Estimation and control in the wet end using CO2

Abstract

A method for controlling the CO2 addition in a wet end process utilizing CO2 addition is disclosed. The method includes combining a papermaking composition and CO2 to create a CO2-enriched papermaking composition, measuring or estimating at least one electrical property of either the papermaking composition or of the CO2-enriched papermaking composition, and controlling the rate of addition of CO2 to maintain the at least one electrical property within a pre-selected range of values.

Description

BACKGROUND OF THE INVENTION

[0002] 1. Field of the Invention

[0003] The disclosure relates to a method for controlling the CO2 addition in a wet end process utilizing CO2 addition.

[0004] 2. Related Art

[0005] A method for controlling the CO2 addition in a wet end process utilizing CO2 addition is disclosed. The assignee of this application, Air Liquide, currently has pending a patent application for CO2 addition in a wet end process.

[0006] In paper processing, due to industrial competition, changes in raw materials, environmental concerns and greater customer demands, higher levels of knowledge and understanding of the chemistry in the wet end are important to commercial success. It has been discovered that the zeta potential (ZP) is an important property in the final paper quality fabrication.

[0007] It has long been understood that zeta potential plays an important role in paper machine process operability by being related to flocculation, retention and drainage characteristics of the pulp. N. Vanderhoek, “Optimizing Paper Machine Performance Through Electrokinetic Measurement”, APPITA, Vol. 47. No. 5, pp 397-405, 1994. Wet-end stability is a key part to getting machine efficiencies. T. Miyanashi, et. al. studied the effects of zeta potential on these phenomena, and concluded that the zeta potential should be controlled to provide better flocculation and drainage additives. The wet end chemistry of optimized paper machines is not operated at equilibrium conditions, and the order of chemical addition is critical. T. Miyanashi, and S. Motegi, “Optimizing Flocculation and Drainage for Microparticle by Controlling Zeta Potential,” TAPPI Journal, pp. 262-270, January 1997.

[0008] The need for better performance of paper machines has triggered the development of better retention aids. This has defined a need for better understanding the effects of these new, wet-end additives and being able to control in real time the additions to obtain optimum paper machine and overall wet-end operation performances. The first step to achieving these objectives relies on available real-time information. It is desirable to provide a process that adapts itself to real time changes. In the wet-end process, fiber characteristics, chemical additives and water properties can change continuously, and so it is desired to detect these variations as they occur in real time.

[0009] As mentioned above, Air Liquide has developed a technology that is capable of altering the zeta potential of cellulose fibers using CO2. M. Muguet and J. M. deRigaurd, “Improvements to Processes for Manufacturing Paper Products by Improving the Physico-Chemical Behavior of the Paper Stock”, International Publication No. WO 03/074788 A2. Air Liquide has also a pending patent application on such technology, Serie 6052 which was filed as a U.S. provisional application on Sep. 30, 2002, bearing Ser. No. 60/414,876, and as a U.S. non-provisional on Sep. 6, 2003, bearing U.S. Ser. No. 10/656,857. Applicant hereby expressly incorporates by reference the entirety of these disclosures as if fully set forth herein.

[0010] Generally in process control, a mathematical model is required correlating input parameters with output variations of the controlled system. To control wet-end parameters such as retention, drainage and formation by wet-end additives, a mathematical model correlating the additive parameters with the zeta potential and cationic demand is first required. Next, a mathematical model correlating the parameters affecting flocculation such as zeta potential, cationic demand and the bridge forming capability of polymeric additives is needed. Since normally these input-output relationships are unknown, it is not easy to construct either a mathematical control model or a simulation model (F. Onabe). F. Onabe, MEASUREMENT AND CONTROL, Chapter 12. W. Scott explains that these are non-linear, interacting relationships. W. Scott, PRINCIPLES OF WET END CHEMISTRY, TAPPI Press, Atlanta, Ga., 1996. Wang, H. et al., describes a neural network that models the relationship between the wet end chemicals and the properties of the resulting paper. H. Wang, B. Oyebande, “On the Application of Neural Networks Modeling to a Wet End Chemical Process in Paper Making,” IEEE Conference on Control Applications—Proceedings 1995. IEEE, Piscataway, N.J., USA pp. 657-662, 1995.

[0011] To implement a real-time control optimization scheme in the wet end, it is useful to have real-time measurements available. The common lack of immediate feedback measurement about the effectiveness of the adsorption process is a serious shortcoming, and this leads to mill practices of minimizing input disturbances by controlling individual parameters. Most of these parameters are typically controlled, such as pH, ionic demand, consistency (Cy), flowrate, etc. However, those properties that are not controlled due to the lack of on-line instruments present challenges. For example, ZP measurement is normally measured off-line. Most mills lack an on-line ZP analyzer, and so it is impossible to attain an on-line ZP control or optimization.

[0012] Thus, a problem associated with paper processing methods that precede the present invention is that they do not provide a method of more closely controlling the performance of wet end chemistry in paper manufacture by controlled CO2 addition to the wet end.

[0013] Still another problem associated with paper processing methods that precede the present invention is that they do not provide controlled CO2 addition into the wet end that permits the control of unmeasured properties to improve the performance of wet end chemistry in paper manufacture.

[0014] An even further problem associated with paper processing methods that precede the present invention is that they do not provide a control mechanism for CO2 addition into the wet end that permits the more reliable control of unmeasured properties, by providing a predictor of disturbances to the system that facilitates refinement of data.

[0015] The present invention seeks to overcome these problems while at the same time providing a cost-effective, simply used mechanism for controlling CO2 addition into the wet end of paper manufacture.

SUMMARY OF THE INVENTION

[0016] A method for controlling the CO2 addition in a wet end process utilizing CO2 addition is disclosed. A papermaking composition and CO2 are combined to create a CO2 -enriched papermaking composition. At least one electrical property of either the papermaking composition or of the CO2 -enriched papermaking composition is either measured or estimated. The rate of addition of CO2 to maintain the at least one electrical property within a pre-selected range of values is then controlled.

[0017] In one embodiment, the electrical property is selected from the group consisting of ZP, CD and ion concentration or any equivalent thereto, and is estimated by measuring at least one property of either the papermaking composition or the CO2-enriched papermaking composition selected from the group consisting of flowrate, CD, ZP, ion concentration, Cy, pH, conductivity and alkalinity and using a model. Preferably, the ZP is estimated. Thus, the measured property can be measured from either the papermaking composition or the CO2-enriched papermaking composition, and is preferably measured from the papermaking composition. Likewise, the estimated electrical property can be estimated for either the papermaking composition or the CO2-enriched papermaking composition, and is preferably estimated for the CO2-enriched papermaking composition.

[0018] Various control schemes are employed to better control the CO2 addition by maintaining the at least one electrical property within a pre-selected range of values.

[0019] Thus, it is an object of the present invention to provide a method of more closely controlling the performance of wet end chemistry in paper manufacture by controlling the CO2 addition to the wet end.

[0020] It is a further object of the present invention to provide a control mechanism for CO2 addition into the wet end that permits the control of unmeasured properties, thereby improving the performance of wet end chemistry in paper manufacture.

[0021] It is still another object of the present invention to provide a control mechanism for CO2 addition into the wet end that permits the more reliable control of unmeasured properties, by providing a predictor of disturbances to the system that facilitates refinement of data and hence better performance of wet end chemistry in paper manufacture.

[0022] These and other objects of the present invention will be apparent from the description of the invention that follows.

BRIEF DESCRIPTION OF THE DRAWINGS

[0023] In the detailed description that follows, reference will be made to the following figures:

[0024] FIG. 1 is a schematic diagram illustrating an embodiment of the control method adapted to a specific papermaking process;

[0025] FIG. 2 is a schematic diagram illustrating another embodiment of the control method;

[0026] FIG. 3. is a schematic diagram illustrating the expected performance of a feed forward control responding to a normalized step change and a charge demand disturbance; and

[0027] FIG. 4 is a schematic diagram illustrating another embodiment of the control method adapted to a specific papermaking process.

DESCRIPTION OF PREFERRED EMBODIMENTS

[0028] A system and method for controlling the parameters in a wet end process by means of CO2 injection in a real-time manner using an advanced controller is presented. The design of the advanced controller maintains the desired set point and rejects the influence of undesirable wet end disturbances. The effects of the disturbances on the wet end are modeled, and their on-line measurements are used to compensate the addition of CO2. This disclosure provides an effective way of controlling parameter in the wet end using multi-variable advanced control and CO2 gas.

