be assured of a hundred percent oxidation of the organic carbon. This assurance can be obtained by a system suitability test that compares the results of a sample of an easy to oxidize component with a sample of a difficult to oxidize component.
The assumptions in the above-discussed algorithm can be too much of a simplification when interfering species are present. Specifically, non-conductive species such as THMs and nitrogen containing species like urea can generate a conductivity change under UV irradiation only partially caused by the presence of carbon atoms thus producing an erroneous TOC reading. The presence of unknown species can also generate errors in the temperature compensation applied in the conductivity measurement, which will impact the TOC reading.
The above interfering species problem is addressed by non in situ methods that remove the produced CO₂from the analyte. The CO₂can then be measured in the gas phase by, e.g., NDIR spectroscopy, although this approach is typically much less sensitive. Alternatively, the CO₂can be separated from the analyte water, e.g., by diffusion across a suitable selective membrane, to generate a conductivity change in a separate UPW (Ultra Pure Water) stream. A drawback of this, more complex, last approach is that the membrane introduces a factor that has to be determined empirically for each individual instrument which requires calibration with TOC standards. This factor can be subject to drift while its behavior at very low concentrations might be compromised.
(d) Conductivity Measurements:
The following paragraphs describing the state of art of conductivity measurements are taken from “Instruments, unique temperature compensation for conductivity and resistivity measurement”, David M. Gray and Anthony C. Bevilacqua, Ph.D., Thornton Associates Inc., Ultrapure Water, January/February 1996, p. 60-62.
Conductivity and resistivity measurements are the most common, reliable, sensitive, accurate, and low-cost means of monitoring water purity for typical mineral contamination. A critical part of this monitoring is to eliminate the temperature dependence. There are three parameters required to make accurate temperature-compensated conductivity measurements: a conductivity measurement, a temperature measurement, and knowledge of the type of impurity. Modern instrumentation is capable of measuring the conductivity and temperature with one sensor device and one meter, but the compensation for a specific impurity depends upon the application or the industry convention. All this presumes that the instrumentation has the capability to compensate for that specific impurity.
Pharmaceutical Industry: With the continuing revision of United States Pharmacopeia 23 (USP 23) water specifications, there is a need to provide limits on a variety of USP-identified contaminating ions. The least conductive of these ions at the allowed levels are chloride (CL⁻), ammonia (as NH₄ ⁺), and innocuous ions that are always present (hydrogen [H⁺], hydroxide [OH⁻], bicarbonate [HCO₃ ⁻]), and counterions to chloride [Cl⁻]. Since a conductivity measurement cannot differentiate among the different ions, it cannot compensate correctly for all possible compositions. In addition, the complex temperature properties of CO₂/HCO₃ ⁻ were studied in detail to help with determination of their influence, particularly for offline, atmosphere-equilibrated samples. As temperature rises, the conductivity of HCO₃ ⁻ increases, but the solubility of CO₂decreases and the equilibrium between them shifts. Because of these complexities, it is now proposed to measure uncompensated conductivity and temperature separately, with worst-case conductivity limits established across the temperature range.
Calibration: It is not surprising that in general, the lower the conductivity, the greater the percentage uncertainty in the value. This is due to the potential for contamination in use, the variable concentration of carbon dioxide in the laboratory environment and the volatility of HCl used in some low standards. A very accurate standard can be obtained at high conductivity levels and standards exist at low conductivity levels, but with much greater percentage uncertainty. A “Catch 22” situation has existed where calibration in the range of measurement sacrifies accuracy while a high accuracy standard requires calibration far above the range of measurement. This situation has resulted in fact in the use of UPW as a standard at the very low end of the scale. The uncertainty of pure water as a standard is primarily due to the limitation on temperature measurement and control and on carbon dioxide exclusion in an actual recirculating loop.
(e) Difficulties in the Determination of Chemical Properties of Ions:
Scientific literature values describing temperature dependencies of the specific equivalent conductance of species and dissociation constants are typically not very precise. This reflects difficulties in the precise measurement of the properties of species such as weakly ionized acids and bases. One problem is that sample solutions typically contain variable concentrations of carbonic acid due to atmospheric carbon dioxide exposure. Another problem is that scanning properties over a pH range will require samples with multiple components introducing difficulties associated with handling complex chemical interactions.
Objects and Advantages
Accordingly, several objects and advantages of the present invention are:
Absolute Principle:
One object and advantage of the invention is to bring the advantage of an “absolute principle” not only to the determination of a single, relatively straightforward related, component but to the determination of complex related entities or a complete array of properties. Applied to analysis, this allows in principle to determine multiple species at low concentrations without having to perform an individual, low level, calibration for each of the species.
Non-Linear Curve Fitting:
The invention addresses the main obstacles preventing more automated use of non-linear curve fitting including:

- a wide scan technique capable to automatically finding the global minimum, making it unnecessary to provide a good set of initial values.
- a reversed use of the invention providing it known sample properties in order to let it determine best matching underlying physical or chemical properties and their dependencies. Knowing such physical or chemical properties with a high precision allows to determine a large number of unknown properties under normal use of the invention.

Other obstacles related to the mathematical model are addressed under ‘Further objects and advantages’.
Water Analysis:
(a), b) Ion Analysis:
To obtain knowledge of the nature and concentrations of the ions in a sample that make up the conductivity of an aquaeous analyte with a simple, robust, low maintenance, on-line instrument based on an absolute principle making it unnecessary to calibrate for each individual contaminant, so without calibrated standards or consumable reagents. Such easy to run, low maintenance, calibration and reagents free, on-line analyzer would overcome limitations in terms of number of sampling points and frequency of analysis for applications that now rely on grab sampling and labor intensive, laboratory style equipment.
(c) Analysis of Organic Components and TOC:
To determine the inorganic ion composition resulting from a full oxidation of an organic contaminant in water thus revealing the atomic components that were part of the organic molecules. This information is much more meaningful than just a total organic carbon (TOC) indication.
To use knowledge about the atomic components of organic contaminants to correct chemical interference problems of current TOC analyzers by recognizing the part of a conductivity change that is due to carbon.
To determine the degree of oxidation of an organic contaminant by identifying intermediate ionic species that will fall further apart into stable end product
(d) Conductivity Measurements:
To use knowledge of the sample composition to produce accurate temperature compensated conductivity and pH values. Expanding the practice to use UPW for the calibration of conductivity cells, the invention can make use of information of the conductivity measurement over a continuous range of temperatures. It can determine final contamination such as trace concentrations of carbon dioxide and take their impact into account when using the water as a calibration standard. Finally, the invention can make the offset & span of the involved conductivity & temperature sensor part of the parameters to be determined. Such determination would solely rely on the quality of knowledge of UPW and not on, e.g., the use of secondary temperature standards.
Further Objects and Advantages are Related to the Creation and Use of a Mathematical Model to Describe Complex Phenomena:
State of the art teaches the use of the computer to calculate according to a provided formula. State of the art even teaches to find analytical solutions, or formulas for problems, as is done by symbolical calculators. The invention teaches the use of computing power in a numerical iterative way building up solutions from scratch on a case by case basis as a foundation for in principle limitless complex mathematical models. This ability overcomes major objections against automated use of non-linear curve fitters related to the use of a mathematical model. The numerical iterative way of the invention makes the calculation time go up roughly linear with the complexity of the model. State of the art translation of analytical derived expressions in computer program code makes calculation go up roughly with the square of the complexity of the model.

DESCRIPTION OF THE DRAWINGS

The invention will be better understood with reference to the accompanying drawings, in which:
FIG. 1 Schematic diagram of an automated analytical device implementing a mathematical model and non-linear curve fitting.
FIG. 2 Schematic diagram of the invention's iterative conductivity calculation algorithm.
FIG. 3 Implementation of the conductivity calculation algorithm in a curve fitting algorithm.
FIG. 4 Boundary determination to distinguish local minimums from the global minimum in the non-linear curve fitting.
FIG. 5 Invention with a stopped flow conductivity cell.
FIG. 6 Stopped flow conductivity sensor with active temperature ranging.
FIG. 7 Continuous flow application with 2 single downstream sensors.
FIG. 8 Continuous flow application with sensor arrays.
FIG. 9 Flow switch based stopped flow cell.
FIG. 10 Flow switch based stopped flow cell with UV oxidation.
FIG. 11 Continuous flow with heat exchanger.
FIG. 12 Exponential dilution based mixing ratio.

