Availability Analysis of Refining System of a Sugar Plant Using Markov Process

Transcription

1 Availability Analysis of Refining System of a Sugar Plant Using Markov Process Er. Aman 1, Dr. V.K. Mahna 2, Dr. Rajiv Khanduja 3 1 Research Scholar, Dept. of Mechanical Engineering, M.R.I.U., Faridabad,Haryana, India 2 Pro-Vice Chancellor and Professor, M.R.I.U., Faridabad, Haryana, India 3 Principal and Professor, Y.I.T. Jaipur, Rajasthan, India Abstract The paper discusses the availability optimization of refining system of sugar plant. It is a repairable and complex system as there are various subsystems involved in it. It includes feeding system, refining system, evaporation system and crystallization system. One of the main parts of a sugar industry is refining system. The refining system includes filter units, clarifier units. Sulphonation units and heating units. If one unit fails, refining system failure takes place. The mathematical modelling using probabilistic approach based on Markov birth-death process is used to analyze the availability. To fulfill this purpose, the first order differential equations are developed. By using normalizing conditions to determine steady state availability, these equations are solved. The result of this paper is useful to analyze the availability and to determine various maintenance strategies in sugar plant. Key words- Refining system, Steady state availability, Maintenance strategy, Markov birth-death process, Mathematical model. 1. INTRODUCTION The raw material is sugar cane which is mostly used to produce the sugar. Its production mainly depends on land s fertility, manure s quality, skills involved in agriculture. It is also very essential that each subsystem should run failure free for long duration with full efficiency and capacity to achieve high productivity. But in real situations, it is seen that the operative units are always subjected to random failures which depends upon maintenance strategies and operative conditions. The analysis is done to achieve the availability. The real system is modeled mathematically and analyzed in actual operating conditions. To quantify the system performance in terms of availability, mathematical models are developed. Markov Birth- Death process is used for the present study in a sugar plant. To analyze the overall availability of a sugar plant, the different differential equations are developed and solved under normalizing conditions. 2. REFINING SYSTEM DESCRIPTION The refining system is having four sub-systems, (i) Filter unit (A) is having n units in series and failure of any one causes failure of system (ii) Clarifier system (B) having n units in series and failure of any one leads to failure of the whole system. (iii) Sulphonation system (C) having n units in parallel, failure of which reduces the capacity and efficiency of system (iv) the heating system (D) having n units in parallel, failure of which reduces efficiency of system. 3. LITERATURE REVIEW The literature suggests that various approaches have been utilized for analyzing the system performance in terms of availability and reliability. These include Markov modeling, reliability block diagram, failure mode and effect analysis, Monte Carlo simulation and Petri nets. Bellman 1962; Misra 1971; Kumar 1977;Weber 1989; Arora 1996 Sunand 1998; 490

