Special Issue "Modeling, Simulation and Design of Membrane Computing System"

A special issue of Processes (ISSN 2227-9717). This special issue belongs to the section "Chemical Systems".

Deadline for manuscript submissions: closed (28 February 2021).

Special Issue Editors

Dr. Luis Valencia Cabrera
E-Mail Website1 Website2
Guest Editor
Research Group on Natural Computing, Department of Computer Science and Artificial Intelligence, Universidad de Sevilla, 41004 Sevilla, Spain
Interests: Computational Modeling, Membrane Computing, Design and Development of Simulation tools for computational models, Computational Complexity, Artificial Intelligence
Prof. Dr. Mario de Jesús Pérez Jiménez
E-Mail Website
Guest Editor
Research Group on Natural Computing, Department of Computer Science and Artificial Intelligence, Universidad de Sevilla, 41004 Sevilla, Spain
Interests: Computational Complexity Theory, Membrane Computing, Computational Modelling for Systems Biology and Population Dynamics, Natural Computing, Bioinformatics
Prof. Dr. Agustín Riscos Núñez
E-Mail Website
Guest Editor
Research Group on Natural Computing, Department of Computer Science and Artificial Intelligence, Universidad de Sevilla, 41004 Sevilla, Spain
Interests: Membrane Computing, Complexity, Bioinspired models of computation, Computational Modelling, Natural Computing, Membrane Systems Simulation, Artificial Intelligence, Machine Learning, Optimization, Genetic Algorithms, Cellular Automata

Special Issue Information

Dear Colleagues,

Membrane Computing has attracted a considerable amount of attention since its inception in 1998. This branch of natural computing is supported by solid foundations on theoretical computer science, from the formal languages theory to studies of computational power and complexity. It provides computational devices (P systems or membrane systems) inspired from cells, tissues, and neural connections, including many variants proved universal and able to solve computationally hard problems. From the point of view of real-life applications, different types of P systems have been successfully applied as suitable and interesting tools for the computational modeling of complex systems in a wide range of areas as systems biology, ecology, robot control or economy, among others. Additionally, hybrid systems known as membrane algorithms, taking elements from membrane computing and other nature-inspired algorithms, have provided competitive solutions to optimization problems. These models, based on membrane computing, have shown interesting features for a modeling framework, such as relevance, understandability, extensibility, and computability. In order for these computational models of complex systems to become useful practical tools for researchers in theoretical computing and in applied sciences, a crucial aspect to focus on is the development of software-hardware simulators to capture the mechanisms of the computational devices and properly represent the behavior of the systems under study. Depending on their scope, these tools must address different challenges in terms of feasibility, reliability, usability, efficiency, etc., and must cover everything from specific-purpose accurate apps for certain problems to general-purpose tools for the modeling, debugging, model checking, verification and virtual experimentation through the simulation of the corresponding models designed.

This Special Issue on the “Modeling, Simulation, and Design of Membrane Computing Systems” aims to provide a relevant compilation of novel significant advances in the computational modeling of complex systems based on membrane computing and the development of software tools to aid in the design and simulation of such models. Ground-breaking contributions are welcomed in the fields of the design of membrane P systems, modeling frameworks, and simulation tools. Topics include, but are not limited to:

  • Novel modeling techniques within membrane computing
  • Complex systems modeling based on P systems
  • Applications of membrane computing models in real problems in Biology, Medicine, Economy, Robotics, etc.
  • Simulation algorithms
  • Software tools to aid in the modeling, verification and simulation of membrane systems
  • Hardware implementations, and High Performance Computing
  • Design of membrane computing solutions to relevant problems
  • Automatic design of membrane systems
  • Membrane algorithms to solve optimization problems
  • Theoretical contributions providing membrane system variants suitable for modelling

Dr. Luis Valencia Cabrera
Prof. Dr. Mario de Jesús Pérez Jiménez
Prof. Dr. Agustín Riscos Núñez
Guest Editors

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Processes is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2000 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Membrane computing
  • Simulation of P systems
  • Computational modeling of complex systems
  • Automatic design of membrane systems
  • Real-life bio-inspired models
  • Natural computing
  • Membrane algorithms
  • High Performance Computing simulators for membrane systems
  • Spiking neural P systems
  • Cell-inspired models

