ﺑﺮﺭﺳﻲ ﺭﻓﺘﺎﺭ ﻓﺎﺯﻱ ﺁﺳﻔﺎﻟﺘﻴﻦ ﺩﺭ ﻳﮏ ﻧﻤﻮﻧﻪ ﻧﻔﺘﻲ
ﺣﻤﻴﺪﺭﺿﺎ ﺣﺴﻴﻦ ﺑﻴﮕﻲ ) ، (۱ﻏﻼﻣﺮﺿﺎ ﭘﺎﺯﻭﮐﻲ ) ،(۲ﻣﺤﺴﻦ ﻋﺪﺍﻟﺖ
)*،(۱
) (۱ﺩﺍﻧﺸﮕﺎﻩ ﺗﻬﺮﺍﻥ،ﺩﺍﻧﺸﮑﺪﻩ ﻓﻨﻲ،ﮔﺮﻭﻩ ﻣﻬﻨﺪﺳﻲ ﺷﻴﻤﻲ
) (۲ﺩﺍﻧﺸﮕﺎﻩ ﺻﻨﻌﺘﻲ ﺷﺮﻳﻒ ،ﺩﺍﻧﺸﮑﺪﻩ ﻣﻬﻨﺪﺳﻲ ﺷﻴﻤﻲ ﻭ ﻧﻔﺖ
moedalat@aol.com
ﻧﻬﻤﻴﻦ ﮐﻨﮕﺮﻩ ﻣﻠﯽ ﻣﻬﻨﺪﺳﯽ ﺷﻴﻤﯽ ﺍﻳﺮﺍﻥ
ﺩﺍﻧﺸﮕﺎﻩ ﻋﻠﻢ ﻭ ﺻﻨﻌﺖ ﺍﻳﺮﺍﻥ
۵-۳ﺁﺫﺭ ﻣﺎﻩ ۱۳۸۳
ﭼﮑﻴﺪﻩ
ﺩﺭ ﮐﺎﺭ ﺣﺎﺿﺮ ﺩﺭ ﺍﺑﺘﺪﺍ ﻳﮏ ﻣﻌﺎﺩﻟﻪ ﺣﺎﻟﺖ ﻣﮑﻌﺒﻲ ﺩﻭ ﭘﺎﺭﺍﻣﺘﺮﻱ ﺑﺮ ﻣﺒﻨﺎﻱ ﻣﺪﻝ ﻫﺴﺘﻪ ﺳﺨﺖ ﺗﻮﺳﻌﻪ ﺩﺍﺩﻩ ﺷﺪﻩ ﺍﺳﺖ.
ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ ﺍﻳﻦ ﻣﻌﺎﺩﻟﻪ ﺣﺎﻟﺖ ﺟﺪﻳﺪ ﺑﺼﻮﺭﺕ ﺗﺎﺑﻌﻲ ﺍﺯ ﺩﻣﺎ ﻭ ﺿﺮﻳﺐ ﺑﻲ ﻣﺮﮐﺰﻱ ﺩﺭ ﻧﻈﺮ ﮔﺮﻓﺘﻪ ﺷﺪﻩ ﺍﺳﺖ .ﺑﺮﺍﻱ
ﻣﺤﺎﺳﺒﻪ ﺧﻮﺍﺹ ﻓﻴﺰﻳﮑﻲ ﻣﻮﺍﺩ ﺧﺎﻟﺺ ﻧﻈﻴﺮ ﻓﺸﺎﺭ ﺑﺨﺎﺭ ﺍﺷﺒﺎﻉ ﻭ ﺩﺍﻧﺴﻴﺘﻪ ﻣﺎﻳﻊ ﺍﺷﺒﺎﻉ ﻭ ﺣﺠﻢ ﺑﺨﺎﺭﺍﺷﺒﺎﻉ ،ﺍﻳﻦ ﻣﻌﺎﺩﻟﻪ
ﺣﺎﻟﺖ ﺑﻪ ﺩﻣﺎﻱ ﺑﺤﺮﺍﻧﻲ ،ﻓﺸﺎﺭ ﺑﺤﺮﺍﻧﻲ ﻭ ﺿﺮﻳﺐ ﺑﻲ ﻣﺮﮐﺰﻱ ﻧﻴﺎﺯ ﺩﺍﺭﺩ.
ﻣﻌﺎﺩﻟﻪ ﺣﺎﻟﺖ ﭘﻴﺸﻨﻬﺎﺩ ﺷﺪﻩ ﺑﺮﺍﻱ ﻣﺤﺎﺳﺒﺎﺕ PVTﻭ VLEﺳﻴﺎﻻﺕ ﺧﺎﻟﺺ ﻭ ﻣﺨﻠﻮﻁ ﮔﻮﻧﺎﮔﻮﻥ ﻣﻮﺭﺩ ﺍﺳﺘﻔﺎﺩﻩ ﻗﺮﺍﺭ
ﮔﺮﻓﺘﻪ ﺍﺳﺖ ﻭ ﺩﺭﺻﺪ ﻣﻴﺎﻧﮕﻴﻦ ﺍﻧﺤﺮﺍﻑ ﻣﻄﻠﻖ ﻓﺸﺎﺭ ﺑﺨﺎﺭ ﻭ ﺩﺍﻧﺴﻴﺘﻪ ﻣﺎﻳﻊ ﺍﺷﺒﺎﻉ ﻭ ﺣﺠﻢ ﺑﺨﺎﺭﺍﺷﺒﺎﻉ ﻣﺤﺎﺳﺒﻪ ﺷﺪﻩ
ﺑﺮﺍﻱ ۳۰ﻣﺎﺩﻩ ﺧﺎﻟﺺ ﺑﺘﺮﺗﻴﺐ %۵/۸۲۵ ،%۰/۸۵۹ﻭ %۲/۷۹۲ﺑﺪﺳﺖ ﺁﻣﺪﻩ ﺍﺳﺖ).ﺷﮑﻠﻬﺎﻱ ۱ﺗﺎ (۴
∆U , ∆H ,Vﻭ ﺳﺎﻳﺮ ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ ﺗﻌﺎﺩﻟﻲ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﻣﻌﺎﺩﻟﻪ ﺣﺎﻟﺖ ﺟﺪﻳﺪ ﻣﺤﺎﺳﺒﻪ ﮔﺮﺩﻳﺪ ﻭ ﺑﺮﺍﻱ ﻣﺤﺎﺳﺒﺎﺕ ﺩﺭﺻﺪ
ﻭﺯﻧﻲ ﺭﺳﻮﺏ ﺁﺳﻔﺎﻟﺘﻴﻦ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﻣﺪﻝ ﻓﻠﻮﺭﻱ-ﻫﺎﮔﻴﻨﺰ ﺑﮑﺎﺭ ﮔﺮﻓﺘﻪ ﺷﺪﻧﺪ.
ﺩﺭ ﻣﺮﺣﻠﻪ ﺑﻌﺪ ،ﻣﺪﻝ ﻓﻠﻮﺭﻱ-ﻫﺎﮔﻴﻨﺰ ﺑﺎ ﺳﻪ ﭘﺎﺭﺍﻣﺘﺮ ﻗﺎﺑﻞ ﺗﻨﻈﻴﻢ b ،aﻭ cﺑﺮﺍﻱ ﭘﻴﺶ ﺑﻴﻨﻲ ﺩﻗﻴﻖ ﺗﺮ ﻣﻘﺪﺍﺭ ﺭﺳﻮﺏ
ﺁﺳﻔﺎﻟﺘﻴﻦ ﺑﻬﺒﻮﺩ ﺑﺨﺸﻴﺪﻩ ﺷﺪ .ﺍﻳﻦ ﭘﺎﺭﺍﻣﺘﺮﻫﺎ ﺑﻌﻨﻮﺍﻥ ﺛﻮﺍﺑﺖ ﻳﮏ ﭼﻨﺪ ﺟﻤﻠﻪ ﺍﻱ ﺩﺭﺟﻪ ﺩﻭﻡ ﺑﺮ ﺣﺴﺐ ﻧﺴﺒﺖ ﺟﺮﻡ
ﻣﻮﻟﮑﻮﻟﻲ ﺁﺳﻔﺎﻟﺘﻴﻦ ﺑﻪ ﺟﺮﻡ ﻣﻮﻟﮑﻮﻟﻲ ﺭﺳﻮﺏ ﺩﻫﻨﺪﻩ ﺩﺭ ﻧﻈﺮ ﮔﺮﻓﺘﻪ ﺷﺪﻩ ﺍﻧﺪ .ﺭﻓﺘﺎﺭ ﻓﺎﺯﻱ ﺁﺳﻔﺎﻟﺘﻴﻦ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ
ﻣﻌﺎﺩﻟﻪ ﺣﺎﻟﺖ ﺟﺪﻳﺪ ﻭ ﻣﺪﻝ ﺗﻮﺳﻌﻪ ﻳﺎﻓﺘﻪ ﻓﻠﻮﺭﻱ-ﻫﺎﮔﻴﻨﺰ ﻣﻮﺭﺩ ﺑﺮﺭﺳﻲ ﻗﺮﺍﺭ ﮔﺮﻓﺘﻪ ﻭ ﻣﻘﺪﺍﺭ ﺭﺳﻮﺏ ﺁﺳﻔﺎﻟﺘﻴﻦ ﺩﺭ
ﻧﺴﺒﺘﻬﺎﻱ ﻣﺨﺘﻠﻒ ﺣﻼﻟﻬﺎﻱ ﮔﻮﻧﺎﮔﻮﻥ ﻣﺤﺎﺳﺒﻪ ﮔﺮﺩﻳﺪ ﮐﻪ ﻣﻘﺎﻳﺴﻪ ﻧﺘﺎﻳﺞ ﭘﻴﺶ ﺑﻴﻨﻲ ﺷﺪﻩ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﺍﻳﻦ ﺭﻭﺵ ﻭ
ﻧﺘﺎﻳﺞ ﺁﺯﻣﺎﻳﺸﮕﺎﻫﻲ ﺩﺭ ﺷﮑﻠﻬﺎﻱ ۵ﺗﺎ ۱۰ﺁﻭﺭﺩﻩ ﺷﺪﻩ ﺍﺳﺖ ﮐﻪ ﮔﻮﻳﺎﻱ ﺩﻗﺖ ﻗﺎﺑﻞ ﻗﺒﻮﻝ ﺍﻳﻦ ﻣﺪﻝ ﺟﺪﻳﺪ ﺑﺮﺍﻱ ﭘﻴﺶ
ﺑﻴﻨﻲ ﺭﻓﺘﺎﺭ ﻓﺎﺯﻱ ﺁﺳﻔﺎﻟﺘﻴﻦ ﺩﺭ ﻧﻔﺖ ﺳﻨﮕﻴﻦ ﻣﻲ ﺑﺎﺷﺪ.
