Apparatus and method for automatic congruent control of multiple boilers sharing a common feedwater line and chemical feed point

• US 5,923,571 A
• Filed: 10/06/1997
• Issued: 07/13/1999
• Est. Priority Date: 10/11/1994
• Status: Expired due to Term

• Current Assignee: BetzDearborn Inc. (Veolia Environnement SA)
• Original Assignee: BetzDearborn Inc. (Veolia Environnement SA)
• Inventors: Muccitelli, John A., Gunther, John C., Chen, Haiwen
• Primary Examiner(s): WACHSMAN, HAL D
• Application Number:
  US08/944,921
• Time in Patent Office: 645 Days
• Field of Search: 702/22, 702/23, 702/27, 702/30-32, 702/45, 702/50, 702/55, 702/176, 702/177, 702/183, 364/528.01, 364/528.02, 364/528.09, 364/528.17, 364/528.2, 364/528.41, 364/151, 364/152, 364/148.01-148.09, 364/148.1, 364/149 , 364/150, 364/153, 364/164-166, 364/578, 364/157, 364/132, 364/159, 422/62, 422/12, 422/14, 422/16, 422/110, 422/111, 422/81, 436/55, 436/56, 436/50, 376/216, 376/217, 237/8 A, 210/743, 210/742, 210/739, 210/96.1, 210/103, 210/311-313, 210/85-89, 706/906, 706/907, 706/914, 706/915
• US Class Current: 700/267
• CPC Class Codes: C02F 5/025 Hot-water softening devices
• CPC Class Codes: G01N 33/18 Water
• CPC Class Codes: G05D 21/02 characterised by the use of electric means

Abstract

Two control methods and systems for automatically achieving and maintaining a desired sodium/phosphate ratio and phosphate concentration of the boiler waters in a plurality of parallel industrial boilers linked by a common feedwater line for minimizing corrosion. The first control system uses an adaptive controller that models the boilers which enables the system to predict boiler pH and phosphate concentrations at any future time given the feed rates, feed concentrations of high and low sodium/phosphate stocks, blowdown rate, mass of the boiler water, initial boiler phosphate concentration and initial pH. Once these future concentrations are determined, the controller then determines a common normalized control (target) region among all the boilers and feed rates that will drive at least one of the boilers into that region in the least amount of time. Subsequent iterations of feed rates are made based on updated boiler water concentrations to drive all of the boiler waters into that target region. The second control system monitors a maximum cycle boiler ratio to keep the boiler waters within the phosphate control range of the system. This arrangement allows for the control of sodium by switching between the high and low ratio sodium/phosphate stocks based on the average sodium-to-phosphate ratio among all the boilers with respect to a desired average predetermined sodium-to-phosphate ratio.

Claims

1. A method for controlling at least two interdependent chemicals in the fluids of at least two continuously stirred tank reactors (CSTRs) having respective blowdown flows and steam rate flows defining respective cycles for each of said CSTRs, said at least two interdependent chemicals being fed to said fluids through a common feedwater to each of said at least two CSTRs, said method comprising the steps of:

(a) establishing a respective mathematical model of each of said CSTRs;

(b) monitoring the concentration of one of said at least two interdependent chemicals in each of the fluids, the temperature at which the pH is measured in each of the fluids, the respective blowdown flow and the respective steam rate flow;

(c) updating the models based on the concentration of said one of said at least two interdependent chemicals in each of the fluids, the pH of each of the fluids, the temperature at which the pH is measured in each of the fluids, the respective blowdown flow and the respective steam rate flow;

(d) defining a respective target region of said at least two interdependent chemicals in said respective continuously stirred tank reactors and wherein said respective target regions are scaled according to the respective cycles, said respective target regions establishing a state of congruency for each of the fluids;

(e) providing a feedstream of a high-pH fluid treatment material comprising a mixture of said at least two interdependent chemicals and a feedstream of a low-pH fluid treatment material comprising a mixture of said at least two interdependent chemicals for feeding, at respective feed rates, to the fluids; and

(f) developing an optimum feed rate program for controlling said feedstreams to automatically minimize the time that said at least two interdependent chemicals in the fluids spend outside of a common normalized target region formed by the intersection of said respective target regions.

2. The method of claim 1 wherein each of said fluids has associated therewith a respective pumpable region in a CSTR state space that defines all reachable concentrations of said at least two interdependent chemicals in the respective fluid and including therein said respective target region for defining congruency of said at least two interdependent chemicals in said respective pumpable region, said respective pumpable region also being scaled according to said respective cycles, said step of developing an optimum feed rate program comprising overlaying said respective pumpable regions and said respective target regions to define a single pumpable region and to establish said common normalized target region defined by the intersection of said overlayed respective target regions.