FIG. 13 Timing chart for stopped flow cell TOC application.



List of Reference Numerals

	1	sample preparation
	1a	stopped flow on/off valve
	1b	UV lamp
	1c	heater rod
	2	analyte
	3	characteristic property
	3a	conductivity sensor
	3b	conductivity sensor electrode
	3c	conductivity sensor electrode
	4	variable property determination
	4a	temperature sensor
	5	variation control
	5a	heater
	5b	thermo-electric element
	5c	thermo-electric lead wires
	5d	heat exchange provision
	6	analyte data collection
	7	mathematical model
	8	Levenberg algorithm
	9	loop provision
	10	start
	11	result update
	21	start solving [H⁺] concentration
	22	sorting of the input data
	23	storage of temperature T
	24	concentrations fully ionized species
	25	concentrations of weak acids
	26	concentrations of weak bases
	27	initial polynomial setting
	28	polynomials storage
	29	numerator polynomial coefficients
	30	denumerator polynomial coefficients
	31	coefficients update per weak acid
	32	control of the weak acid loop
	33	coefficients update per weak base
	34	control of the weak base loop
	35	solution of the final polynomial
	36	resulting, real, solution of [H⁺]
	40	start of the curve fitting routine
	41	get initial concentration values
	42	Levenberg routine
	43	conductivity calculation
	44	difference vector calculation
	45	instrumentation hardware
	46	ramp control and data acquisition
	47	temperature data storage
	48	conductivity data storage
	49	final best fitting concentrations
	50	start global minimum search
	51	get user selection of components
	52	loop over selected components
	53	single component curve fitting
	54	set boundary for component
	55	loop over grid points
	56	low precision fit from grid point
	57	update best fit conditions
	58	high precision fitting of best fit
	59	best fitting concentrations result
	60	end global minimum search
	70	sample inlet
	71	outlet
	72	quartz stopped flow cell
	80	Tee
	81	outlet oxidized sample
	82	outlet regular sample
	83	quartz spiral around UV lamp
	84	spiral around heater rod
	85	continuous flow cell oxidized sample
	86	continuous flow cell regular sample
	90a	outlet oxidized sample array
	90b	outlet regular sample array
	91	cell in oxidized stream sensor array
	92	cell in oxidized stream sensor array
	100	inlet flow switched stopped flow cell
	101	inlet split first branch
	102	inlet split second branch
	103	cell housing
	104a	insulator/seal first electrode
	104b	insulator/seal second electrode
	105	first, outer electrode
	106	second, inner electrode
	107	cell outlet first branch
	108	cell outlet second branch
	109	on/off valve first cell outlet
	110	on/off valve second cell outlet
	111	bleed outlet first cell outlet
	112	bleed outlet second cell outlet
	113	bleed outlets Tee
	114	common outlet
	121	flow restriction first branch
	122	flow restriction second branch
	123	quartz tube spiral
	130	outlet
	131	inlet
	132	heat exchanger TEE
	133	dual coil heat exchanger
	134	heat exchanger TEE
	135	conductivity sensor flow housing
	136	conductivity/temperature sensor
	137	flow housing outlet
	138	heater
	139	needle valve
	140	reservoir
	141	sample flow inlet
	142	sample flow outlet
	143	reservoir inlet isolation valve
	144	reservoir outlet isolation valve
	145	UPW dilution flow inlet
	146	UPW dilution control valve
	147	stopped flow analysis cell
	148	exponential dilution outlet