[0029] As mentioned above, Air Liquide has developed a technology that is capable of altering the zeta potential of cellulose fibers using CO2. M. Muguet and J. M. deRigaurd, “Improvements to Processes for Manufacturing Paper Products by Improving the Physico-Chemical Behavior of the Paper Stock”, International Publication No. WO 03/074788 A2. Air Liquide has also a pending patent application on such technology, Serie 6052 which was filed as a U.S. provisional application on Sep. 30, 2002, bearing Ser. No. 60/414,876, and as a U.S. non-provisional on Sep. 6, 2003, bearing U.S. Ser. No. 10/656,857. Applicant hereby expressly incorporates by reference the entirety of these disclosures as if fully set forth herein.

[0030] The instant disclosure relates to a control method adaptable therefor.

[0031] The alkalinity in water remains unaltered with the addition of CO2 due to the balance of carbonic species. However, when the CO2 is added in the presence of CaCO3, the alkalinity is changed due to the extra production of bicarbonate.

[0032] The utilization of CO2 has proven to improve the efficiency of the wet end process. The design of the application requires a good knowledge of the interactions caused by the CO2 and the extent of these interactions. This knowledge is covered theoretically by equilibrium analysis of water chemistry. In order to maintain the efficiency of the process it is helpful to design control systems that keep the process running under the designed specifications and rejects major disturbances. The most important disturbances can be attributed to the change of concentration in the make up water, temperature, pressure, consistency, or other chemical addition variations. In order to design the control system capable of rejecting these variations, it is helpful to know the dynamic effect on the controlled variables and their dynamic relationship with the CO2 supply. These relationships are obtained either from available process knowledge, or dynamic tests in the mill, or theoretical models.

[0033] Dynamic modeling of the most important species in the aqueous system with gaseous CO2 and CaCO3 and its effect on Zeta Potential (ZP) and Charge Demand (CD) can be performed. The dynamic model assumed a constant alkalinity.

[0034] The CO2—CaCO3 system is well studied in equilibrium conditions, but the studies are limited when it comes to dynamic (kinetic) conditions. When exploring the dynamic modeling of this system, one needs to consider a variety of parameters that play important roles, such as mass transfer and surface reactions. The operating conditions under which the CO2—CaCO3 are chosen to operate, define how fast the equilibrium conditions are met, and are worthwhile considering when designing a model-based control system. The most important effects of various operating conditions such as partial pressure of CO2, temperature, along with system-specific variables such as calcium carbonate surface area and mass transfer coefficient, are also presented here.

[0035] The validation of the proposed models requires the off-line measurements of alkalinity and [Ca2+] which are tedious and time consuming. The potential for using conductivity measurements to predict these off-line measurements is therefore considered.

[0036] MODEL DEVELOPMENT

[0037] Equilibrium

[0038] The dynamic behavior of the species in a CO2—CaCO3 system depends on several variables. The dynamic behavior will be represented in the form of ordinary differential equations (ODE), which require initial conditions in order to have their solution. Some of the initial conditions are known and measured in a typical (batch) experiment, such as pH. However, other initial conditions are not known and rarely measured, such as [CO3−2] concentration. Equilibrium studies can provide the estimates of the values of any component for any given condition assuming the conditions have not changed in order to reach equilibrium. Then, the equilibrium calculations can be used as initial conditions for ODE. Similarly, equilibrium studies can be used to compare the final or steady state results of dynamic equations. In steady state, the ODE results should be consistent with the equilibrium conditions at the new operating conditions.

[0039] The mass transfer coefficient, kx, has an impact on the time response of the variables but does not affect the final steady state or equilibrium values. On the other hand, pCO2 (partial pressure of CO2) directly influences the equilibrium values. So, the value of the pCO2 that attains the experimental steady state parameters needs to be found or closely monitored, if possible. In order to find the operating pCO2 that achieves the equilibrium conditions, an equilibrium problem is then solved.

[0040] Following the example on p. 168 by Stumm & Morgan (Stumm, W. and Morgan, J. J. “Aquatic Chemistry: Chemical Equilibria and Rates in Natural Waters”, John Wiley & Sons, Third Edition, 1996), a Matlab program is utilized to solve the set of nonlinear algebraic equations defined by: 1$\begin{array}{cc}\frac{\left[H^{+}\right]\left[{\mathrm{HCO}}_3^{-}\right]}{\left[H_2{\mathrm{CO}}_3^{*}\right]}=K_1& \left(1\right)\\ \frac{\left[H^{+}\right]\left[{\mathrm{CO}}_3^{2-}\right]}{\left[{\mathrm{HCO}}_3^{-}\right]}=K_2& \left(2\right)\end{array}$ [H2CO3*]=KHpCO2   (3)

[H+][OH−]=KW   (4)

[Ca+2][HCO3−]=KSO   (5)

2[Ca]+[H30 ]=[HCO3−]+2[CO32−]+[OH−]  (6)

[0041] The equilibrium constants are reported in the literature.

Correlations for temperature dependent equilibrium constants (Stumm & Morgan)
	Temp	294.45
	21.3	A1	A2	A3	A4	A5
LogK1
−6.374687	−356.3094	−0.06092	21834	126.8339	−1684915
LogK2
−10.36285	−107.8871	−0.032528	5151.79	38.92561	−563713.9
LogKH
−1.423209	108.3865	0.019851	−6919.53	−40.45154	669365
LogKw
−14.12347	−283.971	13323	−0.050698	102.2445	−1119669
LogKso
−8.459868	−171.9065	−0.077993	2839.319	71.595	0
Log(Ki) = A1 + A2 * T + A3/T + A4Log(T) + A5/T{circumflex over ( )}2

[0042]

T (deg C.)	LogK1	LogK2	LogKH	LogKw	LogKso
20	−6.383133	−10.37557	−1.406868	−14.16818	−8.453297
25	−6.353105	−10.32885	−1.46794	−13.99953	−8.47983
30	−6.329367	−10.28788	−1.524416	−13.83949	−8.509751
35	−6.311358	−10.25227	−1.576641	−13.68751	−8.543034
40	−6.298577	−10.22169	−1.624926	−13.54308	−8.579652
45	−6.290573	−10.19583	−1.669556	−13.40575	−8.619574
50	−6.286946	−10.1744	−1.710789	−13.2751	−8.662766
55	−6.287334	−10.15714	−1.748859	−13.15074	−8.709195
60	−6.291415	−10.14381	−1.783981	−13.03233	−8.758826
65	−6.298898	−10.13418	−1.816351	−12.91953	−8.81162
70	−6.309522	−10.12806	−1.846147	−12.81207	−8.867541
Dependence of Equilibrium constants with Temperature: Stumm & Morgan report the temperature dependent correlations.

[0043] Equations (1)-(6) describe the equilibrium equations of the CO2—CaCO3 in water at a given CO2 pressure, pCO2. These equations can be manipulated in different forms to fit different conditions. For instance, if the calcium is not in equilibrium, then equation (5) is not applicable, and the [Ca+2] is estimated from a rate equation.

[0044] Kinetics (Rate)

[0045] The equilibrium studies determine the steady state conditions or the total changes based on operating conditions. On the other hand, kinetic studies determine also the rate at which changes occur. Process control design depends on both results, the extent of the change and the rate of change. The exchange of CO2 from the gas phase to the bulk liquid for constant alkalinity is presented as the diffusion equation: 2$\begin{array}{cc}\frac{d{C}_T}{dt}=\mathrm{klx}\left(p_{\mathrm{Co2}}H+\mathrm{Alk}-C_T\right)=R_{\mathrm{CO2}}& \left(7\right)\end{array}$

[0046] where,

[0047] CT=Total carbonic species, M=[H2CO3*]+[HCO3−]+[CO3−2]

[0048] klx=Mass transfer coefficient, min−1

[0049] pCO2=CO2 partial pressure in the gas, atm

[0050] H=Henry's equilibrium constant

[0051] Alk=Alkalinity, M (mol HCO3/L)

[0052] Equation (7) is valid when the concentration of [CO3−−] is negligible and CT>>Alk. This occurs when the pressure is significantly higher than the partial pressure of CO2 in the atmosphere. For pressures close to atmospheric, Equation (7) is not valid, but it is assumed that the operating conditions where it will be used are in CO2 rich conditions.

