Dynamic operation of flat sheet desalination-membrane elements: A comprehensive model accounting for organic fouling

Reliable simulation of membrane-module dynamic operation is essential in optimizing its detailed geo-metric characteristics and operation, as well as that of membrane plants, for various types of fluidtreatment applications. This paper is part of systematic efforts toward development of such a compre-hensive model, considering temporal variability caused by organic membrane fouling. To render themathematical problem tractable, justified simplifications (retaining the physical parameter interdepen-dencies) lead to a system of basic equations in two spatial planar coordinates, enabling to obtain a realistictemporal evolution of all process parameters. The flexible model structure allows integration of sub-models, for phenomena occurring (and researched) at small spatial scales, which account for retentatespacer effects on friction losses and mass transfer, and constitutive expressions for fouling rates duringdesalination. The robust numerical algorithm developed to solve the system of differential and algebraicequations exhibits satisfactory convergence, appropriate for applications. The results presented hereindemonstrate the versatility of the numerical code and its potential to analyze the interaction of mecha-nisms involved in fouling evolution, which is impossible by the much simpler one dimensional models.Directions for future developments are indicated.

Kostoglou-Karabelas-Comp-Chem-Eng-2016-1 Download

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Call Stack
#	Time	Memory	Function	Location
1	1.6358	28285944	shutdown_action_hook( )	...\load.php:0
2	1.6358	28285944	do_action( $hook_name = 'shutdown' )	...\load.php:1124
3	1.6358	28286320	WP_Hook->do_action( $args = [0 => ''] )	...\plugin.php:517
4	1.6358	28286320	WP_Hook->apply_filters( $value = '', $args = [0 => ''] )	...\class-wp-hook.php:332
5	1.6358	28287480	wp_ob_end_flush_all( '' )	...\class-wp-hook.php:308
6	1.6358	28287480	ob_end_flush( )	...\functions.php:5279
7	1.6358	28385816	autoptimizeMain->end_buffering( $content = '<!doctype html>\r\n<html lang="en-US">\r\n<head>\r\n\t<meta charset="UTF-8">\r\n\t<meta name="viewport" content="width=device-width, initial-scale=1.0">\r\n\t<meta http-equiv="X-UA-Compatible" content="IE=edge">\r\n\t<link rel="profile" href="https://gmpg.org/xfn/11">\r\n\t<meta name=\'robots\' content=\'index, follow, max-image-preview:large, max-snippet:-1, max-video-preview:-1\' />\n<link rel="alternate" hreflang="el" href="https://nrre.cperi.certh.gr/el/dynamic-operation-of-flat-sheet-desalination-membr', 9 )	...\functions.php:5279
8	1.6364	28388784	autoptimizeScripts->read( $options = ['aggregate' => 'on', 'defer_not_aggregate' => 1, 'defer_inline' => 1, 'justhead' => '', 'forcehead' => '', 'trycatch' => '', 'js_exclude' => 'wp-includes/js/dist/, wp-includes/js/tinymce/, js/jquery/jquery.js', 'cdn_url' => '', 'include_inline' => '', 'minify_excluded' => 'on'] )	...\autoptimizeMain.php:591
9	1.6365	28388784	apply_filters( $hook_name = 'autoptimize_filter_js_dontmove', $value = [0 => 'document.write', 1 => 'html5.js', 2 => 'show_ads.js', 3 => 'google_ad', 4 => 'histats.com/js', 5 => 'statcounter.com/counter/counter.js', 6 => 'ws.amazon.com/widgets', 7 => 'media.fastclick.net', 8 => '/ads/', 9 => 'comment-form-quicktags/quicktags.php', 10 => 'edToolbar', 11 => 'intensedebate.com', 12 => 'scripts.chitika.net/', 13 => '_gaq.push', 14 => 'jotform.com/', 15 => 'admin-bar.min.js', 16 => 'GoogleAnalyticsObject', 17 => 'plupload.full.min.js', 18 => 'syntaxhighlighter', 19 => 'adsbygoogle', 20 => 'gist.github.com', 21 => '_stq', 22 => 'nonce', 23 => 'post_id', 24 => 'data-noptimize', 25 => 'data-cfasync', 26 => 'data-pagespeed-no-defer', 27 => 'logHuman', 28 => 'amp-mobile-version-switcher', 29 => 'data-rocketlazyloadscript', 30 => 'rocket-browser-checker-js-after'] )	...\autoptimizeScripts.php:286
10	1.6365	28389192	WP_Hook->apply_filters( $value = [0 => 'document.write', 1 => 'html5.js', 2 => 'show_ads.js', 3 => 'google_ad', 4 => 'histats.com/js', 5 => 'statcounter.com/counter/counter.js', 6 => 'ws.amazon.com/widgets', 7 => 'media.fastclick.net', 8 => '/ads/', 9 => 'comment-form-quicktags/quicktags.php', 10 => 'edToolbar', 11 => 'intensedebate.com', 12 => 'scripts.chitika.net/', 13 => '_gaq.push', 14 => 'jotform.com/', 15 => 'admin-bar.min.js', 16 => 'GoogleAnalyticsObject', 17 => 'plupload.full.min.js', 18 => 'syntaxhighlighter', 19 => 'adsbygoogle', 20 => 'gist.github.com', 21 => '_stq', 22 => 'nonce', 23 => 'post_id', 24 => 'data-noptimize', 25 => 'data-cfasync', 26 => 'data-pagespeed-no-defer', 27 => 'logHuman', 28 => 'amp-mobile-version-switcher', 29 => 'data-rocketlazyloadscript', 30 => 'rocket-browser-checker-js-after'], $args = [0 => [0 => 'document.write', 1 => 'html5.js', 2 => 'show_ads.js', 3 => 'google_ad', 4 => 'histats.com/js', 5 => 'statcounter.com/counter/counter.js', 6 => 'ws.amazon.com/widgets', 7 => 'media.fastclick.net', 8 => '/ads/', 9 => 'comment-form-quicktags/quicktags.php', 10 => 'edToolbar', 11 => 'intensedebate.com', 12 => 'scripts.chitika.net/', 13 => '_gaq.push', 14 => 'jotform.com/', 15 => 'admin-bar.min.js', 16 => 'GoogleAnalyticsObject', 17 => 'plupload.full.min.js', 18 => 'syntaxhighlighter', 19 => 'adsbygoogle', 20 => 'gist.github.com', 21 => '_stq', 22 => 'nonce', 23 => 'post_id', 24 => 'data-noptimize', 25 => 'data-cfasync', 26 => 'data-pagespeed-no-defer', 27 => 'logHuman', 28 => 'amp-mobile-version-switcher', 29 => 'data-rocketlazyloadscript', 30 => 'rocket-browser-checker-js-after']] )	...\plugin.php:205