DESCRIPTION OF INVENTION

FIG. 1 shows schematically the different elements of the invention enabling to determine a set of SAMPLE FEATURES of a SAMPLE or analyte from information of a scanned CHARACTERISTIC PROPERTY. Block 1 performs sample preparation on the SAMPLE in block 2, adapting the SAMPLE to feature the SAMPLE FEATURES searched for, or to the characteristics of the scanning operations of the CHARACTERISTIC PROPERTY. Block 3 is a sensor provision measuring the CHARACTERISTIC PROPERTY of the SAMPLE as a function of yet another VARIABLE PROPERTY that is determined by measurement, derivation or control performed by block 4. Block 5 actively or passively causes the VARIABLE PROPERTY to fluctuate using eventually information provided by block 4. To adapt the SAMPLE to the SAMPLE FEATURES searched for, the sample preparation done by block 1 on the SAMPLE selectively changes the members of the set of SAMPLE FEATURES that contribute to the CHARACTERISTIC PROPERTY to be measured. To adapt the SAMPLE to the characteristics of the scanning operations, block 1 can take steps to eliminate or reduce changes of the SAMPLE FEATURES of the SAMPLE that are faster than or comparable to the time necessary to scan enough data for a meaningful interpretation. Measured data regarding the VARIABLE PROPERTY's dependency of the CHARACTERISTIC PROPERTY of the SAMPLE are gathered by data acquisition block 6. Block 7 contains a mathematical model that calculates the value of the SAMPLE's CHARACTERISTIC PROPERTY given a CANDIDATE set of values for the SAMPLE FEATURES and given a value for the VARIABLE PROPERTY. Using the mathematical model block 7 generates a set of calculated values of the CHARACTERISTIC PROPERTY for the series of values of the VARIABLE PROPERTY gathered in block 6. Finally, block 7 puts the difference between measured and calculated values of the CHARACTERISTIC PROPERTY for the series of VARIABLE PROPERTY values into an array. This array, or vector, is offered to the curve fitting routine in block 8 who calculates the NORM of the vector as a measure of the quality of the fit. Block 8 further processes the NORM to come up either with a next CANDIDATE set of SAMPLE FEATURES offered to block 7 or when it meets its fitting criteria to exit the loop over block 7 and present its result to block 9. Depending on the mode of operation of the invention, block 9 can undertake a number of actions presented hereunder. One such action, in a single pass mode of operation, is where block 9 passes its results to block 11 where it interfaces the user as the end result. Another action, in an ongoing monitoring mode of operation, is where block 9 updates new results to block 11 but also loops to start a new cycle at block 8 entering the current end result as the new initial values for the non-linear fit of block 8. In this case, block 6 will continuously acquire new data and discard old data, e.g., in a first in, first out fashion. One provision, according to the invention, in particular enables automation and lets block 7 calculate the NORM adding a time dependent weight factor to each of the members of the array differences. The weight factor gives newer data more weight and can take the form of an exponential exp(−t/rc), where t is the time expired since the data was taken and where rc is a time period that, within limits, can be chosen by the user in terms associated with the response time of the instrument. A cutoff point when weight factors get smaller than some value or a limit on the size of the buffers of data acquisition block 6 can be applied to manage the data streams. In this case block 6 will not only contain a collection of CHARACTERISTIC PROPERTY and VARIABLE PROPERTY values, but also timestamp values associated with the time when the corresponding measurement was done. In the ongoing monitoring mode, prior to loop around to start a new cycle, block 9 can additionally evaluate the quality of the fit value associated with the current result. The associated evaluation criteria can be based on detecting a significant increase compared to recently obtained quality of the fit values or compared to priory determined values considered to be acceptable, e.g., at startup. The detection of such an upset in the quality of the fit value indicates a rapid change in the conditions in the actual SAMPLE FEATURES of the SAMPLE. In fact, so rapid that the fit routine is using outdated SAMPLE FEATURES initial values and ends up in a local minimum instead of the global minimum. In this situation block 9 can start to generated a series of SAMPLE FEATURES initial values thus starting a wide scan procedure to find the global minimum, according to a later discussed WIDESCAN provision. The modified conditions could also be cause by the appearance of a component not part of the present set of SAMPLE FEATURES. In this case block 9 can start a series of fits modifying the group of SAMPLE FEATURES adding and removing members. This step might be taken after failure of a wide scan procedure to find a good enough match. WIDESCAN and the modified group scan can be run in the background or, if needed, on an ongoing basis while block 11 continues to update its finding together with individualized error indications for each of the SAMPLE FEATURES.
Wide scan and modified group scan can also be run at startup from block 10 of the device or method according to the invention. It then runs in a kind of warm-up period and will result in a set of startup initial values for the SAMPLE FEATURES. This way, one no longer has to rely on a sophisticated user to perform this task, thus removing another obstacle for automation as discussed in the prior art.
Hereunder, the invention will be further presented mostly narrowed down to a main application which is the analysis of a liquid sample such as water.
Returning to FIG. 1, now used to disclose this specific application, block 2, the SAMPLE is an analyte being an aquaous solution, a liquid or a fluid. The set of SAMPLE FEATURES, in this case, is the nature and concentrations of chemical species present in the analyte. Chemical species can be selected from the group consisting of ions, dissolved gases, neutral species, organic species and inorganic species. The CHARACTERISTIC PROPERTY is the analyte's electrical conductivity while the VARIABLE PROPERTY can be the analyte's temperature or the degree by which the analyte is mixed with another fluid. Block 1, performing sample preparation which can be the selection of only positive or only negative ions by means of ion exchange resins, or the UV light enhanced breakdown of neutral non-conductive organic molecules into smaller basic species such as carbon dioxide and water. This last creation of carbon dioxide effects the conductivity of water as it will be partially present as carbonic acid.
Block 1, performing sample preparation can trap a quantity of analyte by stopping temporarily a flow of analyte to isolate it from changes in chemical composition during the measurement. Block 1 might also simply do nothing when one just wants to see the components in the sample as it is or when changes in the analyte are much slower than the time to acquire a significant number of data points. Block 3 is a conductivity sensor provision and block 4 contains means to determine the value for the VARIABLE PROPERTY. This last determination might take place by a straight measurement as is likely the best way when dealing with the temperature. This determination might be more involved as is likely to be the case when dealing with the mixing ratio. Determination by block 4 might have to be done in conjunction with block 5 that actively or passively causes the VARIABLE PROPERTY to fluctuate. An example of such conjunction is described later for a preferred embodiment where the mixing ratio fluctuation is setup as an exponential dilution and a value for it can be derived from knowledge of the flowrate, the dilution volume and the time expired since the start of the dilution. Determination can involve repeatable hysteresis data correcting for a lag in the indicated and actual temperature of the analyte. In order to reduce response time of the analysis, the conductivity sensor provision of block 3 might be an array of conductivity sensors each scanning the VARIABLE PROPERTY dependency of the conductivity over only a fraction of the total range. Data acquisition block 6 will gather measured and otherwise derived data regarding the relationship between analyte conductivity and/or between analyte conductivity and mixing ratio value while it can also contain timestamp information associated with these measurements or determinations. Block 7 contains a mathematical model that now calculates the conductivity of an analyte at a certain temperature and/or mixing ratio given a CANDIDATE set of concentrations of the components of the analyte. If applicable the mathematical model might also have to be given a set of concentrations of the components in the fluid used for to mix with the analyte. The functions of the remainder of blocks in FIG. 1 in this application are already described in general terms. However, the mathematical model for this application will be further described in FIG. 2 while its implementation will be detailed in FIG. 3. FIG. 4 will described a WIDESCAN provision for this application.
FIG. 2 shows schematically the invention's iterative polynomial coefficients determination as a part of the conductivity calculation algorithm capable of handling the potentially very complex chemistry associated with a multitude of interacting species. The control stream starts at block 21 while required data is sorted at block 22 into a temperature value T stored in 23; a series of WB weak base concentrations, wb₁, wb₂, wb₃, . . . , wb_WBstored in 26; a series of WA weak acid concentrations, wa₁, wa₂, wa₃, . . . , wa_WAstored in 25; and a series of SA+SB fully ionized species sa₁, sa₂, . . . , sa_SA, sb₁, sb₂, . . . , sb_SBstored in 24. Hereafter, the command passes to block 27 where the initial polynomial coefficients are loaded as follows: P₀=−W, P₁=sa₁+sa₂+ . . . +sa_SA+sb₁+sb₂+ . . . +sb_SB, P₂=1.0 & Q₁=1.0, where W is the water dissociation constant at temperature T. Block 27 uses info from storage 24 and updates values in memory block. 28; numerator polynomial coefficients in array P(P₀, P₁, P₂, . . . ) in storage 29 and denumerator polynomial coefficients in array Q (Q₁, Q₂, Q₃, . . . ) in storage 30. Hereafter, the command passes from block 27 to block 31 where the polynomial coefficients are updated in a loop controlled by block 22 going successively over all weak acids getting their concentrations from storage 25. Each weak acid causes the polynomial coefficients arrays P and Q from block 28 to be updated. Hereafter, a similar loop consisting of block 23 & 24 goes through all weak bases getting their concentration from storage 26. Hereafter, final values of the polynomial coefficients are retrieved at 25 where the polynomial is solved numerically giving in principle a number of solutions equal to the degree of the polynomial. The solutions are typically complex and the solution with zero (within machine precision) imaginary part and a non-negative real part is presented as the end result for the hydrogen ion concentration [H⁺] at 26.
The scheme of FIG. 2 can be extended to incorporate species involved in more than one reaction. This leads to the additional sorting and storage by block 22 of the concentrations involved as well as additional loop(s), e.g., after block 23 with their own updating of the polynomial of block 28.
Not shown in FIG. 2 is the calculation of all ionic concentrations from [H⁺] and the final conductivity calculation done by taking the sum of the products of the individual ion concentrations and their specific equivalent conductance.
