Total Number Of Stages Research Articles

A multi-arm multi-stage platform design that allows preplanned addition of arms while still controlling the family-wise error.

There is growing interest in platform trials that allow for adding of new treatment arms as the trial progresses as well as being able to stop treatments part way through the trial for either lack of benefit/futility or for superiority. In some situations, platform trials need to guarantee that error rates are controlled. This paper presents a multi-stage design, that allows additional arms to be added in a platform trial in a preplanned fashion, while still controlling the family-wise error rate, under the assumption of known number and timing of treatments to be added, and no time trends. A method is given to compute the sample size required to achieve a desired level of power and we show how the distribution of the sample size and the expected sample size can be found. We focus on power under the least favorable configuration which is the power of finding the treatment with a clinically relevant effect out of a set of treatments while the rest have an uninteresting treatment effect. A motivating trial is presented which focuses on two settings, with the first being a set number of stages per active treatment arm and the second being a set total number of stages, with treatments that are added later getting fewer stages. Compared to Bonferroni, the savings in the total maximum sample size are modest in a trial with three arms, <1% of the total sample size. However, the savings are more substantial in trials with more arms.

Thermodynamic investigation of a Carnot battery based multi-energy system with cascaded latent thermal (heat and cold) energy stores

Carnot batteries store electricity in thermal form, allowing for power balancing and also multi-vector energy management as a unique asset. Cascaded thermal energy storage therefore has a vital role in Carnot battery, particularly multi-energy systems delivering electricity and thermal energy at various temperatures. Here, we propose a Carnot battery multi-energy system with cascaded latent thermal energy stores. The effects of compressor pressure ratio, total stage number, stage area and fluid velocity in tubes, on system-level coefficient of performance and total exergy efficiency are investigated. The results show that both the coefficient of performance and exergy efficiency increase significantly and then level off with the total stage number and stage area increasing, while they only increase slightly before a significant decrease with the increase of fluid velocity in tubes. The selection of compressor pressure ratios relates to the demands of cold, heat and electricity. The multi-energy system achieves a maximum coefficient of performance of 95.0% in combined cooling, heating and power mode. Although the thermodynamic performance yileds comparable with Carnot battery systems integrated with packed-bed or liquid-based sensible heat stores, the Carnot battery multi-energy system can deliver electricity and multi-grade heat and cold simultaneously, thus increasing flexibility in future energy systems.

Empirical Evidence on the Reliability of Lateral Supramalleolar Flap over Reverse Sural Flap for Local Soft Tissue Coverage of Dorsum of the Foot and Ankle Defects.

Background Soft tissue coverage of the distal foot and ankle region has been an area of debate due to the paucity of local flap options. To provide empirical evidence on the reliability of an underreported local alternative for foot and ankle defects, we aim to compare the lateral supramalleolar flap (LSMF) to the reverse sural flap (RSF). Methods During 2016-2019, 48 patients were divided randomly into two equal groups, LSMF and RSF groups respectively. The patients' demographic, surgical, and clinical outcome details were recorded and analyzed. Results Flap necrosis was found in five patients in the group treated with RSF and none in the LSMF group. The mean total number of stages in RSF group was significantly higher than in LSMF group ( p < 0.05). The mean operative time for patients in LSMF group was 85.8 ± 18.5 and 54.2 ± 11.2 in RSF group ( p < 0.05). Five patients in the RSF group needed additional procedures following flap complications. Nine patients in the LSMF group reported satisfaction outcomes to be "excellent," five patients reported "good" whereas, in the RSF group, 14 patients reported "excellent," 5 reported "good," 3 reported "fair," and 2 reported "poor" outcomes. Compared to the RSF (46.4 ± 4.3) group, the LSMF group had significantly better foot function indices (34.03 ± 3.9). Conclusion The lateral supramalleolar flap for foot and ankle defects offers better results, reduced complications as well a lesser number of stages and secondary procedures over the traditionally used reverse sural flap.