[0053] If the alkalinity is not constant, then the rate of transfer of CO2 moles converted to [H2CO3*] is 3$\begin{array}{cc}\frac{d\left[H_2{\mathrm{CO}}_3^{*}\right]}{dt}=\frac{d}{dt}\left[C_T-\left[{\mathrm{HCO}}_3^{-}\right]\right]=\frac{d{C}_T}{dt}-\frac{d\left[{\mathrm{HCO}}_3^{-}\right]}{dt}& \left(8\right)\end{array}$

[0054] then, the rate of total carbonic species becomes 4$\begin{array}{cc}\frac{d{C}_T}{dt}=R_{{\mathrm{CO}}_2}-\frac{d\left[{\mathrm{HCO}}_3^{-}\right]}{dt}=R_{{\mathrm{CO}}_2}-\frac{d\mathrm{Alk}}{dt}& \left(9\right)\end{array}$

[0055] In order to estimate the time dependant variation of pH, one starts from the relationship: 5$\begin{array}{cc}\left[H^{+}\right]=\left(\frac{{\mathrm{pK}}_1}{\mathrm{Alk}}\right)\left(C_T-\mathrm{Alk}\right)& \left(10\right)\end{array}$

[0056] which can be rewritten as: 6$\begin{array}{cc}\left[H^{+}\right]={\mathrm{pK}}_1\frac{C_T}{\mathrm{Alk}}-{\mathrm{pK}}_1& \left(11\right)\end{array}$

[0057] Taking the derivative with respect to time on Equation (11) reveals that the equation is more complex when considering a time dependent alkalinity: 7$\begin{array}{cc}\frac{d\left[H^{+}\right]}{dt}={\mathrm{pK}}_1\frac{d}{dt}\left(\frac{C_T}{\mathrm{Alk}}\right)& \left(12\right)\end{array}$

[0058] This becomes, 8$\begin{array}{cc}\frac{d\left[H^{+}\right]}{dt}={\mathrm{pK}}_1\left\{\frac{\mathrm{Alk}*R_{\mathrm{CO2}}-C_{T}d\mathrm{Alk}}{{\mathrm{Alk}}^2}\right\}& \left(13\right)\end{array}$

[0059] The evaluation of Equation (13) depends on Equation (9) or RCO2, but also depends on dAlk/dt. To the present time, an analytical expression for dAlk/dt has not been found.

[0060] One tentative expression can be derived from the simplified proton balance expression when CO2is added in a system in the presence of CaCO3:

2[Ca++]˜=Alk   (14)

[0061] Even though Equation (14) is an equilibrium equation for proton balance, it can be used as an approximate relationship between calcium ions and alkalinity at all times. Hence, taking the time derivative in both sides, 9$\begin{array}{cc}\frac{d\mathrm{Alk}}{dt}=2\frac{d\left[{\mathrm{Ca}}^{++}\right]}{dt}& \left(15\right)\end{array}$

[0062] The implementation of Equations (13) and (15) has posed implementation problems and the results have not been successful to this point due to numerical reasons. When solving Equations (13) and (15) simultaneously, the hydrogen proton concentration becomes non-real. So, a simplification is presented.

[0063] It is known that the proton-transfer reactions such as the carbonic reactions are usually very fast with half-lives less than milliseconds. This suggests that it may not be necessary to express in ODEs the equations to estimate the hydrogen proton or the alkalinity. Instead, as the rate limiting equations are solved in ODEs, the rest of the chemical species can be determined solving the appropriate equilibrium equations.

[0064] Equations (9), (13) and (15) describe the kinetic equations of CT, pH and Alk, correspondingly. The calcium dissolution kinetics obtained by Plummer et. al. has the form:

R Ca =k Ca,1 a H +k Ca,2 a H2CO3 +k Ca,3 a H2O −k Ca,4 a Cu a HCO3   (16)

[0065] Plummer, L. N., Wigley, T. M., and Parhurst, D. L. “The kinetics of calcite dissolution in CO2— water systems at 5° to 60° C. and 0.0 to 1.0 ATM CO2”, American Journal of Science, Vol. 278, p. 179-216, February, 1978. The activity coefficients, ai, are equal to concentrations. At 25° C., the parameters are:

[0066] kCa,1=5.115e−02;

[0067] kCa,2=3.4247e−05;

[0068] kCa,3=1.1919e−07;

[0069] kCa,4=4.55e−02;

[0070] The units of RCa are in mmol/(sec−1cm2). The constants kCa,i are temperature dependent and kCa,4 is the backward reaction. Besides converting RCa to mol and min−1, the kinetic expression depends on the total surface area of the calcite particles. Denoting the particle area as ac, defined as the surface area per unit of mass, provides the calcium dissolution in mol/min as: 10$\begin{array}{cc}\frac{d\left[{\mathrm{Ca}}^{+2}\right]}{dt}=a_C\left[{\mathrm{CaCO}}_3\right]V{R}_{\mathrm{Ca}}\left(60/1000\right)& \left(17\right)\end{array}$

[0071] The product [CaCO3]V corresponds to the total grams of CaCO3 in the reactor. Plummer reports a range of polished calcite particles up to 90 cm2/gr.

[0072] The rate expressions of CO2 transfer and calcium dissolutions are the phenomena that dictate the global rates. Hence, it is suggested that in order to identify the time dependant values of all the species in a CO2—CaCO3 system, small increments solving the ODEs of CO2transfer and calcium dissolution (Equations (9) and (17)) will return the [Ca+2] and total carbon species, CT. Then, the following algebraic equations are solved to find alkalinity, [HCO3], and hydrogen proton, [H+]: 11$\begin{array}{cc}\frac{\left[H^{+}\right]\left[{\mathrm{HCO}}_3^{-}\right]}{\left[H_2{\mathrm{CO}}_3^{*}\right]}=K_1& \left(18\right)\\ \frac{\left[H^{+}\right]\left[{\mathrm{CO}}_3^{2-}\right]}{\left[{\mathrm{HCO}}_3^{-}\right]}=K_2& \left(19\right)\end{array}$ [H+][OH31 ]=KW   (20)

CT=[H2CO3*]+[HCO3−]+[CO32−]  (21)

2[Ca]+[H+]=[HCO3−]+2[CO32−]+[OH−]  (22)

[0073] Once these equations are solved, the new values are used to solve the next increment of the ODEs.

[0074] The dynamic modeling of the CO2—CaCO3 is then defined by 2 ODEs (Equations (9) and (17)), and the simultaneous solution of algebraic equations (Equations (18) through (22)). All these equations have a variety of parameters that have to be specified prior to the numerical simulations. These parameters are the temperature, mass transfer coefficient, the Co2partial pressure, and calcium carbonate surface area.

[0075] All the kinetic and equilibrium constants are temperature dependent. The temperature dependence of the kinetic parameters have been presented in a previous report (CRC200343) and have shown above for T=25° C. The temperature dependence of the equilibrium parameters is shown in Appendix A.

[0076] Experiments

[0077] A series of experiments was performed. The experiments utilized 8.125 gr of CaCO3 (equivalent to 20% PCC in pulp) in a 1.3 L of DI water. Two types of CaCO3 were used: ALBACAR HO PCC (Specialty Minerals, Inc) and reagent grade CaCO3 (Fisher Scientific). The CaCO3 stock solution was agitated for 24 hours to reach equilibrium with the CO2in the atmosphere. The initial sample (time zero) was taken from the stock. 1.3 L of the stock was placed in the reactor and agitation was set at 1500 rpm. Timing started when the dosing of CO2 started. The total amount of CO2 was 10.256 Kg/ton assuming a 2.5% Cy slurry, or 2.6e−04 Kg CO2/L. Dosing of CO2 was completed in approximately 40 seconds. The dosage was performed in order to obtain a constant pCO2 pressure in the reactor head. Close to 10-milliliter samples were withdrawn and immediately filtered with 0.02-micrometer filters. Several experiments with the same conditions were run in order to take more samples. Conductivity, pH, alkalinity and calcium concentration, were measured from each sample.

[0078] Experimental Results

[0079] Table 1 shows the experimental results obtained at ˜24° C. using ALBACAR PCC. Notably, the concentrations of calcium and alkalinity increase rapidly to reach equilibrium values in a few minutes.

[0080] From the proton balance indicated in Equation (6), and since the concentration of carbonate, [CO3−−], is negligible at this pH, the relation 2*[Ca+2]˜=Alk must be satisfied (Stumm & Morgan). From the experimental results shown in Table 1 it can be seen that this relationship is not satisfied. These results represent much higher values of alkalinities compared to the calcium dissolved equilibrium. These results gave the indication that the ALBACAR PCC might have some chemicals that affect the CO2—CaCO3 equilibrium

[0081] Table 2 shows the experimental results using reagent grade CaCO3. As with ALBACAR, the concentrations of calcium and alkalinity increase very rapidly towards equilibrium. More in depth explanations on this behavior will be presented later. What is interesting regarding equilibrium is the fact that the relationship between the equilibrium calcium and alkalinity is much closer to meeting the relationship 2*[Ca+2]˜=Alk. Excluding the 1-minute sample, the experimental values have an average error of 5% from the analytical expression. The higher error at 1 minute is attributed to the difficulty to take a representative sample at such an early stage in the experiment.