Published Papers (14 papers)

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Research

Open AccessArticle
Spiking Neural Membrane Computing Models
Processes 2021, 9(5), 733; https://doi.org/10.3390/pr9050733 - 21 Apr 2021
Viewed by 234
Abstract
As third-generation neural network models, spiking neural P systems (SNP) have distributed parallel computing capabilities with good performance. In recent years, artificial neural networks have received widespread attention due to their powerful information processing capabilities, which is an effective combination of a class [...] Read more.
As third-generation neural network models, spiking neural P systems (SNP) have distributed parallel computing capabilities with good performance. In recent years, artificial neural networks have received widespread attention due to their powerful information processing capabilities, which is an effective combination of a class of biological neural networks and mathematical models. However, SNP systems have some shortcomings in numerical calculations. In order to improve the incompletion of current SNP systems in dealing with certain real data technology in this paper, we use neural network structure and data processing methods for reference. Combining them with membrane computing, spiking neural membrane computing models (SNMC models) are proposed. In SNMC models, the state of each neuron is a real number, and the neuron contains the input unit and the threshold unit. Additionally, there is a new style of rules for neurons with time delay. The way of consuming spikes is controlled by a nonlinear production function, and the produced spike is determined based on a comparison between the value calculated by the production function and the critical value. In addition, the Turing universality of the SNMC model as a number generator and acceptor is proved. Full article
(This article belongs to the Special Issue Modeling, Simulation and Design of Membrane Computing System)
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Open AccessArticle
Simulation of Spiking Neural P Systems with Sparse Matrix-Vector Operations
Processes 2021, 9(4), 690; https://doi.org/10.3390/pr9040690 - 14 Apr 2021
Viewed by 351
Abstract
To date, parallel simulation algorithms for spiking neural P (SNP) systems are based on a matrix representation. This way, the simulation is implemented with linear algebra operations, which can be easily parallelized on high performance computing platforms such as GPUs. Although it has [...] Read more.
To date, parallel simulation algorithms for spiking neural P (SNP) systems are based on a matrix representation. This way, the simulation is implemented with linear algebra operations, which can be easily parallelized on high performance computing platforms such as GPUs. Although it has been convenient for the first generation of GPU-based simulators, such as CuSNP, there are some bottlenecks to sort out. For example, the proposed matrix representations of SNP systems lead to very sparse matrices, where the majority of values are zero. It is known that sparse matrices can compromise the performance of algorithms since they involve a waste of memory and time. This problem has been extensively studied in the literature of parallel computing. In this paper, we analyze some of these ideas and apply them to represent some variants of SNP systems. We also provide a new simulation algorithm based on a novel compressed representation for sparse matrices. We also conclude which SNP system variant better suits our new compressed matrix representation. Full article
(This article belongs to the Special Issue Modeling, Simulation and Design of Membrane Computing System)
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Open AccessArticle
Novel Numerical Spiking Neural P Systems with a Variable Consumption Strategy
Processes 2021, 9(3), 549; https://doi.org/10.3390/pr9030549 - 20 Mar 2021
Cited by 1 | Viewed by 352
Abstract
A novel variant of NSN P systems, called numerical spiking neural P systems with a variable consumption strategy (NSNVC P systems), is proposed. Like the spiking rules consuming spikes in spiking neural P systems, NSNVC P systems introduce a variable consumption strategy by [...] Read more.
A novel variant of NSN P systems, called numerical spiking neural P systems with a variable consumption strategy (NSNVC P systems), is proposed. Like the spiking rules consuming spikes in spiking neural P systems, NSNVC P systems introduce a variable consumption strategy by modifying the form of the production functions used in NSN P systems. Similar to the delay feature of the spiking rules, NSNVC P systems introduce a postponement feature into the production functions. The execution of the production functions in NSNVC P systems is controlled by two, i.e., polarization and threshold, conditions. Multiple synaptic channels are used to transmit the charges and the production values in NSNVC P systems. The proposed NSNVC P systems are a type of distributed parallel computing models with a directed graphical structure. The Turing universality of the proposed NSNVC P systems is proved as number generating/accepting devices. Detailed descriptions are provided for NSNVC P systems as number generating/accepting devices. In addition, a universal NSNVC P system with 66 neurons is constructed as a function computing device. Full article