3. The method of claim 2 wherein said fluids comprise respective current concentrations of said at least two interdependent chemicals and wherein said step of developing an optimum feed rate program comprises the steps of:

(a) establishing a respective region formed by the endpoints of all feed trajectories that move said respective current concentrations of said fluids into said common normalized target region;

(b) selecting a new region formed by the intersection of said respective regions, said new region formed by the intersection of said respective regions defining a common normalized pumpable region.

4. The method of claim 3 wherein said common normalized target region comprises vertices, including extreme vertices, and edges and wherein said step of establishing a respective region comprises forming a respective region defined by feed trajectories that originate from said current concentrations and intersect said extreme vertices for each of said respective current concentrations of said fluids.

5. The method of claim 4 wherein said step of developing an optimum feed rate program further comprises the step of evaluating, for each of said continuously stirred tank reactors, sets of feed rate trajectories between the current concentrations of said at least two interdependent chemicals and said common normalized target region to determine the time required to move said current concentrations into said common normalized target region.

6. The method of claim 5 wherein said common normalized pumpable region comprises vertices and edges, together which define a common normalized pumpable region perimeter, and wherein said step of evaluating comprises the steps of:

(a) determining the time associated with driving the current concentrations of said at least two interdependent chemicals in each of said fluids along a first set of feed rate trajectories formed between the current concentrations and said vertices of said common normalized pumpable region;

(b) determining the time associated with driving the current concentrations of said at least two interdependent chemicals in each of said fluids along a second set of feed rate trajectories formed between said current concentrations and said common normalized target region vertices, said second set of feed rates being projected until they intersect said common normalized pumpable region perimeter, if at all, to define a third set of feed rate trajectories; and

(c) selecting one feed rate trajectory, from all of said first and third sets of feed rate trajectories from each of said fluids, that requires the least amount of time for at least one fluid to reach an edge of said common normalized target region.

7. The method of claim 6 wherein said feedstream of a high-pH fluid treatment material comprising a mixture of said at least two interdependent chemicals defines a first feedstream and wherein said feedstream of a low-pH fluid treatment material comprising a mixture of said at least two interdependent chemicals defines a second feedstream and wherein said selected one feed rate trajectory comprises an endpoint and wherein said method further comprises the step of determining how long to feed said first and second feedstreams at said selected one feed rate trajectory, said step of determining how long to feed said first and second feedstreams comprising the steps of:

(a) for each of said at least two CSTR fluids, establishing a respective feed rate trajectory defined by a line from said respective current concentrations of said at least two interdependent chemicals to the endpoint of said selected one feed rate trajectory;

(b) for each of said at least two CSTR fluids, determining the point at which said respective feed rate trajectory intersects an edge of said common normalized target region and determining the time associated with moving said current concentrations to said point, said intersected edge being a common normalized target region edge different from said edge reached by said at least one fluid in the least amount of time; and

(c) selecting the minimum of those times associated with moving said current concentrations to said point.

8. The method of claim 7 further comprising the step of feeding said first and second feedstreams at said selected one feed rate trajectory for an amount of time corresponding to said selected minimum of those times associated with moving said current concentrations to said point.

9. The method of claim 8 wherein each of said CSTR state spaces are updated based on said feeding said first and second feedstreams at said selected one feed rate trajectory for said selected minimum of those times associated with moving said current concentrations to said point.

10. The method of claim 9 further comprising the steps of:

(a) establishing a new common normalized target region that is nested within said common normalized target region; and

(b) repeating the steps of selecting one feed rate trajectory that requires the least amount of time for at least one fluid to reach an edge of said new common normalized target region; and

(c) repeating the steps for determining how long to feed said first and second feedstreams.

11. The method of claim 7 further comprising the step of feeding said first and second feedstream at said selected one feed rate trajectory for an amount of time corresponding to the time it takes for new data to be available, said data being defined as said concentration of said one of said at least two interdependent chemicals in the fluids, said pH of said fluids, said temperature at which the pH is measured, said blowdown flow and said steam rate flow.

12. The method of claim 11 wherein each of said fluid state spaces are updated based on said feeding said first and second feedstreams at said selected one feed rate trajectory for said amount of time corresponding to the time it takes for new data to be available.