[0082] It was noticed that the pH variation of the filtered samples during the experiment was too small between time zero and the last sample. The pH measurements of the samples before filtering were closer to the expected according to equilibrium analysis.

[0083] The results shown in Table 2 are utilized in the remaining of this study to compare with the equilibrium and dynamic models.

[0084] Equilibrium Analysis of Results

[0085] The equilibrium equations allow determining the target steady state conditions of CO2—CaCO3 systems. With this information, one can find in advance what steady state values are expected in experiments and in dynamic models simulations.

[0086] The first step to confirm the validity of the problem set up and its results, consisted in duplicating the problem on p. 186 by Stumm & Morgan. The problem determines the equilibrium concentrations in the CO2—CaCO3 system in the presence of atmospheric pressure (10−3.5 atm=3.16e−04 atm). The solution of this problem was implemented in Matlab (Mathworks, Inc) using a nonlinear algebraic equation solver command. The results obtained in Matlab solving the set of equations (I) through (6) are [Ca]=4.636e−04 M; Alk=9.2721 e−04 M and pH=8.3048. Note also that 2[Ca2+]˜=Alk.

[0087] In order to compare the experimental results obtained with CaCO3 with the equilibrium equations, the partial pressure of CO2 is needed. This pressure has not been reliable or available experimentally. Some early measurements indicated that the partial pressure of CO2 at the beginning of the experiment was around 0.43 psig, equivalent to 0.02 atm, but it declined continuously and its recording was unreliable. Furthermore, the partial pressure characteristic to the system in equilibrium, as represented in Equation (3), assumes to be constant. This is not the case in the experimental apparatus as the system is a batch reactor and variables change with time. However, in order to make the equilibrium equations, one has to find the characteristic CO2 partial pressure that attains the same experimental equilibrium conditions. Table 3 shows a set of results obtained when solving Equations (1) through (6) for a range of CO2 partial pressures.

[0088] Comparing the equilibrium results obtained from equilibrium equations as shown in Table 3 (with extrapolation), and the experimental results from Table 2, it is obtained that the equilibrium conditions that match the experimental results are:

[0089] CASE A: Theoretical Equilibrium at 25° C.

[0090] i. Alk=5e−03 mol HCO3/L=250 mg CaCO3/L=250 ppm CaCO3

[0091] ii. [Ca]=2.5e−03 mol Ca/L=100 mg Ca/L

[0092] iii. pCO2=10−1.049 atm=˜0.09 atm

[0093] iv. pH=6.5 (Matlab), 6.9-7.0 PHREEQ

[0094] The experimental results using ALBACAR HO (Specialty Minerals, Inc.) suggested that the equilibrium indicator to match was the pH. But the partial pressure of CO2 that achieves a 7.3 equilibrium pH achieves a lower theoretical alkalinity than the experimental values. The theoretical equilibrium conditions for this case are labeled as CASE B and are shown below. At this point, it was suspected that the difference in results could be due to the unknown components in the PCC used (ALBACAR HO, Specialty Minerals, Inc).

[0095] CASE B: Final Equilibrium Experimental Results (Dec. 12, 2003)

[0096] i. pH=7.3

[0097] ii. [Ca]=106 ppm=2.7e−03 M

[0098] iii. Alk˜=300 ppm as CaCO3=6e−03 mol [HCO3]/L

[0099] iv. Initial pCO2˜0.4 psig (±0.2 psig)=2.72e−02 atm

[0100] Even though the equilibrium pH values in the theoretical and experimental cases are the same, the calcium and alkalinity concentrations deviate significantly. The experimental calcium concentration almost doubles the theoretical. The theoretical equilibrium calcium concentration depends on the constant KSO. Aside from experimental errors, one possibility for the discrepancy is that the CaCO3 utilized is either not pure or different. Based on the experimental results, and combining some of the previous equations, one can obtain: 12$\begin{array}{cc}\left[{\mathrm{CO}}_3^{-2}\right]=\frac{K_1{K}_2{K}_{H}p{\mathrm{CO}}_2}{{\left[H^{+}\right]}^2}=2.8637e-06M& \left(23\right)\end{array}$

[0101] Substituting in Equation (5) one gets the equilibrium constant KSO, using the experimental calcium concentration (2.65e−03 M):

KSO=[Ca+2][HCO3−]=7.588e−09=10−8.1198   (24)

[0102] This results in a KSO, almost twice the reported in the literature. Running the equilibrium software for the new KSO and the other constants at 21° C., the following results are obtained:

[0103] CASE C: Theoretical with new KSO

[0104] i. pH=7.3061

[0105] ii. pCO2=10−1.985 atm=1.0351e−02 atm

[0106] iii. [Ca]=2.2e−03 M=89.75 ppm

[0107] iv. Alk=4.5e−03 M=274.5 ppm

[0108] Although the predicted equilibrium calcium concentration is now closer to the experimental, the alkalinity estimation is negatively influenced. The summaries of the results are shown in the following table.

	T	pCO2
Case	(° C.)	(atm)	pH	[Ca] (M)	Alk (M)	Comments
Text	25	10−3.5	8.304	4.636e-04	9.2721e-04	As shown
						in Morgan
Text	25	10−3.5	8.304	4.636e-04	9.2721e-04	Duplicated
						in Matlab
A	25	10−1.04	6.8	2.5e-03	5e-03	Theoretical
B	21.3	0-	7.3	2.7e-03	6e-03	ALBACAR
		10−1.45				PCC Experi-
						ment
C	21.3	10−1.985	7.306	2.2e-03	4.5e-03	New Kso
D	21.3	10−2.05	7.3	1.4e-03	2.8e-03	Theoretical
E	25	N/A	7.1 (?)	2.46e-03	5.08e-03	Grade
						CaCO3 ex-
						periment

[0109] The table shows that the experimental results with chemical grade CaCO3 meet the calcium and alkalinity relationship consistently (CASE E). Hence, the dynamic experimental data from this experiment will be used to compare them with the dynamic models. The complete set of operating conditions, such as the pCO2, will be used from the equilibrium calculations (CASE A).

[0110] Kinetic (Rate) Analysis of Results

[0111] The mass transfer coefficient, kx, in Equation (9) defines the speed at which gaseous CO2 is transferred to the liquid. It depends on physical properties and equipment design. Several correlations can be found in the literature for specific designs and operating conditions. Based on published literature, a typical mass transfer coefficient in an agitated tank where the gas is bubbled near the stirrer is in the order of 0.2 min−1. This number was used as a reference for the next simulation.

[0112] It was found that the experimental results shown in Table 2 are the equilibrium conditions when the partial pressure is 0.09 atm. This pressure will be utilized as the nominal operating pressure.

[0113] Finally, the surface area is needed to determine the dissolution rate according to Equation (16). The surface area of the ALBACAR OH (Specialty Minerals, Inc) was found to be equal to 11.5 m2/gr (11.5e+04 cm2/gr) with mean diameter sizes of ˜1.6 micrometers. On the other hand, the CaCO3 from Fisher has a mean diameter of 30 to 50 micrometers. This may represent a surface area in the range of 104 cm2/gr. Note that the maximum surface area of the calcium carbonate reported on the calcium dissolution paper by Plummer et. al. is 90 cm2/gr, which is several orders of magnitude smaller compared to the calcium carbonate tested at CRC. The consequence of the surface area in calcium dissolution and overall kinetics is presented later on.

[0114] Dynamic Model Test

[0115] Using the nominal operating conditions:

[0116] i. pCO2=0.09 atm

[0117] ii. kx=0.2 min−1

[0118] iii. T=25° C.

[0119] iv. ac=calcium carbonate surface area=103 cm2/gr

[0120] This set of conditions will be labeled as Conditions Set A

[0121] The initial conditions correspond to the equilibrium with the atmospheric CO2 partial pressure (10−3.5 atm): pH=8.96; Alk=3.3e−04molHCO3/L; [Ca+2]=1.65e−04 mol Ca/L; CT=3.45e−04 mol/L. In this report, all the alkalinities are expressed on mol/L, meaning mol [HCO3−]/L, and the calcium will be expressed in mol/L, meaning mol Ca/L.

[0122] Table 4 shows the simulation model using the condition Set A compared to the experimental values. The steady state predictions of the model match the experimental values when the nominal partial pressure of CO2 was lowered from 0.09 atm to 0.07 atm. This difference can be attributed to loss of accuracy when discretizing the dynamic models in order to solve it with equilibrium equations. The solution shown in Table 4, furthermore, was difficult to achieve, as it required some “troubleshooting”. When solving the ODE's (Equations (9) and (17)), it was noticed that the solution of dCa/dt was resulting in [Ca2+] values higher than the values that could be obtained in equilibrium. The dynamic solution of dCa/dt in this system cannot resolve in higher concentrations than equilibrium. Under steady state conditions, dCa/dt should only equalize the equilibrium predictions. This problem led to conclude that kinetic expression in Equation (16) over predicts the calcium dissolution when the calcium carbonate surface area is significantly higher than the one used by Plummer et. al. (90 cm2/gr).