ﻛﻠﻤﺎﺕ ﻛﻠﻴﺪﻱ :ﺭﻓﺘﺎﺭ ﻓﺎﺯﻱ ﺁﺳﻔﺎﻟﺘﻴﻦ ،ﻣﻌﺎﺩﻟﻪ ﺣﺎﻟﺖ ﺩﺭﺟﻪ ﺳﻪ ،ﻣﺪﻝ ﻫـﺴﺘﻪ ﺳـﺨﺖ ،ﻣـﺪﻝ ﻓﻠـﻮﺭﻱ-ﻫـﺎﮔﻴﻨﺰ
ﺗﻮﺳﻌﻪ ﻳﺎﻓﺘﻪ ،ﻣﻮﺍﺩ ﺧﺎﻟﺺ ،ﻣﺨﻠﻮﻁ ،ﻣﺤﺎﺳﺒﺎﺕ PVTﻭ ،VLEﺧﻮﺍﺹ PVTﻭ ﺗﺮﻣﻮﺩﻳﻨﺎﻣﻴﮑﻲ
ﻣﺤﻮﺭ ﻋﻠﻤﻲ : ۲ﺗﻌﺎﺩﻝ ﻓﺎﺯﯼ ﻭ ﺗﺮﻣﻮﺩﻳﻨﺎﻣﻴﮏ
٤٨٨
IChEC9
ﻣﻘﺪﻣﻪ
ﻭﺟﻮﺩ ﺁﺳﻔﺎﻟﺘﻴﻦ ﺩﺭ ﻧﻔﺖ ﺧﺎﻡ ﻭ ﺗﺮﺳﻴﺐ ﺁﻥ ﺩﺭ ﻣﺨﺎﺯﻥ ﻭ ﺗﺠﻬﻴﺰﺍﺕ ﭘﺎﻻﻳﺸﮕﺎﻫﻲ ﺍﺯ ﻣﺸﮑﻼﺕ ﻋﻤﺪﻩ ﺩﺭ ﺯﻣﻴﻨﻪ
ﺍﺳﺘﺨﺮﺍﺝ ﻧﻔﺖ ﺑﺸﻤﺎﺭ ﻣﻲ ﺭﻭﺩ ﮐﻪ ﺭﺍﻧﺪﻣﺎﻥ ﺗﻮﻟﻴﺪ ﻭ ﻫﺰﻳﻨﻪ ﻫﺎﻱ ﺁﻧﺮﺍ ﺗﺤﺖ ﺗﺎﺛﻴﺮ ﻗﺮﺍﺭ ﻣﻲ ﺩﻫﺪ .ﺑﻬﻤﻴﻦ ﺩﻟﻴﻞ
ﻣﻄﺎﻟﻌﺎﺕ ﺑﺴﻴﺎﺭﻱ ﺩﺭ ﺯﻣﻴﻨﻪ ﺗﻌﻴﻴﻦ ﺷﺮﺍﻳﻂ ﺗﺮﺳﻴﺐ ﺍﻳﻦ ﻣﻮﺍﺩ ﺍﺯ ﻧﻘﻄﻪ ﻧﻈﺮ ﺍﺛﺮ ﺗﺮﮐﻴﺐ ﻧﻔﺖ ،ﻓﺸﺎﺭ ﻭ ﺩﻣﺎ ﺍﻧﺠﺎﻡ
ﭘﺬﻳﺮﻓﺘﻪ ﺍﺳﺖ .ﻣﻄﺎﻟﻌﺎﺕ ﻧﺸﺎﻥ ﺩﺍﺩﻩ ﺍﺳﺖ ﮐﻪ ﺳﻪ ﻋﺎﻣﻞ ﺫﮐﺮ ﺷﺪﻩ ﻳﻌﻨﻲ ﻣﻘﺪﺍﺭ ﺩﺭﺻﺪ ﻭﺯﻧﻲ ﻣﻮﺍﺩ ﺁﺳﻔﺎﻟﺘﻴﻨﻲ ،ﻓﺸﺎﺭ
ﻭ ﺩﻣﺎ ﺗﻌﻴﻴﻦ ﮐﻨﻨﺪﻩ ﻗﺎﺑﻠﻴﺖ ﺭﺳﻮﺏ ﮔﺬﺍﺭﻱ ﻧﻔﺖ ﻣﻲ ﺑﺎﺷﻨﺪ.
ﺩﺭ ﺍﻳﻦ ﮐﺎﺭ ﺍﺛﺮ ﭘﺎﺭﺍﻣﺘﺮ ﺣﻼﻟﻴﺖ ﺁﺳﻔﺎﻟﺘﻴﻦ ﻭ ﻧﻔﺖ ﺩﺭ ﭘﻴﺸﮕﻮﻳﻲ ﻣﻘﺪﺍﺭ ﺭﺳﻮﺏ ﺗﻮﺳﻂ ﻳﮏ ﻣﺪﻝ ﺗﺮﻣﻮﺩﻳﻨﺎﻣﻴﮑﻲ
ﻣﻮﺭﺩ ﺑﺮﺭﺳﻲ ﻗﺮﺍﺭ ﮔﺮﻓﺘﻪ ﺍﺳﺖ .ﻣﺪﻟﻬﺎﻱ ﺗﺮﻣﻮﺩﻳﻨﺎﻣﻴﮑﻲ ﻣﺨﺘﻠﻔﻲ ﺑﺮﺍﻱ ﭘﻴﺸﮕﻮﻳﻲ ﺭﻓﺘﺎﺭ ﻓﺎﺯﻱ ﺁﺳﻔﺎﻟﺘﻴﻦ ﺍﺭﺍﺋﻪ ﺷﺪﻩ
ﺍﺳﺖ .ﺑﺮﺍﻱ ﻣﺤﺎﺳﺒﻪ ﭘﺎﺭﺍﻣﺘﺮ ﺣﻼﻟﻴﺖ ﺣﺠﻢ ﻣﻮﻟﻲ ﻧﻔﺖ ﺍﺯ ﻳﮏ ﻣﻌﺎﺩﻟﻪ ﺣﺎﻟﺖ ﺟﺪﻳﺪ ﺍﺳﺘﻔﺎﺩﻩ ﺷﺪﻩ ﺍﺳﺖ ﻭ ﺍﺯ ﺗﺌﻮﺭﻱ
ﻣﺤﻠﻮﻟﻬﺎﻱ ﭘﻠﻴﻤﺮﻱ ﻓﻠﻮﺭﻱ-ﻫﺎﮔﻴﻨﺰ ﺑﻬﺒﻮﺩ ﻳﺎﻓﺘﻪ ﺍﺳﺘﻔﺎﺩﻩ ﺷﺪﻩ ﺍﺳﺖ.
