A STUDY OF MATHEMATICAL PROGRAMMING WITH APPLICATION IN PRODUCTION PLANNING AND PETROLEUM SECTOR IN INDIA SUMMARY OF THESIS SUBMITTED TO H.N.B. GARHWAL UNIVERSITY SRINAGAR (UTTARANCHAL) 246174 FOR THE AWARD OF DEGREE OF DOCTOR OF PHILOSOPHY IN MATHEMATICS 2006 Supervisor : By : Dr. P.B. Semwal PremPal Singh Thakur Ex-Scientist E-II Reg. No. HNB/Res/20398 Indian Institute of Petroleum, Indian Institute of Petroleum, DehraDun, (Uttranchal)-248005 DehraDun,(Uttranchal)-248005
2 CHAPTER-1 LITERATURE REVIEW The Indian petroleum industry scenario has changed very significantly over last one decade. The demand of green fuel products has increased many fold with over all domestic consumption of petroleum products rising to 111.92 mmpta. The increasing dependence on imported crudes with its soaring prices of over $72/bbl has swelled the net oil import bill of India to $34.09 billion in 2005-06 from $22.94 billion in 2004-05. This has a drastic effect on the Indian economy. Thus for Indian petroleum industry, the need of the hour is to make petroleum products precisely viable under the constraints of stringent green fuel regulations and free trade scenario. It has been established that a benefit of 15-20 cent/bbl of crude can be achieved by applying the scientific and mathematical decision making techniques for the optimization of production planning and supply chain management of the petroleum industry. The mathematical techniques like linear programming (LP), based on simplex algorithm developed by G.B. Dantzig in 1947, was first applied in refinery industry in 1950 for blending of fuel oil for meeting a certain set of quality specifications of final blend viscosity and octane rating of different grades of aviation gasoline. Since then LP has been utilized very efficiently the world over in decision models mainly for crude selection, crude transportation, crude processing, evaluation of new process technologies, product blending controls, product inventory and distribution management
3 etc. The extended versions of LP like mixed integer linear programming (MILP) are also used very efficiently in petrochemical industry and chemical processing industry for specific problems of capacity expansion of existing processes, selection and capacity expansion policy of new processes, production profiles, sales & purchase of products, raw materials etc. The petroleum refining involves the availability of different type of crudes, processing units, unit capacities, mode of operation, yield patterns etc. Optimal blending compositions and sharing of product streams are decided to meet the quality and quantity of the finished products. Since it is not possible to carry the experimental work in the real life environment due to the complexity of the operational refinery and the huge costs involved, the computer simulation studies of the mathematical models of the refinery system provides a refiner a fair insight into the future production planning strategy and possible best course of actions at minimum cost to make the enterprise successful. The success of a mathematical model of production planning and distribution system depends on the exactness of the formulations and data that represents the given system including the strategies that are employed to work on the model. The first step for the formulation of the mathematical is to trace the material flow path and then representing the individual operations by respective mathematical formulations like crude availability, unit capacity, material balances, property constraints and product distribution including import & export equations. The refinery optimization model
4 so obtained is configured with a global or single objective of minimizing the over all cost of the finished products and hence to maximize the refinery profit. The large size problems like the present one are solved using LP algorithms which are suitable for computer programs. Although, commercially readymade user friendly softwares like RPMS, PIMS, GRMPTS, PETROPLAN etc. on refinery operational and production planning optimization, based on LP techniques, are easily available but they are not exactly suitable for day to day problems of the refinery besides they are very costly. Hence, the need for updating and developing new specialized softwares. CHAPTER-2 PROBLEM DEFINITION AND SCOPE OF STUDY The present work is an attempt to develop a mathematical model of two refineries using Linear Programming (LP) techniques to optimize their production and distribution system to meet their common demands with provisions for import and export of finished products. The model would link these refineries by sharing a common pool of intermediate/finished product to meet the quality and demand of end products, over a given plan period, for achieving maximum profit margin. Further, the study would suitably identify the optimal crude ratio, the selection and mode of operation of processing units, import and sharing of intermediate/finished products etc. at minimum transportation costs. In the development of this optimization model, due consideration would be given for crude composition, its pricing,
5 various refining processes, quality specifications, regional & seasonal consumption habits, storage and transportation of finished products etc. so as to minimize the overall cost of the finished products. It is observed that a minimum of 5-10% profit margin can be achieved by merely applying LP techniques in refining industry. Indian refineries are not fully applying such decision making techniques in their production and distribution planning system as regularly applied by the western countries for maximization of refinery profitability. Hence, under Indian context, it would be a great saving to the nation by applying these LP based optimization techniques for the following potential problem cases which a refiner has to tackle over a variety of scopes viz: (i) to obtain an optimum crude mix of light and heavy crudes to be processed for meeting quality finished products demand at minimum cost of production and option of import and export, (ii) to select the optimal mode of operation of conversion processes like FCC, Catalytic Reforming, Isomeration, HDS etc. so as to meet the quality and quantity of finished products, (iii) to maximizing the gasoline octane and volume in absence of the MTBE and other octane enhancing oxygenates by sharing the high octane intermediate streams from the common pool, (iv) to reduce the sulphur content in diesel fuel to the required specification level. The specialized mathematical LP optimization technique would minimize the over all cost of production and distribution of the quality