Design and Optimization of 4-bit Absolute-value Detector Based on CMOS

With the development of neural signal acquisition systems, spike-sorting algorithms have been paid full attention. As one of the most extensively used spike-detection algorithms, a 4-bit absolute-value detector is designed in the paper, which comprises three types of architecture. The first design is using combinational logic circuit through a truth table of the absolute value of 2′s complement format and a comparator; the second design is a combination of a series of half adders and transmission gates and a comparator; the third design consists of a combinational logic circuit by truth table of 2′s complement and a cascade of full adders. Then the paper compares the total number of stages and consuming transistors of each circuit, and finally chooses the second circuit, which has five stages and 74 transistors of consumption, as the object of following optimization of critical path delay and energy consumption. With gate sizing, the optimized critical path delay is about 43.05 tp0. The original energy consumption under minimum delay is 49.88C, and the optimized energy consumption under 1.5x minimum delay is 30.35C which is reduced by 39.16%. The processing of the functional realization and circuit optimization of absolute-value detectors can both benefit from the design presented in this work.

Thermodynamic investigation of latent-heat stores for pumped-thermal energy storage

As a large-scale energy storage technology, pumped-thermal energy storage uses thermodynamic cycles and thermal stores to achieve energy storage and release. In this paper, we explore the thermodynamic feasibility and potential of exploiting cascaded latent-heat stores in Joule-Brayton cycle-based pumped-thermal energy storage systems. A thermodynamic model of cascaded latent-heat stores is developed, and the effects of the heat store arrangement (i.e., total stage number and stage area) and fluid velocity in the thermal store tubes as key parameters that affect the heat storage and release rates, as well as the roundtrip efficiency, are evaluated. A pure electricity-storage mode and a combined heating and power mode are proposed and investigated, which allows such technologies to transform from a pure electricity storage system to an energy management system supplying power and multi-grade thermal and cold energy, and also to integrate with external waste heat and/or cold sources. Results show that the roundtrip efficiency of cascaded latent-heat stores is higher in the combined heating and power mode than in the pure electricity-storage mode, and that roundtrip efficiencies ranging from 62 % to 100 % can be achieved in the combined heating and power mode, accompanied by a corresponding pressure loss gradient ranging from 10 Pa/m to 2270 Pa/m. A comparison with packed-bed and liquid sensible-heat stores is also performed, and the results indicate that if these can be well designed, cascaded latent-heat stores can deliver comparable performance in terms of the total heat storage and release rates, roundtrip efficiency and flow resistance loss. Therefore, it is concluded that cascaded latent-heat stores can be considered for use in Joule-Brayton cycle-based pumped-thermal energy storage systems aimed at intelligent energy management for the provision of power and multi-grade heat and cold, if the costs can justify this decision.

Mechanical analysis of radial hydraulic force in oil recovery by sliding vane pump

Due to the mechanical structure and operating principle of sliding vane pump (SVP), an all-metal artificial lift equipment with high temperature resistance and high pump efficiency, an unbalanced radial hydraulic force always exists in it during oil recovery, which will cause damage on efficiency, safety and service life of production system. What's more, the flow behavior of fluid through the pump cannot be accurately characterized because current related works fails to capture the influence of the force mentioned. To bridge this knowledge gap, in this paper, the computational fluid dynamics method was introduced and used to analyze the radial hydraulic force under different operating parameters for the first time. On this basis, novel measures to reduce this unbalanced force were put forward, and a design scheme of concentric stator-rotor to completely eliminate the radial hydraulic force was proposed. Main results show that a) increase in eccentricity will contribute to the enhancement of discharge capacity, which will simultaneously aggravate the radial hydraulic force. And this force is proportional to the fluid viscosity, lifting pressure difference and rotation speed. b) The direction of radial hydraulic force of adjacent stages in multistage SVP is opposite. To reduce this unbalanced force, it is recommended to use even-numbered (odd-numbered) multistage pump when the number of total stages is small (large). c) The concentric design eliminates the radial hydraulic force at the expense of the function of self-regulating flow rate. Besides, the stator curve under concentric stator-rotor condition will degrade the kinetic characteristic of vanes.

Production and quality control of high-purity rare-earth metal oxides for scintillator crystals of medical detection systems

The positron emission tomography (PET) detector uses scintillator crystals to provide high image quality. Cerium-activated lutetium orthosilicates are promising crystals for PET detectors. The optical properties of resulting scintillator crystals directly depend on the impurity composition of starting materials, so they are subject to considerably stringent requirements to the basic substance content: Lu 2 O 3 – 99.999 wt.%, CeO 2 – 99.99 wt.%. A starting material used for obtaining lutetium oxide of the required purity was its concentrate with a basic substance content of 99.1 wt.% with REM carbonates containing up to 54 % cerium used to obtain cerium oxide. The paper presents process flow diagrams for obtaining high-purity Lu 2 O 3 and CeO 2 based on a combination of extraction and ion exchange methods. Extraction purification of lutetium and cerium from accompanying rare-earth impurities was carried out using Aliquat 336 and tri- n -butyl phosphate, respectively. Main operating modes of extraction cascades were calculated. The total number of stages was 17 for lutetium purification, and 20 for cerium purification. The purification technology for lutetium and cerium oxides consists in combining purification methods and varying cycles depending on the content of impurities. In this regard, it is necessary to control the quality of resulting substances practically after each stage. The chemical purity of technology products was subjected to analytical control by mass spectrometry with inductively coupled plasma and a spark excitation source.