(This article belongs to the Special Issue Modeling, Simulation and Design of Membrane Computing System)
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Open AccessFeature PaperArticle
An In Vivo Proposal of Cell Computing Inspired by Membrane Computing
Processes 2021, 9(3), 511; https://doi.org/10.3390/pr9030511 - 12 Mar 2021
Cited by 1 | Viewed by 347
Abstract
Intractable problems are challenging and not uncommon in Computer Science. The computing generation we are living in forces us to look for an alternative way of computing, as current computers are facing limitations when dealing with complex problems and bigger input data. Physics [...] Read more.
Intractable problems are challenging and not uncommon in Computer Science. The computing generation we are living in forces us to look for an alternative way of computing, as current computers are facing limitations when dealing with complex problems and bigger input data. Physics and Biology offer great alternatives to solve these problems that traditional computers cannot. Models like Quantum Computing and cell computing are emerging as possible solutions to the current problems the conventional computers are facing. This proposal describes an in vivo framework inspired by membrane computing and based on alternative computational frameworks that have been proven to be theoretically correct such as chemical reaction series. The abilities of a cell as a computational unit make this proposal a starting point in the creation of feasible potential frameworks to enhance the performance of applications in different disciplines such as Biology, BioMedicine, Computer networks, and Social Sciences, by accelerating drastically the way information is processed by conventional architectures and possibly achieving results that presently are not possible due to the limitations of the current computing paradigm. This paper introduces an in vivo solution that uses the principles of membrane computing and it can produce non-deterministic outputs. Full article
(This article belongs to the Special Issue Modeling, Simulation and Design of Membrane Computing System)
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Open AccessArticle
Noises Cutting and Natural Neighbors Spectral Clustering Based on Coupling P System
Processes 2021, 9(3), 439; https://doi.org/10.3390/pr9030439 - 28 Feb 2021
Viewed by 295
Abstract
Clustering analysis, a key step for many data mining problems, can be applied to various fields. However, no matter what kind of clustering method, noise points have always been an important factor affecting the clustering effect. In addition, in spectral clustering, the construction [...] Read more.
Clustering analysis, a key step for many data mining problems, can be applied to various fields. However, no matter what kind of clustering method, noise points have always been an important factor affecting the clustering effect. In addition, in spectral clustering, the construction of affinity matrix affects the formation of new samples, which in turn affects the final clustering results. Therefore, this study proposes a noise cutting and natural neighbors spectral clustering method based on coupling P system (NCNNSC-CP) to solve the above problems. The whole algorithm process is carried out in the coupled P system. We propose a natural neighbors searching method without parameters, which can quickly determine the natural neighbors and natural characteristic value of data points. Then, based on it, the critical density and reverse density are obtained, and noise identification and cutting are performed. The affinity matrix constructed using core natural neighbors greatly improve the similarity between data points. Experimental results on nine synthetic data sets and six UCI datasets demonstrate that the proposed algorithm is better than other comparison algorithms. Full article
(This article belongs to the Special Issue Modeling, Simulation and Design of Membrane Computing System)
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Open AccessFeature PaperArticle
Parallel Multiset Rewriting Systems with Distorted Rules
Processes 2021, 9(2), 347; https://doi.org/10.3390/pr9020347 - 14 Feb 2021
Viewed by 380
Abstract
Most of the parallel rewriting systems which model (or which are inspired by) natural/artificial phenomena consider fixed, a priori defined sets of string/multiset rewriting rules whose definitions do not change during the computation. Here we modify this paradigm by defining level-t distorted [...] Read more.
Most of the parallel rewriting systems which model (or which are inspired by) natural/artificial phenomena consider fixed, a priori defined sets of string/multiset rewriting rules whose definitions do not change during the computation. Here we modify this paradigm by defining level-t distorted rules—rules for which during their applications one does not know the exact multiplicities of at most tN species of objects in their output (although one knows that such objects will appear at least once in the output upon the execution of this type of rules). Subsequently, we define parallel multiset rewriting systems with t-distorted computations and we study their computational capabilities when level-1 distorted catalytic promoted rules are used. We construct robust systems able to cope with the level-1 distortions and prove the computational universality of the model. Full article