[0123] When the calcium carbonate surface area is high (˜104 cm2/gr and higher), the calcium dissolution is so fast that it approaches practically instantaneously to equilibrium, which makes this reaction as fast as the proton-transfer reactions. The fast calcium dissolution then suggests to calculate the calcium at any specific time using the equilibrium equation as given by Equation (5), simultaneously with the other proton-transfer reactions. So, for high surface areas, only one differential equation is solved in each time interval (dCT/dt). Once CT is known from Equation (9) at one sample interval, the following equations are solved to find the equilibrium calcium concentration: 13$\begin{array}{cc}{K}_1=\frac{\left[H^{+}\right]\left[{\mathrm{HCO}}_3^{-}\right]}{\left[H_2{\mathrm{CO}}_3^{*}\right]}& \left(25\right)\\ K_1=\frac{\left[H^{+}\right]\left[{\mathrm{HCO}}_3^{-}\right]}{\left[H_2{\mathrm{CO}}_3^{*}\right]}& \left(26\right)\end{array}$ Ks=[Ca2+][CO32−]  (27)

CT=[H2CO3*]+[HCO3−]+[CO32−]  (28)

[0124] These equations can be combined to find [Ca2+] as a function of CT only: 14$\begin{array}{cc}{C}_T={\frac{4K_2}{K_1{K}_s}\left[{\mathrm{Ca}}^{2+}\right]}^3+2\left[{\mathrm{Ca}}^{2+}\right]+\frac{K_s}{\left[{\mathrm{Ca}}^{2+}\right]}& \left(29\right)\end{array}$

[0125] Equation (29) is faster to solve since does not require initial values to iterate, as is the case of solving simultaneous nonlinear algebraic equations. The simulation results in Table 4 show the calcium calculations from equilibrium, as the kinetics predictions were higher than equilibrium, which is not believed to be possible.

[0126] The temperature and partial pressures of CO2 affect the rate of dissolution, but also the equilibrium conditions. At this point, one is only interested in changing the rate, while keeping the equilibrium (steady state) results according to experimental results. The only available parameter than can achieve this goal is the mass transfer coefficient. The experiments were carried out at very high speeds (1500 rpm), but the mass transfer coefficient is not known. If the mass transfer coefficient is increased from 0.2 min−1 to 2.0min−1, the CO2 is transferred faster to the bulk and the proton-transfer reactions occur earlier.

[0127] Table 5 shows the simulation results with the higher mass transfer coefficient. It can be seen now that the experimental results have much better agreement with the simulations.

[0128] In conclusion, the dynamic modeling of the CO2—CaCO3 system has been developed to represent the experimental results obtained at CRC. However, it must be emphasized that in order to have good modeling results, knowledge of the right operating conditions, such as partial pressure, and mass transfer coefficient, along with the nature of the calcium carbonate, have to be considered in order to have the best model representation. The experimental example has allowed illustrating some of the important features of the modeling. Next, a more detailed explanation of the modeling issues will be shown.

[0129] Surface Area

[0130] The calcium dissolution kinetics is controlled by surface reaction, which leads to the importance of the surface area. It was already shown that for high surface calcium carbonate, a good approximation is to disregard the calcium rate predictions and use the equilibrium equations instead. Nevertheless, a deeper insight on the calcium dissolution in case the surface area is small is presented. From now on, several simulations will be shown using the conditions defined in the following condition Set B:

[0131] Condition Set B:

[0132] i. pCO2=0.025 atm

[0133] ii. kx=0.2 min−1

[0134] iii. T=25° C.

[0135] iv. ac=1e+0.5 cm 2/gr

[0136] Table 4 and Table 5 show simulations that assume that the calcium surface is significantly high (104 cm2/gr+), which makes the dissolution evolve so fast that reaches equilibrium almost instantly and the calcium is calculated from equilibrium equations. Table 6 shows simulations when the surface area is smaller and then the calcium dissolution is described by the kinetic equation reported by Plummer et al.

[0137] In general, it can be seen that the lowest surface area (90 cm2/gr) takes several orders of magnitude longer to reach equilibrium. The highest surface area simulated of 9e+04 cm2/gr was implemented combining the equilibrium equations and the kinetic equations. At the beginning of the simulation and until approximately 5 minutes, the rate predictions were higher than the equilibrium, which is not possible, so the equilibrium predictions are reported. After 5 minutes, the rate predictions were lower than the equilibrium, and hence the rate predictions by Plummer et. al. are plotted. The switching between one model and another causes some numerical discrepancies shown as spikes in the simulations.

[0138] Note the effect that the surface area has on pH. A high surface area enhances the calcium dissolution and the proton transfer equations equilibrate to lower [H+] concentration (high pH). On the other hand, when the surface area is small, the calcium dissolution is very slow and the equilibrium concentration for the proton-transfer species, such as [H+], is similar to when barely there is calcium. For this reason, Table 6 shows the simulation when there is practically no calcium and there is no CaCO3 to dissolve. When CaCO3 is absent, the alkalinity and calcium remain constant, and the pH drops rapidly to lower steady state values.

[0139] Table 7 shows a closer view of the pH of Table 6. It is more clearly seen that when the surface area is small at initial times, the system behaves as if there was no calcium dissolution and the pH decreases rapidly. When the calcium concentration starts building up, then the pH starts increasing towards the corresponding equilibrium with CaCO3.

[0140] Mass Transfer Coefficient

[0141] The mass transfer coefficient does not affect the steady state or equilibrium conditions. It only affects how fast the equilibrium is reached, just as the calcium carbonate surface area. From the process control point of view, these variables have an effect on the time constant of the process and not the gain. Table 8 shows the effect of different mass transfer coefficients in all the variables.

[0142] Temperature

[0143] One factor that affects the equilibrium conditions is the temperature of the system. All the equilibrium and kinetic constants are temperature dependent, and any variation will have an impact on all the concentrations. Table 9 shows a couple of simulations at different temperatures. The highest temperature shown (50° C.) drives the reactions towards lower calcium dissolution. The values of the equilibrium constants in Appendix show that the temperature affects the constants K1, K2 and Ks in different directions.

[0144] Regarding the sensitivity of the variables with respect to temperature, Table 9 shows that the temperature has a bigger effect on the concentrations than on pH. The small change in pH, however, represents a big change in the [H+] concentration change (because of the logarithmic relationship). If small temperature changes occur in the mill, big performance changes are expected when using CO2

[0145] CO2 Partial Pressure

[0146] Table 10 shows the effect of the CO2 partial pressure on the CO2—CaCO3 system. The increase in the partial pressure promotes the transfer of CO2, the pH reduction and the calcium dissolution. The partial pressure also has a direct impact on the steady state conditions (equilibrium). Unlike temperature, the relatively smaller changes in the CO2 partial pressure, the effect on all variables, including the pH, is greater. This remains as the most important manipulating variable that specifies the final operating conditions.

[0147] Conductivity

[0148] During the experiments using ALBACAR OH (Specialty Minerals, Inc), the on-line conductivity measurements were recorded. Table 11 shows the on-line conductivity measurements of one of the CO2—CaCO3 experiments using ALBACAR PCC (Specialty Minerals, Inc). Conductivity is a measure of the ability of an aqueous solution to carry an electric current. The ability depends on the presence of ions; on their total concentration, mobility, and balance; and on the temperature of measurement. A general theoretical method to calculate the conductivity is presented by Clesceri et al. Clesceri, L. S., Greenberg, A. E., and Eaton, A. D. “Standard Methods for the Examination of Water and Wastewater”, 20th Edition, APHA, AWWA, WEF. First, the infinite dilution conductivity is calculated:

k 0 =Σ|z i |(λ−i0)(mMi)+Σ|zi|(λ−i0)(mMi)   (30)

[0149] where:

[0150] |zi|=absolute value of the charge of the i-th ion

[0151] mMi=millimolar concentration of the i-th ion

[0152] □0+i, □0−i=equivalent conductance of the i-th ion

[0153] Then, calculate the ionic strength, IS in molar units:

IS=Σz i 2 (mMi)/2000   (31)