( ! ) Fatal error: Uncaught TypeError: call_user_func_array(): Argument #1 ($callback) must be a valid callback, non-static method wp_jquery_manager_plugin::autoptimize_support() cannot be called statically in C:\wamp64\www\nrre\wp-includes\class-wp-hook.php on line 308

( ! ) TypeError: call_user_func_array(): Argument #1 ($callback) must be a valid callback, non-static method wp_jquery_manager_plugin::autoptimize_support() cannot be called statically in C:\wamp64\www\nrre\wp-includes\class-wp-hook.php on line 308

Call Stack

Time

Memory

Function

Location

1.6358

28285944

shutdown_action_hook( )

...\load.php:0

1.6358

28285944

do_action( $hook_name = 'shutdown' )

...\load.php:1124

1.6358

28286320

WP_Hook->do_action( $args = [0 => ''] )

...\plugin.php:517

1.6358

28286320

WP_Hook->apply_filters( $value = '', $args = [0 => ''] )

...\class-wp-hook.php:332

1.6358

28287480

wp_ob_end_flush_all( '' )

...\class-wp-hook.php:308

1.6358

28287480

ob_end_flush( )

...\functions.php:5279

1.6358

28385816

autoptimizeMain->end_buffering( $content = '<!doctype html>\r\n<html lang="en-US">\r\n<head>\r\n\t<meta charset="UTF-8">\r\n\t<meta name="viewport" content="width=device-width, initial-scale=1.0">\r\n\t<meta http-equiv="X-UA-Compatible" content="IE=edge">\r\n\t<link rel="profile" href="https://gmpg.org/xfn/11">\r\n\t<meta name=\'robots\' content=\'index, follow, max-image-preview:large, max-snippet:-1, max-video-preview:-1\' />\n<link rel="alternate" hreflang="el" href="https://nrre.cperi.certh.gr/el/dynamic-operation-of-flat-sheet-desalination-membr', 9 )

