Question
Reservoir Engineering I
Generate a robust programming to solve the problem below. The program can be wrote by using any computer language, e.g., Matlab, C, VB, Julia, Python.
Problem:
Use the Peng-Robinson equation of state to calculate the compositions and densities of the equilibrium liquid and gas of the mixture given below at 160°F and 2000 psia. Use binary interaction coefficients of 0.02 for methane-n-butane, 0.035 for methane-n-decane, and 0.0 for n-butane-n-decane.
Component Composition, mole fraction
Methane             0.5532
n-Butane            0.2630
n-Decane          0.1838
                           1.0000
Compare your answer with experimental results shown below.
Component Composition, mole fraction
                                 liquid            gas
Methane                   0.458            0.856
n-Butane                   0.304            0.130
n-Decane                  0.238            0.0136
                                  1.000            0.9996
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%% Physical information
% This part is for all physical properties of components that are required
% for calculation.
% it is important the entry order in each varible because the position is
% related to the component, so the first position is for Methane,
% the second one for butane and the last one for decane.

%    C1   C4    C10
Tc = [343 765.3 1111.7];       % Critical temperature, R
Pc = [666.4 550.6 305.2];       % Critical pressure, psia
Omega = [0.0104 0.1995 0.4898]; % Acentric factor, dimensionless
R = 10.732;                     % Universal gas constant, ft3 psia/R/lbmol

%%
% Matrix of binary interaction coefficients
%%
%
% $$\left[\begin{array}{ccc}
% \delta_{11} & \delta_{12} & \delta_{13} \\
% \delta_{21} & \delta_{22} & \delta_{23} \\
% \delta_{31} & \delta_{32} & \delta_{33}
% \end{array} \right] = \left[\begin{array}{ccc}
% 0.000 & 0.020 & 0.035 \\
% 0.020 & 0.000 & 0.000 \\
% 0.035 & 0.000 & 0.000
% \end{array}\right]$$
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      • Illuminate\Cache\Events\CacheHit (129μs)
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      • Illuminate\Cache\Events\CacheHit (147μs)
      • Illuminate\Cache\Events\CacheHit (117μs)
      • Illuminate\Cache\Events\CacheHit (127μs)
      • Illuminate\Cache\Events\CacheHit (101μs)
      • Illuminate\Cache\Events\CacheHit (118μs)
      • Illuminate\Cache\Events\CacheHit (110μs)
      • Illuminate\Cache\Events\CacheHit (121μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheHit (129μs)
      • Illuminate\Cache\Events\CacheHit (105μs)
      • Illuminate\Cache\Events\CacheHit (146μs)
      • Illuminate\Cache\Events\CacheHit (115μs)
      • Illuminate\Cache\Events\CacheHit (125μs)
      • Illuminate\Cache\Events\CacheHit (103μs)
      • Illuminate\Cache\Events\CacheHit (130μs)
      • Illuminate\Cache\Events\CacheHit (106μs)
      • Illuminate\Cache\Events\CacheHit (132μs)
      • Illuminate\Cache\Events\CacheHit (117μs)
      • Illuminate\Cache\Events\CacheHit (140μs)
      • Illuminate\Cache\Events\CacheHit (123μs)
      • Illuminate\Cache\Events\CacheMissed (226μs)
      • Illuminate\Database\Events\StatementPrepared (1.1ms)
      • Illuminate\Database\Events\QueryExecuted (1.1ms)
      • eloquent.retrieved: App\Models\SubjectCat (83μs)
      • Illuminate\Cache\Events\KeyWritten (343μs)
      • Illuminate\Cache\Events\CacheHit (212μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (114μs)
      • Illuminate\Cache\Events\CacheHit (125μs)
      • Illuminate\Cache\Events\CacheHit (103μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheHit (135μs)
      • Illuminate\Cache\Events\CacheHit (103μs)
      • Illuminate\Cache\Events\CacheHit (130μs)
      • Illuminate\Cache\Events\CacheHit (107μs)
      • Illuminate\Cache\Events\CacheHit (116μs)
      • Illuminate\Cache\Events\CacheHit (100μs)
      • Illuminate\Cache\Events\CacheHit (116μs)
      • Illuminate\Cache\Events\CacheHit (99μs)
      • Illuminate\Cache\Events\CacheHit (115μs)
      • Illuminate\Cache\Events\CacheHit (100μs)
      • creating: site.layouts.app (533μs)
      • composing: site.layouts.app (19μs)
      • creating: components.canonical (417μs)
      • composing: components.canonical (81μs)
      • creating: components.open-graph (165μs)
      • composing: components.open-graph (54μs)
