Sequential Iteration Approach Research Articles

Process intensification and dynamic control of a vapor-recompression-assisted heterogeneous azeotropic distillation for separating N-butanol/water

An ecologically beneficial process of vapor-recompression-assisted distillation was proposed, based on the conventional heterogeneous azeotropic distillation, for separating n-butanol and water. The heat integration was also adopted to improve the energy utilization rate of the process. The sequential iterative approach optimized the parameters relating to all those processes. The heat-integrated vapor-recompression-assisted heterogeneous azeotropic distillation arrangement reflects its economic superiority, for reducing total annual cost by 15.121 % and CO2 emissions by 78.860 % and enhancing second-law efficiency by 102.156 %. An exergy analysis was performed on the intensified processes, which showed that the exergy increases in the configuration coupled with vapor recompression and heat integration were higher than those with only vapor recompression. Dynamic control characteristics were investigated for these three intensified configurations, and both product compositions were well controlled when confronting 20% production rate and feed composition disturbances, and no composition measurement loops were noted in the proposed control schemes.

A method to bridge energy and process system optimization: Identifying the feasible operating space for a methanation process in power-to-gas energy systems

The growing adoption of renewable energy is driving the integration of new, complex process technologies into energy systems, presenting operational optimization challenges. Simple models are necessary for computational tractability, yet detailed models are essential for feasible operating decisions. This work introduces a method for optimally operating an energy system with integrated complex process technologies. The proposed method bridges the mathematical modeling and optimization at energy and process system levels. Simple surrogate models and detailed process models are used to represent complex process technologies at their respective system levels. The resulting operational problems are solved through a sequential iterative approach. Applied to a power-to-gas energy system with an integrated methanation process, our method outperforms a benchmark method by capturing interactions between energy and process system levels, and among different process variables. The proposed method integrates more detailed constraints and ramping costs, yielding an optimal, feasible operating strategy within tractable computational time.

Modeling reactive multi-component multi-phase flow for Geological Carbon Sequestration (GCS) with Matlab

We present a reactive multi-component multi-phase flow program for simulating Geological Carbon Sequestration (GCS), an approach that reduces carbon emissions by storing CO2 in deep subsurface formations. The program, called MRST_CO2, is implemented in the library Matlab Reservoir Simulation Toolbox (MRST). It can simulate multi-phase flow and transport of species undergoing chemical reactions and mass exchanges among gas, liquid and solid phases. Equations for flow, mass transport and chemical reactions are solved with a sequential iteration approach. The program was tested with a 1D benchmark. It has also been applied to heterogeneous 2D and 3D cases with a structured or unstructured grid.

A distributed restoration framework for distribution systems incorporating electric buses

Electric buses can enhance the restoration of distribution systems. However, existing studies have focused on centralized restoration between the electric bus and the distribution system, ignoring the subjectivity and privacy of the electric bus company. This paper proposes a distributed restoration framework for distribution systems incorporating electric buses to address the problem. Firstly, a mixed-integer linear scheduling model of electric buses is constructed considering the bus service requirements, space–time characteristics, and energy characteristics. Secondly, a bi-level distributed restoration framework is proposed. The upper level aims to decide the energy restoration tasks of the electric bus company, and the lower level introduces a control center, using a sequential iterative approach to determine each electric bus's energy and bus service tasks. Thirdly, the distributed restoration model is developed using the augmented Lagrangian method and solved via the improved alternating direction multiplier method (ADMM). The improved ADMM can adaptively change the penalty factor to speed up the convergence. Finally, numerical simulations are performed by the IEEE 33-node distribution system. The results show that the participation of electric buses can enhance the restoration of distribution systems and the proposed distributed restoration framework has good convergence and high optimization efficiency.