FIG. 3 shows schematically how the iterative conductivity calculation, that is partially shown in FIG. 2, is implemented into block 43 of a curve fitting algorithm. FIG. 3 shows an independent loop consisting of the block 45 & 46 representing respectively the instrumentation's hardware and the control/data acquisition. Block 46 acquires data pairs (σ_i, T_i) consisting each respectively of a temperature measurement value and a conductivity measurement value which are stored respectively in memory array 47 and 48. The control function of block 46 deals with the temperature and/or dilution ratio ramping of hardware 45.
The actual curve fitting routine starts at 40 while block 41 gets the initial concentration settings being: SA concentrations for strong acids, sa₁ ⁰, sa₂ ⁰, . . . ; SB concentrations for strong bases, sb₁ ⁰, sb₂ ⁰, . . . ; WA concentrations for weak acids, wa₁ ⁰, wa₂ ⁰, . . . ; WB concentrations for weak bases, wb₁ ⁰, wb₂ ⁰, . . . and eventually other species concentrations that are involved in more than one reaction.
The initial concentrations are passed to the Levenberg routine 42 that runs a loop consisting of block 43 and 44 to determine best fitting concentration values that are passed as the final results to block 49.
Block 43 takes a set of m concentration values (sa₁, sa₂, . . . , sb₁, sb₂, . . . , wa₁, wa₂, . . . , wb₁, wb₂, . . . ) generated by block 42 and loops through the series of n temperature values (T₁, T₂, . . . , T_n) from block 47 to calculate a series of n conductivity values σ(sa₁, sa₂, . . . , sb₁, sb₂, . . . , wa₁, wa₂, . . . , wb₁, wb₂, . . . , T_j) where jε{1, 2, . . . , n). Block 44 now takes, these calculated conductivity values and the measures conductivity values from 48 and presents the array of the differences between these conductivity values to the Levenberg routine 48. Block 48 calculates the NORM, which is the square root out of the sum of the square of the differences, as the quality of the fit which either meets Levenberg algorithm's stopping criteria or results in a modified series of concentration values offered to block 43.
FIG. 4 shows the curve fitting routine implemented into a wide-scan algorithm that enables to determine the best fit value, which is the global minimum of the above defined NORM. This global minimum, out of a possibly multitude of local minimum values resulting from starting the Levenberg routine with different initial concentration values. Starting at block 50 the WIDESCAN provision enters block 51 acquiring the user's selection of the different type of chemical species that are member of the SAMPLE FEATURES group. This group is passed to block 52 that sequentially passes each member type to block 53. Block 52 performs a single component non-linear curve fit with the currently available relationships data from block 6, FIG. 1 and passes the resulting concentration to block 54. This resulting best fitting single species concentration for a particular species represents a good approximation for the upper limit of such species in a mixture with other chemical species. The initial concentration value of zero can be used in the mentioned single component non-linear curve fit. Block 54 sets this way the upper boundary for a particular species and passes the command back to block 52. Hereupon block 52 either continues this loop passing the next type of species to block 53 or when all species are done, passes the command to block 55. Having now upper limits for the concentrations of all chemical species and taking zero for the lower limits, restricts the area from which meaningful initial SAMPLE FEATURES values can be chosen for the curve fitting routine. Such boundaries are required for any kind of automated WIDESCAN search that in fact scans for the lowest local minimum for the NORM which then is considered to be the global minimum. Block 55 sets up a grid of points in the multidimensional space defined by the concentrations of all species from the SAMPLE FEATURES group. A good strategy is to take for each species the upper boundary, a certain fraction of the upper boundary, that fraction of the fraction of the upper boundary etc. Each such value will now be combined with any other such value from all other species. The number of points on the grid will be K**N, where K is the number of points per species and N is the number of different species. For an automated WIDESCAN provision predetermined values for the fraction and for K have to be made. Available calculation time is a likely factor in choosing K as such time goes up exponentially steeper for larger K's. Block 55 sequentially offers all grid points as initial SAMPLE FEATURES values to block 56 that does a low precision non-linear fit. The quality of the fit value and the result of the fit from block 56 is passed to block 57. Block 57 keeps track of the resulting SAMPLE FEATURES values for the lowest (note: lower is better) quality of the fit value encountered so far for a grid point. Block 57 passes command back to block 55. Block 55 continues to loop until all grid points are done or until satisfying quality of the fit values are obtained whereupon block 55 passes command to block 58. Block 58 now performs a regular, high, precision non-linear fit using as initial SAMPLE FEATURES values the values from block 57. The end result of block 57 passes to block 59 where upon the WIDESCAN provision can terminate at block 60.
Mathematical Model of Interacting Chemical Species in a Solution:
The math involved in solving the equations that describe the chemistry that takes place in a mixture of interacting species in a solution becomes rapidly unduly complex when increasing the number of species. On the one hand, analytical solutions seize to exist for solutions of the high order polynomial equations involved. On the other hand the expressions for the polynomial coefficients start rapidly to deal with such a large number of parameters that they fall beyond the capacity of symbolic calculators like MathCAD.
Notation & Theory:
Common ions in an aquaous solution are H⁺ and OH⁻ which are related through the dissociation constant of water leaving only one as an independent parameter, arbitrarily chosen in this case H⁺. Molar concentrations of species are indicated with square brackets. Atomic species or parts of molecules or ions that remains unchanged in the chemical reactions under consideration are hereinafter called atomic species and notated with small letters. All species that can have a particular atomic species build into their molecular or ionic structure are hereinafter called the associated group of that particular atomic species, and are notated with capital letters where the ions have a + or − sign. The concentrations of the atomic species in an analyte are, in the hereunder presented application, the SAMPLE FEATURES of the SAMPLE searched to be determined. Where the total molar concentration, [carbon] of an atomic species like carbon remains unchanged by the reactions taking place in an aquaous solution, the distribution of carbon among the members of its associated group, {CO₂, HCO₃ ⁻, CO₃ ²⁻}, is determined by these reactions. As an example: the total concentration of carbon from carbonic acid can be written as: [carbon]=[CO₂]+[HCO₃ ⁻]+[CO₃ ²⁻] where carbonic acid is involved in two reactions: [H⁺].[HCO₃ ⁻]=k_a1.[CO₂] & [H⁺].[CO₃ ²⁻]=k_a2.[HCO₃ ⁻].
The temperature dependent dissociation constants are indicated as k_wfor water and k_a& k_bfor weak acids & bases with an index for different types.
Summation is noted as:
Σ_{j=0, 1, . . . , N}R_j.[H⁺]^j=R₀+R₁.[H⁺]+R₂.[H⁺]²+ . . . +R_N.[H⁺]^N
Mathematical Model of the Chemistry:
Dissociation of Water: [H⁺].[OH⁻ ]=k _w (1)
Dissociation of weak acids: [H⁺].[A⁻ ]=k _a.[A] (2)
Total concentration [a]of species a, in ionic or dissolves form: [a]=[A]+[A⁻] (3)
Rewriting equations (2) & (3) gives: [A⁻]=[a]/(1+[H⁺ ]/k _a) (4)
Dissociation of weak bases: [B⁺].[OH⁻ ]=k _b.[B] (5)
Total concentration [b] of species b, in ionic or dissolves form: [b]=[B]+[B⁺] (6)
Using (1), rewriting equations (5) & (6) gives: [B⁺]=[b]/(1+k _w/([H⁺ ].k _b)) (7)
Strong acids and bases can be treated as fully ionized so that [sa]=[sa⁺] and [sb]=[sb⁺]. Consider an analyte that contains SA strong acids with concentrations sa₁, sa₂, . . . , sa_SA, SB strong bases with concentrations sb₁, sb₂, . . . , sb_SB, WA weak acids with concentrations wa₁, wa₂, . . . , wa_WA, and WB weak bases with concentrations wb₁, wb₂, . . . , Wb_WB.
Charge conservation dictates:
[H⁺]+[sb₁]+[sb₂]+ . . . +[sb_SB]+[b₁].[H⁺]/([H⁺ ]+k _w /k _b1)+[b₂].[H⁺]/([H⁺ ]+k _w
/k_b2)+ . . . +[b_WB].[H⁺]/([H⁺]+k_w /k _bWB)=(k _w/[H⁺])+[sa₁]+ . . . +[sa₂]+ . . . +[sa_SA]+[a₁]/(1+[H⁺ ]/k _a1)+[a₂]/(1+[H⁺ ]/k _a2)+ . . . +[a_WA]/(1+[H⁺ ]/k _aWA) (9)
The product of denumerators of the terms of expression (9) equals:
[H⁺]*([H⁺]+k_w/k_b1)*([H⁺]+k_w/k_b2)* . . . *([H⁺]+k_w/k_bWB)*(1+[H⁺]/k_a1)*(1+[H⁺]/k_a2)* . . . *(1+[H⁺]/k_aWA) (10)
Multiplying (9) with (10) results in a p^thorder polynomial expression in [H³⁰]: P₀+P₁.[H⁺]+P₂.[H⁺]²+ . . . P_p.[H⁺]^p=0.
Equation (10) can also be expressed as a polynomial expression in [H⁺]:
Q₁.[H⁺]+Q₂.[H⁺]²+ . . . +Q_S.[H⁺]^S (11)
The invention's iterative numerical algorithm finds values for the polynomial coefficients P0, P1, . . . , Pp and Q1, Q2, . . . , Qs by adding weakly ionized species one by one. It calculates the polynomial coefficients for a composition with a weakly ionized species from the polynomial coefficient for that composition without that weakly ionized species. If the conservation of charge equation (9) for the composition without the weakly ionized species can be written as:
{P₀+P₁.[H⁺]+P₂.[H⁺]²+ . . . +P_p.[H⁺]^p}/{Q₁.[H⁺]+Q₂.[H⁺]²+ . . . +Q_S.[H⁺]^S}=0
then adding, e.g., a concentration [a]of a weak acid “a” modifies the conservation of charge equation into:
{P₀+P₁.[H⁺]+P₂.[H⁺]²+ . . . +P_p.[H⁺]^p}/{Q₁.[H⁺]+Q₂.[H⁺]²+ . . . +Q_S.[H⁺]^S}=[a]/(1+[H⁺ ]/k _a)
Notation:
{Σ_{j=0, 1, . . . , N}P_j.[H⁺]^j}/{Σ_{r=1, 2, . . . , N−1}Q_r.[H⁺]^r}=[a].k _a/(k _a+[H⁺]) or
k _a*{Σ_{j=0, 1, . . . , N}P_j.[H⁺]^j}+{Σ_{j=1, 2, . . . , N+1}P_j−1.[H⁺]^j}−[a].k _a*{Σ_{r=1, 2, . . . , N−1}Q_r.[H⁺]^r}=0 (12)
This last expression (12) can be dealt with by a computer program combining old coefficient values to calculate the new coefficient values. Species involved in more than one reaction can be dealt with in a similar way as is illustrated for carbonic acid:
[HCO₃ ⁻]+2[CO₃ ²⁻]={[H⁺]+2k _a2}*[carbon]/{[H⁺]**2/k _a1+[H⁺ ]+k _a1} &
{Σ_{j=0, 1, . . . , N}P_j.[H⁺]^j}/{Σ_{r=1, 2, . . . , N−1}Q_r.[H⁺]^r}={[H⁺]+2k _a2}*[carbon]/{[H⁺]**2/k _a1+[H⁺ ]+k _a1}
The iterative numerical method of the invention makes that total concentration value of a each specific atomic species and the values of the reaction constants have to be entered only at one point. State of the art approach would formulate analytical expressions for all coefficients while for each coefficient specific atomic species and the values of the reaction constants have to be entered. The numerical iterative way of the invention makes the calculation time go up roughly linear with the complexity of the model. State of the art translation of analytical derived expressions in computer program code makes calculation go up roughly with the square of the complexity of the model.
Fitting of Offset and Span Values:
Offset and span parameters can also be fitted entering mathematically as follows: {C_span*σ(a, b, c, . . . , (T_span*T_j−T_offset))+C_offset−σ_j ^measured} which is the value of the j^thcomponent of the difference vector. Span values should be close to 1.0 and offset values around 0.0.
where σ(a, b, c, . . . , T) is the calculated conductivity for an analyte at temperature T containing concentrations a, b, c, . . . of species.
Fitting with a Sample Undergoing Known Changes:
In the case of a sample undergoing known changes there is more information to incorporate than the discussed collection of pairs of conductiviy and temperature data.