2 Modarres et al. 1999; Adamyan and Dravid 2004; P. Gupta 2005; Panja and Ray 2007; Kumar 2012; S.P. Sharma and Y. Vishwakarma 2014; Kumar 2014 have frequently used the various approaches for availability analysis. D.Kumar, J. Singh, and I. P. Singh 1988 has explained the availability of the feeding system in the sugar industry. Kumar et al. (1988, 1989 used the Markov modeling in the analysis and evaluation of the performances of and power generation systems in the thermal power plant.rajiv Khanduja, P. Tewari and D. Kumar 2008 has explained the availability analysis of bleaching system in a paper a plant.s. P. Sharma and H. Garg 2011 studied the behavioral analysis of urea decomposition system in a fertilizer plant. P. Gupta 2011 presented his work on Markov Modeling and availability analysis of a chemical production system-a case 4. ASSUMPTIONS AND NOTATIONS (i) Failure/repair rates are constant over time and independent statistically.. (ii) A repaired unit is as good as new. (iii) Standby units are of same nature and capacity as the active units. (iv) Service includes repair and replacement. (v) Sufficient repair facilities are provided i.e. no waiting time to start the repair. Notations:,, represents full, reduced and failed state respectively. A,B,C,D are operative states of all four subsystems and a, b,c, d arefailed states of systems A,B,C,D. (i) α A, α B, α C, α D are repair rates of system A,B,C,D. (ii) β A, β B, β C, β D are complete failure rates of system A,B,C,D. 0 represents operative state 1,2,3,4,5 reduced state 7,8,9,10,11,12,13,14,15,16,17,18,19,20,21 and 22 represents failed state. P n (t) represents probability that the system is in state n at time t. 5. MODELLING USING MARKOV PROCESS The system is modeled as we consider that time involved in repair as well as failure free time must be distributed exponentially. 491 sugar and urea fertilizers plant. D. Kumar and N. Arora 1997 has explained the availability analysis of air circulation system using Markov approach. For failure-free operation of the refining units in a sugar plant, the steady- state availability expressions has been developed, and each subsystem s behavior has also been analyzed in the present study. Fig- 1: Transition Diagram of Refining System State 0 full working State 1 to 5 Reduced capacity state State 6 to 22 is failed state due to failure of one or more units of a system. The associated differential equations are given as:- P 0 '(t) + β r P 0 (t) = α j P k (t) (1) P 1 ' (t) + (β r +α D )P 1 (t) = α j P k (t) + β D P 0 (t) (2) P 2 ' (t) + (β r +α D )P 2 (t) = α j P k (t) + β D P 1 (t)(3) P 3 ' (t) + (β r +α c )P 3 (t) = α j P k (t) + β c P 0 (t) (4) P 4 ' (t) + (β r +α c )P 4 (t) = α j P k (t) + β c P 1 (t)(5) P 5 ' (t) + (β r +α c )P 5 (t) = α j P k (t) + β c P 2 (6) P i ' (t) + α m P i (t) =β m P 1 (t) (7) For steady state availability By putting d/dt=0 as t in equations (1 to 7), the steady state probabilities are given by, P 1 =p P 0 P 2 =( β D /α D ) p P 0 P 3 =p P 0 P 4 =( β C /α C ) p P 0 P i =( β m /α m ) P 1.(8) The probability of full working i.e. P 0 is determined by using normalizing conditions, 22 P i =1 i=0

3 Substituting the values of P 1 to P 22 in terms of P 0 into normalizing condition, we get P 0 A 0 =1 or P 0 [ A 0 ] -1 Where P 0 [1 + β A /α A + β B /α B + q{1 + β A /α A + β B /α B + β C /α C } + p {1 + β A /α A + β B /α B + β C /α C + β D /α D } + (β D /α D ) + { β C /α C + β B /α B + β A /α A ) + (β C /α C ) + (β C /α C ) + (β A /α A ) (β D /α D ) } + (β B /α B ). (β D /β D ) + (β C /α C ). (β D /α D ) + (β D /α D ) 2 ] = 1 P 0 A 0 =1 or P 0 [ A 0 ] -1 Where A 0 =1 + repeat the [1+.+() 2 ] The steady state availability of refining subsystem may be obtained as summation of all six working state probabilities. 5 A vst = P i i=0 A vst = P 0 [1+p+( β D /α D ) p +q +(β C /α C ) p +(β C /α C ) (β D /α D ) p] A vst =1/G 0 [1+p{1+ β c /α c +β D /α C + β D (α D + β C /α C ). (β D /α D )}+q}] (9) Where p= β D β C + β D - β D. α D q= β C + β D -pα D α C 6. AVAILABILITY ANALYSIS OF REFINING SYSTEM The performance of availability of refining system is mainly affected by failure repair rates and failure rate of each subsystem in a sugar industry. The availability evaluation model includes all possible repair priorities. Table 1 and 2 shows effect of different combinations of failure and repair rates on availability of various subsystems of refining system. Best possible combination of repair and failure rates may be selected on the basis of this analysis α B α A β A Table-1: Availability matrix for filter subsystem of refining system Where β D =0.002, α B =0.55, β C =0.002, α C =0.05, β D =0.002, α D =0.05. Table 1 and graph in figure 2(a) and 2(b) show the effect on availability of refining system by using various combinations of failure rate and repair rates of filter subsystem. In the analysis, it is observed that for some known values of failure and repair rates of filter, as failure rate of filter subsystem increases from 0.01 to 0.07, the system availability