ﻣﻌﺎﺩﻟﻪ ﺣﺎﻟﺖ ﻣﮑﻌﺒﻲ ﺟﺪﻳﺪ
ﺑﺮ ﭘﺎﻳﺔ ﺗﺌﻮﺭﻱ ﺍﻏﺘﺸﺎﺵ ١ﺩﺭ ﺗﺮﻣﻮﺩﻳﻨﺎﻣﻴﮏ ﺁﻣﺎﺭﻱ ،ﺿﺮﻳﺐ ﺗﺮﺍﮐﻢ ﭘﺬﻳﺮﻱ ﺳﻴﺎﻻﺕ ،ﺑﺼﻮﺭﺕ ﺣﺎﺻﻞ ﺟﻤﻊ ﺩﻭ ﺟﻤﻠﻪ
ﻣﺮﺑﻮﻁ ﺑﻪ ﻧﻴﺮﻭﻫﺎﻱ ﺩﺍﻓﻌﻪ ﻭ ﺟﺎﺫﺑﻪ ﺩﺭ ﻧﻈﺮ ﮔﺮﻓﺘﻪ ﻣﻲ ﺷﻮﺩ .ﺑﻨﺎﺑﺮﺍﻳﻦ ﻣﻲ ﺗﻮﺍﻥ ﻧﻮﺷﺖ ]: [۱
)(۱
Z = Z rep + Zattr
ﮐﻪ ﺯﻳﺮﻧﻮﻳﺴﻬﺎﻱ repﻣﻌﺮﻑ ﺳﻬﻢ ﻧﻴﺮﻭﻫﺎﻱ ﺩﺍﻓﻌﻪ ﻭ attrﻣﻌﺮﻑ ﺳﻬﻢ ﻧﻴﺮﻭﻫﺎﻱ ﺟﺎﺫﺑﻪ ﺍﺳﺖ.
ﺩﺭ ﺍﻳﻦ ﻣﻌﺎﺩﻟﻪ ﺣﺎﻟﺖ ﺑﺮ ﻣﺒﻨﺎﻱ ﺟﻤﻼﺕ Packing fractionﻳﮏ ﺟﻤﻠﻪ ﺑﺮﺍﻱ ﻣﺤﺎﺳﺒﻪ ﺍﺛﺮ ﻧﻴﺮﻭﻫﺎﻱ ﺩﺍﻓﻌﻪ ﺗﻌﺮﻳﻒ
ﻣﻲ ﺷﻮﺩ:
)(۲
1 + εy
1 − ηy
= Z rep
ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ εﻭ ηﻃﻮﺭﻱ ﺗﻨﻈﻴﻢ ﻣﻲ ﺷﻮﻧﺪ ﮐﻪ ﻣﻘﺎﺩﻳﺮ Packing fractionﺩﺭ ﮔﺴﺘﺮﻩ * 0 < y < yﺻﺎﺩﻕ ﺑﺎﺷﺪ
ﮐﻪ * yﻣﺮﺑﻮﻁ ﺑﻪ ﺑﺎﻻﺗﺮﻳﻦ ﺣﺪ Packing fractionﻣﻲ ﺑﺎﺷﺪ .ﺑﻨﺎﺑﺮﺍﻳﻦ ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﺗﻌﺮﻳﻒ ﻓﻮﻕ ﻭ ﺟﻤﻠﻪ ﺟﺪﻳﺪ
ﻣﺮﺑﻮﻁ ﺑﻪ ﻧﻴﺮﻭﻱ ﺩﺍﻓﻌﻪ ﻣﻌﺎﺩﻟﻪ ﺣﺎﻟﺖ ﺟﺪﻳﺪ ﺑﺼﻮﺭﺕ ﺯﻳﺮ ﺗﻌﺮﻳﻒ ﻣﻲ ﺷﻮﺩ ]:[۲
)(۳
v + εb
a
−
1+ n
) v − ηb RT (v + ηγb
=Z
Perturbation
ﻧﻬﻤﻴﻦ ﮐﻨﮕﺮﻩ ﻣﻠﯽ ﻣﻬﻨﺪﺳﯽ ﺷﻴﻤﯽ ﺍﻳﺮﺍﻥ ،ﺩﺍﻧﺸﮕﺎﻩ ﻋﻠﻢ ﻭ ﺻﻨﻌﺖ ﺍﻳﺮﺍﻥ ۳ ،ﺍﻟﯽ ۵ﺁﺫﺭﻣﺎﻩ ۱۳۸۳
1
ﻣﺤﻮﺭ ﻋﻠﻤﻲ : ۲ﺗﻌﺎﺩﻝ ﻓﺎﺯﯼ ﻭ ﺗﺮﻣﻮﺩﻳﻨﺎﻣﻴﮏ
٤٨٩
IChEC9
ﮐﻪ ﭘﺮﺍﻣﺘﺮﻫﺎﻱ nﻭ γﻣﻘﺎﺩﻳﺮ ﺩﻟﺨﻮﺍﻩ ﻣﻲ ﺑﺎﺷﻨﺪ ﮐﻪ ﺑﺎﻳﺪ ﺑﮕﻮﻧﻪ ﺍﻱ ﻣﻨﺎﺳﺐ ﺍﻧﺘﺨﺎﺏ ﺷﻮﻧﺪ .ﺑﺎ ﻓﺮﺽ n = 0
ﻭ γ = 1ﺟﻤﻠﻪ ﻣﺮﺑﻮﻁ ﺑﻪ ﻧﻴﺮﻭﻫﺎﻱ ﺟﺎﺫﺑﻪ ﺑﺸﮑﻞ ﺗﺮﻡ ﻣﺮﺑﻮﻁ ﺑﻪ ﺟﺎﺫﺑﻪ ﺩﺭ ﻣﻌﺎﺩﻟﻪ ﺣﺎﻟﺖ ﺳﻮ-ﺭﺩﻟﻴﺶ-ﮐﻮﺍﻧﮓ ﻣﻲ
ﺑﺎﺷﺪ.
ﺑﻪ ﮐﻤﮏ ﺷﺮﺍﻳﻂ ﻣﺮﺑﻮﻁ ﺑﻪ ﻧﻘﻄﻪ ﺑﺤﺮﺍﻧﻲ ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ a cﻭ bcﻗﺎﺑﻞ ﻣﺤﺎﺳﺒﻪ ﻫﺴﺘﻨﺪ ﻭ ﺑﺮ ﭘﺎﻳﻪ ﺍﻳﻦ ﻣﻘﺎﺩﻳﺮ ﺑﺪﺳﺖ
ﺁﻣﺪﻩ ﻭ ﺑﻪ ﮐﻤﮏ ﻣﻘﺎﺩﻳﺮ ﻣﺮﺑﻮﻁ ﺑﻪ ﺩﺍﻧﺴﻴﺘﻪ ﻧﻘﻄﻪ ﺑﺤﺮﺍﻧﻲ ﻭ ﻧﻘﻄﻪ ﺳﻪ ﮔﺎﻧﻪ ﻣﺎﮐﺰﻳﻤﻢ ﻣﻘﺪﺍﺭ Packing fraction
ﺑﺮﺍﻱ ﺳﻴﺎﻻﺕ ﻣﺨﺘﻠﻒ ﺍﺯ ﺭﺍﺑﻄﻪ
ρ tp
ρc
ymax ≈ 0.103ﻣﺤﺎﺳﺒﻪ ﻣﻲ ﺷﻮﺩ.
ﻣﻘﺎﺩﻳﺮ yﺑﺪﺳﺖ ﺁﻣﺪﻩ ﺑﺎﻳﺪﺍﺯ * yﮐﻤﺘﺮ ﺑﺎﺷﺪ ﺩﺭ ﻏﻴﺮ ﺍﻳﻨﺼﻮﺭﺕ ﺑﺎ ﺗﻐﻴﻴﺮ ﻣﻘﺎﺩﻳﺮ εﻭ ηﺑﺎﻳﺪ ﺑﮕﻮﻧـﻪ ﺍﻱ ﻣﻌﺎﺩﻟـﻪ ﺭﺍ
ﺗﻐﻴﻴﺮ ﺩﻫﻴﻢ ﺗﺎ ﻣﻘﺪﺍﺭ yﺑﺪﺳﺖ ﺁﻣﺪﻩ ﺍﺯ ﻣﻌﺎﺩﻟﻪ ﺍﺯ * yﮐﻤﺘﺮ ﮔﺮﺩﺩ .ﺍﺯ ﺁﻧﺠﺎ ﮐﻪ ﺗـﺮﻡ ﺩﺍﻓﻌـﻪ ﺩﺭ ﺍﻳـﻦ ﻣﻌﺎﺩﻟـﻪ ﺣﺎﻟـﺖ
ﺑﻌﻨﻮﺍﻥ ﺗﺮﻡ ﺭﻓﺮﻧﺲ ﻗﺮﺍﺭ ﮔﺮﻓﺘﻪ ﻭ ﻧﻴﺮﻭﻫﺎﻱ ﺟﺎﺫﺑﻪ ﺳﻴﺎﻝ ﺑﻪ ﻋﻨﻮﺍﻥ ﺗﺮﻡ ﺍﻏﺘﺸﺎﺵ ﻳﺎﻓﺘﻪ ﺭﻭﻱ ﭘﺘﺎﻧﺴﻴﻞ ﮐﺮﺍﺕ ﺳـﺨﺖ
ﺩﺭ ﻧﻈﺮ ﮔﺮﻓﺘﻪ ﺷﺪﻩ ﺍﺳﺖ ،ﺻﺎﺩﻕ ﺑﻮﺩﻥ ﺷﺮﻁ ﻓﻮﻕ ﺩﺭ ﺍﺭﺍﺋﻪ ﺩﻗﻴﻖ ﺧﻮﺍﺹ ﻣﺪ ﻧﻈﺮ ﺍﺯ ﺍﻫﻤﻴـﺖ ﺧﺎﺻـﻲ ﺑـﺮ ﺧـﻮﺭﺩﺍﺭ
ﺍﺳﺖ.