An investigation of the interactions between system characteristics and controllability for reactive distillation systems

Reactive distillation is an emerging process intensification technology, although its operation and control are complex due to the interactions between reaction and separation within the column. In this work, the impact of reaction and separation, as well as design parameters, on the controllability of reactive distillation processes is investigated, using a systematic methodology developed. Case studies of industrial interest are considered, varying in the key (reaction, separation and design) parameters, in order to investigate the relative impact of the latter on the controllability of the reactive distillation systems. It is shown that the system with slower kinetics demonstrates an increased difficulty in rejecting feed disturbances for both one point (V-only) and two-point (LV) control configurations. Even when linear model predictive control (MPC) is considered based on a state-space representation of the model, the system with slower reaction kinetics is still more difficult to control, for both set point change and load disturbance. It is also shown that revision of the optimal steady state design variables, such as the total number of stages, may be beneficial for the controllability of the process. The importance of maintaining feed ratio in stoichiometric processes is identified and discussed, as failure to do so may result in failure to maintain both product purities when two point control is considered.

Stack Thermo-Osmotic System for Low-Grade Thermal Energy Conversion.

Thermo-osmotic energy conversion (TOEC) technology, developed from membrane distillation, is an emerging method that has the potential of obtaining electricity efficiently from a low-grade heat source but faces the difficult problem of pump power loss. In this study, we build a novel TOEC system with a multistage architecture that can work without pump assistance. The experiment system, made of cheap commercial materials, can obtain a power density of 1.39 ± 0.25 W/m2, with a heating temperature of 80 °C, and its efficiency increased linearly with the total stage number. A theory calculation shows that a 30-stage system with a specific membrane and a working pressure of 5.0 MPa can obtain an efficiency of 2.72% with a power density of 14.0 W/m2. By a molecular dynamics simulation, it is shown that a high-performance membrane has the potential to work at 40 MPa. This study proves that TOEC technology is a practical and competitive approach to covert low-grade thermal energy into power efficiently.

Recovery of high-purity NO2 and SO2 products from iron-ore sintering flue gas by distillation: process design, optimization and analysis

High-purity NO2 and SO2 have significant economic values and are widely used in many fields. The large amounts of NO2 and SO2 in industrial flue gases are worthy of recovery for environmental protection and economic benefits. In this work, a dual-column distillation separation process was proposed to further separate and upgrade NO2 and SO2 following a flue gas adsorption capture process. The feasibility of distillation separation of NO2/SO2 from the desorbed gas, and the advantage of liquid-phase feeding way over gas-phase counterpart in terms of lower energy consumption (1286.39 kW) were demonstrated. Key process parameters such as the number of total stages, the feed stage number, the mole flow rate at bottom of column, the reflux ratio and operating pressure for the two columns (15, 6, 16.66 kmol/h, 0.16, 4 bar; 21, 10, 4.43 kmol/h, 0.50, 1 bar) were determined. Heat and mass transfers along the column height as well as the process robustness against feed composition fluctuation indicate its applicability for practical operation and adaptation to industrial needs. An economic analysis shows a significant annual revenue of 14,333.52 thousand USD based on high-purity (>99.5%) SO2 and NO2 products recovered from a typical scale (~1000,000 m3/h) of iron-ore sintering flue gas, not only offsetting the total operating cost of the entire adsorption capture-distillation recovery process but also generating net profit.