13. The method of claim 11 wherein a new common normalized target region is recomputed based on said new data.

14. The method of claim 2 wherein said feedstream of a high-pH fluid treatment material comprising a mixture of said at least two interdependent chemicals defines a first feedstream and wherein said feedstream of a low-pH fluid treatment material comprising a mixture of said at least two interdependent chemicals defines a second feedstream and wherein said fluids comprise respective current concentrations of said at least two interdependent chemicals and wherein said step of developing an optimum feed rate program comprises the steps of:

(a) evaluating, for each of said CSTRs, sets of feed rate trajectories between the current concentrations of said at least two interdependent chemicals and said common normalized target region to determine the time required to move said current concentrations into said common normalized target region;

(b) selecting that feed rate trajectory that moves at least one fluid current concentrations into said common normalized target region in the least amount of time; and

(c) feeding said first and second feedstreams at said selected feed rate trajectory.

15. The method of claim 14 further comprising the steps of:

(a) establishing a new common normalized target region that is nested within said common normalized target region; and

(b) evaluating, for each of said CSTRs, sets of feed rate trajectories between the current concentrations of said at least two interdependent chemicals and said new common normalized target region to determine the time required to move said current concentrations into said new common normalized target region;

(b) selecting a feed rate trajectory that moves at least one fluid current concentrations into said new common normalized target region in the least amount of time; and

(c) feeding said first and second feedstreams at said selected feed rate trajectory.

16. The method of claim 1 wherein each of said CSTRs is an industrial boiler having a boiler fluid.

17. The method of claim 16 wherein said one of said at least two interdependent chemicals is phosphate.

18. The method of claim 17 wherein said one of said at least two interdependent chemicals is sodium.

19. The method of claim 18 wherein said method further includes the step of estimating the blowdown flow.

20. The method of claim 19 wherein said method further includes the steps of calculating the phosphate concentration and the sodium concentration in the boiler fluid.

21. The method of claim 20 wherein said method further includes the step of estimating a feedwater contaminant ingress.

22. The method of claim 21 wherein said steps of estimating a blowdown flow and a feedwater contaminant ingress are based on a series of phosphate and pH measurements of the boiler fluid wherein said method uses small sample intervals.

23. The method of claim 1 wherein said method further includes a step that accounts for dead time in each of the continuously stirred tank reactors.

24. The method of claim 1 wherein said method further comprises the step of controlling the blowdown flow of each of said CSTRs.

25. An automatic control system for controlling at least two interdependent chemicals in the fluids of at least two continuously stirred tank reactors (CSTRs) linked in parallel by a common feedwater line and wherein each CSTR includes a respective blowdown flow and steam rate flow that define respective cycles for each of said CSTRs and wherein each CSTR has associated therewith a respective target region of said at least two interdependent chemicals, said respective target regions being scaled according to the respective cycles of said CSTRs, said control system comprising:

input means for receipt of fluid parameters and control means responsive to said input means;

said control means using non-proportional control for automatically minimizing the time that said at least two interdependent chemicals in the fluids spend outside of a common normalized target region formed by the intersection of said respective target regions of said at least two CSTRs;

wherein one of said fluid parameters comprises the pH of the fluid and wherein said input means comprises means for determining the pH value of each of the fluids; and

wherein said control means comprises a first feedstream and a second feedstream for feeding first and second fluid treatment materials, respectively, to the common feedwater line at respectively determined feed rates, said first material comprising a mixture of sodium and phosphate having a first predetermined sodium-to-phosphate ratio and said second material comprising a mixture of sodium and phosphate having a second predetermined sodium-to-phosphate ratio.

26. The control system of claim 25 wherein said control means further comprises an adaptive controller, said adaptive controller modeling of each of said at least two CSTRs.

27. The control system of claim 26 wherein said control means further comprises monitoring means for monitoring the concentration of said at least two interdependent chemicals in said fluids, the temperature at which the pH is measured, the blowdown flow and the steam rate flow, said monitoring means being coupled to said adaptive controller in order to update said modeling of each of said at least two CSTRs, the concentration of said at least two interdependent chemicals in said fluids, the temperature at which the pH is measured, the blowdown flow and the steam rate flow being defined as data.

28. The control system of claim 27 wherein said adaptive controller generates said respective target regions of congruency! in a CSTR state space for each of said at least two CSTRs.

29. The control system of claim 28 wherein said adaptive controller overlays said respective target regions to generate said common normalized target region.