ﺩﺭ ﮐﺎﺭ ﺣﺎﺿﺮ ﻣﻘﺎﺩﻳﺮ ε = η = 1ﺩﺭ ﻧﻈﺮ ﮔﺮﻓﺘﻪ ﺷﺪﻩ ﺍﺳﺖ ﮐﻪ ﺩﺭ ﺍﻳﻨﺼﻮﺭﺕ ﺑﻪ ﻣﻌﺎﺩﻟﻪ ﭘﻴﺸﻨﻬﺎﺩﻱ ﺗﻮﺳﻂ ﺍﺳﮑﺎﺕ
ﻣﻲ ﺭﺳﻴﻢ[۳] .
v+b
v−b
)(۴
= Z rep
ﮐﻪ ﻣﻌﺎﺩﻟﻪ ﻓﻮﻕ ،ﻣﻌﺎﺩﻟﻪ ﺍﺻﻼﺡ ﺷﺪﻩ ﮐﺎﺭﻧﺎﻫﺎﻥ-ﺍﺳﺘﺎﺭﻟﻴﻨﮓ ﺑﺮﺍﻱ ﻣﻘﺎﺩﻳﺮ y < 0.6ﺍﺳﺖ .ﺑﻨﺎﺑﺮﺍﻳﻦ ﺑﺮ ﻣﺒﻨﺎﻱ ﺭﻭﺵ
ﺍﺭﺍﺋﻪ ﺷﺪﻩ ﻭ ﺑﺎ ﺍﻧﺘﺨﺎﺏ ﻣﻘﺎﺩﻳﺮ n = 0 ، ε = η = 1ﻭ γ = 1ﺑﻪ ﻣﻌﺎﺩﻟﻪ ﺣﺎﻟﺖ ﺟﺪﻳﺪ ﺩﻭ ﭘﺎﺭﺍﻣﺘﺮﻱ ﺯﻳﺮ ﻣﻲ ﺭﺳﻴﻢ:
v+ b
a
−
))v − b RT (v + b
)(۵
=Z
ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﺧﻮﺍﺹ ﻣﺮﺑﻮﻁ ﺑﻪ ﻧﻘﻄﻪ ﺑﺤﺮﺍﻧﻲ ،ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ a cﻭ bcﻭ ﻣﻘﺪﺍﺭ ﺿﺮﻳﺐ ﺗﺮﺍﮐﻢ ﭘﺬﻳﺮﻱ ﺩﺭ ﻧﻘﻄﻪ ﺑﺤﺮﺍﻧﻲ
ﺑﺼﻮﺭﺕ ﺯﻳﺮ ﻣﺤﺎﺳﺒﻪ ﻣﻲ ﺷﻮﺩ:
R 2Tc2
a c = 0.47448
Pc
)(۶
RTc
Pc
)(۷
bc = 0.06824
)(۸
Z c = 0.333
ﺑﻨﺎﺑﺮﺍﻳﻦ ﻓﺸﺎﺭ ﺑﺼﻮﺭﺕ ﺗﺎﺑﻌﻲ ﺻﺮﻳﺢ ،ﺍﺯ ﻣﻌﺎﺩﻟﻪ ﻓﻮﻕ ﺑﺪﺳﺖ ﻣﻲ ﺁﻳﺪ:
)(۹
) RT (v + b
a
−
) v(v − b ) v(v + b
ﻧﻬﻤﻴﻦ ﮐﻨﮕﺮﻩ ﻣﻠﯽ ﻣﻬﻨﺪﺳﯽ ﺷﻴﻤﯽ ﺍﻳﺮﺍﻥ ،ﺩﺍﻧﺸﮕﺎﻩ ﻋﻠﻢ ﻭ ﺻﻨﻌﺖ ﺍﻳﺮﺍﻥ ۳ ،ﺍﻟﯽ ۵ﺁﺫﺭﻣﺎﻩ ۱۳۸۳
=P
٤٩٠
ﻣﺤﻮﺭ ﻋﻠﻤﻲ : ۲ﺗﻌﺎﺩﻝ ﻓﺎﺯﯼ ﻭ ﺗﺮﻣﻮﺩﻳﻨﺎﻣﻴﮏ
IChEC9
ﺩﺭ ﮐﺎﺭ ﺟﺪﻳﺪ ﻫﺮ ﺩﻭ ﭘﺎﺭﺍﻣﺘﺮ aﻭ bﺍﺻﻼﺡ ﮔﺮﺩﻳﺪﻩ ﺍﻧﺪ .ﺍﻳﻦ ﭘﺎﺭﺍﻣﺘﺮﻫﺎ ﺭﺍ ﺑﻌﻨﻮﺍﻥ ﺗﺎﺑﻌﻲ ﺍﺯ ﺩﻣﺎﻱ ﮐﺎﻫﻴﺪﻩ ﻭ ﺿﺮﻳﺐ
ﺑﻲ ﻣﺮﮐﺰﻱ ﻣﻮﺍﺩ ﺩﺭ ﻧﻈﺮ ﮔﺮﻓﺘﻪ ﻣﻲ ﺷﻮﻧﺪ .ﺑﻨﺎﺑﺮﺍﻳﻦ:
) a = a cα (Tr , ω
)(۱۰
) b = bc β (Tr , ω
)(۱۱
ﺍﻟﺒﺘﻪ ﺿﺮﺍﻳﺐ ﺗﺼﺤﻴﺢ ﺑﺎﻳﺪ ﺑﻪ ﮔﻮﻧﻪ ﺍﻱ ﺍﺭﺍﺋﻪ ﺷﻮﻧﺪ ﮐﻪ ﺷﺮﻁ ﺯﻳﺮ ﺭﺍ ﺍﺭﺿﺎ ﮐﻨﻨﺪ:
Tr = 1 α (Tr , ω ) = β (Tr , ω ) = 1
)(۱۲
at
ﻳﺎ ﺑﻌﺒﺎﺭﺗﻲ ﺩﺭ ﻧﻘﻄﻪ ﺑﺤﺮﺍﻧﻲ ﻣﻮﺍﺩ ﺭﻓﺘﺎﺭ ﻓﺎﺯﻱ ﺭﺍ ﺑﺘﻮﺍﻧﺪ ﺑﺪﻗﺖ ﭘﻴﺶ ﺑﻴﻨﻲ ﮐﻨﺪ.
ﺑﺮﺍﻱ ﻣﺤﺎﺳﺒﺔ ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ αﻭ βﺑﺮﺣﺴﺐ ﺩﻣﺎﻱ ﮐﺎﻫﻴﺪﻩ ﻭ ﺿﺮﻳﺐ ﺑﻲ ﻣﺮﮐﺰﻱ ﻣﻮﺍﺩ ،ﺗﺎﺑﻊ ﻫﺪﻑ ﺯﻳﺮ ﻓﺮﺽ ﺷﺪ
ﮐﻪ ﺍﻳﻦ ﭘﺎﺭﺍﻣﺘﺮ ﺑﺮ ﻣﺒﻨﺎﻱ ﺭﻭﺷﻬﺎﻱ ﺑﻬﻴﻨﻪ ﺳﺎﺯﻱ ﺑﺎﻳﺪ ﺍﺻﻼﺡ ﺷﻮﺩ:
)(۱۳
v
v
l
l
Pcal
ρ cal
,i − Pexp, i
,i − ρ exp, i
Ω = ∑ wp
+ wd
v
l
ρ exp,
Pexp,
i
i
i
n
ﺩﺭ ﻣﻌﺎﺩﻟﻪ ﻓﻮﻕ wp = 0.8ﻭ wd = 0.2ﺩﺭ ﻧﻈﺮ ﮔﺮﻓﺘﻪ ﺷﺪﻩ ﺍﻧﺪ.