      • creating: site.headers.header (222μs)
      • composing: site.headers.header (49μs)
      • Illuminate\Cache\Events\CacheHit (1.35ms)
      • creating: components.footer (72μs)
      • composing: components.footer (71μs)
      • Illuminate\Cache\Events\CacheHit (715μs)
      • Illuminate\Cache\Events\CacheMissed (340μs)
      • Illuminate\Database\Events\StatementPrepared (1.21ms)
      • Illuminate\Database\Events\QueryExecuted (1.01ms)
      • eloquent.retrieved: App\Models\SubjectCat (73μs)
      • Illuminate\Cache\Events\KeyWritten (1.57ms)
      • Illuminate\Cache\Events\CacheHit (344μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (136μs)
      • Illuminate\Cache\Events\CacheHit (123μs)
      • Illuminate\Cache\Events\CacheHit (145μs)
      • Illuminate\Cache\Events\CacheHit (247μs)
      • Illuminate\Cache\Events\CacheHit (247μs)
      • Illuminate\Cache\Events\CacheHit (131μs)
      • Illuminate\Cache\Events\CacheHit (139μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (153μs)
      • Illuminate\Cache\Events\CacheHit (141μs)
      • creating: components.forms.contact-us (193μs)
      • composing: components.forms.contact-us (116μs)
      • creating: components.forms.get-started (112μs)
      • composing: components.forms.get-started (47μs)
      • creating: components.forms.free-tool-download (73μs)
      • composing: components.forms.free-tool-download (40μs)
      • creating: components.forms.claim-free-worksheet (65μs)
      • composing: components.forms.claim-free-worksheet (39μs)
      • creating: components.forms.tutor-subscription-waitlist (62μs)
      • composing: components.forms.tutor-subscription-waitlist (37μs)
      • creating: components.forms.tutor-subscription-join (64μs)
      • composing: components.forms.tutor-subscription-join (38μs)
      • creating: components.forms.tutor-support (61μs)
      • composing: components.forms.tutor-support (40μs)
      • 311 x Illuminate\Cache\Events\CacheHit (16.73%)
        63.34ms
        20 x Illuminate\Database\Events\StatementPrepared (14.8%)
        56.01ms
        20 x Illuminate\Database\Events\QueryExecuted (7.35%)
        27.83ms
        11 x Illuminate\Cache\Events\CacheMissed (2.29%)
        8.68ms
        11 x Illuminate\Cache\Events\KeyWritten (1.59%)
        6.03ms
        1 x Illuminate\Foundation\Events\LocaleUpdated (1.19%)
        4.49ms
        12 x eloquent.retrieved: App\Models\SubjectCat (0.38%)
        1.44ms
        1 x Illuminate\Routing\Events\Routing (0.31%)
        1.16ms
        1 x Illuminate\Database\Events\ConnectionEstablished (0.24%)
        912μs
        1 x creating: site.layouts.app (0.14%)
        533μs
        1 x Illuminate\Routing\Events\RouteMatched (0.12%)
        448μs
        1 x creating: components.canonical (0.11%)
        417μs
        1 x eloquent.booting: App\Models\SubjectCat (0.1%)
        384μs
        1 x creating: homework.show (0.1%)
        376μs
        1 x creating: components.breadcrumbs (0.09%)
        357μs
        2 x eloquent.retrieved: App\Models\Subject (0.07%)
        261μs
        7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.06%)
        243μs
        1 x creating: site.headers.header (0.06%)
        222μs
        10 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.06%)
        219μs
        1 x creating: components.forms.contact-us (0.05%)
        193μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.05%)
        190μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.05%)
        175μs
        1 x composing: components.breadcrumbs (0.05%)
        174μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.05%)
        173μs
        1 x composing: homework.show (0.04%)
        165μs
        1 x creating: components.open-graph (0.04%)
        165μs
        1 x composing: components.forms.contact-us (0.03%)
        116μs
        1 x creating: components.forms.get-started (0.03%)
        112μs
        1 x eloquent.booting: App\Models\Subject (0.03%)
        101μs
        1 x composing: components.canonical (0.02%)
        81μs
        1 x creating: components.forms.free-tool-download (0.02%)
        73μs
        1 x creating: components.footer (0.02%)
        72μs
        1 x composing: components.footer (0.02%)
        71μs
        1 x creating: components.forms.claim-free-worksheet (0.02%)
        65μs
        1 x creating: components.forms.tutor-subscription-join (0.02%)
