Papers by Rosendo Monroy-Loperena
Fluid Phase Equilibria, 2022
A useful procedure for finding all the roots of the type of equation indicated in the title, typi... more A useful procedure for finding all the roots of the type of equation indicated in the title, typically used in vapor-liquid separations, is presented. The proposed procedure is the result of a matrix-based analysis to generate a Standard Eigenvalue Problem. The eigenvalues of the resulting matrix system are exactly the roots of the equation indicated in the title. Numerical experiments are presented to show the goodness of the proposed procedure.
Industrial & Engineering Chemistry Research, 2012
... Distillation Columns, with a Draw-Stream in the Middle-Vessel Rosendo Monroy-Loperena 1,2,∗ a... more ... Distillation Columns, with a Draw-Stream in the Middle-Vessel Rosendo Monroy-Loperena 1,2,∗ and José Alvarez-Ramírez 3 1. ROMON ... However, other control configurations can be derived along the same lines (see, for instance, Bezzo and Barolo 6 ). ...
Industrial & Engineering Chemistry Research, 2012
This work address the problem of round-off errors in the analytical solution (Cardano's Method) o... more This work address the problem of round-off errors in the analytical solution (Cardano's Method) of cubic equations of state inside the simulation of chemical processes in the low-temperature region, as it is the case of cryogenic processes involving hydrates calculations. It is proposed as a strategy that can be taken as an iterative refinement of the solution obtained by the analytical method and allows one to take advantage of the calculations fulfilled in the application of the analytical solution (Cardano's Method). Numerical experimentations are presented in order to show the application of the proposed strategy.
Industrial & Engineering Chemistry Research, 2012
Flash calculations are used extensively in computer-aided process simulation programs. Inherent t... more Flash calculations are used extensively in computer-aided process simulation programs. Inherent to flash calculations is the determination of the vapor−liquid split. Currently, to calculate the vapor−liquid split, the Rachford−Rice equation is the most accepted method. In this work, it is shown that the Rachford−Rice equation can be posed as a generalized eigenvalue problem, where each eigenvalue of the resulting system is exactly a root of the Rachford−Rice equation. In this way, an ad hoc strategy based on linear algebra is proposed for finding the vapor−liquid split. The main advantage of the proposed strategy is that the resulting linear system has an almost-diagonal structure and generates a discrepancy function with a more linear shape than that of the Rachford−Rice equation. In this way, the solution of the system is simple and computationally inexpensive. Numerical experiments show the reliability of the proposed solution strategy for calculating the vapor−liquid split.
Industrial & Engineering Chemistry Research, 2004
Internal model control (IMC) tuning rules have proven to yield acceptable performance and robustn... more Internal model control (IMC) tuning rules have proven to yield acceptable performance and robustness properties when used in the control of typical processes (e.g., distillation columns, chemical reactors). In general, analytical IMC tuning rules are derived for proportional-integral (PI)/proportional-integral-derivative compensators by matching an approximate process model to a low-dimensional reference model. In the case of time-delay processes, an approximate model is obtained by taking a finite-dimensional approximation to the delay operator by means of Pade or Taylor expansions. For some typical cases arising commonly in process control, including first-order plus time-delay plants, this paper studies the optimality of PI-IMC tuning rules to match the prescribed closed-loop behavior (i.e., the reference model response). To this end, optimal PI settings are computed by means of numerical optimization based on random search algorithms. Small deviations of IMC tuning from optimality are found for moderate time delays. However, significant deviations are displayed for large time delays, which motivate the use of tuning techniques based on numerical optimization to refine IMC settings.
Industrial & Engineering Chemistry Research, 1999
The proportional plus double-integral (PI 2) controller was proposed by Belanger and Luyben (Ind.... more The proportional plus double-integral (PI 2) controller was proposed by Belanger and Luyben (Ind. Eng. Chem. Res. 1997, 36, 5339-5347) as a low-frequency compensator. The objective of the additional double-integral compensation is to reject the effects of ramplike disturbances. The aim of this work is to provide a parametrization of the PI 2 controller gains in terms of a nominal closed-loop and disturbance estimation time constants. A reduced-order observer is constructed to estimate ramplike disturbances, which is subsequently coupled with a feedback loop to counteract the effects of the disturbance. It is shown that such control configuration is equivalent to a PI 2 compensator. Some robustness issues of the PI 2 compensator with respect to unmodeled dynamics and nonlinearities are discussed and illustrated with two numerical examples.
Industrial & Engineering Chemistry Research, 1999
An ethylene glycol column is studied in this paper, where the main objective is to describe the b... more An ethylene glycol column is studied in this paper, where the main objective is to describe the bifurcation diagram with respect to the reboiler boilup ratio. The bifurcation analysis reveals the existence of a unique equilibrium point at low reboiler heat inputs and three equilibrium points (two stable and one unstable) at high reboiler heat inputs. Moreover, the existence of input multiplicities at moderate and high product purity is also revealed.