COMPARISON OF ENERGY SAVING METHODS FOR DISTILLATION OF LIQUID MIXTURES

The analysis and review of the scientific literature on methods and approaches to energy saving in distillation, as one of the most energy-intensive processes for the separation of binary and multicomponent mixtures was carried out. Directions of the scientific literature are highlighted, showing the relevance of the thermodynamic method assessment of separation processes. A comparative analysis of various methods of energy conservation in the separation of liquid binary mixtures by the distillation method is performed (a binary mixture of benzene-toluene was chosen as an example). A conventional distillation column as well as a column with a heat pump and a column with heat integration were considered. As a result of the calculation experiment for each option performed using the Aspen Plus software package the optimal column parameters were determined - the total number of stages and the position of feed stage. The heat consumption in the column boiler was taken as the objective function. It is also shown that with the same characteristics of the columns, the best way to organize the process for separating the selected mixture is to compress the steam stream from rectifying profile of the column with its subsequent use in the boiler of the stripping profile according to the principle of a heat pump. It was established by a calculation experiment that heat integration by compressing steam from rectifying profile of the column and supplying it to the stripping profile gives significantly less energy saving. The calculation of internal energy saving by distillation column was carried out and it was shown that the distributed heat removal from the plates of the rectifying profile of the column and the supply of this heat to the stripping profile plates reduces internal energy saving and leads to an additional increase in heat consumption in the boiler.

PDB68 Maximum-Likelihood Estimation of Transition Probabilities between Fibrosis Stages in Nonalcoholic Steatohepatitis (NASH)

NASH is a disease characterized by progression of hepatic fibrosis through five stages, from F0 (no fibrosis) to F4 (compensated cirrhosis). Singh, 2015 estimated a fibrosis progression rate (FPR) between fibrosis stages as the total number of stages progressed from any starting stage divided by the total number of person years of follow up. The FPR has been used in Markov cost-effectiveness models as a proxy for transition probabilities between fibrosis stages (Tapper, 2015; ICER, 2016; ICER, 2020). Gal, 2017 presented a method to calibrate model specific transition probabilities to match detailed study data that gives a better model of disease progression than FPR. This research improves on our previous methodology by leveraging the advantages of maximum-likelihood estimation (MLE). Our model restricted transitions by at most one stage per cycle. The observed data include the number of patients for all 25 combination of initial and final F-stages, and the total number of patient years for each initial stage. The elements of the transition probability matrix were considered as model parameters implying a multinomial distribution across the final stages for each starting stage. The lengths of follow-up periods were available on an aggregated level, therefore the MLE assumed an average follow-up time from each starting stage. The MLE achieved convergence and the resulting transition probabilities were found to be consistent with the estimated FPR, and the probabilities given by our prior calibration method. MLE is recommended to estimate transition probabilities over the use of FPR or the prior calibration method. The method incorporates all available information from the data source and benefits from the favorable statistical properties of MLE. In particular, the MLE method also provides covariance between the estimated parameters that can be used in probabilistic sensitivity analysis required in cost-effectiveness models for HTA submissions.

Accelerated implicit-explicit Runge-Kutta schemes for locally stiff systems

In this paper we introduce a family of accelerated implicit-explicit (AIMEX) schemes for the solution of stiff systems of equations. Similar to conventional IMEX schemes, AIMEX schemes allow a problem to be split into its stiff and non-stiff constituent parts. These are then advanced in time using an implicit and explicit scheme, respectively. By design, AIMEX schemes have an arbitrarily large number of stages. This allows for optimization of the explicit part to improve its stability properties, increasing the allowable time step size. Importantly, only two implicit stages are required regardless of the total number of stages, meaning a larger global time step can be taken with significantly fewer implicit stages for a given simulation time. Numerical results demonstrate that AIMEX schemes achieve their designed order of accuracy for linear and non-linear problems involving mesh induced stiffness. Simulations of unsteady flow over an SD7003 airfoil using the compressible Navier-Stokes equations demonstrate that AIMEX schemes can significantly outperform classical explicit Runge-Kutta schemes by over a factor of 20, and conventional IMEX schemes by over a factor of two, with negligible impact on quantitative results. Finally, a demonstration case of Implicit Large Eddy Simulation (ILES) of flow over a stalled NACA0020 airfoil shows the utility of AIMEX schemes for wall-bounded turbulent flows.