[0154] The monovalent ion activity coefficient, y, is calculated using the Davies equation for IS<=0.5M and for temperatures from 20 to 30° C. 15$\begin{array}{cc}y={10}^{-0.5\left(a-0.3/S\right)};a=\frac{{\mathrm{IS}}^{0.5}}{1+{\mathrm{IS}}^{0.5}}& \left(32\right)\end{array}$

[0155] Finally, the conductivity is calculated as:

k calc =k 0 y2   (33)

[0156] Equivalent ionic conductivities in aqueous solutions can be found in different sources, including Lange's Handbook of Chemistry. Dean, J. A. “Lange's Handbook of Chemistry”, McGraw-Hill, Thirteen Edition. The equations to calculate the conductivity as a function of the molar concentration of the ions in solution are then used to “back-calculate” the ion concentrations based on the conductivity measurements. Since DI water was used in the experiments, it is known that only two main components can be found in the solution: [Ca2+] and [HCO3−]. However, there are an infinite number of ion concentration combinations that can produce the same conductivity. For this, an additional relationship is needed. The proton balance equation in a CO2—CaCO3 for the range of pH of interest, is simplified as

2[Ca2+]˜=[HCO3−]=Alk   (34)

[0157] Then, an optimization problem to calculate the concentration of the [Ca+2] and [HCO3−] ions is used and defined as: 16$\begin{array}{cc}\underset{\left[{\mathrm{Ca}}^{2+}\right],\left[{\mathrm{HCO}}_3^{-}\right]}{\min }J={\min \left(k_{\exp }-{\hat{k}}_{\mathrm{calc}}\right)}^2& \left(35\right)\end{array}$

[0158] such that Equation (32) is true. The back calculation is solved by minimizing the objective factor, J. This factor consists of the squared error of the measured or experimental conductivities, kexp, and the estimation of the calculated conductivities from Equation (kcalc). The solution will be the minimization of the problem that meets the proton balance equation. This problem is solved numerically in Matlab with the minimization of a constrained multivariable function.

[0159] Table 12 shows the experimental on-line conductivity measurements and off-line [Ca2+] and alkalinity measurements of an experiment using ALBACAR PCC (Specialty Minerals, Inc). Aside from the first off-line sample, which may be considered inaccurate due to sampling difficulties, the calcium predictions from the conductivity measurements match very close the off-line experimental measurements. The alkalinities, on the other hand, have larger estimation errors. The maximum error is up to 40 units.

[0160] Table 13 shows the estimations of [Ca 2+] and alkalinity of the experiment using chemical grade CaCO3. The calcium estimates are almost as good as in the previous case. The alkalinities, on the other hand, have smaller prediction errors. This suggests that this experiment consists of ions closer to the expected. The experiment with ALBACAR could have some components or ions that affect the conductivity, and may drive Equation (32) off. In summary, it can be said that the conductivity measurement has the potential to predict the evolution of the most important ions in the CO2—CaCO3 system.

[0161] In the preferred embodiments thus described, phenomena that help determine the rate of species in a CO2—CaCO3 system are the CO2 transfer and calcium dissolution. The other reactions are proton-transfer reactions that occur quickly and can be considered in equilibrium, including the alkalinity. This disclosure presents the calculation of the proton-transfer reactions calculated and updated at every integration step of the rate equations.

[0162] The calcium dissolution can be calculated with equilibrium equations if the calcium carbonate surface area is significantly large (over 104 cm2/gr). The CaCO3 used in the experiments of this report have high surface areas and the best predictions results considered equilibrium calculations of calcium. The increase of alkalinity with the supply of CO2 has a big impact on the pH, and hence on the calcium dissolution.

[0163] Once the alkalinity was calculated in a time dependent manner, the CO2—CaCO3 system was simulated for a variety of conditions in CO2 partial pressure, temperature, mass transfer coefficient and calcium carbonate surface area. If the calcium carbonate surface area is large, the most important factor that controls the rate of the system is the mass transfer coefficient. If the surface area is small (large particle diameters), the time constant of the system can be increased dramatically due to slower calcium dissolution rate.

[0164] Unlike the mass transfer coefficient and the particle surface area, the temperature of the system and the CO2 partial pressure have an effect on the equilibrium (steady state) conditions. The partial pressure has a bigger impact on the equilibrium conditions than temperature, so it is important to have a well-controlled operation of CO2.

[0165] Finally, it is shown that the conductivity measurements can be used to predict the calcium and alkalinity of CO2—CaCO3 systems. A more detailed development would be needed if other ionic species were present.

[0166] Referring now to FIG. 1, a schematic diagram illustrating an embodiment of the control method adapted to a specific papermaking process is shown. A mixing chest 1 receives a regulated inlet flow of CO2 and a papermaking composition such as a fiber flow, 7, and provides a CO2—enriched papermaking composition, such as an outlet fiber flow. Properties of the fiber flow such as, for example, flowrate, CD (charge demand), ZP (Zeta Potential), ion concentration, Cy (consistency), pH, conductivity and alkalinity are measured on-line before the fiber flow reaches the mixing chest, and measurements 2 are generated. At the same time, on-line properties of the outlet fiber flow are measured by instrument 3, and can be chosen from the same set of properties as described above. An advanced controller, in this case a feed forward controller, uses the measurements of the inlet flow and compensates the feedback controller, 5, by adding the controller outputs, 6. The resulting controller output is used to manipulate the inlet CO2 that will maintain the desired wet end properties while minimizing variations in the inlet fiber flow.

[0167] Note that certain properties can be described as electrical properties, such as ZP, CD and ion concentration. Since an ion is an atom or molecule which has gained or lost one or more electrons, it thereby has a net negative or positive electrical charge. For example, a fusion plasma is so hot that virtually all the electrons are stripped from the atoms creating ions that have a net positive charge equal to the number of protons in their nucleus. Ion concentration is related to the amount of such ions in per unit volume. Thus, there is a direct link of a concentration of ions having an electrical charge.

[0168] However, if there are two different ions A and B with concentration [A] and [B] mixed in a solution, there is still a total electrical charge, but measuring this electrical charge, for example with a conductivity meter in the solution, will not enable distinction and measurement of [A] and [B]. The present disclosure anticipates separately distinguishing and measuring [A] and [B] individually. It is to be generally noted that ion concentration, as used herein, anticipates performing this operation where desired.

[0169] FIG. 2 shows the block diagram for the feed forward controller. It requires the mathematical relationship between the disturbance and the wet end measure, in this case the Zeta Potential (ZP), GL, and the relationship between the input CO2 and the same wet end measure, Gp. The advanced controller design consists on finding the mathematical relationship of the feed forward controller F, and the feedback controller Gc.

[0170] This embodiment is applicable in the wet end of pulp mills to control the properties of the paper by the controlled addition of additives. More specifically, this embodiment considers the addition of CO2 in the wet end in a mixing chest. The measurement of the most important variables in the inlet and outlet fiber flows such as Zeta Potential, charge demand, alkalinity, pH, etc. are taken in real-time, collected and made available to a data acquisition system. The mathematical relationship in the form of transfer function or any time dependent form are utilized to relate the CO2 addition and the desired wet end property, or controlled variable, such as Zeta Potential or charge demand. In addition, similar relationships are utilized between possible variations or disturbances in the inlet fiber flow and the controlled variable. Any feedback controller that tends to minimize the variations between the desired controlled value and the real-time measurements in the outlet fiber flow is used.

[0171] In addition, the available real-time measurements from the inlet fiber flow are used to design a predictive controller, such as feed forward controller, model predictive control (MPC), or any advanced controller. The feed forward controller modifies in a coordinated manner the output of the feedback controller. The feedback and feed forward signals are added and sent to a linear proportional control valve that controls the CO2 flow into the mixing tank.

[0172] FIG. 3 shows the performance of a feed forward control responding to a normalized step change and a charge demand disturbance. It can be seen that the feedback controller can respond with no problems to the set point change, and that due to the feed forward controller, the disturbance is rejected almost immediately, returning the plant to the desired set point.

[0173] Illustrating another preferred embodiment, FIG. 4 shows a mixing chest 11, where a regulated inlet flow of CO2 is supplied, 7. Some properties of the fiber flow are measured on-line before going to the mixing chest by measurements 12. At the same time, some on-line properties of the outlet fiber flow are measured by 13. All available on-line measurements are used to compute the unobservable variables or states, 14, using a real-time model, 15, and an observer or optimal estimator, such as Kalman Filter, 16.

[0174] The Kalman Filter observer is normally known as a model-based observer as it relies on the real-time model, 15. Data-driven observers such as neural networks, do not require a real-time model, but require larger amounts of data to be trained. The observer then estimates in real-time the unobserved variables and passes this information to a controller, 18, that manipulates the input of CO2 that changes the unobserved variable to the desired set point.