Optimal novel approach for estimating the pavement transition probabilities used in Markovian prediction models

ABSTRACT An optimal novel approach is proposed to estimate the transition probabilities associated with both homogeneous and non-homogeneous Markov chains. The approach applies an exhaustive optimisation technique to search for the optimal transition probabilities associated with minimal sum of squared errors (SSE), wherein the error defined as the difference between predicted and observed pavement condition ratings. Three state transitions are allowed in constructing the relevant transition probability matrix (TPM). In the homogenous chain, the approach yields one optimal TPM applicable to an analysis period of (n) years. Whereas, one distinct optimal TPM can be derived for each year if non-homogenous chain is deployed. A sequential iterative optimisation approach is proposed wherein the optimal TPM for a given year becomes the input for the subsequent year. Sample results are presented for two projects (A & B) with superior and inferior performances, respectively. The sample results indicate that the non-homogenous chain provided significant reduction in the SSE compared to the homogeneous one. However, the use of 10 condition states instead of 5 resulted in moderate reduction in the SSE considering both homogeneous and non-homogeneous Markov chains. Also, the results indicate that the use of three state transitions made significant impact when deploying 10 condition states instead of 5 especially in the case of inferior performance.

Modeling and analysis of the acidizing process in carbonate rocks using a two-phase thermal-hydrologic-chemical coupled model

We present a two-phase thermal-hydrologic-chemical coupled model for simulating the dissolution process during the acidization of carbonate rocks. In particular, we develop a new model to describe the change in irreducible water saturation, residual oil saturation, and the maximum relative permeability of oil and water phases with dissolution proceeding. We also present a new method for the generation of the initial porosity field with controllable correlation length. In numerical calculation, the sequential iteration approach is adopted to solve the presented model, and the operator splitting method is used to deal with the reaction relevant equations. The involved equations are discretized using the finite-volume method, where the convection term is discretized by the MINMOD scheme which can prevent overshoot/undershoot of the numerical solution. Additionally, sensitivity analysis of the dissolution process concerning rock properties, the exothermic heat of reaction, and two-phase flow, is carried out. Based on the predicted results, several recommendations for the carbonate acidizing operation are given, and the potential extensions of the current work are summarized.

A fully implicit finite volume scheme for single phase flow with reactive transport in porous media

Single phase flow and reactive transport modelling involve solving a highly nonlinear coupled system of partial differential equations to algebraic or ordinary differential equations requiring special numerical treatment. In this paper, we propose a fully implicit finite volume method using a direct substitution approach to improve the efficiency and the accuracy of numerical computations for such systems. The approach has been developed and implemented in the framework of the parallel open-source platform DuMuX. The object oriented code allows solving reactive transport problems considering different coupling approaches. A number of 2D and 3D numerical tests were performed for verifying and demonstrating the capability of the coupled fully implicit approach for single phase flow and reactive transport in porous media. Numerical results for the reactive transport benchmark of MoMaS and long-term fate of injected CO2 for geological storage including a comparison between the direct substitution approach and the sequential iterative approach are presented. Parallel scalability is investigated for simulations with different grid resolutions.

Improvement of numerical approximation of coupled multiphase multicomponent flow with reactive geochemical transport in porous media

In this paper, we consider a parallel finite volume algorithm for modeling complex processes in porous media that include multiphase flow and geochemical interactions. Coupled flow and reactive transport phenomena often occur in a wide range of subsurface systems such as hydrocarbon reservoir production, groundwater management, carbon dioxide sequestration, nuclear waste repository or geothermal energy production. This work aims to develop and implement a parallel code coupling approach for non-isothermal multiphase multicomponent flow and reactive transport simulation in the framework of the parallel open-source platform DuMuX. Modeling such problems leads to a highly nonlinear coupled system of degenerate partial differential equations to algebraic or ordinary differential equations requiring special numerical treatment. We propose a sequential fully implicit scheme solving firstly a multiphase compositional flow problem and then a Direct Substitution Approach (DSA) is used to solve the reactive transport problem. Both subsystems are discretized by a fully implicit cell-centred finite volume scheme and then an efficient sequential coupling has been implemented in DuMuX. We focus on the stability and robustness of the coupling process and the numerical benefits of the DSA approach. Parallelization is carried out using the DUNE parallel library package based on MPI providing high parallel efficiency and allowing simulations with several tens of millions of degrees of freedom to be carried out, ideal for large-scale field applications involving multicomponent chemistry. As we deal with complex codes, we have tested and demonstrated the correctness of the implemented software by benchmarking, including the MoMaS reactive transport benchmark, and comparison to existing simulations in the literature. The accuracy and effectiveness of the approach is demonstrated through 2D and 3D numerical simulations. Parallel scalability is investigated for 3D simulations with different grid resolutions. Numerical results for long-term fate of injected CO2 for geological storage are presented. The numerical results have demonstrated that this approach yields physically realistic flow fields in highly heterogeneous media and showed that this approach performs significantly better than the Sequential Iterative Approach (SIA).

