(441b) Plantwide Optimization of a Pulp Mill Process

Paper products are indispensable parts of the modern daily life. The production of this essential commodity is also an important part of the global economy with annual revenues of 500 billion dollars from sales of over 300 million tons of products [1]. The production facilities to process the requisite amounts of timber into finished pulp and paper products are massive in size and technologically very complex. A modern pulp mill with a production capacity of 300,000 tons per year is estimated to cost more than a billion dollars [2]. The principle of economies of scale is valid for the industry and high capacity mills are necessary to lower the cost of production. However, in recent years changes in the global economy affected the pulp and paper industry dramatically and resulted in serious price-based international competition. The high capacity producers are facing another challenge from the digital alternative media and storage technologies. The decline in demand combined with the international competition is forcing the sector to reductions in capacity. In the face of decreasing demand and excess capacity, it is essential for the industry to improve the productivity of existing mill operations.

The pulp mill process is comprised of several important material and energy recycle loops, which lead to highly interactive multivariate process behavior among different unit operations. This characteristic of the process motivates a plantwide approach to both control and optimization problems. Recently, Castro and Doyle provided a benchmark for the operation of a complete pulp mill and presented an analysis of the benchmark for plantwide control [3, 4]. There are also several publications in the literature that consider selection of optimal inventory levels and production rates for millwide operation using simple mass and energy balances [5, 6]. However, the development of an economic optimization system that can be interfaced with the millwide process control structure for real-time applications is lacking.

In this study, the benchmark problem of Castro and Doyle was chosen to provide a virtual pulp mill for the formulation of a plantwide economic optimization problem. In the first step, the costs and revenues associated with the various mill operations were identified along with a set of process variables that were involved in the process economics. This set consisted of a total of 28 controlled (CV), 61 manipulated (MV) and 11 disturbance variables (DV) chosen from a total of 115 CV's, 82 MV's and 58 DV's of the pulp mill benchmark. The calculation of total steady state profit from these variables generated the objective function for the optimization problem. This information is then used to develop an optimization relevant model by linearizing the benchmark problem at its nominal operating conditions to establish the relationships among the chosen set of process variables. The linearized model and the operational limits for the variables formed the constraint set of the optimization problem.

The solution of the problem provided a new set of operating conditions and according to model predictions these new operating conditions increased the steady state profit by 47% compared to the nominal case. As a next step, an optimization module was interfaced with the model predictive and regulatory control structures, as well as with the free MV's of the benchmark to carry the actual nonlinear process to this more profitable operating regime. The transition was conducted relatively slowly and took about 85 hours of mill operation to prevent any violation of process constraints and to minimize the deviation of quality variables from their targets. The results showed that the new operating regime improved the steady state profitability over the base case by 24%. The discrepancy between the predicted improvement and the actual result can be explained either by the unaccounted relationships between the variables, which constrained the achievement of target values, or by the change of model parameters at the new operating conditions due to the nonlinearity of the actual process. The size of the problem impedes an online update of the full linearized model, however it may be possible to identify more important model parameters and update them during operation to lessen the effects of plant-model mismatch.

This work provides important insight for the understanding of the pulp mill structure for process optimization and offers an analysis of the problem from a process control point of view. Such an analysis will be very helpful for the design of real-time optimization systems and their connection to the existing process control structures in the mill. Even though there is a difference between the predicted improvement and the actual result, a 24% increase in mill profits is very significant and encouraging.

[1] Noel DeKing (Editor). Pulp & Paper Global Fact & Price Book 2003-2004. Paperloop, Inc, 2004.

[2] G.A. Smook. Handbook for Pulp and Paper Technologists. Angus Wilde Publications, Vancouver, BC, second edition, 1992.

[3] J. J. Castro, F. J. Doyle III. A Pulp Mill Benchmark Problem for Control: Problem Description. J. Proc. Cont., 14: 17-29, 2004.

[4] J. J. Castro, F. J. Doyle III. A Pulp Mill Benchmark Problem for Control: application of plantwide control design. J. Proc. Cont., 14: 329-347, 2004.

[5] H. Kivijarvi, M. Tuominen. A Decision Aid in Strategic Planning and Analysis of a Wood-Processing Company. Comp. Ind. Eng., 31: No. 1/2, 467-470, 1996.

[6] A. Santos, A. Dourado. Global Optimization of Energy and Production in Process Industries: A Genetic Algorithm Application. Control Eng. Pract., 7: 549-554, 1999.