...\functions.php:5279

1.6364

28388784

autoptimizeScripts->read( $options = ['aggregate' => 'on', 'defer_not_aggregate' => 1, 'defer_inline' => 1, 'justhead' => '', 'forcehead' => '', 'trycatch' => '', 'js_exclude' => 'wp-includes/js/dist/, wp-includes/js/tinymce/, js/jquery/jquery.js', 'cdn_url' => '', 'include_inline' => '', 'minify_excluded' => 'on'] )

...\autoptimizeMain.php:591

1.6365

28388784

apply_filters( $hook_name = 'autoptimize_filter_js_dontmove', $value = [0 => 'document.write', 1 => 'html5.js', 2 => 'show_ads.js', 3 => 'google_ad', 4 => 'histats.com/js', 5 => 'statcounter.com/counter/counter.js', 6 => 'ws.amazon.com/widgets', 7 => 'media.fastclick.net', 8 => '/ads/', 9 => 'comment-form-quicktags/quicktags.php', 10 => 'edToolbar', 11 => 'intensedebate.com', 12 => 'scripts.chitika.net/', 13 => '_gaq.push', 14 => 'jotform.com/', 15 => 'admin-bar.min.js', 16 => 'GoogleAnalyticsObject', 17 => 'plupload.full.min.js', 18 => 'syntaxhighlighter', 19 => 'adsbygoogle', 20 => 'gist.github.com', 21 => '_stq', 22 => 'nonce', 23 => 'post_id', 24 => 'data-noptimize', 25 => 'data-cfasync', 26 => 'data-pagespeed-no-defer', 27 => 'logHuman', 28 => 'amp-mobile-version-switcher', 29 => 'data-rocketlazyloadscript', 30 => 'rocket-browser-checker-js-after'] )

...\autoptimizeScripts.php:286

1.6365

28389192

WP_Hook->apply_filters( $value = [0 => 'document.write', 1 => 'html5.js', 2 => 'show_ads.js', 3 => 'google_ad', 4 => 'histats.com/js', 5 => 'statcounter.com/counter/counter.js', 6 => 'ws.amazon.com/widgets', 7 => 'media.fastclick.net', 8 => '/ads/', 9 => 'comment-form-quicktags/quicktags.php', 10 => 'edToolbar', 11 => 'intensedebate.com', 12 => 'scripts.chitika.net/', 13 => '_gaq.push', 14 => 'jotform.com/', 15 => 'admin-bar.min.js', 16 => 'GoogleAnalyticsObject', 17 => 'plupload.full.min.js', 18 => 'syntaxhighlighter', 19 => 'adsbygoogle', 20 => 'gist.github.com', 21 => '_stq', 22 => 'nonce', 23 => 'post_id', 24 => 'data-noptimize', 25 => 'data-cfasync', 26 => 'data-pagespeed-no-defer', 27 => 'logHuman', 28 => 'amp-mobile-version-switcher', 29 => 'data-rocketlazyloadscript', 30 => 'rocket-browser-checker-js-after'], $args = [0 => [0 => 'document.write', 1 => 'html5.js', 2 => 'show_ads.js', 3 => 'google_ad', 4 => 'histats.com/js', 5 => 'statcounter.com/counter/counter.js', 6 => 'ws.amazon.com/widgets', 7 => 'media.fastclick.net', 8 => '/ads/', 9 => 'comment-form-quicktags/quicktags.php', 10 => 'edToolbar', 11 => 'intensedebate.com', 12 => 'scripts.chitika.net/', 13 => '_gaq.push', 14 => 'jotform.com/', 15 => 'admin-bar.min.js', 16 => 'GoogleAnalyticsObject', 17 => 'plupload.full.min.js', 18 => 'syntaxhighlighter', 19 => 'adsbygoogle', 20 => 'gist.github.com', 21 => '_stq', 22 => 'nonce', 23 => 'post_id', 24 => 'data-noptimize', 25 => 'data-cfasync', 26 => 'data-pagespeed-no-defer', 27 => 'logHuman', 28 => 'amp-mobile-version-switcher', 29 => 'data-rocketlazyloadscript', 30 => 'rocket-browser-checker-js-after']] )

...\plugin.php:205