30. The control system of claim 29 wherein each fluid comprises a current concentration for each of said at least two interdependent chemicals and wherein said adaptive controller analyzes all feed rate trajectories of said first and second feedstreams that will drive said current concentrations in each of said fluids from said current concentrations to concentrations within said common normalized target region in said CSTR state space, said analyzation determining a respective region for each of said fluids that is formed by the endpoints of all said feed rate trajectories.

31. The control system of claim 30 wherein said adaptive controller selects that region in said CSTR state space that is formed by the intersection of said respective regions, said selected region forming a common normalized pumpable region that defines all reachable concentrations of said at least two interdependent chemicals among said at least two CSTR fluids, said common normalized pumpable region comprising a first set of edges and a first set of vertices.

32. The control system of claim 31 wherein said common normalized target region comprises a second set of vertices and second set of edges, said adaptive controller determining for each of said CSTRs:

(a) the time associated with driving said current concentrations of said at least two interdependent chemicals along a first set of feed rate trajectories formed between said current concentrations and said second set of vertices; and

(b) the time associated with driving said current concentrations of said at least two interdependent chemicals along a second set of feed rate trajectories formed between said current concentrations and said second set of vertices, said second set of feed rate trajectories being projected until they intersect said first set of edges of said common normalized pumpable region to define a third set of feed rate trajectories, said adaptive controller selecting one feed rate trajectory from all of said first and third sets of feed rate trajectories that requires the least amount of time for at least one fluid to reach one of said second set of edges.

33. The control system of claim 32 wherein said adaptive controller calculates how long to feed said first and second feedstreams at said selected feedrate trajectory, said adaptive controller:

(a) establishing, for the other CSTRs of said at least two CSTRs whose current concentrations have not reached one of said second set of edges, a respective feedrate trajectory between said current concentrations and said selected feedrate trajectory;

(b) said adaptive controller determining, for the other CSTRs whose current concentrations have not reached one of said second set of edges, the point at which each of said respective feedrate trajectories intersects one of said second set of edges and determining the time associated with moving said current concentrations to said point, said intersected edge being a common normalized target region edge different from said edge of said common normalized target region reached by said at least one CSTR fluid in the least amount of time, said adaptive controller selecting the minimum of those times associated with moving said current concentrations to said point and feeding said first and second feedstreams at said selected feedrates for said selected minimum time.

34. The control system of claim 33 wherein said monitoring means updates said fluid state spaces for each of said CSTRs based on said adaptive controller feeding said first and second feedstreams at said selected feedrate trajectories for said selected minimum time.

35. The control system of claim 34 wherein said adaptive controller establishes a new common normalized target region that is nested within said common normalized target region and wherein said adaptive controller determines one feedrate trajectory that requires the least amount of time for at least one of said CSTRs to reach an edge of said new common normalized target region and determines how long to feed said first and second feedstreams at said one feedrate trajectory.

36. The control system of claim 32 wherein said adaptive controller feeds said first and second feedstreams at said selected feedrates for an amount of time corresponding to the time it takes for new data to be available.

37. The control system of claim 36 wherein said monitoring means updates said CSTR state spaces for each of said CSTRs based on said adaptive controller feeding said first and second feedstreams at said selected feedrate trajectories for said time it takes for new data to be available.

38. The control system of claim 37 wherein said adaptive controller recomputes a new common normalized target region based on said new data.

39. A method for controlling the sodium-to-phosphate ratio of the fluids of at least two continuously stirred tank reactors (CSTRs) having respective blowdown flows and steam rate flows defining respective cycles for each of said at least two continuously stirred tank reactor, said fluids of said at least two CSTRs being fed a through a common feedwater line, said method comprising the steps of:

(a) providing a supply of a first sodium phosphate fluid treatment material to said common feedwater, said first sodium phosphate fluid treatment material having a first predetermined sodium-to-phosphate ratio and a first known phosphate concentration;

(b) providing a supply of a second sodium phosphate fluid treatment material to said common feedwater, said second sodium phosphate fluid treatment material having a second predetermined sodium-to-phosphate ratio and a second known phosphate concentration;

(c) measuring a fluid parameter of each of said fluids substantially continuously;

(d) determining the cycle of each of said at least two CSTRs substantially continuously;

(e) estimating the phosphate concentration in each of said fluids;

(f) determining the effective sodium in each of said fluids;

(g) determining the sodium-to-phosphate ratio in each of said fluids and identifying a maximum sodium-to-phosphate ratio and a minimum sodium-to-phosphate ratio among said fluids, said minimum and maximum sodium-to-phosphate ratios defining a first range having a first midpoint; and

(h) feeding said first sodium phosphate fluid treatment material if said first midpoint is less than or equal to a second midpoint of a predetermined ratio range of sodium-to-phosphate, or feeding said second sodium phosphate fluid treatment material if said first midpoint is greater than said second midpoint.