Optimal synthesis and design of catalytic distillation columns: A rate-based modeling approach

This work presents the optimal synthesis and design of a rigorous catalytic distillation (CD) column that explicitly considers the multiscale and multiphase nature of this intensification process. A rate-based model that couples micro and macroscale events taking place inside the CD column is explicitly considered. The direct solution of such intensive optimization problems is challenging due to nonlinearities introduced by heterogeneous reactions, transport phenomena, and interactions between discrete and continuous variables. Also, combinatorial complexity involved in the selection of multiple structural decisions complicates the problem, e.g., distribution of reactive stages along the column, location of feed stages, and total number of stages. A discrete-steepest descent-based optimization framework recently developed is used to address the optimal synthesis and design of rate-based CD columns. A case study involving the production of ethyl tert-butyl ether (ETBE) has been considered. The results show that the multiscale events occurring in this process intensification (PI) unit cannot be ignored since they produce process designs different from those obtained with an equilibrium-based CD model. The results also show that neglecting multiscale phenomena may result in infeasible CD designs. The outcomes gained through this study illustrate the critical need to systematically consider multiscale and multiphase events in CD columns for the optimal design of realistic, cost-effective, and attractive process intensification (PI) systems.

Development of Value Stream Mapping from L’Oreal’s Artwork Process

ABSTRACT This research develops value stream mapping (VSM) for L’Oreal’s artwork process, to eliminate waste, reduce lead-time, and identify stages that should be automated, which makes the process less prone to human error and more responsive to fulfilling B2B (B2B) customer requirements. Additionally, amendments frequently occur slowing down the artwork process. In this context, VSM is applied to L’Oreal’s artwork process to reduce lead-time, human error, and missed deadlines. This practitioner note uses data from L’Oreal’s artwork tracker from 2018 to 2019, which is manually tracked by the launch team. The service level agreement and task time data has been collected from 12 employees representing the launch, factory, and marketing teams working on the artwork process. Qualitative feedback was also obtained from nine employees to validate the VSM for L’Oreal’s artwork process. VSM identified stages that should be streamlined and automated in L’Oreal’s artwork process, which makes the process more efficient and responsive to the changing scope of the artworks. Fifty percent of the stages have been eliminated from the manual artwork process, resulting in a reduced lead-time of 10.5 days and a reduction of 28% time spent on the process. This allows the artwork process to be more agile to the requirements of B2B customers. Moreover, the proposed VSM shows a 73% increase in value added time for a renovation and a 75% increase in value added time for new product developments (NPD). VSM has been used within many functions in a business, such as operations and supply chain management, however, its application within marketing has not been extensively explored. This practitioner note attempts to fill this gap by applying VSM to L’Oreal’s artwork process (AP). Moreover, this research extends the understanding of the concept and application of VSM within the context of lean in a marketing process. VSM has successfully identified the inefficiencies in the artwork process and highlighted the stages in the process that should be removed or automated thereby, making the process responsive and agile to meet the changing requirements of B2B customers. VSM has been successfully applied to L’Oreal’s artwork process that resulted in a significant reduction in the total number of stages in the proposed process by eliminating non-value added activities. Efficiency gained through the application of VSM will lead to increased B2B customer satisfaction, reduced lead-time, and reduction in human errors and missed deadlines. VSM has been specifically designed, developed, and analyzed for L’Oreal’s artwork process, in order to make the process more efficient and responsive to B2B customers' requirements.

Desorption of VOC from polymer adsorbent in multistage fluidized bed

Abstract The desorption process of volatile organic compounds (VOC) from a polymer adsorbent in counter-current multistage fluidized bed was studied. And a mathematical model considering the mass transfer dynamics was developed, which was validated from experiment data. The gaseous ethyl acetate mass transfer was discussed, and the limiting step is the intraparticle mass transfer of the desorption process. The value of intraparticle mass transfer coefficient is between 1.85 × 10−6 and 1.38 × 10−5 m·s−1 under temperature of 100–160 °C. Experiments under different operating conditions were carried out. The effects of operating conditions such as gas–solid flow ratio, gas inlet temperature and total stage number of multistage fluidized bed on outlet VOCs concentration and desorption efficiency were discussed. The maximum outlet VOCs concentration and corresponding desorption efficiency of the multistage fluidized bed desorber was calculated under different gas inlet temperatures and total stage numbers.

Application of Microemulsions in Liquid Chromatography and Electrokinetic Methods of Analysis: Advantages and Disadvantages of the Approach

The review surveys the works of staff members, students, and graduate students of the Divison of Analytical Chemistry, Department of Chemistry, Lomonosov Moscow State University on the use of microemulsions in liquid and electrokinetic chromatography. Microemulsions are used as promising extractants for the extraction of hydrophobic target substances from food, pharmaceutical, environmental, etc., samples. The possibility of the subsequent separation of microemulsions and the preconcentration of components to be determined in an organic phase was demonstrated. The approaches proposed are characterized by low detection limits; they considerably simplify a sample preparation process to shorten the total analysis time and to decrease the total number of stages, which decreases the error of determination.

