A demethaniser process is characterised by interactions between the complex distillation column and other flowsheet units, including the turbo-expander, flash units, multistream exchangers and refrigeration system. When a design problem dealing with demethaniser flowsheets is approached in a systematic way, the number of alternatives to be studied is generally very large. The assessment of all possible flowsheets with numerous options is a time consuming task with many simulations required to select the most economic option. This research presents a systematic approach for demethaniser flowsheet synthesis to generate cost-effective designs with minimal time and effort. A demethaniser column has many degrees of freedom, including the operating pressure, multiple feeds, the number and duty of side reboilers and the flow rate of the external reflux stream. The additional feed and side reboiler streams enhance the efficiency of the process, but complicate process modelling. The number of design variables is also augmented by additional degrees of freedom such as the location and the order of feeds, the number of stages and the reflux ratio in the column. The complexity of the demethaniser column precludes the use of the Fenske–Underwood–Gilliland shortcut design method. A semi-rigorous boundary value method is proposed for the design of complex demethaniser columns for application within an optimisation framework for process synthesis and evaluation. The results of the proposed design methodology are shown to be in good agreement with those of rigorous simulation. A simplified flowsheet simulation model based on a sequential modular approach is developed that is able to account for various configurations and inter-connections in the demethaniser process. Improved shortcut models for flash units, the turbo-expander, compressor and refrigeration cycle have been proposed for exploitation in a synthesis framework. A methodology accounting for heat integration in multistream exchangers is proposed. The simplified simulation model is applied for the optimisation of a flowsheet of fixed configuration. The nonlinear programming technique of sequential quadratic programming (SQP) is used as the optimisation method. A case study is presented to illustrate the application of the optimisation approach for maximising the annual profit. A generalised superstructure has been proposed for demethaniser flowsheet synthesis that includes various structural combinations in addition to the operational parameters. The various options included in the superstructure and their effects on flowsheet performance are discussed. A stochastic optimisation technique, simulated annealing, is applied to optimise the superstructure and generate energy-efficient and cost-effective flowsheets. The application of the developed synthesis methodology is illustrated by a case study of relevance to natural gas processing. The results allow insights to be obtained into the important trade-offs and interactions and indicate that the synthesis methodology can be employed as a tool for quantitative evaluation of preliminary designs as well as to facilitate evaluation, selection and optimisation of licensed demethaniser flowsheets.

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The Linear Discrete Method (LDM; SIMMEL 2000; SIMMEL ET AL. 2000) is used to solve the Stochastic Collection Equation (SCE) numerically. Comparisons are made to the Method of Moments (MOM; TzIVION ET AL. 1999) which is suggested as a reference for numerical solutions of the SCE. Simulations for both methods are shown for the GoLOVIN kernel (for which an analytical solution is available) and the hydrodynamic kernel after LONG (1974) as it is used by TZIVION ET AL. (1999). Different bin resolutions are investigated and the simulation times are compared. In addition, LDM simulations using the hydrodynamic kernel after BÖHM (1992b) are presented. The results show that for the GoLOVIN kernel, LDM is slightly closer to the analytic solution than MOM. For the LONG kernel, the low resolution results of LDM and MOM are of similar quality compared to the reference solution. For the BÖHM kernel, only LDM simulations were carried out which show good correspondence between low and high resolution results. / Die lineare diskrete Methode (LDM; SIMMEL 2000; SIMMEL ET AL. 2000) wird dazu benutzt, die Gleichung für stochastisches Einsammeln (stochastic collection equation, SCE) numerisch zu lösen. Dabei werden Vergleiche gezogen zur Methode der Momente (Method of Moments, MOM; TzIVION ET AL. 1999), die als Referenz für numerische Lösungen der SCE vorgeschlagen wurde. Simulationsrechnungen für beide Methoden werden für die Koaleszenzfunktion nach GoLOVIN (für die eine analytische Lösung existiert) und die hydrodynamische Koaleszenzfunktion nach LONG (1974) wie sie von TZIVION ET AL. (1999) verwendet wird, gezeigt. Verschiedene Klassenauflösungen werden untersucht und die Simulationszeiten verglichen. Zusätzlich werden LDM-Simulationen mit der hydrodynamischen Koaleszenzfunktion nach BÖHM (1992b) gezeigt. Die Ergebnisse für die Koaleszenzfunktion nach GoLOVIN zeigen, daß die LDM der analytischen Lösung etwas näher kommt als MOM. Für die Koaleszenzfunktion nach LONG sind die Ergebnisse von LDM und MOM mit niedriger Auflösung von ähnlicher Qualität verglichen mit der Referenzlösung. Für die Koaleszenzfunktion nach BÖHM wurden nur Simulationen mit der LDM durchgeführt, die eine gute Übereinstimmung der Ergebnisse mit niedriger und hoher Auflösung zeigen.

