Multi‐period planning,design, and strategic models for long‐term,quality‐sensitive shale gas development

In this work we address the long‐term, quality‐sensitive shale gas development problem. This problem involves planning, design, and strategic decisions such as where, when, and how many shale gas wells to drill, where to lay out gathering pipelines, as well as which delivery agreements to arrange. Our objective is to use computational models to identify the most profitable shale gas development strategies. For this purpose we propose a large‐scale, nonconvex, mixed‐integer nonlinear programming model. We rely on generalized disjunctive programming to systematically derive the building blocks of this model. Based on a tailor‐designed solution strategy we identify near‐global solutions to the resulting large‐scale problems. Finally, we apply the proposed modeling framework to two case studies based on real data to quantify the value of optimization models for shale gas development. Our results suggest that the proposed models can increase upstream operators’ profitability by several million U.S. dollars. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2296–2323, 2016     

湍流系统的能量最小多尺度模型研究进展

湍流一直被视为经典物理中百年未解的难题,也被认为是检验新理论和新方法的试金石。新兴的介科学,由气固流态化中能量最小多尺度（energy-minimization multi-scale,EMMS）模型发展而来,基于各主导因素在竞争中协调的观点,致力于分析挑战性的介尺度现象。基于介科学框架,介绍了湍流系统中介尺度行为的共性原理和最新的介尺度观点,包括黏性机制和惯性机制的竞争中协调、湍流稳定性条件。在此基础上发展了EMMS湍流模型并实现与计算流体力学（computational fluid dynamics, CFD）的耦合,贡献于层湍转捩预测和全球气候模型的改进。EMMS湍流模型复现了介区域内黏性控制机制与惯性控制机制的竞争中协调,为介科学理论作为复杂系统的普适理论提供依据。     

Meso‐scale statistical properties of gas–solid flow—a direct numerical simulation (DNS) study

Statistical properties of particles in heterogeneous gas–solid flow were numerically investigated based on the results of a three‐dimensional large‐scale direct numerical simulation (DNS). Strong scale‐dependence and local non‐equilibrium of these properties, especially the particle fluctuating velocity (PFV) or granular temperature, were observed to be related to the effect of meso‐scale structures formed by the compromise in competition between fluid and particle dominated mechanisms. To quantify such effects, the heterogeneous structures were partitioned into a gas‐rich dilute phase and a solid‐rich dense phase according to the particle‐scale voidage defined through the Voronoi tessellation. Non‐equilibrium features, such as the deviation of PFV from Gaussian distribution and anisotropy, were found even in phase‐specific properties. A new distribution function for the PFV well characterizing these features was obtained by fitting the DNS results, which takes a typical bi‐disperse mode, with phase‐specific granular temperatures. The implications of these findings to the kinetic theory of granular flow and traditional continuum models of gas–solid flow were also discussed. © 2016 American Institute of Chemical Engineers AIChE J, 63: 3–14, 2017     

Quantitative assessment of fine‐grid kinetic‐theory‐based predictions of mean‐slip in unbounded fluidization

The quantitative ability of a kinetic‐theory‐based, two‐fluid model is demonstrated in a clustering (unstable) gas‐solid system via highly resolved simulations. Unlike previous works, this assessment is validated against ideal computational fluid dynamics‐discrete element method data to minimize sources of discrepancy. Overall, good agreement in mean‐slip velocities is observed with relative errors less than 20% over a mean solids concentration range of 0.02–0.25. Local concentration gradient distributions are also studied, showing a distinct shift toward higher gradients at higher mean solids concentrations which is proposed as the bottleneck in obtaining grid‐independence rather than the cluster length scale. © 2015 American Institute of Chemical Engineers AIChE J, 62: 11–17, 2016     

流态化与物质相变的相似性

通常单组分多相系统随着温度的变化会呈现固态、液态和气态三种不同的结构和性质，而固体颗粒和流体组成的多相系统在循环流化床中随着气体流速的升高也会经历鼓泡、湍动和快速流化三种结构。两类体系虽然呈现不同的结构和性质，但是用介科学的概念对体系状态、区域过渡参数、驱动系统状态演变的能力、体系的控制机制等进行类比和分析，其物理根源却大同小异，均为复杂系统中不同控制机制在竞争中协调的必然结果。在对比了流态化与物质的相变两类体系之后，提出了基于能量最小多尺度模型（EMMS）的思想来构建相变理论的主张，从而期望能够充分理解物质的相变这一非平衡动力学过程。     