[0175] This embodiment can be applied to control and optimization of the wet end of paper mills. It is intended to control the wet end in real-time when the intended control variable is not measured or available in real-time. The available on-line measurements, 12 and 13, are related to control variables or states in what is called an observation equation. The observation equation is part of the estimator or observer 6. The observation equation can assume that there is some noise in the instruments and that the rate of acquisition varies. This way, the information used by the estimator can also use off-line information that is available in long time intervals.

[0176] The observation equation is related to the observer, as is the state equation. The state equation is the transformation of the model, 15, which is suitable for an estimation algorithm along with the observation equation. The state equation also includes some model uncertainty, which corresponds to the inaccuracies of the model. There are several estimation algorithms, but one of the most common is the Kalman Filter (Kalman, R. E.) prediction for being an optimal estimator. The KF estimator is a real-time estimator that estimates the unobservable variables using the available measurements and the available model. The KF observer depends on the process model, 15, and so it is called a model-based observer.

[0177] If no model was available, a data-based observer such as neural network can be employed, but this requires a larger amount of data. The real-time optimal estimates, 14, become the process variable measurements required by the controller 18, which compares the estimates with user-defined set points, and calculates a control output based on the errors. The control output is sent to a linear proportional valve that changes the addition of CO2 into the reactor.

[0178] A method for controlling the CO2 addition in a wet end process utilizing CO2 addition is disclosed. A papermaking composition and CO2 are combined to create a CO2-enriched papermaking composition. At least one electrical property of either the papermaking composition or of the CO2-enriched papermaking composition is either measured or estimated. The rate of addition of CO2 to maintain the at least one electrical property within a pre-selected range of values is then controlled.

[0179] In one preferred embodiment, the electrical property is selected from the group consisting of ZP, CD and ion concentration or any equivalent thereto, and is estimated by measuring at least one property of either the papermaking composition or the CO2-enriched papermaking composition selected from the group consisting of flowrate, CD, ZP, ion concentration, Cy, pH, conductivity and alkalinity and using a model. Preferably, the ZP is estimated. Thus, the measured property can be measured from either the papermaking composition or the CO2-enriched papermaking composition, and is preferably measured from the papermaking composition. Likewise, the estimated electrical property can be estimated for either the papermaking composition or the CO2-enriched papermaking composition, and is preferably estimated for the CO2-enriched papermaking composition.

[0180] In another preferred embodiment, a method for controlling the CO2 addition in a wet end process utilizing CO2 addition includes more sophisticated controls. A papermaking composition and CO2 are combined to create a CO2 -enriched papermaking composition. At least one property of the papermaking composition is measured or estimated and papermaking composition property data is generated. The papermaking composition property data is provided to an advanced controller which generates a papermaking composition output component.

[0181] At least one property of the CO2-enriched papermaking composition is measured or estimated and CO2-enriched papermaking composition property data is generated. The CO2-enriched papermaking composition property data is provided to a feedback controller which generates an outlet controller output component. The feedback controller is compensated by analyzing the inlet controller output component and the outlet controller output component. The inlet flow of CO2 is controlled to maintain at least one property of the CO2-enriched papermaking composition within a pre-selected range of values.

[0182] The at least one property of the papermaking composition is preferably selected from the group consisting of flowrate, ZP, CD, ion concentration, Cy, pH, conductivity and alkalinity. The at least one property of the CO2-enriched papermaking composition is preferably selected from the group consisting of ZP, CD and ion concentration, and is most preferably ZP. Most prerably, the advanced controller comprises a feed forward controller.

[0183] In alternatives of this embodiment, the advanced controller comprises a feed forward controller, and the feed forward controller uses either predictive control or inferential control.

[0184] In yet another preferred embodiment, a method for controlling the CO2 addition in a wet end process utilizing CO2 addition includes somewhat different controls. A papermaking composition and CO2 are combined to create a CO2-enriched papermaking composition. On-line measurements of at least one property of the papermaking composition selected from the group consisting of flowrate, ZP, CD, ion concentration, Cy, pH, conductivity and alkalinity are made, papermaking composition property data is generated and transmitted to an observer. On-line measurements of at least one property of the CO2-enriched papermaking composition selected from the group consisting of flowrate, ZP, CD, ion concentration, Cy, pH, conductivity and alkalinity are made and CO2-enriched papermaking composition data is generated. These data are provided to an observer that generates at least one estimated electrical property of the CO2-enriched papermaking composition selected from the group consisting of ZP, CD and ion concentration. The observer transmits the papermaking composition property data, the CO2—enriched papermaking composition property data and the estimated electrical property data to a controller, and the controller controlling the inlet flow of CO2 to maintain at least one electrical property of the CO2-enriched papermaking composition within a pre-selected range of values.

[0185] The observer can comprise a model, and can further refine the estimated electrical property data by analyzing inaccuracies presented by the model and by analyzing expected errors in measurement. The papermaking composition property data, the CO2-enriched papermaking composition property data and the estimated electrical property data can be incorporated into a software sensor. The estimated electrical property data can be used to evaluate a set point and implement a real time closed loop control.

[0186] Note that, in all of the embodiments described above, in a wet end process utilizing CO2 to control chemical properties in the wet end by injecting CO2 at specific locations in the process, the CO2 injection can be controlled to impart the desired properties either to the liquid or to the fibers, both of which can be present in the papermaking composition. These can be achieved using properties of the fibers or the liquid and rejecting process disturbances.

[0187] For example, the CO2 can be injected in at least one point of the wet end either directly to the fiber flow or to a fiber free liquid that will mix later on with the fibers. Alternatively, the CO2 can be injected into a tank. The controlled injection can be either manual if the measurements are off-line or automatic if the measurements are on-line.

[0188] The manual control takes off-line samples and the properties are measured from these samples. The CO2 is then manually regulated based on some recipes. The recipes for manual control are based on multivariable linear or nonlinear regressions between the CO2 injection, the measurements and the desired set points.

[0189] The automatic control can either be feedback, feedforward, a combination or an advanced controller. The feedback control takes at least one measurement of the process after the mixing the fiber flow and the CO2 rich flow (pure CO2 or water mixed with CO2). The feedforward takes at least one measurement of the process before the CO2 (pure CO2 or water mixed with CO2) is injected and adjusts the CO2 before the process is affected. An advanced controller is either a combination of the feedforward and the feedback or an advanced controller such as but not limited to cascade control, adaptive control, optimum control, robust control, neural network controller, fuzzy control, model predictive control, etc. The advanced controller adjusts the CO2 to maintain the desired chemical property in the wet end, while rejecting any disturbance or minimizing the use of chemical additives in the wet end.

[0190] The chemical properties to be maintained by the CO2 controller in the wet are but not limited to ZP (Zeta Potential), CD (Charge demand), pH, ion concentration, etc. The disturbances that can be rejected by the CO2 controller are but not limited to broke recirculation, variations in inlet charge demand, variations in inlet ZP, variations in pH, temperature, consistency, etc. The CO2 controller uses properties of the process that can be either intrinsic or extensive. Intrinsic information can be at least one but not restricted to pH, conductivity, CD, ZP, ion concentration, etc. Extensive information can be at least but not restricted to flow, volume, etc.

[0191] The on-line properties used by the controller can either be measured or unmeasurable. The measured properties can be at least one but not limited to pH, conductivity, temperature, flow, CD, ZP, etc. The unmeasurable or unobservable properties can be at least one but not limited to CD, ZP, ion concentration, etc. The unmeasurable or unobservable properties can be estimated on-line and used by the CO2 controller using an observer or estimator. The observer or estimator can predict the unmeasurable or unobservable properties based on algorithms provided by, e.g., Kalman filters or neural networks. Observers use process knowledge either from fundamental models, empirical models or heuristic models.

[0192] Note further that, in the embodiments described above, ion concentrations can be from [H+],[OH−],[Ca+2], [Na+], [HCO3−], [CO3−−], etc.

[0193] Moreover, in the embodiments described above, there are at least three techniques for performing automatic control: using properties in the papermaking composition, using properties in the CO2-enriched papermaking composition, and using properties in both. For the first case, it is desired to use feed forward that can be typical feedforward or inferential or predictive control. In the second case, a typical feedback becomes advanced when using adaptive, model predictive, robust, optimal, neural networks, fuzzy control, dynamic matrix control, etc. For the third case, combinations of both techniques can be employed.

[0194] While in the foregoing specification this invention has been described in relation to certain preferred embodiments thereof, and many details have been set forth for purpose of illustration, it will be apparent to those skilled in the art that the invention is susceptible to additional embodiments and that certain of the details described herein can be varied considerably without departing from the basic principles of the invention.