- exponential dilution. Giving the data pairs σ_j& T_ja timestamp t_jtogether with the knowledge of the starting moments, composition of the diluting flow (a₀, b₀, c₀, . . . ), volume V and flowrate F of the setup enables to fit with:
  - {σ(α_j.a+a₀,α_j.b+b₀,α_j.c+c₀, . . . T_j)−σ_j ^measured} where α_j=exp(−tj*F/V)
    Measuring the Temperature Dependency of a Species' Specific Equivalent Conductance or the Temperature Dependency of a Dissociation Constant Involving Several Species:

In this case we provide data from one or more samples with accurately known compositions. The unknowns to be fitted are the Taylor expansion coefficients of the involved specific equivalent conductance or dissociation constant. The calculated vector now is: {σ(p₀, p₁, p₂, . . . , p_n, a_j, b_j, c_j, . . . , T_j)−σ_j ^measured}
In this case, the p₀, p₁, p₂, . . . , p_nparameters are the unknowns to be fitted while the a_j, b_j, c_j, . . . and T_jvalues are the given known parameters. The non-linear curve fitter works basically the same as in the analysis case.
This makes it possible to, e.g., acidify a sample with a known concentration of carbonic acid with HCl in various concentrations allowing to measure the dissociation constant over a wide pH range. As pointed out in the state of the art description, without using the invention's techniques, complex interaction makes it hard to distinguish temperature effects of the specific conductivity from those of the dissociation constant.

Description of the Invention's Preferred Embodiment Number 1

This embodiment of the invention allows to acquire periodically a set of electric conductivity data from a single sensor over a range of temperatures on a trapped quantity of analyte. FIG. 5 illustrates the hardware of the first-preferred embodiment while the time chart of FIG. 13 illustrates the hereunder-mentioned stages and the method of operation. A water analysis according to this embodiment of the invention consists of the following steps:

- stage 1 By opening valve 7, fresh sample enters through inlet 70, flows through the stopped flow cell 72 and exits through outlet 71. Measure initial UPW sample's conductivity & temperature with respectively sensor 3 a & 4 a and calculate the corresponding total carbon from carbonate, ICC, value assuming all initial conductivity is related to carbonic acid. Note that as the conductivity is strongly dependent on the sample's temperature, both conductivity and temperature has to be measured.
- stage 2 Trap sample water with the stopped flow technique, conductivity and temperature measurements at this point should result identical ICC values as in stage 1
- stage 3 Turn on lamp 1 b to apply UV irradiation while determining the end point of chemical oxidizing activity. Oxidation turns non conductive organic species into water and carbon dioxide and possible some other simple molecular species. The carbon dioxide will contribute to the conductivity as carbonic acid. See U.S. Pat. Nos. 4,626,413 and 4,666,860 for possible algorithms for end point detection, where it should be noted that the actual data used for the TOC measurement does not come from this stage but from stage 4. A possible exception might be the case when the curve in stage 3 ends in a linear ramping slope which is, e.g., an indication of a CO₂leak which impact can be taken into account subtracting the leakrate integrated over the expired time from the total carbon.
- stage 4 After the extinction of the UV irradiation by turning off lamp 1 b, monitor with sensors 3 a & 4 a the conductivity and temperature of the analyte as it remains now trapped according to the invention. Heated by the previous UV irradiation the sample will cool down toward ambient temperature. The monitoring during the cool down will provide the empirical temperature profile of the sample in the form of data pairs of a temperature and the corresponding conductivity over a range of temperatures.

As the data from stage 4 comes in, perform curve fitting matching sets of total atomic species such as carbon, chlorine, nitrogen, etc. The match should gain accuracy as more and more data over a growing temperature range is taken into account. The fitting algorithm should provide a quantitative number for the accuracy of the fit.
Compare the accuracy number of the fit with some minimal accuracy requirement. This minimal requirement number can be established in relationship with the specified accuracy of the analyzer. When the minimal accuracy requirements are achieved, step 4 can be halted, the results are reported, and a now measurement cycle can begin by opening the valve that gets a fresh flow of sample into the measuring cell.
Note that a time limit might be set on stage 4, reporting the results, e.g., in combination with a warning regarding any reduced accuracy.
FIG. 5 features also heater 5 a that enables to determine the nature of the ions responsible for conductivity prior to any conversion of species by oxidation with UV light. Hereto, after a fresh stage 1 purge, with lamp 1 b off, sample is trapped by closing valve 1 a. The trapped sample hereafter is heated by heater 5 a while monitoring the empirical temperature profile of the sample in the form of data pairs of a temperature and the corresponding conductivity over a range of temperatures. As such data comes in, perform curve fitting by matching sets of total atomic species such as carbon, chlorine, nitrogen, etc. If more data is desired, one can continue the data acquisition when the sample cools down after turning of the heater.
The heater can also be used in conjunction with a control provision based on temperature feedback from sensor 4 a. This way, the stage 4 cool down can be controlled by the heater to go at a desirable pace and the above mentioned heat up of an un oxidized sample can take place in a controlled fashion.
Comparing the conductivity temperature dependency of a sample while rising the temperature and while cooling down at various speeds might reveal hysteresis effects. This is caused by a lag between the reading of the temperature sensor and between the actual temperature of the sample. In this preferred embodiment, as well as most of the hereafter presented embodiments, the hysteresis lag should be highly repeatable and can eventually be addressed by a form of lookup table kind of correction.