Improving the operational stability of the multi‐chamber spout‐fluid bed via the insertion of a submerged partition plate

The effect of a submerged partition plate on improving the gas–solid flow robustness and stability in a three‐dimensional spout‐fluid bed with multiple inter‐connected chambers is numerically investigated by means of computational fluid dynamics coupled with discrete element method (CFD‐DEM). Notably, multiple‐chamber beds are necessary in scaling up the spout‐fluid bed. The influence of plate height on gas–solid distribution, spout‐annulus interaction and chamber interaction are also studied to optimize the design. The results demonstrate that inserting a partition plate with height above a certain threshold can effectively improve the stability of spouting and uniformly re‐distribute the flux load in each chamber, giving rise to parallel fountains and lower circulation flux of the solid phase. Results indicate that the plate height should be at least 80% of the packed bed height investigated, with the most optimal being about 92% based on steady spouting, and the maximum solid and gas exchanging fluxes between the chambers. © 2016 American Institute of Chemical Engineers AIChE J, 63: 485–500, 2017     

3‐D full‐loop simulation of an industrial‐scale circulating fluidized‐bed boiler

Three‐dimensional (3‐D) simulations using an Eulerian multiphase model were employed to explore flow behaviors in a full‐loop industrial‐scale CFB boiler with and without fluidized‐bed heat exchanger (FBHE), where three solids phases were employed to roughly represent the polydisperse behavior of particles. First, a simulation of the boiler without FBHE is implemented to evaluate drag models, in terms of pressure profiles, mixing behaviors, radial velocity profiles, etc. Compared to the conventional model, the simulation using the energy‐minimization multiscale (EMMS) model successfully predicts the pressure profile of the furnace. Then, such method is used to simulate the boiler with FBHE. The simulation shows that solid inventory in the furnace is underpredicted and reduced with an increase of the valve opening, probably due to the underevaluated drag for FBHE flows. It is suggested to improve EMMS model which is now based on a single set of operating parameters to match with the full‐loop system. © 2012 American Institute of Chemical Engineers AIChE J, 59: 1108–1117, 2013     

Minimum fluidization velocity in gas‐liquid‐solid minifluidized beds

The initial fluidization characteristics of gas‐liquid‐solid minifluidized beds (MFBs) were experimentally investigated based on the analyses of bed pressure drop and visual observations. The results show that U_Lmf in 3–5 mm MFBs can not be determined due to the extensive pressure drop fluctuations resulting from complex bubble behavior. For 8–10 mm MFBs, U_Lmf can be confirmed from both datum analyses of pressure drop and Hurst exponent at low superficial gas velocity. But at high superficial gas velocity, U_Lmf was not obtained because the turning point at which the flow regime changes from the packed bed to the fluidized bed disappeared, and the bed was in a half fluidization state. Complex bubble growth behavior resulting from the effect of properties of gas‐liquid mixture and bed walls plays an important role in the fluidization of solid particles and leads to the reduction of U_Lmf. An empirical correlation was suggested to predict U_Lmf in MFBs. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1940–1957, 2016     

Direct numerical simulations of dynamic gas‐solid suspensions

Direct numerical simulation results for gas flow through dynamic suspensions of spherical particles is reported. The simulations are performed using an immersed boundary method, with careful correction for the grid resolution effect. The flow systems we have studied vary with mean flow Reynolds number, solids volume fraction, as well as particle/gas density ratio. On the basis of the simulation results, the effect of particle mobility on the gas‐solid drag force is analyzed and introduced into the existing drag correlation that was derived from simulations of stationary particles. This mobility effect is characterized by the granular temperature, which is a result of the particle velocity fluctuation. The modified drag correlation is considered so‐far the most accurate expression for the interphase momentum exchange in computational fluid dynamics models, in which the gas‐solid interactions are not directly resolved. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1958–1969, 2016     

A spatially‐averaged two‐fluid model for dense large‐scale gas‐solid flows

We present a spatially‐averaged two‐fluid model (SA‐TFM), which is derived from ensemble averaging the kinetic‐theory based TFM equations. The residual correlation for the gas‐solid drag, which appears due to averaging, is derived by employing a series expansion to the microscopic drag coefficient, while the Reynolds‐stress‐like contributions are closed similar to the Boussinesq‐approximation. The subsequent averaging of the linearized drag force reveals that averaged interphase momentum exchange is a function of the turbulent kinetic energies of both, the gas and solid phase, and the variance of the solids volume fraction. Closure models for these quantities are derived from first principles. The results show that these new constitutive relations show fairly good agreement with the fine grid data obtained for a wide range of particle properties. Finally, the SA‐TFM model is applied to the coarse grid simulation of a bubbling fluidized bed revealing excellent agreement with the reference fine grid solution. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3544–3562, 2017     