Claims

1. In a wet end process utilizing CO2 addition, a method for controlling the CO2 addition comprising, in combination: combining a papermaking composition and CO2 to create a CO2-enriched papermaking composition; measuring or estimating at least one electrical property of either the papermaking composition or of the CO2-enriched papermaking composition; and controlling the rate of addition of CO2 to maintain the at least one electrical property within a preselected range of values.

2. The method of claim 1, wherein the at least one electrical property is selected from the group consisting of ZP, CD and ion concentration.

3. The method of claim 2, wherein the electrical property is estimated by measuring at least one property of either the papermaking composition or the CO2 -enriched papermaking composition and estimating the ZP.

4. The method of claim 3, the electrical property being ZP.

5. The method of claim 3, the electrical property being CD.

6. The method of claim 3, the electrical property being ion concentration.

7. The method of claim 3, wherein the at least one property is selected from the group consisting of flowrate, CD, ZP, ion concentration, Cy, pH, conductivity and alkalinity.

8. The method of claim 4 wherein the at least one property is selected from the group consisting of flowrate, CD, ion concentration, Cy, pH, conductivity and alkalinity.

9. The method of claim 5 wherein the at least one property is selected from the group consisting of flowrate, ZP, ion concentration, Cy, pH, conductivity and alkalinity.

10. The method of claim 6 wherein the at least one property is selected from the group consisting of flowrate, CD, ZP, Cy, pH, conductivity and alkalinity.

11. The method of claim 3, wherein the at least one electrical property is estimated in the papermaking composition.

12. The method of claim 3, wherein the at least one electrical property is measured in the CO2-enriched papermaking composition.

13. The method of claim 11, wherein the at least one electrical property is estimated in the papermaking composition.

14. The method of claim 12, wherein the at least one electrical property is estimated in the papermaking composition.

15. The method of claim 11, wherein the at least one electrical property is measured in the CO2-enriched papermaking composition.

16. The method of claim 12, wherein the at least one electrical property is measured in the CO2-enriched papermaking composition.

17. In a wet end process utilizing CO2 addition, a method for controlling the CO2 addition comprising, in combination: combining a papermaking composition and CO2 to create a CO2-enriched papermaking composition; measuring or estimating at least one property of the papermaking composition and generating papermaking composition property data, and providing the papermaking composition property data to an advanced controller constructed and arranged to receive the papermaking composition property data and generate a papermaking composition output component; measuring or estimating at least one property of the CO2-enriched papermaking composition, generating CO2-enriched papermaking composition property data and providing the CO2-enriched papermaking composition property data to a feedback controller constructed and arranged to receive the CO2-enriched papermaking composition property data and generate an outlet controller output component; compensating the feedback controller by analyzing the inlet controller output component and the outlet controller output component; and controlling the inlet flow of CO2 to maintain at least one property of the CO2-enriched papermaking composition within a preselected range of values.

18. The method of claim 17, wherein the at least one property of the papermaking composition is selected from the group consisting of flowrate, ZP, CD, ion concentration, Cy, pH, conductivity and alkalinity.

19. The method of claim 17, wherein the at least one property of the CO2-enriched papermaking composition is selected from the group consisting of ZP, CD and ion concentration.

20. The method of claim 18, wherein the at least one property of the CO2-enriched papermaking composition is selected from the group consisting of ZP, CD and ion concentration.

21. The method of claim 17, wherein the advanced controller comprises a feed forward controller.

22. The method of claim 21, wherein the at least one property of the papermaking composition is selected from the group consisting of flowrate, ZP, CD, ion concentration, Cy, pH, conductivity and alkalinity and the at least one property of the CO2-enriched papermaking composition is selected from the group consisting of ZP and CD.

23. In a wet end process utilizing CO2 addition, a method for controlling the CO2 addition comprising, in combination: combining a papermaking composition and CO2 to create a CO2-enriched papermaking composition; measuring or estimating at least one property of the papermaking composition selected from the group consisting of flowrate, ZP, CD, Cy, pH, conductivity, ion concentration and alkalinity, generating papermaking composition property data and providing the papermaking composition property data to an advanced controller constructed and arranged to receive the papermaking composition property data and generate an inlet controller output component; measuring or estimating at least one property of the CO2-enriched papermaking composition selected from the group consisting of ZP, CD and salt ion concentration and generating CO2-enriched papermaking composition property data, providing the CO2-enriched papermaking composition property data to a feedback controller constructed and arranged to receive the CO2-enriched papermaking composition property data and generate an outlet controller output component; compensating the feedback controller by analyzing the inlet controller output component and the outlet controller output component; and controlling the inlet flow of CO2 to maintain at least one property of the CO2-enriched papermaking composition within a preselected range of values.

24. The method of claim 23, wherein the advanced controller comprises a feed forward controller.

25. The method of claim 24 wherein the feed forward controller uses predictive control.

26. The method of claim 24 wherein the feed forward controller uses inferential control.

27. In a wet end process utilizing CO2 addition, a method for controlling the CO2 addition comprising, in combination: combining a papermaking composition and CO2 to create a CO2-enriched papermaking composition; on-line measuring at least one property of the papermaking composition selected from the group consisting of flowrate, ZP, CD, ion concentration, Cy, pH, conductivity and alkalinity, generating papermaking composition property data and providing the papermaking composition property data to an observer; on-line measuring at least one property of the CO2-enriched papermaking composition selected from the group consisting of flowrate, ZP, CD, ion concentration, Cy, pH, conductivity and alkalinity, generating CO2-enriched papermaking composition property data and providing the CO2-enriched papermaking composition property data to the observer; the observer receiving the papermaking composition property data and the CO2-enriched papermaking composition property data and generating at least one estimated electrical property of the CO2-enriched papermaking composition selected from the group consisting of ZP, CD and ion concentration, the observer generating estimated electrical property data for the at least one electrical property and transmitting the papermaking composition property data, the CO2-enriched papermaking composition property data and the estimated electrical property data to a controller; and the controller controlling the inlet flow of CO2 to maintain at least one electrical property of the CO2-enriched papermaking composition within a preselected range of values.

28. The method of claim 27, the observer comprising a model.

29. The method of claim 27, the papermaking composition property data, the CO2-enriched papermaking composition property data and the estimated electrical property data being incorporated into a software sensor.

30. The method of claim 28, the papermaking, composition property data, the CO2-enriched papermaking composition property data and the estimated electrical property data being incorporated into a software sensor.

31. The method of claim 28, the observer further refining the estimated electrical property data by analyzing inaccuracies presented by the model.

32. The method of claim 28, the observer further refining the estimated electrical property data by analyzing expected errors in measurement.

33. The method of claim 28, the observer further refining the estimated electrical property data by analyzing inaccuracies presented by the model and by analyzing expected errors in measurement.

34. The method of claim 30, the observer further refining the estimated electrical property data by analyzing inaccuracies presented by the model.

35. The method of claim 30, the observer further refining the estimated electrical property data by analyzing expected errors in measurement.

36. The method of claim 30, the observer further refining the estimated electrical property data by analyzing inaccuracies presented by the model and by analyzing expected errors in measurement.

37. The method of claim 28 further comprising using the estimated electrical property data to evaluate a set point and implement a real time closed loop control.

38. The method of claim 30 further comprising using the estimated electrical property data to evaluate a set point and implement a real time closed loop control.

39. The method of claim 36 further comprising using the estimated electrical property data to evaluate a set point and implement a real time closed loop control.

40. In a wet end process utilizing CO addition, a method for controlling the CO2 addition comprising, in combination: combining a papermaking composition and CO2 to create a CO2-enriched papermaking composition; on-line measuring at least one property of the papermaking composition selected from the group consisting of flowrate, ZP, CD, ion concentration, Cy, pH, conductivity and alkalinity, generating papermaking composition property data and providing the papermaking composition property data to an observer; on-line measuring at least one property of the CO2-enriched papermaking composition selected from the group consisting of flowrate, ZP, CD, ion concentration, Cy, pH, conductivity and alkalinity, generating CO2-enriched papermaking composition property data and providing the CO2-enriched papermaking composition property data to the observer; the observer receiving the papermaking composition property data and the CO2-enriched papermaking composition property data and using a model to generate at least one estimated electrical property of the CO2-enriched papermaking composition selected from the group consisting of ZP, CD and ion concentration; the observer refining the estimate for the at least one electrical property by analyzing inaccuracies presented by the model and by analyzing expected errors in measurement; the observer transmitting the papermaking composition property data, the CO2-enriched papermaking composition property data and the refined estimated electrical property data to a controller; and the controller controlling the inlet flow of CO2 to maintain at least one electrical property of the CO2-enriched papermaking composition within a preselected range of values.