Description of the Invention's Preferred Embodiment Number 2

FIG. 6 shows also an embodiment where a quantity of a flowing sample stream is trapped in a conductivity/temperature measurement cell 72 by closing valve 1 a. When valve 1 a is open analyte will flow entering at inlet 70 and exiting at outlet 71. The difference with preferred embodiment number 1 is that heater 5 a now is replaced by thermo electric heatpump means. Temperature ramping of a trapped sample is obtained by active temperature control that is applied to this cell by Peltier element 5 b allowing to pump heat between the cell 72 and heat exchange finned structure 5 d. Heating and cooling can be achieve by changing the direction of the electrical current through the Peltier element leads 5 c. This embodiment's active heating or cooling provides a way to achieve a wider temperature range while also the speed of the scan can be increased giving a faster response time of the instrument.

Description of the Invention's Preferred Embodiment Number 3

FIG. 7 shows the third preferred embodiment. Also this embodiment of the invention allows acquiring periodically a set of electric conductivity data from a measurement sensor (conductivity & temperature) over a range of temperatures. However, this embodiment works with a flowing stream of analyte. A sample stream enters at inlet 70 into Tee 80 that splits the stream into two legs. One leg connects to spirally coiled quartz tube 83 where the analyte stream gets irradiated with UV light from lamp 1 b positioned on the axis of the spiral. After being irradiated with UV light, the stream exits spiral quartz tube 83 into continuous flow analysis cell 85 that is equipped with a conductivity sensor and a temperature sensor 4 a. The analyte flow exits of cell 85 at outlet 81 downstream of which not shown flow rate controlling means might be positioned. The second leg connects to conduit 84 where it might optionally be heated. Hereafter, conduit 84 connects to continuous flow analysis cell 86. Conduit 84 is shown as a heated, 1 c, spiraled coil to illustrate the possibility to give analyte arriving at both analysis cells the same history of travel in terms of delay, spread and diffusion thus enabling a meaningful comparison. Both analysis cells, 85 and 86, are equipped with means to vary the temperature of the analyte shown as thermo electric 5 b and heat exchange means 5 d.
This preferred embodiment can analyze species with and without oxidation. A higher concentration of species in analysis cell 85, compared to analysis cell 86, can be considered to result from the breakdown of non conductive, organic species.

Description of the Invention's Preferred Embodiment Number 4

FIG. 8 shows an embodiment of the invention that allows acquiring continuously a set of electric conductivity data from a number of measurement sensors over a range of temperatures on a flowing stream of analyte. A sample stream enters at inlet 70 where after it is split into two legs similarly as preferred embodiment number 3. However, in this embodiment, the analysis is not done by ramping the temperature over time such as is the case in analysis cell 85 and 86. In this embodiment, the analysis is done by an array of cell connected in series. FIG. 8 shows two such arrays, one for the oxidized sample and one for a regular, non oxidized sample. The temperature of the analyte, heated respectively in quartz spiral 83 and by heater 1 c, will gradually come down going to the more downstream sensors. This way, continuous acquisition of the conductivity of the oxidized sample will be obtained at a number of different temperatures, each temperature corresponding with one of the sensors. This embodiment number 4 has the potential of responding very fast, and correctly, to changes in the composition of the analyte. A large number of sensors could be integrated in a MEMS devices opening the potential of a high speed, low cost, miniature device.

Description of the Invention's Preferred Embodiment Number 5

FIG. 9 shows an innovative embodiment of the invention that provides the stopped flow advantages of making an isolated sample quantity available for scanning while addresses the contamination issue troubling this mode of operation. Analyte enters at inlet 100 where after the flow is split into a left leg 101 and a right leg 102. Both legs enter the main cell body 103 at opposite ends. Leg 101 enters the into the cavity around the foot of the outer electrode 105 of the pair of electrodes that constitutes the coaxial conductivity sensor. Leg 102 enters the cavity around the foot of the inner electrode 106. Outer electrode 105 has a hollow cylindrical drilled out space at its extremity that encloses the cylindrical top of electrode 106. The capacity for the conductivity measurement is formed by the inner wall of the hollow cylindrical space of electrode 105 and the facing outer wall of the cylindrical top of electrode 106. Electrode 105 has, e.g., three flow passage holes drilled perpendicular to its longitudinal axis in the thin walled part just bordering the solid part. This embodiment number 5 isolates a stagnant flow contained in the just described space of the capacity by opening simultaneously both valves 109 and 110. These valves are connected at opposite positions on the cylindrical main cell body 103 of the entrance points of respectively leg 101 and 102 on the main cell body 103. Tubing pieces 107 and 108 constitute respectively the actual connections between the valves and cell body 103. Upstream of each valve is a teed off small diameter tubing; 111 for valve 109 and 112 for valve 110. The other ends of tubing 111 and 112 are teed into conduit 113 that connects to the outlet 114. The outlets of valve 109 and 110 equally connect to outlet 114.
In this mode of operation, contamination emitting from the insulation 104 a at the foot of electrode 105 and similarly, the insulation 104 b at the foot of electrode 106, will not build up but will be dragged away from the volume of trapped analyte in the measurement area. Closing only one of the valves, say 109, will create a flow from the cavity at the foot of electrode 105 through the measurement area toward the cavity at the foot of electrode 106 continuing toward open valve 110 and the outlet 114. Contaminant buildup in the now small stagnant flow area just upstream of closed valve 109 will have to move counter a small flow in tubing 107 in order to contribute to the measurement. This small flow moves from the cavity around the foot of electrode 105 toward tubing 111 through which it will exit. If valve 110 would have been closed instead of 109, then a flow would have been create from the cavity at the foot of electrode 106 through the measurement area toward the cavity at the foot of electrode 105 continuing toward open valve 109 and the outlet 114. Contaminant buildup in the now small stagnant flow area just upstream of closed valve 110 will have to move counter a small flow in tubing 108 in order to contribute to the measurement. This last small flow moves from the cavity around the foot of electrode 106 to tubing 111 through which it will exit. These on valve open, one valve closed mode of operation allow to replace the analyte in the measurement area by new analyte. The axis of cylindrical cell body 103 might have to be secured in a horizontal position to avoid perturbing effects from gravity.
Varying the temperature of a trapped analyte in this preferred embodiment can be done by taking away from or sending heat into main cell body 103 by means of a cooling or heating provision. This provision can transport heat by direct contact with cell body 103 but also by using the stream of fluid passing through cell body 103 as its means of heat transportation, see preferred embodiment number 8 hereunder.
It should be noted that choosing valves with minimal flow restriction makes that the two discussed cavities around the foot of each electrode are basically interconnected through large diameter tubing downstream of the opened valves. This makes that the cavities will be at the same pressure and the trapped volume will not flow one way or the other.

Description of the Invention's Preferred Embodiment Number 6

FIG. 10 shows the same setup as FIG. 9 but the right leg of the tee at inlet 100 is now replaces by a quartz tubing spiral around a UV lamp. Moreover, flow restrictions 121 and 122, respectively for the left and the right leg of this tee, are positioned at the points of entrance of the legs into cell body 103. Most of the pressure drop will take place over these restriction thus taking away effects of the asymmetry in the legs of the tee. Now, opening valve 109 and closing 110 will flush the measuring area of the capacity with oxidized sample, provided that the UV lamp is on. Opening now both valves will trap this oxidized sample in the measurement area. Alternatively, opening valve 110 and closing 109 will flush the measuring area of the capacity with non-oxidized sample, even when the lamp is still on. Opening now both valves will trap this non-oxidized sample in the measurement area. Preferred embodiment 6 can analyze species in a non-oxidized, regular, analyte as well as the additional species created by the oxidation.
To preserve the symmetry in the tee at inlet 100, both legs could be equipped with a quartz spiral around a UV lamp while operating such unit with one lamp on and one lamp off.