ﺑﻨﺎﺑﺮﺍﻳﻦ ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ αﻭ βﺑﺮ ﺣﺴﺐ ﺩﻣﺎﻱ ﮐﺎﻫﻴﺪﻩ ﻭ ﺿﺮﻳﺐ ﺑﻲ ﻣﺮﮐﺰﻱ ﺑﺼﻮﺭﺕ ﺯﻳﺮ ﻣﺤﺎﺳﺒﻪ ﺷﺪﻩ ﺍﻧﺪ:
)(۱۴
)(۱۵
)
3
(
+ m3 1 − Tr2 / 3
)
2
(
)
(
α (T , ω ) = 1 + m1 1 − Tr2 / 3 + m2 1 − Tr2 / 3
) β (T , ω ) = 1 + n1 (1 − Tr
ﺑﻨﺎﺑﺮﺍﻳﻦ ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﺭﻭﺵ ﺭﮔﺮﺳﻴﻮﻥ ﺑﻴﻦ ﻧﺘﺎﻳﺞ ﺿﺮﺍﻳﺐ m3 ، m2 ، m1ﻭ nﺑﺮ ﺣﺴﺐ ﺿﺮﻳﺐ ﺑﻲ ﻣﺮﮐﺰﻱ ﺑﺼﻮﺭﺕ
ﺯﻳﺮ ﺑﺪﺳﺖ ﻣﻲ ﺁﻳﻨﺪ:
)(۱۶
m1 = 0.7389 + 1.0841ω + 0.1414ω 2
)(۱۷
m2 = −0.7221 − 0.2672ω − 2.5291ω 2
)(۱۸
m3 = 1.2288 + 2.6501ω − 0.1814ω 2
)(۱۹
n = 0.1972 − 0.8881ω + 0.1679ω 2
ﻧﻬﻤﻴﻦ ﮐﻨﮕﺮﻩ ﻣﻠﯽ ﻣﻬﻨﺪﺳﯽ ﺷﻴﻤﯽ ﺍﻳﺮﺍﻥ ،ﺩﺍﻧﺸﮕﺎﻩ ﻋﻠﻢ ﻭ ﺻﻨﻌﺖ ﺍﻳﺮﺍﻥ ۳ ،ﺍﻟﯽ ۵ﺁﺫﺭﻣﺎﻩ ۱۳۸۳
ﻣﺤﻮﺭ ﻋﻠﻤﻲ : ۲ﺗﻌﺎﺩﻝ ﻓﺎﺯﯼ ﻭ ﺗﺮﻣﻮﺩﻳﻨﺎﻣﻴﮏ
٤٩١
IChEC9
ﻧﺘﺎﻳﺞ ﻣﻌﺎﺩﻟﻪ ﺣﺎﻟﺖ ﺩﺭﺟﻪ ﺳﻪ ﺟﺪﻳﺪ )ﺧﺎﻟﺺ ﻭ ﻣﺨﻠﻮﻁ(
ﺍﺯ ﺍﻳﻦ ﻣﻌﺎﺩﻟﻪ ﺣﺎﻟﺖ ﺑﺮﺍﻱ ﭘﻴﺶ ﺑﻴﻨﻲ ﺭﻓﺘﺎﺭ ﻓﺎﺯﻱ ﻣﻮﺍﺩ ﺧﺎﻟﺺ ﻭ ﻣﺨﻠﻮﻁ ﻣﺘﻔﺎﻭﺕ ﺍﺳﺘﻔﺎﺩﻩ ﺷﺪﻩ ﺍﺳﺖ .ﻓﺸﺎﺭ ﺑﺨﺎﺭ ﻭ
ﺩﺍﻧﺴﻴﺘﻪ ﻣﺎﻳﻊ ﺍﺷﺒﺎﻉ ﺍﺯ ﻣﻬﻤﺘﺮﻳﻦ ﺧﻮﺍﺹ ﻣﻮﺍﺩ ﺧﺎﻟﺺ ﺑﺸﻤﺎﺭ ﻣﻲ ﺁﻳﻨﺪ ﮐﻪ ﻧﺘﺎﻳﺞ ﺍﻳﻦ ﺧﺼﻮﺻﻴﺎﺕ ﺑﺮﺍﻱ ۴۰ﻣﺎﺩﻩ
ﺧﺎﻟﺺ ﺷﺎﻣﻞ ﻣﻮﺍﺩ ﻫﻴﺪﺭﻭﮐﺮﺑﻨﻲ ﻭ ﻏﻴﺮ ﻫﻴﺪﺭﻭﮐﺮﺑﻨﻲ )ﻗﻄﺒﻲ ﻭ ﻏﻴﺮ ﻗﻄﺒﻲ( ﻣﺤﺎﺳﺒﻪ ﺷﺪﻩ ﺍﺳﺖ.
ﻣﺠﻤﻮﻉ ﺧﻄﺎﻱ ﻣﻴﺎﻧﮕﻴﻦ ﺑﺮﺍﻱ ﻣﻌﺎﺩﻟﻪ ﺣﺎﻟﺖ ﺟﺪﻳﺪ PR ،ﻭ SRKﺑﻪ ﺗﺮﺗﻴﺐ %۱/۳۱۳ ، %۰/۸۵۹ﻭ %۱/۵۸۵ﻣﻲ
ﺑﺎﺷﺪ.
ﻣﺠﻤﻮﻉ ﺧﻄﺎﻱ ﻣﻴﺎﻧﮕﻴﻦ ﺩﺍﻧﺴﻴﺘﻪ ﻓﺎﺯ ﻣﺎﻳﻊ ﺑﺮﺍﻱ ﻣﻌﺎﺩﻟﻪ ﺣﺎﻟﺖ ﺟﺪﻳﺪ PR ،ﻭ SRKﺑﻪ ﺗﺮﺗﻴﺐ %۶/۸۶۳ ، %۵/۸۲۵
ﻭ %۹/۸۲۴ﻣﻲ ﺑﺎﺷﺪ.
ﻣﺠﻤﻮﻉ ﺧﻄﺎﻱ ﻣﻴﺎﻧﮕﻴﻦ ﺣﺠﻢ ﻣﻮﻟﻲ ﻓﺎﺯ ﺑﺨﺎﺭ ﺑﺮﺍﻱ ﻣﻌﺎﺩﻟﻪ ﺣﺎﻟﺖ ﺟﺪﻳﺪ PR ،ﻭ SRKﺑﻪ ﺗﺮﺗﻴﺐ ، %۲/۷۹۲
%۲/۳۷۰ﻭ %۲/۳۳۳ﻣﻲ ﺑﺎﺷﺪ.
ﺟﻬﺖ ﻣﺤﺎﺳﺒﻪ ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ aﻭ bﻣﺨﻠﻮﻁ ﺑﺮ ﻣﺒﻨﺎﻱ ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ ﻣﻮﺍﺩ ﺧﺎﻟﺺ،ﺑﻪ ﻗﻮﺍﻧﻴﻦ ﺍﺧﺘﻼﻁ ﻧﻴﺎﺯ ﺍﺳﺖ.
ﺳﺎﺩﻩ ﺗﺮﻳﻦ ﻗﻮﺍﻧﻴﻦ ﺍﺧﺘﻼﻁ ،ﻗﻮﺍﻧﻴﻦ ﺍﺧﺘﻼﻁ ﻭﻧﺪﺭﻭﺍﻟﺲ ﻣﻲ ﺑﺎﺷﺪ ﮐﻪ ﺑﺼﻮﺭﺕ ﺯﻳﺮ ﺗﻌﺮﻳﻒ ﻣﻲ ﺷﻮﻧﺪ :
n
n
j
i
a = ∑ ∑ xi x j a ij
)(۲۰
n
b = ∑ xi bi
)(۲۱
i
) a ij = (a ii a jj ) (1 − kij
)(۲۲
12
kijﺿﺮﻳﺐ ﺗﺄﺛﻴﺮ ﻣﺘﻘﺎﺑﻞ ﺍﺳﺖ ﮐﻪ ﺑﺮﺍﻱ ﺗﺼﺤﻴﺢ ﻣﻌﺎﺩﻻﺕ ﺣﺎﻟﺖ ﻭﺍﺭﺩ ﺭﻭﺍﺑﻂ ﻣﻲ ﺷﻮﺩ .ﺩﺭ ﺍﻳﻦ ﺗﺤﻘﻴﻖ ﺑﻪ ﺧﺎﻃﺮ
ﺳﺎﺩﮔﻲ ﻭ ﺟﻠﻮﮔﻴﺮﻱ ﺍﺯ ﻣﺤﺎﺳﺒﺎﺕ ﭘﻴﭽﻴﺪﻩ ﺗﺮ ،ﻣﻘﺪﺍﺭ kij = 0ﺑﺮﺍﻱ ﮐﻠﻴﻪ ﻣﻮﺍﺩ ﻓﺮﺽ ﺷﺪﻩ ﺍﺳﺖ.