Industrial & Engineering Chemistry Research, 2001
This paper presents a PI control configuration for a class of multi-input multi-output (MIMO) pla... more This paper presents a PI control configuration for a class of multi-input multi-output (MIMO) plants. The control design procedure consists of a modeling error estimator based on a reducedorder observer structure and a nominal feedback function. The estimated modeling error signals are used in the feedback loop to counteract the effects of uncertain parameters. It is shown that this design procedure leads to a classical multivariable PI control configuration with novel parametrization of the controller gains. An advantage of the proposed control design is that easy tuning procedures can be designed. In addition, several special two-input two-output PI control configurations with decentralized structure can be obtained. As an application example, the separation control in an integrated three-product (Petlyuk) distillation column is studied. Sufficient conditions to achieve decentralized regulation in terms of the steady-state gain matrix are provided. Numerical simulations are used to show the effectiveness of the proposed PI controller under measurement dead times and uncertain parameters.
Industrial & Engineering Chemistry Research, 2005
This paper studies the limitations in the operation and control of a continuous middle-vessel dis... more This paper studies the limitations in the operation and control of a continuous middle-vessel distillation column with a draw stream in the middle vessel. This separation layout can be of interest to cases where the most and less volatile components of fractions of a mixture are desired in high concentrations, as in the processing of some oil streams. It was found that to maintain distillate and bottoms products within specifications, large recycling rates can be required to compensate for the storage effects of the middle vessel. This is because, contrary to the case where a draw stream is not present, in the studied distillation column layout the middle vessel alters material balances. In this form, the middle vessel acts as both a dynamical damper to reduce bottoms and distillate control loops and an accumulator for intermediate fractions. That includes some residuals of nonseparated most and less volatile components. The control objective is to track prescribed product compositions of the most and less volatile components by means of manipulations of the reflux and vapor boilup rates. Given that the middle vessel introduces a sluggish controlled response, the recycling stream from the middle vessel to the column is taken as an additional control input to improve the operation of the column and the control performance. In this way, a rectangular control configuration is obtained, which is regularized (i.e., squared) with a habituating control parameter. It is shown that this habituating control configuration can satisfy the control objectives more easily because it provides a balance between the separation and mixing tasks provided by the distillation column and the middle vessel, respectively.
Industrial & Engineering Chemistry Research, 2004
The simple reactor/separator process with recycle has recently been used as a benchmark case to g... more The simple reactor/separator process with recycle has recently been used as a benchmark case to gain insights into the problem of plantwide control structure selection. This paper explores the use of a balanced control scheme aimed at improving the disturbance rejection capabilities of the controlled process. The idea is to change the operating conditions in both the reactor and the separator so that the composition control effort in the presence of production rate changes is distributed. To this end, a parallel control structure is proposed where the product composition is regulated by means of simultaneous feedback manipulations of the vapor boilup rate and the reactor temperature. In this way, the use of the reactor temperature as a secondary control input reduces the snowball effects reflected in large vapor boilup rate changes in response to relatively small production rate changes. Nonlinear simulations show that effective composition control can be obtained with moderate vapor boilup control efforts.
Industrial & Engineering Chemistry Research, 2003
It is shown that the well-known and extensively used bubble-point methods, such as the one propos... more It is shown that the well-known and extensively used bubble-point methods, such as the one proposed by Wang and Henke for simulating vapor-liquid multistage distillation problems, can be used efficiently for the simulation of other types of vapor-liquid multistage separation problems, such as absorption and reboiled-absorption processes, even when the thermodynamic properties are a strong function of the composition. Via numerical simulations, it is shown that a robust bubble-point temperature iteration scheme provides convergence stability in the whole bubble-point method. The proposed robust bubble-point temperature iteration scheme is a combination of an equation decoupling method and a simultaneous method. This hybrid bubblepoint temperature iteration scheme exploits the reliability of the equation decoupling method, which makes good convergence progress from a poor starting point. However, if the initial point in the bubble-point temperature calculation is good enough, only the equation decoupling method is used, to avoid excessive successive substitution steps when the separation factors are updated. As a consequence of the extension of the bubble-point method to simulate absorption cases, a didiagonal matrix with an off column is generated, when the interstage vapor rates are calculated. An efficient and simple algorithm derived from the Gaussian elimination method to solve the didiagonal matrix with an off column is presented. Results are reported for distillation, absorption, and reboiled-absorption processes, using the Soave-Redlich-Kwong equation of state.