40. The method of claim 39 wherein said step of determining the cycle of each of said at least two CSTRs substantially continuously comprises the steps of:

(a) measuring each of said blowdown flows substantially continuously; and

(b) measuring the total feedwater flow substantially continuously.

41. The method of claim 40 wherein said step of feeding said first sodium phosphate fluid treatment material or said second sodium phosphate fluid treatment material comprises feeding said first or second sodium phosphate fluid treatment material at a rate which maintains the respective phosphate concentration of each boiler fluid between a respective predetermined upper phosphate control limit and a respective predetermined lower phosphate control limit.

42. The method of claim 41 wherein said respective predetermined upper phosphate control limits are identical and which form a first phosphate control limit, and wherein said respective predetermined lower phosphate control limits are identical and which form a second phosphate control limit.

43. The method of claim 42 wherein said step of feeding said first sodium phosphate fluid treatment material or said second sodium phosphate fluid treatment material is fed at a rate given by:

##EQU6## where TotalFeedwater is said total feedwater flow;

FeedPO4 is said first known phosphate concentration or said second known phosphate concentration, depending on which fluid treatment material is being fed;

PO4Bound_max is said first phosphate control limit;

PO4Bound_min is said second phosphate control limit;

Cycles_imax is said CSTR having a maximum cycle value wherein said cycle is defined as;

##EQU7## and Cycles_imin is said CSTR having a minimum cycle value, Steam (i) is the steam flow rate for the "ith" boiler and Blowdown (i) is the blowdown flow for the "ith" CSTR and i=CSTR index for identifying a particular CSTR of said at least two CSTRs.

44. The method of claim 43 wherein said step of feeding said first sodium phosphate fluid treatment material or said second sodium phosphate fluid treatment material at said rate occurs as long as the following condition is met:

Cycles_imax /Cycles_imin ≦

PO4Bound_max /PO4Bound_min.

45. The method of claim 41 wherein said step of feeding said first sodium phosphate fluid treatment material or said second sodium phosphate fluid treatment material is fed at a rate given by:

##EQU8##

46. The method of claim 45 wherein said step of feeding said first sodium phosphate fluid treatment material or said second sodium phosphate fluid treatment at said rate occurs as long as the following condition is met:

max(PO4Bound_min(i) /Cycle(i))≦

min(PO4Bound_max(i) /Cycle(i)).

47. The method of claim 46 wherein said step of determining the effective sodium in each of said fluids comprises back calculating sodium using a model projected phosphate concentration given by:

##EQU9## where PO4Est(i,t) is the estimated concentration in the fluid at time t;

i=CSTR index for identifying a particular CSTR of said at least two CSTRs;

PO4(i) is the steady-state phosphate concentration;

T is the characteristic time of the fluid; and

dt is the time between interval samples.

48. The method of claim 41 wherein said fluid parameter is the pH of the fluid.

49. The method of claim 41 wherein said first known phosphate concentration is identical to said second known phosphate concentration.

50. The method of claim 39 wherein said method further comprises the step of controlling the blowdown flow of each of said CSTRs.

51. A system for simultaneously controlling respective sodium-to-phosphate ratios of at least two boiler fluids of respective industrial boilers that are fed through a common feedwater, the industrial boilers having respective blowdown flows and steam rate flows that define respective cycles for each boiler fluid, said system comprising:

input means for receipt of a boiler fluid parameter for each of the at least two boiler fluids and a parameter indicative of the cycles of each of said industrial boilers; and

control means responsive to said input means for automatically driving the respective sodium-to-phosphate ratios of said at least two boiler fluids to a desired sodium-to-phosphate ratio region, said control means comprising model phosphate projecting means for estimating the sodium-to-phosphate ratios in each of said at least two boiler fluids.

52. The system of claim 51 wherein said boiler fluid parameter comprises the pH of the boiler fluid, the respective pH of each of the boiler fluids being defined by the respective sodium-to-phosphate ratio and the respective cycles and wherein said input means comprises a respective pH meter for determining the respective pH value of each of the boiler fluids and providing the respective pH value to said control means.