Description of the Invention's Preferred Embodiment Number 7

FIG. 11 shows preferred embodiment 7 which contains a sampling manifold equipped with a dual coil heat exchanger 133, consisting of a spiraled inner tubing within an outer tubing. The outer tubing is terminated by heat exchanger tees 132 and 134. Analyte entering at inlet 131 flows into this inner tubing, passes through the heat exchanger into conductivity cell housing 135 that contains conductivity/temperature sensor 136. This analyte will have exchanged heat with counter flowing analyte that passes through the outer tubing. This counter flowing analyte consists of the stream exiting the conductivity cell housing at 137 and is heated by heater 138 prior to entering the outer tubing at heat exchange tee 134. Exiting the outer tubing at heat exchange tee 132, this counter flowing analyte stream passes through flow controlling needle valve 139 to exit the manifold at outlet 130. The temperature of the analyte being measured can be varied by controlling heater 138. A cooling provision can be used to lower the temperature of the incoming analyte in order to expand the measuring range.

Description of the Invention's Preferred Embodiment Number 8

Preferred embodiment number 8 uses the sampling manifold of preferred embodiment number 7 where conductivity cell housing 135 and its sensor 136 are replaced by flow switch based stopped flow cell of preferred embodiment 5 or 6. Varying the temperature of a trapped analyte in the flow switch based stopped flow cell can now be done by varying the temperature of the analyte flow that continues to stream around the trapped volume. The intimate contact of this stream around the trapped volume with cell body 103 and the feet of the electrode bodies 105 and 106 will minimize local temperature gradients when changing the temperature over time. This will ensure a homogeneous temperature distribution in the measuring volume at any point in time.
In order to prevent bubble formation in the trapped volume that might impact the measurement the invention can start flushing the volume with the highest temperature analyte, trapping a volume and then start to measure ramping the temperature down. Bubbles are typically formed when raising the temperature which frees dissolved gases in the fluid.

Description of the Invention's Preferred Embodiment Number 9

FIG. 12 shows an exponential dilution setup allowing to scan the conductivity dependency of a single sample on two variable properties: the temperature and the mixing ratio with another fluid. This represents a scan in two dimensions with the potential of generating a wide range of precise information regarding the composition of the sample. A stream of fluid enters inlet 141, passes through isolation valve 143, enters reservoir 140 and leaves through the reservoir through isolation valve 144 to exit at outlet 142. As soon as it is decided to analyze the fluid, isolation valves 143 and 144 are closed to seal a representative analyte volume in the reservoir. At that point in time, valve 146 is opened to allow a flow of mixing fluid to enter the reservoir 140 through conduit 146. Whenever a flow of mixing fluid enters the sealed reservoir 140, a similarly sized flow of analyte/mixing fluid mixture will leave the reservoir through analysis cell 147 and its valve 1 a to exit through outlet 148. Measuring or controlling the flowrate F of this last flow together with the knowledge of the volume of the reservoir 140 enables to calculate the mixing ratio as it evolves over time. For example, the evolution of a concentration C(t) of a component in the fluid exiting the reservoir will be:
C(t)=C(0)*exp(−t*F/V)
where C(0) is the concentration of the component in the analyte, and where the mixing fluid contains zero concentration of the component while the flowrate F is fixed over time.
The mixing fluid can be a strong acid or base which enables to take species properties into account that show more characteristic behavior at extreme pH values.

Description of the Invention's Preferred Embodiment Number 10

The accuracy of the measurement of the conductivity's temperature dependency could be compromised when it involves a ramping up or down of the temperature. The actual water temperature might trail the temperature at the position of the temperature probe or vise versa. This could, e.g., be the case when the temperature probe is attached to the cell's housing and contacts the sample water only indirectly. This preferred embodiment maps such relationship by performing an analysis on a known sample. Looking at the conductivity versus temperature plots show typically monotonously rising curves which enable to define a one on one relationship between a specific conductivity and a specific temperature. Taking a known sample, e.g., containing only a known amount of carbonate, allows to link a conductivity to a temperature. This way, mentioned trailing of the actual analyte temperature with the temperature at the temperature sensor can be determined. A model can now be made, e.g., assigning a certain “inertia” to the “thermal mass” of the cell, to predict the correct analyte temperature from a series of prior temperature measurements made with the temperature sensor. It can be expected that the underlying phenomena leading to the here described effects will be very stable and repeatable. Mentioned correction can also be made using a lookup table or equivalent analytical expression.

Description of the Invention's Preferred Embodiment Number 11

Superimposed on the conductivity signal will be effects from the UV lamp. Effects so far discussed are typically the irreversible breaking down and oxidizing of species. U.S. Pat. No. 4,666,860's FIG. 13 shows a relative fast reversible conductivity effect where turning the UV lamp on results in a temporary rise in conductivity that disappears again when the UV light is turned off. Such effects might take place immediately after the extinction of the UV lamp at the onset of the series of measurements to determine the temperature dependency of the conductivity of an oxidized sample according to the current invention disclosure. As these UV related reversible effects are relatively fast compared to the thermal cool down of the sample, this preferred embodiment introduces a wait period at the beginning of stage 4 in FIG. 13 prior to the beginning of the data acquisition for the temperature dependency. Alternatively, this preferred embodiment can subtract the reversible UV effect once it is empirically determined and features sufficient repeatability.

Description of the Invention's Preferred Embodiment Number 12

Prolonged, intense, high energetic UV irradiation and the oxidation it provokes will decompose complex species, such as organic species, in a water sample into fragments that will ultimately recombine into molecular and ionic species of the most simple, typically lowest energy, chemical forms. The carbon, nitrogen, chlorine atoms etc. that constituted the original species in the sample prior to the UV irradiation, will end up in the form of only a limited number of mentioned simple species such as CO₂, HCO₃ ⁻, CO₃ ²⁻, NH₄ ⁺, NH₃, NO₃ ⁻, Cl⁻, etc.
This embodiment applies UV light for the above purpose as its sample preparation step 1, but does not rely on the completeness of the transformation of complex species into simple molecular or ionic species. It can include intermediate transformation products to the set of sample features used for the curve fitting and takes their atomic composition into account when reporting the analysis result.

Description of the Invention's Preferred Embodiment Number 13

This embodiment provides additional means to check the degree of oxidation of the analyte by the UV irradiation. During the oxidation large organic molecules are little by little broken down in smaller pieces. If the oxidation is not complete, larger ions will be present with a corresponding relatively low ion mobility compared to the simplest, smallest form of ions. Matching the temperature dependency of such not fully oxidized analyte with calculated conductivities of an analyte consisting only of simple fully oxidized species will lead to a poor fit. In this embodiment, the curve fitting procedure provides a number for the quality of the fit. A poor number for the fit quality will be an indicator that the sample is not fully oxidized. Detecting such incomplete oxidation could be followed up by slowing down the stream of analyte thus increasing the exposure time to UV.
Summary, Ramifications, and Scope
Accordingly, the reader will see that the invention can create a device or method providing an automated stream of information on hard to determine parameters by scanning easy to measuring parameters while circumventing potentially difficult calibration issues. In its application on water analysis, the measured trace concentrations of ionic contaminants are certainly considered hard to determine while measuring the water conductivity as a function of temperature is much easier. Summarizing this application, the invention measures the temperature and/or dilution ratio dependency of the electrical conductivity of a sample and compares this with calculated conductivity dependencies for various possible sample compositions. The calculation includes the laws of chemistry governing the dependencies including common ion effects that cause non-linear behavior of the conductivity as a function of the concentration of species. The comparison uses a non-linear curve fitting routine such as that of Levenberg-Marquardt to determine the best fit in terms of lowest sum of the squares of the differences between measured and calculated curves. The sample composition with the best fit is then presented as the analysis result.
The invention has various sampling configurations typically trading off speed of response and accuracy of the analysis. Non conductive organic contaminants in water can also be analyzed this way by converting them into basic conductive inorganic species by UV generated oxidation.
The acquired knowledge of the analytical composition of a sample enables also precise calculation of the pH, temperature compensated conductivity values, and calibration of the sensors.
Although the description above contains many specificities, these should not be construed as limiting the scope of the invention but as merely providing illustrations of some of the presently preferred embodiments of this invention. For example, apart from analysis, wider applications of are typically in the field of monitoring chemical or mechanical processes and equipment, machines, engines or even vehicles. To picture the wideness of the scope, based on a mathematical model describing the collaborative functioning of the parts of a car given a number of semi-empirical determined parameters, the invention enables to construct an automated provision that determines the current viscosity of the engine oil by monitoring the engine temperature as a function of the rpm number, speedometer reading and outside temperature.
Thus the scope of the invention should be determined by the appended claims and their legal equivalents, rather than by the examples given.

