Sensor arrangement and method for determining orthophosphate content of a liquid

1. A method for determining the orthophosphate content of a liquid, comprising the steps of:

contacting the liquid with an ion selective dihydrogen phosphate sensor, including an ion selective dihydrogen phosphate electrode, which thereupon generates a first measurement signal;

contacting the liquid with an ion selective hydrogen phosphate sensor, including an ion selective hydrogen phosphate electrode, which thereupon generates a second measurement signal;

registering the first measurement signal to an electronic control unit configured to receive and to digitize measurement signals generated by ion selective sensors;

registering the second measurement signal to the control unit; and

determining the orthophosphate content of the liquid based on the first and the second measurement signals using the control unit, wherein:

a dihydrogen phosphate concentration is determined from the first measurement signal, and a hydrogen phosphate concentration is determined from the second measurement signal;

the dihydrogen phosphate concentration determined from the first measurement signal and the hydrogen phosphate concentration determined from the second measurement signal are corrected by determining a corrected dihydrogen phosphate concentration using a cross-sensitivity of the dihydrogen phosphate electrode to hydrogen phosphate present in the liquid and by determining a corrected hydrogen phosphate concentration using a cross-sensitivity of the hydrogen phosphate electrode to dihydrogen phosphate present in the liquid; and

the corrected dihydrogen phosphate concentration and the corrected hydrogen phosphate concentration are determined from the concentrations determined based on the measurement signals with application of selectivity coefficients of the dihydrogen phosphate electrode and the hydrogen phosphate electrode, based on a system of equations comprising:

c 1 =c DHP +( k 1 c MHP ) 1/2

and

c 2 =c MHP +( k 2 c DHP ) 2 ,

wherein c 1 is the dihydrogen phosphate concentration determined from the first measurement signal, c 2 is the hydrogen phosphate concentration determined from the second measurement signal, k 1 is the selectivity coefficient of the dihydrogen phosphate electrode, and k 2 is the selectivity coefficient of the hydrogen phosphate electrode.

2. The method as claimed in claim 1 , wherein:

the corrected dihydrogen phosphate concentration is ascertained based on the equation:

c

DHP

=

c

1

-

k

1

⁡

(

k

1

⁢

k

2

2

+

1

)

⁢

c

2

-

k

1

⁢

k

2

2

⁢

c

1

2

k

1

⁢

k

2

2

+

1

,

wherein c 1 is the dihydrogen phosphate concentration ascertained from said first measurement signal, c 2 is the hydrogen phosphate concentration ascertained from said second measurement signal, k 1 is the selectivity coefficient of the dihydrogen phosphate electrode, and k 2 is the selectivity coefficient of the hydrogen phosphate electrode; and

based on the corrected dihydrogen phosphate concentration, a corrected hydrogen phosphate concentration is calculated based on the equation:

c MHP =c 2 −( k 2 c DHP ) 2 .

3. The method as claimed in claim 1 , wherein:

the corrected hydrogen phosphate concentration is ascertained based on the equation:

c

MHP

=

c

2

-

k

2

2

(

c

1

-

k

1

⁡

(

k

1

⁢

k

2

2

+

1

)

⁢

c

2

-

k

1

⁢

k

2

2

⁢

c

1

2

k

1

⁢

k

2

2

+

1

)

2

,

wherein c 1 is the dihydrogen phosphate concentration ascertained from said first measurement signal, c 2 is the hydrogen phosphate concentration ascertained from said second measurement signal, k 1 is the selectivity coefficient of the dihydrogen phosphate electrode, and k 2 is the selectivity coefficient of the hydrogen phosphate electrode; and

based on the corrected hydrogen phosphate concentration, a corrected dihydrogen phosphate concentration is calculated based on the equation:

c DHP =c 1 −( k 1 c DHP ) 1/2 .

4. The method as claimed in claim 1 , wherein:

the orthophosphate concentration is determined by adding the corrected dihydrogen phosphate concentration and the corrected hydrogen phosphate concentration.

5. The method as claimed in claim 1 , wherein:

the liquid is an aqueous liquid.

6. The method as claimed in claim 1 , wherein:

the liquid has a pH-value between 5 and 10.

7. The method as claimed in claim 1 , wherein:

the liquid is waste water treated in an industrial or municipal clarification plant.

8. A method for determining the orthophosphate content of a liquid, comprising the steps of:

contacting the liquid with an ion selective dihydrogen phosphate sensor, including an ion selective dihydrogen phosphate electrode, which thereupon generates a first measurement signal;

contacting the liquid with an ion selective hydrogen phosphate sensor, including an ion selective hydrogen phosphate electrode, which thereupon generates a second measurement signal;

registering the first measurement signal to an electronic control unit configured to receive and to digitize measurement signals generated by ion selective sensors;

registering the second measurement signal to the control unit;

determining a dihydrogen phosphate concentration and a hydrogen phosphate concentration from the first and second measurement signals, respectively;

correcting the dihydrogen phosphate concentration for a cross-sensitivity of the dihydrogen phosphate electrode to hydrogen phosphate and thereby ascertaining a corrected dihydrogen phosphate concentration using the control unit;

correcting the hydrogen phosphate concentration for a cross-sensitivity of the hydrogen phosphate electrode to dihydrogen phosphate and thereby ascertaining a corrected hydrogen phosphate concentration using the control unit; and

ascertaining the orthophosphate content of the liquid as a sum of the corrected dihydrogen phosphate concentration and the corrected hydrogen phosphate concentration using the control unit, wherein:

the corrected dihydrogen phosphate concentration and the corrected hydrogen phosphate concentration are determined from the concentrations determined based on the measurement signals with application of selectivity coefficients of the dihydrogen phosphate electrode and the hydrogen phosphate electrode, based on a system of equations comprising:

c 1 =c DHP +( k 1 c MHP ) 1/2

and

c 2 =c MHP +( k 2 c DHP ) 2 ,

wherein c 1 is the dihydrogen phosphate concentration determined from the first measurement signal, c 2 is the hydrogen phosphate concentration determined from the second measurement signal, k 1 is the selectivity coefficient of the dihydrogen phosphate electrode, and k 2 is the selectivity coefficient of the hydrogen phosphate electrode.

9. The method as claimed in claim 8 , wherein:

the liquid is waste water treated in an industrial or municipal clarification plant.

10. A method of monitoring or controlling phosphate elimination from water, phosphate reclamation from water, or water treatment in a clarification plant, comprising:

contacting the water with an ion selective dihydrogen phosphate sensor, including an ion selective dihydrogen phosphate electrode, which thereupon generates a first measurement signal;

contacting the water with an ion selective hydrogen phosphate sensor, including an ion selective hydrogen phosphate electrode, which thereupon generates a second measurement signal;

registering the first measurement signal to an electronic control unit configured to receive and to digitize measurement signals generated by ion selective sensors;

registering the second measurement signal to the control unit;

determining a dihydrogen phosphate concentration and a hydrogen phosphate concentration from the first and second measurement signals, respectively;

correcting the dihydrogen phosphate concentration for a cross-sensitivity of the dihydrogen phosphate electrode to hydrogen phosphate and ascertaining a corrected dihydrogen phosphate concentration using the control unit;

correcting the hydrogen phosphate concentration for a cross-sensitivity of the hydrogen phosphate electrode to dihydrogen phosphate and ascertaining a corrected hydrogen phosphate concentration using the control unit;

determining the orthophosphate content of the water based on the corrected dihydrogen phosphate concentration and on the corrected hydrogen phosphate concentration using the control unit; and

controlling the phosphate elimination, phosphate reclamation or water treatment in the clarification plant based on the determined orthophosphate content.