Industrial & Engineering Chemistry Research, 2001
In this paper the problem of single-stage vapor-liquid flash calculations using equations of stat... more In this paper the problem of single-stage vapor-liquid flash calculations using equations of state is addressed. A solution scheme in the framework of complex domain is used in conjunction with a Newton-based formulation in block algebra, providing an efficient, robust, and reliable computation scheme. The new scheme minimizes the number of iterations, because it always ensures a direct-forward step toward the solution, making fewer calls to thermodynamic property evaluations during iterations and avoiding the use of pseudophases along the calculation path. Convergence to unambiguous results is assured for all cases of practical interest, because derivative discontinuities inherent to real-domain models, including the need for bounding mole fractions to lie between 0 and 1, are avoided. The efficiency and robustness of the proposed scheme are shown by calculations in the retrograde region and in the construction of phase envelopes for model mixtures.
Industrial & Engineering Chemistry Research, 2001
The design of distillation columns requires the calculation of the minimum reflux. For ideal mixt... more The design of distillation columns requires the calculation of the minimum reflux. For ideal mixtures, the well-known Underwood equations, which can also be applied to complex columns, are used to calculate it (e.g., several feeds and side products and side-stream strippers and enrichers). In this work, it is shown that Underwood's equations of an N-component mixture can be represented as a polynomial of degree N and general relations for its coefficients are derived. In addition, the advantage of solving Underwood's equations in a polynomial form is shown. Any conventional numeric method may be used to find the roots of this polynomial because it is continuous and smooth (the discontinuities are eliminated).
Computers & Chemical Engineering, 1999
The control problem of an ethylene glycol reactive distillation column is studied in this work. T... more The control problem of an ethylene glycol reactive distillation column is studied in this work. The control objective is to regulate the ethylene glycol composition in the product by manipulating the reboiler boil-up ratio. By using an estimator of the input-output modeling error, a first-order output-feedback compensator is designed which is shown to be equivalent to a PI controller with
Computers & Chemical Engineering, 2008
The polynomial finite difference method, an easy-to-use variant of the finite difference method f... more The polynomial finite difference method, an easy-to-use variant of the finite difference method for the numerical solution of differential and differential–algebraic equations, has been recently presented [Wu, B., & White, R.E. (2004). Computers & Chemical Engineering, 28, 303–309]. In this work, it is shown that the polynomial finite difference method can be seen as a collocation method with finite elements
Computers & Chemical Engineering, 2012
A bordered matrix is proposed, that with block-algebra manipulations rebuilds the form of the equ... more A bordered matrix is proposed, that with block-algebra manipulations rebuilds the form of the equation given in the title. It is shown that the determinant of the bordered matrix results in a Standard Eigenvalue Problem, where the roots are exactly the eigenvalues of the resulting problem. Even more, the blockalgebra operations involved are extremely simple. Likewise, a specialized iterative procedure to find one eigenvalue for a Standard Eigenvalue Problem, based on multivariable Newton, is presented. Numerical experiments are presented to show the reliability of the proposed approach taken to find one or all the roots of the equation given in the title.
Chemical Engineering Science, 2012
The design of distillation columns requires the calculation of the minimum reflux. For ideal mixt... more The design of distillation columns requires the calculation of the minimum reflux. For ideal mixtures, the well-known Underwood's equations, which can also be applied to complex columns (e.g., several feeds and side products and side-stream strippers and enrichers) are used to calculate it. When distributed components other than the light and the heavy key are considered in the separation, the knowledge of all the roots of the Underwood's feed equation is essential. However, the discontinuous form of the Underwoods feed equation; makes the search of all roots a hard task. Using the fact that the Underwood's equation can be transform into a polynomial form, in this work a companion matrix of the polynomial is presented, permitting the solution of the equation as a Generalized Eigenvalue Problem, arriving to a reliable and efficient method for the calculation of all roots of the Underwood's equations. One main feature of the proposed approach is that not initial guesses are required to find all the roots of the Underwood's equation. Open, robust and reliable software such as EISPACK can be used to routinely calculate the minimum reflux ratio by Underwood's equations.
Chemical Engineering Science, 2003
A method for the identiÿcation and control of a batch distillation process is presented in this n... more A method for the identiÿcation and control of a batch distillation process is presented in this note. The proposed model consists of a ÿrst-order integrating process in composition with a high-frequency gain. The feedback controller is designed in the framework of robust nonlinear control with modeling error compensation techniques for the control of distillate composition via manipulations of the re ux ratio. The proposed identiÿcation and control procedures are illustrated via numerical simulations.
Chemical Engineering Science, 2000
The control problem of an ethylene glycol reactive distillation column is studied in this work. T... more The control problem of an ethylene glycol reactive distillation column is studied in this work. The control objective is to regulate the ethylene glycol composition in the product by manipulating the reboiler boil-up ratio. A preliminary input/output bifurcation analysis reveals the ...
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Papers by Rosendo Monroy-Loperena