Theoretical analysis of LC-refining – pressure screening systems in TMP

Jorge Enrique Rubiano Berna; Christer Sandberg; Mark Martinez; James Olson

doi:10.1515/npprj-2018-0040

Published by De Gruyter February 1, 2019

Theoretical analysis of LC-refining – pressure screening systems in TMP

Jorge Enrique Rubiano Berna , Christer Sandberg , Mark Martinez and James Olson

From the journal Nordic Pulp & Paper Research Journal

https://doi.org/10.1515/npprj-2018-0040

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Abstract

LC refining of mechanical pulps has proven to save energy in the production of TMP pulps. However, the specific role of LC refining as part of a TMP system has not been thoroughly studied since it is difficult to conceive any particular system at industrial-scales and impractical at pilot-scales. In this study, pressure screening and LC refining models that describe fibre length distributions, together with correlations to predict refining power were used to model three basic refining systems. From the simulation results, the impact of important variables such as reject ratio, refiner gap and refining net-power was studied. Performance curves of length-weighed average fibre length were generated from simulation results and were used to assess each system behaviour and also to make comparisons between systems. Data from an industrial scale TMP mill sub-system was gathered and compared to simulation results showing relative errors between 0–18 % on the predicted variables.

Keywords: low consistency; mechanical pulp; pressure screening; refining systems; system modeling

Funding source: Natural Sciences and Engineering Research Council of Canada

Award Identifier / Grant number: CRDPJ 437223-12

Funding statement: This work was funded by the Natural Sciences and Engineering Research Council of Canada (NSERC) Collaborative Research and Development (CRD) grant CRDPJ 437223-12 and the support of the industrial partners AB Enzymes, Alberta Newsprint Company, Andritz, BC Hydro, Canfor, Catalyst Paper, FPInnovations, Holmen, Meadow Lake Pulp (Paper Excellence), Millar Western, NORPAC, West Fraser, Westcan Engineering and Winstone Pulp International who are thanked for their support.

Conflict of interest: The authors declare no conflicts of interest.

Appendix A Mathematical analysis of a system

Flows fibre length distributions

The following mathematical procedure includes matrix operations. To simplify the notation, matrices for the screening and refining operations and vectors for the fibre length distributions are defined and presented in bold fonts.

(A.1a) H = diag R v P ( l i ) − 1 ∑ i = 1 p R v P ( l i ) − 1

For refining:

(A.1b) J = exp m π α β ω R o 2 Q ( 1 − λ 2 ) A

For the fibre length distribution of the flow k:

(A.1c) Y k = { y i k }

Consider the Feed-back reject-refining system with the notation shown in the Figure A.1. The rejects are related to the screen feed as:

(A.2) Y r = H Y f s

The accepts are related to the screen feed as:

(A.3) Y a = ( I − R v H ) Y f s

The refined pulp is related to the screen rejects as:

(A.4) Y r r = J Y r

Figure A.1

Feed-back reject-refining.

Combining Equation A.2 and A.4 yields:

(A.5) Y r r = J H Y f s

Now, from a mass balance at the mixing point:

(A.6) Q f s C f s Y f s = Q f C f Y f + Q r r C r r Y r r

Dividing Equation A.6 by Q f s C f s , the FLD of the screen feed Y f s is obtained as:

(A.7) Y f s = ( 1 − R v ) T Y f + R v T Y r r

Replacing Equation A.5 in Equation A.7:

(A.8) Y r r = J H [ ( 1 − R v ) T Y f + R v T Y r r ]

And finally, finding an explicit expression for Y r r in terms of the initial pulp Y f :

(A.9) Y r r = ( 1 − R v ) T J H [ I − R v T J H ] − 1 Y f

Where I is the identity matrix. Once Y r r is known, it is used in Equation A.7 to calculate Y f s . Subsequently it is possible to calculate Y r and Y a using Equation A.2 and A.3 respectively.

Calculation of E

If the mass flow rate flowing through the screen is set to 1, one has:

(A.10a) 1 = m ˙ a + m ˙ r

Expressing the mass flow rates as the product of volumetric flow rate times consistency:

(A.10b) 1 = Q a C a + Q r C r

(A.10c) 1 Q a C a = 1 + Q r C r Q a C a

(A.10d) 1 1 − R v T − 1 = Q r C r Q a C a

Since the mass flow leaving the system Q a C a is the same as the mass flow feeding the system Q f C f :

(A.10e) Q r C r Q f C f = R v T 1 − R v T

On the left-hand side one has the ratio mass flow rate flowing through the refiner over the mass flow rate leaving the system which is the definition of E.

(A.10f) E = R v T 1 − R v T

The alternate definition of E in terms of energy content is also derived. Setting m ˙ f s = 1 and e f = 0.

(A.11a) e r r = e r + e R

Where e R is the energy supplied by the refiner (SEC). At the mixing point:

(A.11b) e f s = m ˙ r r e r r

Since m ˙ r r = m ˙ r = R v T, combining Equation A.11a and A.11b leads to:

(A.11c) e f s = R v T ( e r + e R )

(A.11d) e f s − ( R v T ) e r = ( R v T ) e R

As e f s = e r = e a , the interest is on finding an expression for the ratio e a / e R (energy content of the flow leaving the system over the energy supplied by the refiner), which is the alternate definition of E.