Com o objetivo de propor um modelo estocástico para estimação da produtividade potencial da cultura de milho em Piracicaba (SP), em função de temperatura e radiação solar média diária, foi desenvolvido um programa computacional em linguagem Visual Basic para ambiente Windows, o qual foi utilizado em diferentes períodos agroclimáticos (datas de semeadura). Em função dos resultados obtidos, pode-se concluir que: (i) em escala diária, as variáveis temperatura média do ar e radiação solar em Piracicaba (SP) (períodos de 1917 a 2002 e 1978 a 2002, respectivamente) apresentaram distribuição normal; (ii) as distribuições normal truncada, triangular simétrica, e triangular assimétrica podem ser utilizadas no modelo estocástico para previsão da produtividade de milho; (iii) o programa computacional é uma ferramenta que viabiliza a operacionalização da estimação da produtividade potencial de milho utilizando a opinião de especialistas. / With the purpose of proposing a stochastic model for estimating potential maize productivity in Piracicaba (SP), as function of mean values of daily air temperature and solar radiation, a software was developed using Visual Basic for Windows, where it was applied for different agro climatic periods (sowing dates). The results allowed the following conclusions: (i) at daily scale, the variables air temperature and solar radiation (periods from 1917 to 2002 and 1978 to 2002, respectively) presented normal distribution; (ii) the normal and triangular (symmetric and asymmetric) distributions can be used in the stochastic model to forecast potential maize productivity; (iii) the software is a tool that allows to estimate the potential maize productivity using the specialist opinion.

Waterflood optimization via rate control is receiving increased interest because of rapid developments in the smart well completions and I-field technology. The use of inflow control valves (ICV) allows us to optimize the production/injection rates of various segments along the wellbore, thereby maximizing sweep efficiency and delaying water breakthrough. It is well recognized that field scale rate optimization problems are difficult because they often involve highly complex reservoir models, production and facilities related constraints and a large number of unknowns. Some aspects of the optimization problem have been studied before using mainly optimal control theory. However, the applications to-date have been limited to rather small problems because of the computation time and the complexities associated with the formulation and solution of adjoint equations. Field-scale rate optimization for maximizing waterflood sweep efficiency under realistic field conditions has still remained largely unexplored. We propose a practical and efficient approach for computing optimal injection and production rates and thereby manage the waterflood front to maximize sweep efficiency and delay the arrival time to minimize water cycling. Our work relies on equalizing the arrival times of the waterfront at all producers within selected sub-regions of a water flood project. The arrival time optimization has favorable quasi-linear properties and the optimization proceeds smoothly even if our initial conditions are far from the solution. We account for geologic uncertainty using two optimization schemes. The first one is to formulate the objective function in a stochastic form which relies on a combination of expected value and standard deviation combined with a risk attitude coefficient. The second one is to minimize the worst case scenario using a min-max problem formulation. The optimization is performed under operational and facility constraints using a sequential quadratic programming approach. A major advantage of our approach is the analytical computation of the gradient and Hessian of the objective which makes it computationally efficient and suitable for large field cases. Multiple examples are presented to support the robustness and efficiency of the proposed optimization scheme. These include several 2D synthetic examples for validation purposes and 3D field applications.