(This article belongs to the Special Issue Modeling, Simulation and Design of Membrane Computing System)
Open AccessArticle
On Numerical 2D P Colonies Modelling the Grey Wolf Optimization Algorithm
Processes 2021, 9(2), 330; https://doi.org/10.3390/pr9020330 - 11 Feb 2021
Viewed by 445
Abstract
The 2D P colonies is a version of the P colonies with a two-dimensional environment designed for observing the behavior of the community of very simple agents living in the shared environment. Each agent is equipped with a set of programs consisting of [...] Read more.
The 2D P colonies is a version of the P colonies with a two-dimensional environment designed for observing the behavior of the community of very simple agents living in the shared environment. Each agent is equipped with a set of programs consisting of a small number of simple rules. These programs allow the agent to act and move in the environment. The 2D P colonies have been shown to be suitable for the simulations of various (not only) multi-agent systems, and natural phenomena, like flash floods. The Grey wolf algorithm is the optimization-based algorithm inspired by social dynamics found in packs of grey wolves and by their ability to create hierarchies, in which every member has a clearly defined role, dynamically. In our previous papers, we extended the 2D P colony by the universal communication device, the blackboard. The blackboard allows for the agents to share various information, e.g., their position or the information about their surroundings. In this paper, we follow our previous research on the numerical 2D P colony with the blackboard. We present the computer simulator of the numerical 2D P colony with the blackboard and the results of the computer simulation, and we compare these results with the original algorithm. Full article
(This article belongs to the Special Issue Modeling, Simulation and Design of Membrane Computing System)
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Open AccessArticle
Improved Hybrid Heuristic Algorithm Inspired by Tissue-Like Membrane System to Solve Job Shop Scheduling Problem
Processes 2021, 9(2), 219; https://doi.org/10.3390/pr9020219 - 25 Jan 2021
Viewed by 347
Abstract
In real industrial engineering, job shop scheduling problem (JSSP) is considered to be one of the most difficult and tricky non-deterministic polynomial-time (NP)-hard problems. This study proposes a new hybrid heuristic algorithm for solving JSSP inspired by the tissue-like membrane system. The framework [...] Read more.
In real industrial engineering, job shop scheduling problem (JSSP) is considered to be one of the most difficult and tricky non-deterministic polynomial-time (NP)-hard problems. This study proposes a new hybrid heuristic algorithm for solving JSSP inspired by the tissue-like membrane system. The framework of the proposed algorithm incorporates improved genetic algorithms (GA), modified rumor particle swarm optimization (PSO), and fine-grained local search methods (LSM). To effectively alleviate the premature convergence of GA, the improved GA uses adaptive crossover and mutation probabilities. Taking into account the improvement of the diversity of the population, the rumor PSO is discretized to interactively optimize the population. In addition, a local search operator incorporating critical path recognition is designed to enhance the local search ability of the population. Experiment with 24 benchmark instances show that the proposed algorithm outperforms other latest comparative algorithms, and hybrid optimization strategies that complement each other in performance can better break through the original limitations of the single meta-heuristic method. Full article
(This article belongs to the Special Issue Modeling, Simulation and Design of Membrane Computing System)
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Open AccessArticle
Snapse: A Visual Tool for Spiking Neural P Systems
Processes 2021, 9(1), 72; https://doi.org/10.3390/pr9010072 - 30 Dec 2020
Cited by 1 | Viewed by 453
Abstract
Spiking neural P (SN P) systems are models of computation inspired by spiking neurons and part of the third generation of neuron models. SN P systems are equivalent to Turing machines and are able to solve computationally hard problems using a space-time trade-off. [...] Read more.
Spiking neural P (SN P) systems are models of computation inspired by spiking neurons and part of the third generation of neuron models. SN P systems are equivalent to Turing machines and are able to solve computationally hard problems using a space-time trade-off. Research in SN P systems theory is especially active, more so in recent years as more efforts are directed towards their real-world applications. Usually, SN P systems are represented visually as a directed graph and simulated through mainly text-based simulations or tables. Thus, there is a need for tools that can simulate and create SN P Systems in a visual and easy-to-use manner. Snapse is such a tool which aims to hasten the speed and ease at which researchers may create and experiment with SN P systems. Furthermore, visual tools such as Snapse can help further bring SN P systems outside of theoretical computer science. Full article