ﭘﻴﺸﮕﻮﻳﻲ ﺭﻓﺘﺎﺭ ﻓﺎﺯﻱ ﺁﺳﻔﺎﻟﺘﻴﻦ
ﻣﺪﻟﻬﺎﻱ ﺗﺮﻣﻮﺩﻳﻨﺎﻣﻴﮑﻲ ﺑﺮ ﺍﺳﺎﺱ ﺻﺒﻴﻌﺖ ﻭ ﻣﺎﻫﻴﺖ ﺁﺳﻔﺎﻟﺘﻴﻦ ﺩﺭ ﻧﻔﺖ ﺗﻮﺳﻌﻪ ﻳﺎﻓﺘﻪ ﺍﻧﺪ ﮐﻪ ﻏﺎﻟﺒﺎ ﺑﻪ ﺩﻭ ﻗﺴﻤﺖ
ﺗﺮﻣﻮﺩﻳﻨﺎﻣﻴﮏ ﻣﻮﻟﮑﻮﻟﻲ ﻭ ﮐﻠﻮﺋﻴﺪﻱ ﺗﻘﺴﻴﻢ ﺷﺪﻩ ﺍﻧﺪ ﮐﻪ ﻣﺪﻟﻬﺎﻱ ﺗﺮﻣﻮﺩﻳﻨﺎﻣﻴﮑﻲ ﺑﺮ ﻣﺒﻨﺎﻱ ﺣﻼﻟﻴﺖ ﻣﻮﻟﮑﻮﻟﻲ
ﺑﻴﺸﺘﺮ ﻣﺮﺩ ﺗﻮﺟﻪ ﻗﺮﺍﺭ ﮔﺮﻓﺘﻪ ﺍﻧﺪ ۵ ،۴] .ﻭ [۶
ﻣﺪﻟﻲ ﮐﻪ ﺩﺭ ﺍﻳﻦ ﮐﺎﺭ ﻣﻮﺭﺩ ﺍﺳﺘﻔﺎﺩﻩ ﻗﺮﺍﺭ ﮔﺮﻓﺘﻪ ﺍﺳﺖ ،ﻣﺪﻝ ﻓﻠﻮﺭﻱ-ﻫﺎﮔﻴﻨﺰ ٢ﻣﻲ ﺑﺎﺷﺪ .ﺑﺮﻣﺒﻨﺎﻱ ﺍﻳﻦ ﻣﺪﻝ ،ﺭﺳﻮﺏ
ﺁﺳﻔﺎﻟﺘﻴﻦ ﺑﻌﻨﻮﺍﻥ ﻳﮏ ﻓﺎﺯ ﻣﺠﺰﺍ ﺑﻤﻨﻈﻮﺭ ﻣﺤﺎﺳﺒﻪ ﻣﻘﺪﺍﺭ ﺭﺳﻮﺏ ﺁﺳﻔﺎﻟﺘﻴﻦ ﺩﺭ ﺩﺭﺻﺪﻫﺎﻱ ﻣﺨﺘﻠﻒ ﺣﻼﻝ ﺩﺭ ﻧﻈﺮ
ﮔﺮﻓﺘﻪ ﺷﺪﻩ ﺍﺳﺖ ،ﺑﻨﺎﺑﺮﺍﻳﻦ ﭘﺘﺎﻧﺴﻴﻞ ﺷﻴﻤﻴﺎﻳﻲ ﺟﺰﺀ ﺁﺳﻔﺎﻟﺘﻴﻦ ﺩﺭ ﻓﺎﺯ ﻣﺎﻳﻊ ﻭ ﺟﺎﻣﺪ ﺩﺭ ﺗﻌﺎﺩﻝ ﺑﺎ ﻫﻢ ﻣﻲ ﺑﺎﺷﻨﺪ.
ﺑﻨﺎﺑﺮﺍﻳﻦ:
Flory-Huggins
ﻧﻬﻤﻴﻦ ﮐﻨﮕﺮﻩ ﻣﻠﯽ ﻣﻬﻨﺪﺳﯽ ﺷﻴﻤﯽ ﺍﻳﺮﺍﻥ ،ﺩﺍﻧﺸﮕﺎﻩ ﻋﻠﻢ ﻭ ﺻﻨﻌﺖ ﺍﻳﺮﺍﻥ ۳ ،ﺍﻟﯽ ۵ﺁﺫﺭﻣﺎﻩ ۱۳۸۳
2
ﻣﺤﻮﺭ ﻋﻠﻤﻲ : ۲ﺗﻌﺎﺩﻝ ﻓﺎﺯﯼ ﻭ ﺗﺮﻣﻮﺩﻳﻨﺎﻣﻴﮏ
٤٩٢
IChEC9
)(۲۳
µ as = µ al
ﭘﺘﺎﻧﺴﻴﻞ ﺷﻴﻤﻴﺎﻳﻲ ﺟﺰﺀ ﺁﺳﻔﺎﻟﺘﻴﻦ ﺩﺭ ﺩﻭ ﻓﺎﺯ ﺟﺎﻣﺪ ﻭ ﺣﻼﻝ ﺑﺮ ﻣﺒﻨﺎﻱ ﻣﺪﻝ ﻓﻠﻮﺭﻱ-ﻫﺎﮔﻴﻨﺰ ﺑﺎ ﺭﺍﺑﻄﻪ ) (۲۴ﺑﻴﺎﻥ
ﺷﺪﻩ ﺍﺳﺖ:[۷] .
)(۲۴
s
2
φ o + Vas (δ a − δ o )2 φ os
)(۲۵
l
2
φ o + Val (δ a − δ o )2 φ ol
Vas
s
= RT ln φ a + 1 −
Vo
s
a
µ −µ
s
a
Vl
µ al − µ al = RT ln φ al + 1 − a
Vo
ﮐﻪ ﺩﺭ ﻣﻌﺎﺩﻻﺕ ﻓﻮﻕ µ i j ،ﻧﺸﺎﻥ ﺩﻫﻨﺪﻩ ﭘﺘﺎﻧﺴﻴﻞ ﺷﻴﻤﻴﺎﻳﻲ ﺟﺰﺀ iﺩﺭ ﻓﺎﺯ ، φ i j ،jﮐﺴﺮ ﺣﺠﻤﻲ ﺟﺰﺀ iﺩﺭ ﻓﺎﺯ jﻭ
δ aﻭ δ oﺑﻪ ﺗﺮﺗﻴﺐ ﭘﺎﺭﺍﻣﺘﺮ ﺣﻼﻟﻴﺖ ﺁﺳﻔﺎﻟﺘﻴﻦ ﻭ ﻧﻔﺖ ﻣﻲ ﺑﺎﺷﻨﺪ.
ﺑﺎ ﻓﺮﺽ ﺍﻳﻨﮑﻪ ﺭﺳﻮﺏ ﺁﺳﻔﺎﻟﺘﻴﻦ ﺩﺭ ﻓﺎﺯ ﺟﺎﻣﺪ ﻋﺎﺭﻱ ﺍﺯ ﻫﺮﮔﻮﻧﻪ ﺣﻼﻝ ﺑﺎﺷﺪ ،ﺩﺍﺭﻳﻢ:
)(۲۶
φ os = 0
ﺑﺎ ﻣﺴﺎﻭﻱ ﻗﺮﺍﺭ ﺩﺍﺩﻥ ﭘﺘﺎﻧﺴﻴﻞ ﻫﺎﻱ ﺷﻴﻤﻴﺎﻳﻲ ﺁﺳﻔﺎﻟﺘﻴﻦ ﺩﺭ ﺩﻭ ﻓﺎﺯ ) (۲۳ﺑﻪ ﺭﺍﺑﻄﻪ ﺯﻳﺮ ﻣﻲ ﺭﺳﻴﻢ:
l Val
Val φ ol
φ = φ exp φ o l − 1 −
(δ a − δ o )2
RT
Vo
2
)(۲۷
s
a
l
a
ﺑﺎ ﺩﺭ ﻧﻈﺮ ﮔﺮﻓﺘﻦ ﺭﻭﺍﺑﻂ ) (۲۷ﻭ ) (۲۸ﺭﺍﺑﻄﻪ ) (۲۶ﺑﻪ ﺭﺍﺑﻄﻪ ) (۲۹ﺳﺎﺩﻩ ﻣﻲ ﺷﻮﺩ:
)(۲۸
δ l = φ al .δ a + φ ol .δ o
)(۲۹
V l = xa .Val + xoVol
ﮐﻪ δ lﻭ V lﺑﻪ ﺗﺮﺗﻴﺐ ﭘﺎﺭﺍﻣﺘﺮ ﺣﻼﻟﻴﺖ ﻭ ﺣﺠﻢ ﻣﻮﻻﺭ ﻣﺨﻠﻮﻁ ﻧﻔﺖ ﻭ ﺁﺳﻔﺎﻟﺘﻴﻦ ﻣﻲ ﺑﺎﺷﺪ xa .ﻭ xsﻧﻴﺰ ﺑﻪ
ﺗﺮﺗﻴﺐ ﮐﺴﺮ ﻣﻮﻟﻲ ﻣﺨﻠﻮﻁ ﻧﻔﺖ ﻭ ﺁﺳﻔﺎﻟﺘﻴﻦ ﻣﻲ ﺑﺎﺷﺪ.
V l
Vl
2
φ al = φ as exp al − 1 − a (δ a − δ l )
RT
V
)(۳۰
ﭘﺎﺭﺍﻣﺘﺮ ﺣﻼﻟﻴﺖ ﺩﺭ ﻣﻌﺎﺩﻟﻪ ﻓﻮﻕ ﺍﺯ ﺭﺍﺑﻄﻪ ﺯﻳﺮ ﺑﺪﺳﺖ ﻣﻲ ﺁﻳﺪ:
)(۳۱
0.5
∆H − RT
=
V
0.5
∆U
δ =
V
ﮐﻪ ∆H ، ∆Uﻭ Vﻭ ﺩﺭ ﻧﺘﻴﺠﻪ ﭘﺎﺭﺍﻣﺘﺮ ﺣﻼﻟﻴﺖ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﻣﻌﺎﺩﻟﻪ ﺣﺎﻟﺖ ﺟﺪﻳﺪ ﻣﺤﺎﺳﺒﻪ ﺷﺪﻩ ﺍﺳﺖ.