53. The system of claim 51 wherein said control means comprises a first feedstream and a second feedstream for feeding first and second fluid treatment materials, respectively, to the common feedwater, said first material comprising a mixture of sodium and phosphate having a first predetermined sodium-to-phosphate ratio and a first predetermined concentration of phosphate, said second material comprising a mixture of sodium and phosphate having a second predetermined sodium-to-phosphate ratio and a second predetermined concentration of phosphate.

54. The system of claim 53 wherein said first predetermined concentration of phosphate and said second predetermined concentration of phosphate are identical.

55. The system of claim 53 wherein said control means comprises feeding means for feeding said first feedstream or said second feedstream at a rate which maintains the respective phosphate concentration of each boiler fluid between a respective predetermined upper phosphate control limit and a respective predetermined lower phosphate control limit.

56. The system of claim 55 wherein said respective predetermined upper phosphate control limits are identical, referred to as a first phosphate control limit, and wherein said respective predetermined lower phosphate control limits are identical, referred to as a second phosphate control limit.

57. The system of claim 56 wherein said control means further comprises means for feeding said first feedstream or said second feedstream at a rate given by:

##EQU10## where TotalFeedwater is the flow of said common feedwater;

FeedPO4 is said first predetermined phosphate concentration or said second predetermined phosphate concentration;

PO4Bound_max is a predetermined maximum phosphate concentration;

PO4Bound_min is a predetermined minimum phosphate concentration;

Cycles_imax is said boiler having a maximum cycle value wherein said cycle is defined as;

##EQU11## and Cycles_imin is said boiler having a minimum cycle value, Steam (i) is the steam flow rate for the "ith" boiler and Blowdown (i) is the blowdown flow for the "ith" boiler and i=boiler index for identifying a particular boiler of said at least two boilers.

58. The system of claim 57 wherein said feeding means includes monitoring means that permits said feeding means to feed at said rate whenever the following condition is met:

Cycles_imax /Cycles_imin ≦

PO4Bound_max /PO4Bound_min.

59. The system of claim 58 wherein said monitoring means alerts an operator if said condition is not met.

60. The system of claim 55 wherein said feeding means feeds said first feedstream or said second feedstream at a rate given by:

FeedRate=a*max(FeedRate_min(i))+(1-a)*min(FeedRate_max(i)),

where

0≦

a≦

1;

i=boiler index for identifying a particular boiler of said at least two boilers;

FeedRate_min(i) =PO4Bound_min /Cycle(i)*(TotalFeedWater)/FeedPO4;

FeedRate_max(i) =PO4Bound_max(i) /Cycle(i)*(TotalFeedWater)/FeedPO4

TotalFeedwater is the flow of said common feedwater;

FeedPO4 is said first predetermined phosphate concentration or said second predetermined phosphate concentration, depending on which fluid treatment material is being fed;

PO4Bound_max(i) is said respective predetermined upper phosphate control limit;

PO4Bound_min(i) is said respective predetermined lower phosphate control limit; and

Cycle(i) is defined as;

##EQU12##

61. The system of claim 60 wherein said feeding means includes monitoring means that permits said feeding means to feed at said rate whenever the following condition is met:

max(PO4Bound_min(i) /Cycle(i))≦

min(PO4Bound_max(i) /Cycle(i)).

62. The system of claim 61 wherein said control means further comprises means for estimating the phosphate concentration in each of the boiler fluids.

63. The system of claim 62 wherein said control means further comprises means for back-calculating the sodium concentration in each of said boiler fluids.

64. The system of claim 63 wherein said means for back-calculating the sodium concentration in each of said boiler fluids uses the following model projected phosphate concentration:

##EQU13## where PO4Est(i,t) is the estimated concentration in the fluid at time t;

i=boiler index for identifying a particular boiler of said at least two boilers;

PO4(i) is the steady-state phosphate concentration;

T is the characteristic time of the fluid; and

dt is the time between interval samples.

65. The system of claim 62 wherein said control means further comprises means for determining a sodium-to-phosphate ratio for each of said boiler fluids and for identifying a maximum sodium-to-phosphate ratio and a minimum sodium-to-phosphate ratio from all of said boiler fluids to define a first range having a first midpoint.

66. The system of claim 62 wherein said feeding means feeds said first feedstream if said first midpoint is less than or equal to a second midpoint of a predetermined ratio range of sodium-to-phosphate, or feeding said second feedstream if said first midpoint is greater than said second midpoint.

67. The system of claim 61 wherein said monitoring means alerts an operator if said condition is not met.

68. The system of claim 51 wherein said system does not control the blowdown flow of each of said boilers.