Investigation of the operability for four-product dividing wall column with two partition walls

Abstract For separating some specific four component mixtures into four products, the four-product dividing wall column (FPDWC) with two partition walls can provide the same utility consumption with the extended Petlyuk configuration, although with structure simplicity. However, the reluctance to implement this kind of four product dividing wall column industrially also consists in the two uncontrollable vapor splits associated with it. The vapor split ratios are set at the design stage and might not be the optimal value for changed feed composition, thus minimum energy consumption could not be ensured. In the present work, a sequential iterative optimization approach was initially employed to determine the parameters of cost-effective FPDWC. Then the effect of maintaining the vapor split ratios at their nominal value on the energy penalty was investigated for the FPDWC with two partition walls, in case of feed composition disturbance. The result shows that no more than + 2% above the optimal energy requirements could be ensured for 20% feed composition disturbances, which is encouraging for industrial implementation.

A sequential approach for numerical simulation of two-phase multicomponent flow with reactive transport in porous media

We develop a new scheme for numerical solution of immiscible compressible two-phase flow in porous media with geochemistry. The problem is modelled by the mass balance law for each phase, Darcy–Muskat’s law, and the capillary pressure law. Coupling with chemistry occurs through reactions rates. These rates can be either given nonlinear functions of concentrations in the case of kinetic chemical reactions or unknown for equilibrium chemical reactions. Each kinetic reaction produces an ordinary differential equation while each equilibrium reaction gives rise to a mass action law that is an algebraic relation that links the activities of concerned species. An implicit finite volume scheme is applied to solve the two-phase flow equations, which is then sequentially coupled to a method for solving the reactive transport problem. More precisely, we used firstly the module 2p2c implemented in the parallel open-source simulator DuMuX to solve a simplified two-phase two-component flow with two dominant species without chemistry. Secondly, we have developed and integrated a reactive transport module in the DuMuX framework to deal with the other species using a sequential iterative approach (SIA) where transport, equilibrium chemical reactions and kinetic chemical reactions are solved sequentially. A new module for transport and a code using the GSL library for the chemical problem have been coupled. Finally, our approach has been validated by solving several test cases. Here we will present two benchmark tests to demonstrate the ability of our method to approximate solutions of single and two-phase flows with reactive transport in heterogeneous porous media.

Optimal Sequential Sampling Plans Using Dynamic Programming Approach

In this paper we proposed a dynamic programming procedure to develop an optimal sequential sampling plan. A suitable cost model is employed for depicting the cost of sampling, accepting or rejecting the lot. This model is based on sequential approach. A sequential iterative approach is used for modeling the cost of different decisions in each stage. In addition a backward recursive algorithm is developed that can be adapted to a computer program. At the end of this paper a numerical example is solved to show how this model works.

Technologies comparison for iterative data acquisition strategies

The present work proposes a new experimental strategy based on a general model which describes and includes different reactor technologies. The strategy is based on a sequential iterative approach where, in a predictive step, the model is used to propose optimal experimental conditions, and, in a validation step, experimental data are used to improve the parameter estimation.A specific work bench with three types of reactors (batch, semi-batch stirred tank and continuous plug flow reactor) has been developed. The demonstration of the strategy is performed by using a classical parallel-consecutive reaction scheme, for which it has been demonstrated experimentally that the use of several reactors enlarges the experimental window, which enables to improve the accuracy on kinetic constants by comparison to using a restricted experimental window, with only one kind of reactor.

Quantitative reactive transport modeling of Portland cement in CO 2-saturated water

A modular reactive transport model, Dynaflow ™ , is used to simulate the reactivity of cement in CO 2-saturated water of intermediate salinity (0.5 M). Methodology for coupling transport and geochemical modules is derived and its assumptions are discussed. The modules are coupled in a sequential iterative approach to accurately model: (1) mineral dissolution/precipitation (2) aqueous phase speciation and (3) porosity-dependent transport properties. Simulation results reproduce qualitatively the dissolution of cement hydrates (CH, C-S-H, AFm, AFt) and intermediate products (CaCO 3) that have been observed experimentally. However, when using a standard power law to relate effective transport properties to porosity, modeling and experimental results do not coincide; here, agreement between simulations and observations is obtained by modifying the functional dependence of effective diffusivity on mineralogy. Furthermore, for this particular system for which concentration gradients are the only driving force, the assumption of neglecting the mass balance of water or density changes might show its limits. Therefore, future work should investigate the likely need to account for reaction-driven advection.