Data‐driven mathematical modeling and global optimization framework for entire petrochemical planning operations

In this work we develop a novel modeling and global optimization‐based planning formulation, which predicts product yields and properties for all of the production units within a highly integrated refinery‐petrochemical complex. Distillation is modeled using swing‐cut theory, while data‐based nonlinear models are developed for other processing units. The parameters of the postulated models are globally optimized based on a large data set of daily production. Property indices in blending units are linearly additive and they are calculated on a weight or volume basis. Binary variables are introduced to denote unit and operation modes selection. The planning model is a large‐scale non‐convex mixed integer nonlinear optimization model, which is solved to ε‐global optimality. Computational results for multiple case studies indicate that we achieve a significant profit increase (37–65%) using the proposed data‐driven global optimization framework. Finally, a user‐friendly interface is presented which enables automated updating of demand, specification, and cost parameters. © 2016 American Institute of Chemical Engineers AIChE J, 62: 3020–3040, 2016     

基于MP-PIC方法改进EMMS/DP曳力模型

改进了面向离散粒子法的能量最小多尺度曳力模型(EMMS/DP)的颗粒参数生成方式,并将非均匀因子(HD)与固相浓度和滑移速度关联以考虑介尺度结构动态效应的影响,用改进的EMMS/DP模型与多相流质点网格模型(MP-PIC)耦合模拟气固两相流提升管系统,模拟结果与实验值吻合很好,考察了MP-PIC方法的网格无关性和粗粒化模型参数.     

Outer approximation algorithm with physical domain reduction for computer‐aided molecular and separation process design

Integrated approaches to the design of separation systems based on computer‐aided molecular and process design (CAMPD) can yield an optimal solvent structure and process conditions. The underlying design problem, however, is a challenging mixed integer nonlinear problem, prone to convergence failure as a result of the strong and nonlinear interactions between solvent and process. To facilitate the solution of this problem, a modified outer‐approximation (OA) algorithm is proposed. Tests that remove infeasible regions from both the process and molecular domains are embedded within the OA framework. Four tests are developed to remove subdomains where constraints on phase behavior that are implicit in process models or explicit process (design) constraints are violated. The algorithm is applied to three case studies relating to the separation of methane and carbon dioxide at high pressure. The process model is highly nonlinear, and includes mass and energy balances as well as phase equilibrium relations and physical property models based on a group‐contribution version of the statistical associating fluid theory (SAFT‐γ Mie) and on the GC⁺ group contribution method for some pure component properties. A fully automated implementation of the proposed approach is found to converge successfully to a local solution in 30 problem instances. The results highlight the extent to which optimal solvent and process conditions are interrelated and dependent on process specifications and constraints. The robustness of the CAMPD algorithm makes it possible to adopt higher‐fidelity nonlinear models in molecular and process design. © 2016 The Authors AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers AIChE J, 62: 3484–3504, 2016     

Experiment design for control‐relevant identification of partially known stable multivariable systems

Design of experiments for identification of control‐relevant models is at the heart of robust controller design. In a number of prior publications, experiment designs have been developed that generate input/output data for efficient identification of models satisfying the integral controllability (IC) condition. The design of process inputs for such experiments is often, but not always, based on the concept of independent random rotated inputs, with appropriately proportioned amplitudes. However, prior publications do not account for models that may already be partially known before identification. In this work, this issue is addressed by developing a general experiment design framework for efficient identification of partially known models that must satisfy the IC condition. This framework produces optimal designs by solving appropriately formulated optimization problems, based on a number of rigorous theoretical results. Numerical simulations illustrate the proposed approach and potential future extensions are suggested. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2986–3001, 2016     

Gas‐liquid mass transfer behavior in a surface‐aerated vessel stirred by a novel long‐short blades agitator