6 petroleum products subject to meeting the demand for each time period over the entire planning horizon. CHAPTER-3 CRUDE OIL EVALUATION REFINERY CONFIGURATION AND PRODUCT QUALITY SPECIFICATIONS The refinery configuration, operation and end product quality are affected by the type of crudes processed. The crudes from different sources and even from the same region vary significantly in their composition and price. The crude oils contain thousands of hydrocarbons with varied amount of composition impurities and are classified in three broad groups viz: Paraffinic, Naphthenic and Aromatic. The API gravity, Sulfur content (wt %), Viscosity, Characterization Factor (K) are the key properties of a crude oil which influence its distillation, refinery conversion process and the quality of finished products for its market value. The value of K gives idea against the paraffinic, naphthenic and aromatics type of crudes. The composition of the crude from different fields has carbon range 83-87%, hydrogen range 10-14%, sulfur range 0.05-6% and others from 0.05-1.5%. It is observed that the API gravity of crude oil has been declining rapidly at the rate of 0.20 API per year and the sulfur content is increasing at about 0.023 wt % per year. The high sulphur sour or heavy crudes are cheap but not suitable for the production of middle distillates. The low sulphur light paraffinic, sweet crudes are suitable for the middle distillates but are comparatively costly. Also the refining strategy for the light crude is
7 quite different from that of heavy crude. Hence selection of crude or crude mix is highly significant factor for a given refinery configuration. Here LP applications has a great role in identifying the optimum crude mix for a given refinery for maximum profit margin. Petroleum refining industry involves three important phases (i) the crude supply (ii) refining & processing (iii) product blending & distribution, where application of LP is made frequently. The selection of right type of crude is important keeping in view the crude prices, refinery configuration and end product quality & quantity requirements. The modern refineries essentially consist of the main processes of Reforming, Catalytic Cracking (FCC) to convert heavy oil to lighter streams and Desulphurization (HDS) to remove the sulfur, mainly from cracked blend components of gasoline and diesel fuel, for meeting their quality norms. After the complete ban of lead compounds as anti-knock additive in India the next stage is set for the stringent regulations on the content of benzene, oxygenate in gasoline, ultra low sulfur in gasoline & diesel. The sulfur standard on diesel fuel requires special attention as the consumption of it is more than five times to that of lighter fuels. The performance quality of gasoline is expressed in term of its octane number. High octane gasoline like the reformulated gasoline (RFG) contains high-octane oxygenated fuels like alcohols and ethers. Studies have established that the MTBE, an important octane enhancer is animal carcinogen and also that its desired phase out will reduce the refining margin very drastically. Thus the need for
8 application of innovative mathematical techniques in production planning and distribution systems to use the existing resources very judiciously and effectively while maintaining the product quality & quantities has become much more important. CHAPTER-4 OPTIMIZATION MODEL OF A TYPICAL REFINERY R1 WITH IMPORT AND EXPORT SCENARIO The application of scientific decision making actions on the level of Indian refineries and over all economy, leads to the utilization of new concepts and solution for refinery planning and economy. This includes multistage set of models. For the optimization of the production planning of a typical refinery configuration with constraints of unit capacity, type of crudes, crude ratio, demand, quality and environmental specification limits on petroleum fuel products with special provision for import and export of intermediate and finished products, specialized mathematical linear programming method has been applied under this study. Firstly, a base model is proposed to identify the right use of crude mix ratio for given refinery configuration which minimizes the over all cost of production subject to various constraints on crude prices & its availability, product demand their quality specification limits for a given planned period. The mathematical linear constraints and equations which described the model consist of the unit capacity constraints, crude availability, material balances,
9 product quality constraints, blend composition, demand, importexport of intermediate and finished products along with a linear objective function based on cost of crude oils, unit processing, import and export. A total of 48 constrained equations comprising of 20 inequalities and 28 equalities were described. Twenty slack variables are introduced to convert these inequalities into equations. Based on two phase Simplex Method a suitable computer programme in programming language C/C++ run on a Pentium III computer, is developed to solve the above LP optimization problem. The base model converged in 102 iterations giving a minimum cost of production 90.178x10 6 units. The optimum total crude processed is 538.65 units with share of crude-1 at 278.65 units and crude-2 at 260.00 units. From the analysis of the result, it is observed that the refinery can meet all the domestic demands of desired quality products with present configuration but to meet the product demand and quality specification, 7.4 units of the reformer feed (heavy naphtha) is desired to be imported. The production of Jet Fuel in F1 mode is more economical than F2 mode under given refinery configuration with export option of 5.62 units per month. Further a quantity of 12.77 units per month of gasoline (ES95) can also be used as export for increasing refinery profit margin. Different case studies are carried on two main parameters, first the reduction of sulphur content in high speed diesel (HSD) and second the variation of ratio of crude mix processed, to analyze its effect on product blend composition, import & export and over all refinery profit