Claims

1. An instrument, device, method or procedure to determine one or more features, properties or parameters, hereinafter called analyzed feature, of an object, sample or process, hereinafter called object, where the object has another feature, property or parameter, hereinafter called the characteristic feature that is measurable as a function of yet another feature, property, or parameter, of the object hereinafter called the scanned feature, comprising the following

(a) a mathematical model that given a value of the object's analyzed feature and given a value of the object's scanned feature calculates the corresponding value of the object's characteristic feature, and

(b) measurement means measuring the object's characteristic feature, and

(c) variable entity determination means to measure or to control the value of the object's scanned feature, and

(d) scanning means to actively or passively vary the object's scanned feature, and

(e) object preparation means to set the scope of the analyzed feature, or to adapt the object to the characteristics of the scanning means, and

(f) data collection means that, in conjunction with the scanning means, collects data from the measuring means and the variable entity determination means regarding the relationship between the object's characteristic feature and object's scanned feature, and

(g) data interpretation means determining the most likely object's analyzed feature based on the comparison between the relationship's data from the data collection means and calculated relationships based on the said mathematical model where the calculated relationships are given candidate analyzed feature values by a non-linear regression or curve fitting algorithm such as that of Levenberg-Marquardt to find the candidate analyzed feature value that provides the best match in the comparison.

2. An instrument, device, method or procedure of claim 1 wherein the best matching candidate analyzed feature value is frequently updated using ongoing scanning, data acquisition and interpretation with means that takes older data less into account when doing the comparisons.

3. An instrument, device, method or procedure of claim 2 wherein upon startup or otherwise the data interpretation means can activate a wide scan means generating a grid of initial analyzed feature values with whom a series of runs of a non-linear regression or curve fitting algorithm such as that of Levenberg-Marquardt is started in order to distinguish the overall best fit out of a possible multiple local best fitting analyzed feature values.

4. An instrument, device, method or procedure of claim 3 wherein a quality of the fit value is generated by the data interpretation means that is used as a decision criteria to activate said wide scan means.

5. An instrument, device, method or procedure of claim 1 wherein the best matching candidate analyzed feature value is generated as an automated operation on a given set of recently acquired or stored data.

6. An instrument, device, method or procedure of claim 5 wherein upon startup or otherwise the data interpretation means can activate a wide scan means generating a grid of initial analyzed feature values with whom a series of runs of a non-linear regression or curve fitting algorithm such as that of Levenberg-Marquardt is started in order to distinguish the overall best fit out of a possible multiple local best fitting analyzed feature values.

7. An instrument, device, method or procedure of claim 6 wherein a quality of the fit value is generated by the data interpretation means that is used as a decision criteria to activate said wide scan means.

8. An instrument, device, method or procedure of claim 1 where the analyzed feature include offset or span correction parameters for sensors involved in the measurement means or involved in the variable entity determination means.

9. An instrument, device, method or procedure to determine chemical species selected from the group consisting of ions, dissolved gases and neutral species, hereinafter called the composition, present in analytes selected from the group consisting of aquaous solutions, liquids and fluids, hereinafter called the analyte, whereby the analyte features an electrical conductivity property that is measurable as a function of a scannable parameter selected from the group consisting of the analyte's temperature and the degree by which the analyte is mixed with another fluid, hereinafter called the scannable parameter, comprising the following

(a) model calculation means that given values of a composition and given an analyte temperature produces the corresponding calculated value of an analyte's conductivity, and

(b) measurement means measuring the analyte's conductivity, and

(c) scannable parameter determination means for the determination of the value of the analyte's scannable parameter, where determination is selected from the group measurement, derivation and control, and

(d) scanning means to actively or passively vary the value of the analyte's scannable parameter, and

(e) analyte preparation means to selectively change the type of chemical species that contribute to the analyte's conductivity or to adapt the analyte to the characteristics of the scanning means, and

(f) data collection means that in conjunction with the scanning means collects data from the measuring means and the scannable parameter determination means regarding the relationship between the analyte's conductivity and the analyte's scannable parameter, and

(g) data interpretation means determining the analyte's composition based on the comparison between the relationship's data from the data collection means and relationships calculated by the mathematical model where the calculated relationships are given candidate analyte's composition values by a non-linear regression or curve fitting algorithm such as that of Levenberg-Marquardt to find the candidate analyte's composition value that provides the best match in the comparison.

10. An instrument, device, method or procedure of claim 9 wherein the analyte preparation means selectively changes the type of chemical species that contribute to the analyte's conductivity by irradiating the analyte with UV light converting non conductive species such as organic molecules into other species from which some of them conductive.

11. An instrument, device, method or procedure of claim 9 wherein the analyte preparation means adapt the analyte to the characteristics of the scanning means by isolating, stopping or stabilizing part of the analyte stream so that its analyte's composition is no longer subject to further changes while it is being measured, other than changes resulting from the scanning means or resulting from other analyte preparation means, while its conductivity is measured by the measuring means.

12. An instrument, device, method or procedure of claim 11 where the actual isolating, stopping or stabilizing of a part of the analyte stream takes place by analyte streams redirecting means that flush areas suspect of building up contamination with bypassed, non measured, analyte thus preventing their interfering with the measurement.

13. An instrument, device, method or procedure of claim 10 wherein the analyte preparation means adapt the analyte to the characteristics of the scanning means by isolating, stopping or stabilizing part of the analyte stream so that its analyte's composition is no longer subject to further changes, other than those resulting from the scanning means or resulting from UV light irradiation, while its conductivity is measured by the measuring means.

14. An instrument, device, method or procedure of claim 9 wherein the analyte is flowing while the analyte's conductivity is measured by the measurement means and where the measuring means can consist of more than one conductivity sensor or an array of miniaturized conductivity sensors.

15. An instrument, device, method or procedure of claim 10 wherein the analyte is flowing while the analyte's conductivity is measured by the measurement means and where the measuring means can consist of more than one conductivity sensor or an array of miniaturized conductivity sensors.

16. An method, procedure, instrument or device to generate numerical values for unknown parameters in a mathematical model describing a phenomena involving multiple known or given values for known parameters where known and unknown parameters are linked by a number of mathematically described relationships and where one still has a valid but simpler phenomena by successively leaving unknown parameters out and where an analytical solution is available for an initial simple case featuring none or only few unknown parameters consisting of the following

(a) the initialization step creating numerical values using formulas derived from the analytical solution for the initial simple case, and

(b) an iterative step that calculates numerical solutions for a certain phenomena based on the numerical solution for the same but slightly simpler phenomena featuring one unknown parameter less, and

(c) an loop step that starts with the solution from the initialization step (a) to which it adds successively new unknown parameters while solving each time the next more complex case using the iterative step (b) to end up with a solution for the original phenomena.

17. An method, procedure, instrument or device as claim 16 where the phenomena is the chemistry taking place in aquaous solutions and where the known parameters are the total concentrations of species added to a pure water independent of the ionic or molecular forms that will end up having in the solution and where said ionic or molecular forms are the unknown parameters and where the mathematical model is based on the laws of chemistry associated with aquaous solutions.

18. An method, procedure, instrument or device as claim 17 aking activity coefficients into account build into the mathematical model calculation to reflect effects taking place when dealing with higher concentrations of species.

19. An method, procedure, instrument or device of claim 17 wherein the involved pH range is such that certain strong acids or bases can be considered fully ionized and are treated mathematically that way in the mathematical model.