(A.11e) e a ( 1 − R v T ) = ( R v T ) e R

(A.11f) E = R v T 1 − R v T

References

AFT Aikawa Fibre Technologies. Introduction to stock prep refining. Last accessed: 29-Sep-2017.Search in Google Scholar

Andersson, S. (2011). Low Consistency Refining of Mechanical Pulp – Process Conditions and Energy Efficiency. Licentiate Thesis, Mid Sweden University, Sundsvall, Sweden.Search in Google Scholar

Andersson, S., Sandberg, C., Engstrand, P. (2012) Effect of long fibre concentration on low consistency refining of mechanical pulp. Nord. Pulp Pap. Res. J. 27:702–706.10.3183/npprj-2012-27-04-p702-706Search in Google Scholar

Cannell, E. (2002) Low consistency refining of TMP. Solutions! 12:30–32.Search in Google Scholar

Gorski, D., Mörseburg, K., Olson, J.A., Luukkonen, A. (2012) Fibre and fines quality development in pilot scale high and low consistency refining of ATMP. Nord. Pulp Pap. Res. J. 27:871–881.10.3183/npprj-2012-27-05-p872-881Search in Google Scholar

Kerekes, R.J. (2015) Perspectives on high and low consistency refining in mechanical pulping. BioResoruces 10(4):8795–8811.10.15376/biores.10.4.8795-8811Search in Google Scholar

Lemrini, M., Lanouette, R., Michaud, G. (2015) Merging interstage fractionation and low consistency advantages during the TMP refining process: Part III – How fibre morphology impacts paper properties. BioResources 10(1):1048–1059.10.15376/biores.10.1.1048-1059Search in Google Scholar

Luukkonen, A., Olson, J.A., Martinez, D.M. (2010) Low consistency refining of mechanical pulp: A methodology to relate operating conditions to paper properties. J. Pulp Pap. Sci. 36:28–34.Search in Google Scholar

Miller, M., Luukkonen, A., Olson, J.A. (2017) Effect of LC refining intensity on fractionated and unfractionated mechanical pulp. Nord. Pulp Pap. Res. J. 27(3):386–394.10.3183/npprj-2017-32-03-p386-394Search in Google Scholar

Olson, J.A. (2001) Fibre length fractionation cause by pulp screening, slotted screen plates. J. Pulp Pap. Sci. 27(8):255–261.Search in Google Scholar

Olson, J., Allison, B., Roberts, N. (2000) Fibre length fractionation cause by pulp screening. Smooth-hole screen plates. J. Pulp Pap. Sci. 26(1):12–16.Search in Google Scholar

Olson, J., Roberts, N., Allison, B., Gooding, R. (1998) Fibre length fractionation caused by pulp screening. J. Pulp Pap. Sci. 24(12):393–397.Search in Google Scholar

Olson, J., Wherrett, G. (1998) A model of fibre fractionation by slotted screen apertures. J. Pulp Pap. Sci. 24(12):398–403.Search in Google Scholar

Rubiano Berna, J.E., Martinez, D.M., Olson, J.A. (2018a). A comminution model parametrization for low consistency refining. Powder Technol. 328:288–299.10.1016/j.powtec.2018.01.031Search in Google Scholar

Rubiano Berna, J.E., Martinez, M., Olson, J. (2018b). Power–Gap relationships in low consistency refining. Nord. Pulp Pap. Res. J. DOI: 10.1515/npprj-2018-0039.Search in Google Scholar PubMed PubMed Central

Sandberg, C., Berg, J.E., Engstrand, P. (2017a) Low consistency refining of mechanical pulp – System design. Tappi J. 16(7):419–429.10.32964/TJ16.7.419Search in Google Scholar

Sandberg, C., Berg, J.E., Engstrand, P. (2017b) Mill evaluation of an intensified mechanical pulping process. Nord. Pulp Pap. Res. J. 32(2):204–210.10.3183/npprj-2017-32-02-p204-210Search in Google Scholar

Sandberg, C., Sundström, L., Nilsson, L. (2009) Potential of low conistency refininer of TMP – Mill evaluation. In: International Mechanical Pulping Refining Conference. pp. 186–189.Search in Google Scholar

Scott, G.M., Abubakr, S. (1994) Fractionation of secondary fiber – A review. Prog. Pap. Recycl. 3(3):50–59.Search in Google Scholar

Young, E., Olson, J.A. (2004) Development of a continuous high-efficiency laboratory fibre fractionator. Can. J. Chem. Eng. 82:433–441.10.1002/cjce.5450820303Search in Google Scholar

Received: 2018-08-06

Accepted: 2018-10-19

Published Online: 2019-02-01

Published in Print: 2019-03-26

Theoretical analysis of LC-refining – pressure screening systems in TMP

Abstract

Appendix A Mathematical analysis of a system

Flows fibre length distributions

Calculation of E

References

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