        64μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.02%)
        63μs
        1 x creating: components.forms.tutor-subscription-waitlist (0.02%)
        62μs
        1 x creating: components.forms.tutor-support (0.02%)
        61μs
        1 x composing: components.open-graph (0.01%)
        54μs
        1 x composing: site.headers.header (0.01%)
        49μs
        1 x composing: components.forms.get-started (0.01%)
        47μs
        1 x eloquent.booted: App\Models\SubjectCat (0.01%)
        46μs
        1 x eloquent.booted: App\Models\Subject (0.01%)
        42μs
        1 x composing: components.forms.free-tool-download (0.01%)
        40μs
        1 x composing: components.forms.tutor-support (0.01%)
        40μs
        1 x composing: components.forms.claim-free-worksheet (0.01%)
        39μs
        1 x composing: components.forms.tutor-subscription-join (0.01%)
        38μs
        1 x composing: components.forms.tutor-subscription-waitlist (0.01%)
        37μs
        1 x composing: site.layouts.app (0.01%)
        19μs
      14 templates were rendered
      • 1x homework.showshow.blade.phpblade
      • 1x components.breadcrumbsbreadcrumbs.blade.phpblade
      • 1x site.layouts.appapp.blade.phpblade
      • 1x components.canonicalcanonical.blade.phpblade
      • 1x components.open-graphopen-graph.blade.phpblade
      • 1x site.headers.headerheader.blade.phpblade
      • 1x components.footerfooter.blade.phpblade
      • 1x components.forms.contact-uscontact-us.blade.phpblade
      • 1x components.forms.get-startedget-started.blade.phpblade
      • 1x components.forms.free-tool-downloadfree-tool-download.blade.phpblade
      • 1x components.forms.claim-free-worksheetclaim-free-worksheet.blade.phpblade
      • 1x components.forms.tutor-subscription-waitlisttutor-subscription-waitlist.blade.phpblade
      • 1x components.forms.tutor-subscription-jointutor-subscription-join.blade.phpblade
      • 1x components.forms.tutor-supporttutor-support.blade.phpblade
      uri
      GET college-homework-library/{category}/{subject}/{id}
      middleware
      web, utm.parameters
      controller
      App\Http\Controllers\HomeworkLibraryController@show
      namespace
      where
      as
      homework.show
      file
      app/Http/Controllers/HomeworkLibraryController.php:79-176
      20 statements were executed, 5 of which were duplicates, 15 unique. Show only duplicated68.19ms
      • Connection Establishedtwenty4_siteHomeworkLibraryController.php#91
        Backtrace
        • 13. app/Http/Controllers/HomeworkLibraryController.php:91
        • 14. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 15. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 16. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary` where `status` = 'published' and `price` > 0 and `solutionslibrary`.`id` = '37565' limit 1
        35.12mstwenty4_siteHomeworkLibraryController.php#97
        Bindings
        • 0: published
        • 1: 0
        • 2: 37565
        Backtrace
        • 16. app/Http/Controllers/HomeworkLibraryController.php:97
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 18. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 19. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 20. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subjects` where `subjects`.`id` in (356)
        4.91mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` in (37565)
        3.7mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subject_cats` where `subject_cats`.`id` = 10 limit 1
        1.06mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 10
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 26. app/Http/Controllers/HomeworkLibraryController.php:105
        • 27. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 28. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 29. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
      • select * from `solutionslibrary` where `id` <> 37565 and `subject` = 356 and `status` = 'published' and `price` > 0 order by RAND() limit 6
        5.07mstwenty4_siteHomeworkLibraryRepository.php#30
        Bindings
        • 0: 37565
        • 1: 356
        • 2: published
        • 3: 0
        Backtrace
        • 14. app/Repositories/HomeworkLibraryRepository.php:30