(This article belongs to the Special Issue Modeling, Simulation and Design of Membrane Computing System)
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Open AccessArticle
A Novel Consensus Fuzzy K-Modes Clustering Using Coupling DNA-Chain-Hypergraph P System for Categorical Data
Processes 2020, 8(10), 1326; https://doi.org/10.3390/pr8101326 - 21 Oct 2020
Cited by 1 | Viewed by 561
Abstract
In this paper, a data clustering method named consensus fuzzy k-modes clustering is proposed to improve the performance of the clustering for the categorical data. At the same time, the coupling DNA-chain-hypergraph P system is constructed to realize the process of the clustering. [...] Read more.
In this paper, a data clustering method named consensus fuzzy k-modes clustering is proposed to improve the performance of the clustering for the categorical data. At the same time, the coupling DNA-chain-hypergraph P system is constructed to realize the process of the clustering. This P system can prevent the clustering algorithm falling into the local optimum and realize the clustering process in implicit parallelism. The consensus fuzzy k-modes algorithm can combine the advantages of the fuzzy k-modes algorithm, weight fuzzy k-modes algorithm and genetic fuzzy k-modes algorithm. The fuzzy k-modes algorithm can realize the soft partition which is closer to reality, but treats all the variables equally. The weight fuzzy k-modes algorithm introduced the weight vector which strengthens the basic k-modes clustering by associating higher weights with features useful in analysis. These two methods are only improvements the k-modes algorithm itself. So, the genetic k-modes algorithm is proposed which used the genetic operations in the clustering process. In this paper, we examine these three kinds of k-modes algorithms and further introduce DNA genetic optimization operations in the final consensus process. Finally, we conduct experiments on the seven UCI datasets and compare the clustering results with another four categorical clustering algorithms. The experiment results and statistical test results show that our method can get better clustering results than the compared clustering algorithms, respectively. Full article
(This article belongs to the Special Issue Modeling, Simulation and Design of Membrane Computing System)
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Open AccessArticle
A Representation of Membrane Computing with a Clustering Algorithm on the Graphical Processing Unit
Processes 2020, 8(9), 1199; https://doi.org/10.3390/pr8091199 - 22 Sep 2020
Cited by 1 | Viewed by 653
Abstract
Long-timescale simulations of biological processes such as photosynthesis or attempts to solve NP-hard problems such as traveling salesman, knapsack, Hamiltonian path, and satisfiability using membrane systems without appropriate parallelization can take hours or days. Graphics processing units (GPU) deliver an immensely parallel mechanism [...] Read more.
Long-timescale simulations of biological processes such as photosynthesis or attempts to solve NP-hard problems such as traveling salesman, knapsack, Hamiltonian path, and satisfiability using membrane systems without appropriate parallelization can take hours or days. Graphics processing units (GPU) deliver an immensely parallel mechanism to compute general-purpose computations. Previous studies mapped one membrane to one thread block on GPU. This is disadvantageous given that when the quantity of objects for each membrane is small, the quantity of active thread will also be small, thereby decreasing performance. While each membrane is designated to one thread block, the communication between thread blocks is needed for executing the communication between membranes. Communication between thread blocks is a time-consuming process. Previous approaches have also not addressed the issue of GPU occupancy. This study presents a classification algorithm to manage dependent objects and membranes based on the communication rate associated with the defined weighted network and assign them to sub-matrices. Thus, dependent objects and membranes are allocated to the same threads and thread blocks, thereby decreasing communication between threads and thread blocks and allowing GPUs to maintain the highest occupancy possible. The experimental results indicate that for 48 objects per membrane, the algorithm facilitates a 93-fold increase in processing speed compared to a 1.6-fold increase with previous algorithms. Full article
(This article belongs to the Special Issue Modeling, Simulation and Design of Membrane Computing System)
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Open AccessArticle
Membrane System-Based Improved Neural Networks for Time-Series Anomaly Detection
Processes 2020, 8(9), 1168; https://doi.org/10.3390/pr8091168 - 17 Sep 2020
Cited by 1 | Viewed by 771
Abstract