Com o objetivo de propor um modelo estocástico para estimação da produtividade potencial da cultura de milho em Piracicaba (SP), em função de temperatura e radiação solar média diária, foi desenvolvido um programa computacional em linguagem Visual Basic para ambiente Windows, o qual foi utilizado em diferentes períodos agroclimáticos (datas de semeadura). Em função dos resultados obtidos, pode-se concluir que: (i) em escala diária, as variáveis temperatura média do ar e radiação solar em Piracicaba (SP) (períodos de 1917 a 2002 e 1978 a 2002, respectivamente) apresentaram distribuição normal; (ii) as distribuições normal truncada, triangular simétrica, e triangular assimétrica podem ser utilizadas no modelo estocástico para previsão da produtividade de milho; (iii) o programa computacional é uma ferramenta que viabiliza a operacionalização da estimação da produtividade potencial de milho utilizando a opinião de especialistas. / With the purpose of proposing a stochastic model for estimating potential maize productivity in Piracicaba (SP), as function of mean values of daily air temperature and solar radiation, a software was developed using Visual Basic for Windows, where it was applied for different agro climatic periods (sowing dates). The results allowed the following conclusions: (i) at daily scale, the variables air temperature and solar radiation (periods from 1917 to 2002 and 1978 to 2002, respectively) presented normal distribution; (ii) the normal and triangular (symmetric and asymmetric) distributions can be used in the stochastic model to forecast potential maize productivity; (iii) the software is a tool that allows to estimate the potential maize productivity using the specialist opinion.

The Linear Discrete Method (LDM; SIMMEL 2000; SIMMEL ET AL. 2000) is used to solve the Stochastic Collection Equation (SCE) numerically. Comparisons are made to the Method of Moments (MOM; TzIVION ET AL. 1999) which is suggested as a reference for numerical solutions of the SCE. Simulations for both methods are shown for the GoLOVIN kernel (for which an analytical solution is available) and the hydrodynamic kernel after LONG (1974) as it is used by TZIVION ET AL. (1999). Different bin resolutions are investigated and the simulation times are compared. In addition, LDM simulations using the hydrodynamic kernel after BÖHM (1992b) are presented. The results show that for the GoLOVIN kernel, LDM is slightly closer to the analytic solution than MOM. For the LONG kernel, the low resolution results of LDM and MOM are of similar quality compared to the reference solution. For the BÖHM kernel, only LDM simulations were carried out which show good correspondence between low and high resolution results. / Die lineare diskrete Methode (LDM; SIMMEL 2000; SIMMEL ET AL. 2000) wird dazu benutzt, die Gleichung für stochastisches Einsammeln (stochastic collection equation, SCE) numerisch zu lösen. Dabei werden Vergleiche gezogen zur Methode der Momente (Method of Moments, MOM; TzIVION ET AL. 1999), die als Referenz für numerische Lösungen der SCE vorgeschlagen wurde. Simulationsrechnungen für beide Methoden werden für die Koaleszenzfunktion nach GoLOVIN (für die eine analytische Lösung existiert) und die hydrodynamische Koaleszenzfunktion nach LONG (1974) wie sie von TZIVION ET AL. (1999) verwendet wird, gezeigt. Verschiedene Klassenauflösungen werden untersucht und die Simulationszeiten verglichen. Zusätzlich werden LDM-Simulationen mit der hydrodynamischen Koaleszenzfunktion nach BÖHM (1992b) gezeigt. Die Ergebnisse für die Koaleszenzfunktion nach GoLOVIN zeigen, daß die LDM der analytischen Lösung etwas näher kommt als MOM. Für die Koaleszenzfunktion nach LONG sind die Ergebnisse von LDM und MOM mit niedriger Auflösung von ähnlicher Qualität verglichen mit der Referenzlösung. Für die Koaleszenzfunktion nach BÖHM wurden nur Simulationen mit der LDM durchgeführt, die eine gute Übereinstimmung der Ergebnisse mit niedriger und hoher Auflösung zeigen.