        • 15. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 16. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 18. app/Repositories/HomeworkLibraryRepository.php:39
        • 19. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `subjects` where `subjects`.`id` in (356)
        1.28mstwenty4_siteHomeworkLibraryRepository.php#30
        Backtrace
        • 19. app/Repositories/HomeworkLibraryRepository.php:30
        • 20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 21. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 23. app/Repositories/HomeworkLibraryRepository.php:39
        • 24. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 37565 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        1.39mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 37565
        • 1: question
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:58
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 37565 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc
        1.1mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 37565
        • 1: teaser
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:69
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 37565 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'solution' order by `order` asc, `id` asc
        1.07mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 37565
        • 1: solution
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:80
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `subject_cats` where `subject_cats`.`id` = 10 limit 1
        1.03mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 10
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 32. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 33. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 34. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
        • 35. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        1.15mstwenty4_siteSubject.php#100
        Bindings
        • 0: 1
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 3 limit 1
        1.11mstwenty4_siteSubject.php#100
        Bindings
        • 0: 3
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 4 limit 1
        1.1mstwenty4_siteSubject.php#100
        Bindings
        • 0: 4
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 10 limit 1
        1.14mstwenty4_siteSubject.php#100
        Bindings
        • 0: 10
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 33 limit 1
        1.18mstwenty4_siteSubject.php#100
        Bindings
        • 0: 33
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 11 limit 1
        1.45mstwenty4_siteSubject.php#100
        Bindings
        • 0: 11
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 5 limit 1
        1.12mstwenty4_siteSubject.php#100
        Bindings
        • 0: 5
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 34 limit 1
        1.19mstwenty4_siteSubject.php#100
        Bindings
        • 0: 34
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 31 limit 1
        1.54mstwenty4_siteSubject.php#100
        Bindings
        • 0: 31
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 36 limit 1
        1.48mstwenty4_siteSubject.php#100
        Bindings
        • 0: 36
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 28. view::components.footer:170
      App\Models\SubjectCat
      12SubjectCat.php
      App\Models\HomeworkLibrary\HomeworkLibraryFile
      10HomeworkLibraryFile.php
      App\Models\HomeworkLibrary\HomeworkLibrary
      7HomeworkLibrary.php
      App\Models\Subject
      2Subject.php
          _token
          zOEyxkC2e7cVnsdCykfzlK3JSj4qsZmBYKRFYjhb
          utm_source
          direct
          redirectUrl
          /college-homework-library/Engineering/Petroleum-Engineering/37565
          _previous
          array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Engineering/Pet...
          _flash
          array:2 [ "old" => [] "new" => [] ]
          PHPDEBUGBAR_STACK_DATA
          []
          path_info
          /college-homework-library/Engineering/Petroleum-Engineering/37565
          status_code
          200
          
          status_text
          OK
          format
          html
          content_type
          text/html; charset=UTF-8
          request_query
          []
          
          request_request
          []
          
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