10 From this study it is concluded that the processing cost increases significantly with reduction of sulfur content in diesel fuel and hence import of HSD becomes more economical under present refinery configuration. Also the profit margin increases significantly within the feasibility region with increase of light crude ratio and the profit margin is maximum at light crude processing of 53.9% with potential of exports of excess products but there is no significant gain in profit on processing above 53% of crude-1. The study also predicts that the import of Heavy Naphtha decreases with the increase in crude ratio and stabilizes at about 53% of light crude processing. Hence the LP suggests that refiner can process up to 47% of heavy crude with high profit margin for the given refinery configuration. CHAPTER-5 TWO REFINERY MODEL WITH COMMON MARKETS AND COMMON POOL Under this study a model linking two refineries with three common markets is attempted to develop. The purpose of the model is to determine the optimum allocation of environment friendly finished product from these refineries to the common demand markets while meeting demands of their individual market. The mathematical model is formed by linking two refineries R1 and R2. The configuration & formulations of R1 is that of the refinery described under chapter 4. The refinery R2 is considered to be a simplified simulation ( Black Box ) processing three crudes viz: light
11 & expensive (crude-1), heavy & cheap (crude-2) and an average crude (crude-3). For the mathematical formulations it is assumed that (i) The property specifications of intermediate and finished products of R2 are same as that of R1. (ii) Any surplus of liquefied gas (LG) and light naphtha (LN) from either of the refinery is being used for meeting demand as well as and quality specifications of finished products. (iii) Burnt fuel and losses amount to 6% (wt) of crude for R2 and is comprised of refinery gas and liquid heavy fuel. Further, that the potential excesses of LG & LN may replace some liquid fuel. The formulations of LP model are described as detailed linear equations and constraints representing crude availability, unit capacity, mode of operations, material balances, quality specifications, besides equation of market demands, export/import etc. The mathematical model minimizes the linear objective cost function of production of the finished products with minimum transportation costs to meet the demand of common markets. The model consists of a total of 68 constrained equations comprising of 25 inequalities & 43 equalities having 75 decision variables were developed. Twenty five slack variables are introduced to convert the inequalities into equations. The two phase simplex method is used to solve above constrained mathematical problem. The model converged in 132 iterations giving a minimum cost of production 151.135x10 6 units. From the optimal results, it is observed that the optimum crude processed in refinery R1 is 542.85 units with the share of crude-1 as 282.85 units and crude-2 as
12 260.00 units. The optimum crude processed in R2 is 338.93 units of which crude-2 is 200.0 units; crude-3 is 138.93 units however, crude-1 is not processed. From the analysis of the result obtained, the following important observations are made that (i) The capacity utilization of CDU of R1 (77.55%) is higher than that of R2 (67.79%). (ii) Both refineries can meet all the domestic demands of desired quality gasoline ES95 and HSD, however it is more economical to import JP (by 6.1 units) to meet its demand. Further to meet the product demand and quality specification, 7.2 units of the reformer feed (heavy naphtha) has to be imported in R1. (iii) The production of gasoline (ES95) and HSD from R1 is in surplus by 5.22 and 5.57 units respectively which can be used for export. Under the given transportation cost structures the major demands of common markets A & B are met from R1 while that of C are met by products from R2. To find the operational utility of this model, different case studies are under taken on three broad parameters viz; ratio of crude mix, clean diesel fuel norms and common market demand. For this each parameter is changed in steps, while keeping the others fixed to study its effect on operation of refineries, import & export of finished products and finally the profit margin of the refinery system. Further an attempt is also made to study the linking of the two refineries by sharing a common pool of intermediate/finished products of liquefied gas (LG) and light naphtha (LN) for meeting the quality & quantity of the finished products from either of the two refineries R1 and R2.
13 From this study it is concluded that (i) the margins of the refineries R1 & R2 is high with the processing of higher quantity (up to 64.2%) of light crude-1 in refinery R1, but there is no significant gain in profit for above 63% of crude-1 processed, while refinery R2 can process entirely the heavy (crude-2) and the average (crude-3) in the ratio of 10:7. (ii) The processing cost increases significantly with reduction of sulphur content in diesel fuel and thus import of HSD becomes more economical with present configurations of the refineries. (iii) Demand fluctuation can affect the refinery inventory and/or export & import of clean finished products and hence the refinery profit margin but has no other significant effect on refinery operations. (iv) The study of common pool suggests that refineries can increase the quality of finished product by sharing the intermediate products. Further the common pool case study predicts a large increase in profit margin for the refineries. The concept of linking of refineries can be extended to more than two refineries with common pool for sharing intermediate /finished products. The concept is more useful in context of Indian refinery industry, where more than one refinery are owned and managed by large public sector companies, for efficient utilization of blend streams for the production of green fuel products, higher sale realization and hence the improved profitability. This study is very well applicable to the IOC Mathura and Panipat refineries while catering to the demands of common markets of adjoining Northern States like Delhi, Haryana, Punjab, H.P., U.P., Uttranchal etc.