A global strategy for solving reactive transport equations

Reactive transport models are complex nonlinear Partial Differential Algebraic Equations (PDAE), coupling the transport engine with the geochemical operator. We propose an efficient and robust global numerical method, based on a method of lines and Differential Algebraic Equations (DAE) solvers, combined with a Newton method using a powerful sparse linear solver. Numerical experiments show the performances of the method. We also propose a unified framework to describe classical methods such as Sequential Non-Iterative Approach, Sequential Iterative Approach, Direct Substitution Approach and compare them with our global method.

A sequential partly iterative approach for multicomponent reactive transport with CORE2D

CORE2D V4 is a finite element code for modeling partly or fully saturated water flow, heat transport, and multicomponent reactive solute transport under both local chemical equilibrium and kinetic conditions. It can handle coupled microbial processes and geochemical reactions such as acid–base, aqueous complexation, redox, mineral dissolution/precipitation, gas dissolution/exsolution, ion exchange, sorption via linear and nonlinear isotherms, and sorption via surface complexation. Hydraulic parameters may change due to mineral precipitation/dissolution reactions. Coupled transport and chemical equations are solved by using sequential iterative approaches. A sequential partly iterative approach (SPIA) is presented which improves the accuracy of the traditional sequential non-iterative approach (SNIA) and is more efficient than the general sequential iterative approach (SIA). While SNIA leads to a substantial saving of computing time, it introduces numerical errors which are especially large for cation exchange reactions. SPIA improves the efficiency of SIA because the iteration between transport and chemical equations is only performed in nodes with a large mass transfer between solid and liquid phases. The efficiency and accuracy of SPIA are compared to those of SIA and SNIA using synthetic examples and a case study of reactive transport through the Llobregat Delta aquitard in Spain. SPIA is found to be as accurate as SIA while requiring significantly less CPU time. In addition, SPIA is much more accurate than SNIA with only a minor increase in computing time. A further enhancement of the efficiency of SPIA is achieved by improving the efficiency of the Newton–Raphson method used for solving chemical equations. Such an improvement is obtained by working with increments of log concentrations and ignoring the terms of the Jacobian matrix containing derivatives of activity coefficients. A proof is given for the symmetry and non-singularity of the Jacobian matrix. Numerical analyses performed with synthetic examples confirm that these modifications improve the efficiency and convergence of the iterative algorithm.

A Subgrid-Scale Stabilized Finite Element Method for Multicomponent Reactive Transport through Porous Media

Standard Galerkin finite element methods (GFEM) lack stability in solving advection-dominated solute transport in porous media. They usually require prohibitively fine grids and extremely small time steps to solve for advection-dominated problems. The algebraic subgrid-scale stabilized (ASGS) finite element method has been proved to overcome such problems for single-species reactive transport. Its potential for dealing with multicomponent reactive transport has not yet been explored. Here we present a numerical formulation of ASGS for steady and transient multicomponent reactive transport. Subgrid-scale transport equations are solved first by using an ASGS approximation and their solutions are substituted back into the grid-scale equations. A sequential iteration approach (SIA) is used to solve for coupled transport and chemical equations. Coupling of ASGS and SIA, ASGS+SIA, has been implemented in a reactive transport code, CORE2D V4, and verified for conservative solute transport. ASGS+SIA has been tested for a wide range of 1-D transient multicomponent reactive transport problems involving different types of chemical reactions such as: (1) Kinetically controlled aqueous species degradation, (2) Kinetic mineral dissolution, (3) Serial-parallel decay networks, and (4) Cation exchange and pyrite oxidation at local equilibrium. ASGS+SIA always provides accurate solutions and therefore offers an efficient option to solve for advection-dominated multicomponent reactive transport problems.