Anomaly detection in time series has attracted much attention recently and is quite a challenging task. In this paper, a novel deep-learning approach (AL-CNN) that classifies the time series as normal or abnormal with less domain knowledge is proposed. The proposed algorithm combines [...] Read more.
Anomaly detection in time series has attracted much attention recently and is quite a challenging task. In this paper, a novel deep-learning approach (AL-CNN) that classifies the time series as normal or abnormal with less domain knowledge is proposed. The proposed algorithm combines Convolutional Neural Networks (CNNs) and Long Short-Term Memory (LSTM) to effectively model the spatial and temporal information contained in time-series data, the techniques of Squeeze-and-Excitation are applied to implement the feature recalibration. However, the difficulty of selecting multiple parameters and the long training time of a single model make AL-CNN less effective. To alleviate these challenges, a hybrid dynamic membrane system (HM-AL-CNN) is designed which is a new distributed and parallel computing model. We have performed a detailed evaluation of this proposed approach on three well-known benchmarks including the Yahoo S5 datasets. Experiments show that the proposed method possessed a robust and superior performance than the state-of-the-art methods and improved the average on three used indicators significantly. Full article
(This article belongs to the Special Issue Modeling, Simulation and Design of Membrane Computing System)
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Open AccessArticle
A Grid-Density Based Algorithm by Weighted Spiking Neural P Systems with Anti-Spikes and Astrocytes in Spatial Cluster Analysis
Processes 2020, 8(9), 1132; https://doi.org/10.3390/pr8091132 - 11 Sep 2020
Cited by 1 | Viewed by 580
Abstract
In this paper, we propose a novel clustering approach based on P systems and grid- density strategy. We present grid-density based approach for clustering high dimensional data, which first projects the data patterns on a two-dimensional space to overcome the curse of dimensionality [...] Read more.
In this paper, we propose a novel clustering approach based on P systems and grid- density strategy. We present grid-density based approach for clustering high dimensional data, which first projects the data patterns on a two-dimensional space to overcome the curse of dimensionality problem. Then, through meshing the plane with grid lines and deleting sparse grids, clusters are found out. In particular, we present weighted spiking neural P systems with anti-spikes and astrocyte (WSNPA2 in short) to implement grid-density based approach in parallel. Each neuron in weighted SN P system contains a spike, which can be expressed by a computable real number. Spikes and anti-spikes are inspired by neurons communicating through excitatory and inhibitory impulses. Astrocytes have excitatory and inhibitory influence on synapses. Experimental results on multiple real-world datasets demonstrate the effectiveness and efficiency of our approach. Full article
(This article belongs to the Special Issue Modeling, Simulation and Design of Membrane Computing System)
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Open AccessFeature PaperArticle
Performance Assessment of SWRO Spiral-Wound Membrane Modules with Different Feed Spacer Dimensions
Processes 2020, 8(6), 692; https://doi.org/10.3390/pr8060692 - 14 Jun 2020
Cited by 5 | Viewed by 890
Abstract
Reverse osmosis is the leading process in seawater desalination. However, it is still an energy intensive technology. Feed spacer geometry design is a key factor in reverse osmosis spiral wound membrane module performance. Correlations obtained from experimental work and computational fluid dynamics modeling [...] Read more.
Reverse osmosis is the leading process in seawater desalination. However, it is still an energy intensive technology. Feed spacer geometry design is a key factor in reverse osmosis spiral wound membrane module performance. Correlations obtained from experimental work and computational fluid dynamics modeling were used in a computational tool to simulate the impact of different feed spacer geometries in seawater reverse osmosis spiral wound membrane modules with different permeability coefficients in pressure vessels with 6, 7 and 8 elements. The aim of this work was to carry out a comparative analysis of the effect of different feed spacer geometries in combination with the water and solute permeability coefficients on seawater reverse osmosis spiral wound membrane modules performance. The results showed a higher impact of feed spacer geometries in the membrane with the highest production (highest water permeability coefficient). It was also found that the impact of feed spacer geometry increased with the number of spiral wound membrane modules in series in the pressure vessel. Installation of different feed spacer geometries in reverse osmosis membranes depending on the operating conditions could improve the performance of seawater reverse osmosis systems in terms of energy consumption and permeate quality. Full article
(This article belongs to the Special Issue Modeling, Simulation and Design of Membrane Computing System)
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