Multi-Person Pose Estimation Using Bounding Box Constraint and LSTM

This paper presents a new method for single-image pose estimation of multiple people combining the traditional bottom-up and the top-down methods. Specifically, we extract features from the input image by a residual network and use a multistage CNN to learn both the confidence maps of joints and the connection relationships, between joints. During testing, we perform the network feedforwarding in a bottom-up manner, and then use the predicted confidence maps, the connection relationships, and the corresponding bounding boxes to parse the poses of all people in a top-down manner. In contrast to the previous top-down methods, our method is robust to bounding box shift and tightness, works well for largely overlapped people, and achieves faster running speed. In contrast to the bottom-up method, our method avoids mistake propagation across different people, and addresses disconnected joints effectively. To estimate human pose from videos, we impose a weight-sharing scheme to the multi-stage CNN, and rewrite it as a recurrent neural network. Thus, we can reuse the prediction results from the previous frames so as to reduce the total stage number, yielding significantly faster speed in invoking the network on videos. And we adopt LSTM units between frames to capture the temporal correlation among video frames. We found that LSTM handles input-quality degradation in videos well and successfully stabilizes the sequential outputs.

Simulating reactive distillation of HIx (HI–H2O–I2) system in Sulphur-Iodine cycle for hydrogen production

Abstract In this article, we develop a reactive distillation (RD) column configuration for the production of hydrogen. This RD column is in the HI decomposition section of the sulphur - iodine (SI) thermochemical cycle, in which HI decomposition and H2 separation take place simultaneously. The section plays a major role in high hydrogen production efficiency (that depends on reaction conversion and separation efficiency) of the SI cycle. In the column simulation, the rigorous thermodynamic phase equilibrium and reaction kinetic model are used. The tuning parameters involved in phase equilibrium model are dependent on interactive components and system temperature. For kinetic model, parameter values are adopted from the Aspen flowsheet simulator. Interestingly, there is no side reaction (e.g., solvation reaction, electrolyte decomposition and polyiodide formation) considered aiming to make the proposed model simple that leads to a challenging prediction. The process parameters are determined on the basis of optimal hydrogen production as reflux ratio = 0.87, total number of stages = 19 and feeding point at 8th stage. With this, the column operates at a reasonably low pressure (i.e., 8 bar) and produces hydrogen in the distillate with a desired composition (H2 = 9.18 mol%, H2O = 88.27 mol% and HI = 2.54 mol%). Finally, the results are compared with other model simulations. It is observed that the proposed scheme leads to consume a reasonably low energy requirement of 327 MJ/kmol of H2.

Kinetic modeling of countercurrent saccharification

BackgroundCountercurrent saccharification is a promising way to minimize enzyme loading while obtaining high conversions and product concentrations. However, in countercurrent saccharification experiments, 3–4 months are usually required to acquire a single steady-state data point. To save labor and time, simulation of this process is necessary to test various reaction conditions and determine the optimal operating point. Previously, a suitable kinetic model for countercurrent saccharification has never been reported. The Continuum Particle Distribution Modeling (CPDM) satisfactorily predicts countercurrent fermentation using mixed microbial cultures that digest various feedstocks. Here, CPDM is applied to countercurrent enzymatic saccharification of lignocellulose.ResultsCPDM was used to simulate multi-stage countercurrent saccharifications of a lignocellulose model compound (α-cellulose). The modified HCH-1 model, which accurately predicts long-term batch saccharification, was used as the governing equation in the CPDM model. When validated against experimental countercurrent saccharification data, it predicts experimental glucose concentrations and conversions with the average errors of 3.5% and 4.7%, respectively. CPDM predicts conversion and product concentration with varying enzyme-addition location, total stage number, enzyme loading, liquid residence time (LRT), and solids loading rate (SLR). In addition, countercurrent saccharification was compared to batch saccharification at the same conversion, product concentration, and reactor volume. Results show that countercurrent saccharification is particularly beneficial when the product concentration is low.ConclusionsThe CPDM model was used to simulate multi-stage countercurrent saccharification of α-cellulose. The model predictions agreed well with the experimental glucose concentrations and conversions. CPDM prediction results showed that the enzyme-addition location, enzyme loading, LRT, and SLR significantly affected the glucose concentration and conversion. Compared to batch saccharification at the same conversion, product concentration, and reactor volume, countercurrent saccharification is particularly beneficial when the product concentration is low.