Power flow algorithm and practical contingency analysis for distribution systems with distributed generation

AbstractDistributed generation (DG) is playing an important role in enhancing the social sustainability. Because DGs connected to distribution network will impact power flow, it is necessary to develop a new approach of power flow analysis. In this paper, the interfaces between DGs and distribution network are introduced, the operating principles and control schemes of typical DGs, including asynchronous generators and solar batteries, are studied. A DC–AC sequential iteration approach is applied for calculating power flow with DGs. In addition, a practical sensitivity based contingency analysis approach is proposed in this paper. A 15‐bus distribution network with wind power generation and solar energy is analyzed to exhibit the effectiveness of the proposed approaches. Copyright © 2008 John Wiley & Sons, Ltd.

Modelling water distribution systems with deficient pressure

The pressure dependency of withdrawals from water distribution systems under conditions of abnormal stress, such as mains failure or fire fighting, is well accepted. A simple sequential solution seeking iterative approach to obtain a solution for pressure constrained outflows (including leakage) based on repetitive substitution into conventional computational algorithms, where demands are generally predetermined, has been developed. The methods are presently configured to use the computational efficiency and versatility of the widely used EPANET-2 software routine, offering the benefits of full network operational specifications at the level of ‘commercial’ network applications. Application of the new algorithm to UK water networks under various partial failure conditions has given insight into the ‘true’ extent and scale of supply deficiency as a consequence of pressure shortfall. The failures of one link of the network at a time have been simulated. The results suggest that, in terms of the nodes (properties) affected by shortfall in pressure, the more rigorous approach reduces the zone of deficient service compared with that flagged by conventional investigations. A case study used the methodology to investigate loss of resilience arising from pressure management and to assess the susceptibility to supply interruption of sensitive customers.

Hydrogeochemical modeling of organo-metallic colloids in the Nsimi experimental watershed, South Cameroon

This paper presents a hydrogeochemical modeling code HYDROS, which combines the multi-component transport model with equilibrium speciation module MINTEQA2. The processes of adsorption, aqueous speciation and mineral precipitation/dissolution are represented in the model. The numerical model uses a sequential iterative approach for solving the solute transport and the equilibrium geochemistry modules. Further the transport part is solved using an operator split approach wherein a finite volume method is used for solving the advective equations while a classical finite difference method is employed for solving the dispersive equations. The model performance is evaluated by comparing it with MINTOX for a literature problem. HYDROS is then applied to the case study of the transfer of transition metals with organic colloids in the swamp groundwater system of the experimental Nsimi watershed, representative of the humid tropical ecosystem of the South Cameroon Plateau. Field observations at the site swamp system suggest that the carbon is mainly transferred as organic colloids (i.e., dissolved organic carbon) produced by the slow biodegradation of the swamp organic matter. Using HYDROS, the behaviour of Al(III) and Fe(III) elements in the base flow system is simulated during inter rain events of a short rainy season (May–June 1996). The elemental time-series for Al, Fe, Cl, pH compare well with the simulation results. The colloids are found to have a strong impact on the mobilization and transfer of Al(III) and Fe(III), which are considered to have low mobility in weathering environment.

Investigation of a modified sequential iteration approach for solving coupled reactive transport problems

When contaminants enter the soil or groundwater, they may interact physically, geochemically and biochemically with the native water, microorganisms and solid matrix. A realistic description of a reactive transport regime that includes these processes requires joint consideration of multiple chemical species. Currently there are three common numerical approaches for coupling multispecies reaction and solute transport: the one-step approach, the sequential non-iterative approach (SNIA), and the sequential iterative approach (SIA). A modification of the SNIA method is the Strang-splitting method. In this study, a new modified sequential iteration approach (MSIA) for solving multicomponent reactive transport in steady state groundwater flow is presented. This coupling approach has been applied to two realistic reactive transport problems and its performance compared with the SIA and the Strang-splitting methods. The comparison shows that MSIA consistently converges faster than the other two coupling schemes. For the simulation of nitrogen and related species transport and reaction in a riparian aquifer, the total CPU time required by MSIA is only about 38% of the total CPU time required by the SIA, and only 50% of the CPU time required by the Strang-splitting method. The test problem results indicate that the SIA has superior accuracy, while the accuracy of MSIA is marginally better than that of the Strang-splitting method. The overall performance of MSIA is considered to be good, especially for simulations in which computational time is a critical factor. Copyright © 2005 John Wiley & Sons, Ltd.