For a recently developed long‐short blades (LSB) agitator, its critical rotational speed for the onset of gas entrainment, power number, and gas‐liquid mass transfer behavior in the case of surface aeration is investigated. The effect of the LSB configurations and the liquid level on the agitator performance has been studied in details. The obtained results clearly show several advantages of the LSB agitator in gas‐liquid mass transfer with respect to the agitators in the literature. It is found that its gas‐liquid volumetric mass‐transfer coefficient at a given specific power can be several times larger than those shown in the literature. It can also avoid decrease in the gas‐liquid mass transfer rate as the liquid level increases. In addition, the bubble distribution in the system is more uniform with respect to conventional agitators, resulting from better distribution of the dissipated energy for the LSB agitator. © 2015 American Institute of Chemical Engineers AIChE J, 62: 1322–1330, 2016     

A bubble-based EMMS model for gas–solid bubbling fluidization

An EMMS/bubbling model for gas–solid bubbling fluidized bed was proposed based on the energy-minimization multi-scale (EMMS) method (Li and Kwauk, 1994). In this new model, the meso-scale structure was characterized with bubbles in place of clusters of the original EMMS method. Accordingly, the bubbling fluidized bed was resolved into the suspending and the energy-dissipation sub-systems over three sub-phases, i.e., the emulsion phase, the bubble phase and their inter-phase in-between. A stability condition of minimization of the energy consumption for suspending particles (N_s→min) was proposed, to close the hydrodynamic equations on these sub-phases. This bubble-based EMMS model has been validated and found in agreement with experimental data available in literature. Further, the unsteady-state version of the model was used to calculate the drag coefficient for two-fluid model (TFM). It was found that TFM simulation with EMMS/bubbling drag coefficient allows using coarser grid than that with homogeneous drag coefficient, resulting in both good predictability and scalability.     

Euler–euler anisotropic gaussian mesoscale simulation of homogeneous cluster‐induced gas–particle turbulence

An Euler–Euler anisotropic Gaussian approach (EE‐AG) for simulating gas–particle flows, in which particle velocities are assumed to follow a multivariate anisotropic Gaussian distribution, is used to perform mesoscale simulations of homogeneous cluster‐induced turbulence (CIT). A three‐dimensional Gauss–Hermite quadrature formulation is used to calculate the kinetic flux for 10 velocity moments in a finite‐volume framework. The particle‐phase volume‐fraction and momentum equations are coupled with the Eulerian solver for the gas phase. This approach is implemented in an open‐source CFD package, OpenFOAM, and detailed simulation results are compared with previous Euler–Lagrange simulations in a domain size study of CIT. The results demonstrate that the proposed EE‐AG methodology is able to produce comparable results to EL simulations, and this moment‐based methodology can be used to perform accurate mesoscale simulations of dilute gas–particle flows. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2630–2643, 2017     

Mathematical modeling of a moving bed reactor for post‐combustion CO2 capture

A mathematical model for a moving bed reactor with embedded heat exchanger has been developed for application to solid sorbent‐based capture of carbon dioxide from flue gas emitted by coal‐fired power plants. The reactor model is one‐dimensional, non‐isothermal, and pressure‐driven. The two‐phase (gas and solids) model includes rigorous kinetics and heat and mass transfer between the two phases. Flow characteristics of the gas and solids in the moving bed are obtained by analogy with correlations for fixed and fluidized bed systems. From the steady‐state perspective, this work presents the impact of key design variables that can be used for optimization. From the dynamic perspective, the article shows transient profiles of key outputs that should be taken into account while designing an effective control system. In addition, the article also presents performance of a model predictive controller for the moving bed regenerator under process constraints. © 2016 American Institute of Chemical Engineers AIChE J, 62: 3899–3914, 2016     

Comparative analysis of subgrid drag modifications for dense gas‐particle flows in bubbling fluidized beds

Many subgrid drag modifications have been put forth to account for the effect of small unresolved scales on the resolved mesoscales in dense gas‐particle flows. These subgrid drag modifications significantly differ in terms of their dependencies on the void fraction and the particle slip velocity. We, therefore, compare the hydrodynamics of a three‐dimensional bubbling fluidized bed computed on a coarse grid using the drag correlations of the groups of (i) EMMS, (ii) Kuipers, (iii) Sundaresan, (iv) Simonin, and the homogenous drag law of (v) Wen and Yu with fine grid simulations for two different superficial gas velocities. Furthermore, we present an (vi) alternative approach, which distinguishes between resolved and unresolved particle clusters revealing a grid and slip velocity dependent heterogeneity index. Numerical results are analyzed with respect to the time‐averaged solids volume fraction and its standard deviation, gas and solid flow patterns, bubble size, number density, and rise velocities. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4077–4099, 2013