ﺑﺎ ﻣﺤﺎﺳﺒﻪ ﮐﺴﺮ ﺣﺠﻤﻲ ﺁﺳﻔﺎﻟﺘﻴﻦ ﺩﺭ ﻓﺎﺯ ﻣﺎﻳﻊ ،ﮐﺴﺮ ﻭﺯﻧﻲ ﺁﺳﻔﺎﻟﺘﻴﻦ ﺭﺳﻮﺏ ﮐﺮﺩﻩ ﺍﺯ ﺭﺍﺑﻄﻪ ﺯﻳﺮ ﺑﺪﺳﺖ ﻣﻲ ﺁﻳﺪ
]:[۸
ﻧﻬﻤﻴﻦ ﮐﻨﮕﺮﻩ ﻣﻠﯽ ﻣﻬﻨﺪﺳﯽ ﺷﻴﻤﯽ ﺍﻳﺮﺍﻥ ،ﺩﺍﻧﺸﮕﺎﻩ ﻋﻠﻢ ﻭ ﺻﻨﻌﺖ ﺍﻳﺮﺍﻥ ۳ ،ﺍﻟﯽ ۵ﺁﺫﺭﻣﺎﻩ ۱۳۸۳
ﻣﺤﻮﺭ ﻋﻠﻤﻲ : ۲ﺗﻌﺎﺩﻝ ﻓﺎﺯﯼ ﻭ ﺗﺮﻣﻮﺩﻳﻨﺎﻣﻴﮏ
٤٩٣
IChEC9
MWl
Vl
)(۳۲
) (1 − φ al
MWl
MWa
) (1 − φ
+ φ al
Vl
Va
= Wa
l
a
ﺭﺍﺑﻄﻪ ) (۳۰ﻳﮏ ﺭﺍﺑﻄﻪ ﺑﺪﻭﻥ ﭘﺎﺭﺍﻣﺘﺮ ﺗﻨﻈﻴﻤﻲ ﺍﺳﺖ ﻭ ﺩﺭ ﻣﺤﺎﺳﺒﺎﺕ ﺭﻓﺘﺎﺭ ﻓﺎﺯﻱ ﺁﺳﻔﺎﻟﺘﻴﻦ ﺩﺍﺭﺍﻱ ﺧﻄﺎﻱ ﺯﻳﺎﺩﻱ
ﻣﻲ ﺑﺎﺷﺪ ،ﺑﻬﻤﻴﻦ ﻣﻨﻈﻮﺭ ﺭﺍﺑﻄﻪ ) (۳۰ﺑﺎ ﻳﮏ ﭘﺎﺭﺍﻣﺘﺮ ﺗﻨﻈﻴﻤﻲ ﺑﺼﻮﺭﺕ ﺯﻳﺮ ﺗﺼﺤﻴﺢ ﻣﻲ ﺷﻮﺩ:
)(۳۳
}
Val
Val
φ = φ exp{ ( l − 1) −
] [(δ a − δ l ) 2 + 2 alδ a δ l
V
RT
s
a
l
a
ﮐﻪ ﺩﺭ ﺭﺍﺑﻄﻪ ﻓﻮﻕ l al ،ﭘﺎﺭﺍﻣﺘﺮ ﺗﻨﻈﻴﻤﻲ ﺑﻮﺩﻩ ﻭ ﺗﺎﺑﻌﻲ ﺩﺭﺟﻪ ﺩﻭ ﺑﺮ ﺣﺴﺐ ﻧﺴﺒﺖ ﺟﺮﻡ ﻣﻮﻟﮑﻮﻟﻲ ﺁﺳﻔﺎﻟﺘﻴﻦ ﺑﻪ
ﺭﺳﻮﺏ ﺩﻫﻨﺪﻩ ﻣﻲ ﺑﺎﺷﺪ:
MWa
MWa 2
() + c
)
MWs
MWs
)(۳۴
( al = a + b
ﺿﺮﺍﻳﺐ ﻣﻌﺎﺩﻟﻪ ) (۳۴ﺑﺮﺍﻱ ﺳﻪ ﺭﺳﻮﺏ ﺩﻫﻨﺪﻩ ﻧﺮﻣﺎﻝ ﭘﻨﺘﺎﻥ ،ﻧﺮﻣﺎﻝ ﻫﮕﺰﺍﻥ ﻭ ﻧﺮﻣﺎﻝ ﻫﭙﺘﺎﻥ ﺩﺭ ﺟﺪﻭﻝ ) (۵ﺁﻣﺪﻩ
ﺍﺳﺖ.
ﺑﺤﺚ ﻭ ﺑﺮﺭﺳﻲ ﻧﺘﺎﻳﺞ ﻣﺪﻝ ﺟﺪﻳﺪ:
ﺩﺭ ﺍﻳﻦ ﻣﻄﺎﻟﻌﻪ ،ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﻣﺪﻝ ﺗﺮﻣﻮﺩﻳﻨﺎﻣﻴﮑﻲ ﻓﻮﻕ ﻣﻘﺪﺍﺭ ﺭﺳﻮﺏ ﺁﺳﻔﺎﻟﺘﻴﻦ ﺗﻮﺳﻂ ﻧﺮﻣﺎﻝ ﭘﻨﺘﺎﻥ ،ﻧﺮﻣﺎﻝ ﻫﮕﺰﺍﻥ
ﻭ ﻧﺮﻣﺎﻝ ﻫﭙﺘﺎﻥ ﺑﺮﺍﻱ ﻳﮑﻲ ﺍﺯ ﻣﺨﺎﺯﻥ ﺟﻨﻮﺏ ﻏﺮﺑﻲ ﺍﻳﺮﺍﻥ ﻣﺤﺎﺳﺒﻪ ﺷﺪﻩ ﺍﺳﺖ ﮐﻪ ﻣﺸﺨﺼﺎﺕ ﺳﻴﺎﻝ ﻣﺨﺰﻥ ﺩﺭ
ﺟﺪﻭﻝ ۴-ﺁﻣﺪﻩ ﺍﺳﺖ .ﺍﺯ ﺁﻧﺠﺎ ﮐﻪ ﭘﺎﺭﺍﻣﺘﺮ ﺣﻼﻟﻴﺖ ﺁﺳﻔﺎﻟﺘﻴﻦ ﻭ ﻧﻔﺖ ﺑﺮ ﭘﻴﺶ ﺑﻴﻨﻲ ﺩﻗﻴﻖ ﻣﻘﺪﺍﺭ ﺭﺳﻮﺏ ﺁﺳﻔﺎﻟﺘﻴﻦ
ﺑﺴﻴﺎﺭ ﺗﺎﺛﻴﺮ ﮔﺬﺍﺭ ﺍﺳﺖ ،ﺑﻬﻤﻴﻦ ﻣﻨﻈﻮﺭ ﺍﺯ ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ ﺗﻨﻈﻴﻤﻲ ﺑﺮﺍﻱ ﺗﻌﻴﻴﻦ ﺩﻗﻴﻖ ﭘﺎﺭﺍﻣﺘﺮ ﺣﻼﻟﻴﺖ ﻧﻔﺖ ﺍﺳﺘﻔﺎﺩﻩ
ﺷﺪﻩ ﺍﺳﺖ.ﺑﺮﺍﻱ ﭘﻴﺶ ﮔﻮﺋﻲ ﻣﻘﺪﺍﺭ ﺩﻗﻴﻖ ﺭﺳﻮﺏ ﺁﺳﻔﺎﻟﺘﻴﻦ ﺑﺎﻳﺪ ﺩﺭ ﻫﺮ ﻧﺴﺒﺖ ﺣﻼﻝ ﻣﻘﺪﺍﺭ ﭘﺎﺭﺍﻣﺘﺮ ﺣﻼﻟﻴﺖ
ﺁﺳﻔﺎﻟﺘﻴﻦ ﺭﺍ ﺗﻐﻴﻴﺮ ﺩﺍﺩ ﺑﻄﻮﺭﻳﮑﻪ ﻣﻘﺪﺍﺭ ∆ ﺑﺎ ﺍﻓﺰﺍﻳﺶ ﻧﺴﺒﺖ ﺣﻼﻝ ﺍﻓﺰﺍﻳﺶ ﭘﻴﺪﺍ ﮐﻨﺪ ﺟﺪﺍﻭﻝ ۷ ،۶ﻭ ۸ﻣﻴﺰﺍﻥ
ﺍﺧﺘﻼﻑ ﭘﺎﺭﺍﻣﺘﺮ ﺣﻼﻟﻴﺖ ﺁﺳﻔﺎﻟﺘﻴﻦ ﻭ ﻧﻔﺖ ﻳﺎ ∆ ﺭﺍ ﺍﺭﺍﺋﻪ ﻣﻴﺪﻫﺪ ﻭ ﻫﻤﺎﻧﻄﻮﺭ ﮐﻪ ﻣﺸﺎﻫﺪﻩ ﻣﻲ ﺷﻮﺩ ﺑﺎ ﺍﻓﺰﺍﻳﺶ ﻧﺴﺒﺖ
ﺣﻼﻝ ﻣﻘﺪﺍﺭ ∆ ﺍﻓﺰﺍﻳﺶ ﻣﻲ ﻳﺎﺑﺪ ﮐﻪ ﺑﺎ ﻧﺘﺎﻳﺞ ﺁﺯﻣﺎﻳﺸﮕﺎﻫﻲ ﻣﻄﺎﺑﻘﺖ ﺩﺍﺭﺩ.ﮐﻪ ﻫﻤﻴﻦ ﻣﻮﺿﻮﻉ ﺩﺭ ﺷﮑﻠﻬﺎﻱ ۶ ،۵ﻭ ۷
ﮐﺎﻣﻼ ﻣﺸﻬﻮﺩ ﺍﺳﺖ.