4 decreases by 29.69%. Similarly as repair rate of filter subsystem increases from to 0.175, the system availability increases by 31%. α B β B Table-2: Availability matrix for clarifier subsystem of refining system where β A =0.045, α A =0.100, β C =0.002, α C =0.05, β B =0.002, α D =0.05 Table 2 and graph in figure 3(a) and 3(b) show the effect on availability of clarifier subsystem in refining system by using various combinations of failure rate and repair rates of clarifier subsystem. In the analysis, it is observed that for some known values of failure and repair rates of clarifier, as failure rate of clarifier subsystem increases from to 0.07, the system availability decreases by 4.2%. Similarly as repair rate of clarifier subsystem increases from 0.50 to 0.200, the system availability increases by 2.14%. From this analysis, it is clear that for subsystems G and H, the failure and repair rates do not affect the working capacity when run for long time. 7. CONCLUSION It is concluded that for the analysis of availability of various subsystems of refining system in a sugar plant, the performance evaluating model is used effectively. It also explains the relationship between various failure and repair rates for each subsystem of refining system in a sugar plant. It also gives different availability levels for various combinations of failure and repair rates for each subsystem. Best possible combination of failure and repair priorities may be selected for each subsystem. The optimal maintenance strategies may be determined to ensure maximum availability of refining system in sugar plant. For every subsystem, the optimum values of failure and repair rates of each subsystem are given in Table 3. Beyond these optimum values of failure and repair rates, there is very less increase in availability levels. Therefore, we have selected the optimum values for highest possible availability level. So, findings are discussed with concerned sugar plant management. These results are beneficial to sugar plant management for analysis of availability and decide repair priorities of various subsystems of refining system in sugar plant to enhance the performance of the system.

5 Sr. No. 494 Failure rates Repair rates Maximum Availability Level 1 β A = 0.01 α A = β B =0.001 α B = Table-3: Optimal values of failure and repair rates Availibilit y Fig-2(a): Effect of Repair rate of filter subsystem on refining system availability Availibilit y Repair rate------> Failure Rate Fig-2(b): Effect of Failure rate of filter subsystem on refining system availability Fig-3(a): Effect of Repair rate of clarifier subsystem on refining system availability Fig- 3(b): Effect of Failure rate of clarifier subsystem on refining system availability REFERENCES [1]. Arora N. and Kumar D., Availability analysis of steam and power generation systems in the thermal power plant, Micro-electronics Reliability, vol. 37, no. 5, pp , [2].Dhillon B.S. and Singh C. (1981), Engineering Reliability, New Techniques and Applications, John Willey and Sons, New York. [3]. Garg H. and Sharma S.P., Behavior analysis of synthesis unit in fertilizer plant, International Journal of Quality and Reliability Management, vol. 29, no. 2, pp , [4]. Gupta P., Markov Modeling and availability analysis of a chemical production system-a case study, in Proceedings of the World Congress on Engineering (WCE 11), pp , London, UK, July [5]. Khanduja R., Tewari P. and Kumar D., Availability analysis of bleaching system in a paper a plant vol. 32, no. 1, [6]. Komal, Sharma S.P., and Kumar D., RAM analysis of the press unit in a paper plant using genetic algorithm and lambda-tau methodology, in Proceeding of the 13th Online International Conference (WSC 08), vol. 58 of Applications of Soft computing (Springer Book Series), pp , [7]. Kumar D., Singh J., and Pandey P.C., Availability of a washing system in the paper industry, Microelectronics Reliability, vol. 29, no. 5, pp , [8]. Kumar S. and Tewari P.C., Mathematical Modelling and performance optimization of CO 2 cooling system of a Fertilizer plant, International Journal of Industrial Engineering Computations, vol. 2, no. 3, pp , [9]. Kumar R., Sharma A.K., and Tewari P.C., Markov approach to evaluate the availability simulation

6 model for power generation system in a thermal power plant, International Journal of Industrial Engineering Computations, vol. 3, no. 5, pp , [10].Sharma S.P. and Vishwakarma Y., Application of Markov Process in Performance Analysis of Feeding System of Sugar Industry Research article, Hindawi publishing corporation, journal of industrial mathematics,volume Dr. V.K. Mahna is Pro-Vice Chancellor of Manav Rachna International University Faridabad, Haryana, India BIOGRAPHIES Aman is a research Scholar at Department of Mechanical Engineering, Manav Rachna international University, Faridabad, Haryana, India Dr. Rajiv Khanduja is working as Principal of Y.I.T. Jaipur, Rajasthan, India 495