ﺩﺭ ﺷﮑﻠﻬﺎﻱ ۹ ،۸ﻭ ۱۰ﺍﺭﺗﺒﺎﻁ ﺑﻴﻦ ﻣﻴﺰﺍﻥ ﺭﺳﻮﺏ ﺁﺳﻔﺎﻟﺘﻴﻦ ﻭ ∆ ﺍﺭﺍﺋﻪ ﺷﺪﻩ ﺍﺳﺖ.
ﻧﻬﻤﻴﻦ ﮐﻨﮕﺮﻩ ﻣﻠﯽ ﻣﻬﻨﺪﺳﯽ ﺷﻴﻤﯽ ﺍﻳﺮﺍﻥ ،ﺩﺍﻧﺸﮕﺎﻩ ﻋﻠﻢ ﻭ ﺻﻨﻌﺖ ﺍﻳﺮﺍﻥ ۳ ،ﺍﻟﯽ ۵ﺁﺫﺭﻣﺎﻩ ۱۳۸۳
٤٩٤
ﺗﻌﺎﺩﻝ ﻓﺎﺯﯼ ﻭ ﺗﺮﻣﻮﺩﻳﻨﺎﻣﻴﮏ: ۲ ﻣﺤﻮﺭ ﻋﻠﻤﻲ
IChEC9
ﻓﻬﺮﺳﺖ ﻋﻼﺋﻢ
6
-2
attraction parameter (MPa.m .kmol )
molar co-volume (m3.kmol-1)
enthalpy (KJ.Kmol-1)
parameters in Eq. (23)
molecular weight
pressure (MPa)
universal gas constant
entropy (KJ.Kmol-1.K-1)
temperature (K)
Molar volume (m3.kmol-1)
weighting factors
liquid phase mole fraction
vapor phase mole fraction
compressibility factor
a
b
h
m1 , m2 , m3
Mw
P
R
s
T
V
wd , wp
x
y
z
ﻋﻼﺋﻢ ﻳﻮﻧﺎﻧﻲ
volume fraction
density (Kg.m-3)
Pitzer acentric factor
objective function
packing factor
parameter in Eq. (4)
adjustable parameter
parameter in Eq. (7)
chemical potential
difference between asphaltene and oil solubility parameter
φ
ρ
ω
Ω
η
τ
al
ξ
µ
Δ
ﺯﻳﺮﻧﻮﻳﺲ
asphaltene
attraction
critical
dummy index
liquid
reduced
repulsion
oil mixture
solvent
a
attr
c
i, j
l
r
rep
o
s
ﺑﺎﻻﻧﻮﻳﺲ
liquid
solid
vapor
ideal gas property
ideal gas state property
۱۳۸۳ ﺁﺫﺭﻣﺎﻩ۵ ﺍﻟﯽ۳ ، ﺩﺍﻧﺸﮕﺎﻩ ﻋﻠﻢ ﻭ ﺻﻨﻌﺖ ﺍﻳﺮﺍﻥ،ﻧﻬﻤﻴﻦ ﮐﻨﮕﺮﻩ ﻣﻠﯽ ﻣﻬﻨﺪﺳﯽ ﺷﻴﻤﯽ ﺍﻳﺮﺍﻥ
l
s
v
∗
°
٤٩٥
ﺗﻌﺎﺩﻝ ﻓﺎﺯﯼ ﻭ ﺗﺮﻣﻮﺩﻳﻨﺎﻣﻴﮏ: ۲ ﻣﺤﻮﺭ ﻋﻠﻤﻲ
IChEC9
ﻣﻨﺎﺑﻊ ﻭ ﻣﺮﺍﺟﻊ
1. S. Malanowski, A. Anderko, Modeling Phase Equilibria, Second Edition, New York, John
Wiley, (1992).
2.
M. Mohsen-Nia, H. Modarres, G.A. Mansoori, Chem. Eng. Comm. 131 (1995) 15-31.
3. J.V. Sengers, R.F. Kayser, C.J. Peters and H.J. White Jr., Equations of State for Fluids
and Fluid Mixtures, First Edition, Elsevier, Amsterdam, (2000).
4. Burke N. E. et al, “Measurement and modeling of asphaltene
November, 1990.
precipition”,
IPT,
5. Leontaritis, K. J. and G. A. Mansoori “Asphaltene flocculation during oil production and
processing: Thermodynamic colloidal model”. SPE 16258.
6. Lian, H, etal. “Peptization studies of asphaltene and solubility parameter spectra” Fuel.
Vol 73 No 3. 1994
7. Edmister. W. G. and B. I. Lee “Applied hydrocarbon”, Vol 1, second Edition, Gulf
publishing, 1984.
8.
M.Edalat, MGhanei: Prediction of Asphaltene phase behavior in oil .PHD thesis.
9. R.H. Perry, D.W. Green, Perry’s Chemical Engineers’ Handbook, 6th Edition, McGraw
Hill, Tokyo, Japan, (1988).
10. B.D. Smith, R. Srivastava, Thermodynamic data for pure compounds, Elsevier (1986).
11. S., Laugier, D., Richon, J. Chem. Eng. Data 41(1996) 282-284.
12. C.-Y., Day, C.J., Chang, , C.-Y., Chen, , J. Chem. Eng. Data. 44 (1999) 365.
13. M.V., da Silva, , D., Barbosa, Fluid Phase Equilibria 198 (2002) 229-237.
14. J., Winnick, Chemical Engineering Thermodynamics, New York, John Wiley, (1997).
15. A.M. Scurto, Christopher M. Lubbers, Gang Xu and Joan F. Brennecke, Fluid Phase
Equilibriria 190 (2001) 135-147.
16. S.D., Fink, C., Hershey, Ind. Eng. Chem. Res. 29 (1990) 295-306.
۱۳۸۳ ﺁﺫﺭﻣﺎﻩ۵ ﺍﻟﯽ۳ ، ﺩﺍﻧﺸﮕﺎﻩ ﻋﻠﻢ ﻭ ﺻﻨﻌﺖ ﺍﻳﺮﺍﻥ،ﻧﻬﻤﻴﻦ ﮐﻨﮕﺮﻩ ﻣﻠﯽ ﻣﻬﻨﺪﺳﯽ ﺷﻴﻤﯽ ﺍﻳﺮﺍﻥ
٤٩٦
ﺗﻌﺎﺩﻝ ﻓﺎﺯﯼ ﻭ ﺗﺮﻣﻮﺩﻳﻨﺎﻣﻴﮏ: ۲ ﻣﺤﻮﺭ ﻋﻠﻤﻲ
IChEC9
ﺩﺍﻧﺴﻴﺘﻪ ﻣﺎﻳﻊ ﺍﺷﺒﺎﻉ ﻭ ﺣﺠﻢ ﺑﺨﺎﺭ ﺍﺷﺒﺎﻉ ﻣﻮﺍﺩ ﺧﺎﻟﺺ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ، ﻣﻘﺎﻳﺴﻪ ﻧﺘﺎﻳﺞ ﺧﻄﺎﻱ ﻓﺸﺎﺭ ﺑﺨﺎﺭ-۱-ﺟﺪﻭﻝ
SRK ﻭPR ،ﻣﻌﺎﺩﻟﻪ ﺣﺎﻟﺖ ﺟﺪﻳﺪ
Compound
n
New
PR
SRK
New
PR
SRK
New
PR
SRK
Reference
Percent of average absolute deviation (%AAD)
Tr
range
Vapor Pressure
Saturated liquid density
Vapor volume
CH4
19
0.500.97
0.791
0.584
1.820
4.235
8.886
4.472
1.899
0.930
2.335
a
C2H6
15
0.520.98
0.351
0.757
1.216
5.303
6.570
7.775
1.671
1.173
1.075
a
C3H8
17
0.510.95
0.691
1.401
0.758
4.517
5.049
8.164
1.590
1.571
0.318
a
n-C4H10
20
0.540.99
0.315
0.814
1.037
6.146
4.875
10.479
2.000
1.138
0.717
a
i-C4H10
17
0.540.98
1.018
1.569
1.658
5.775
5.216
9.518
2.011
2.179
1.479
a
n-C5H12
22
0.640.97
0.522
0.348
1.061
5.986
3.379
12.236
2.550
1.103
0.713
b
i-C5H12
28
0.530.97
0.925
0.244
1.348
6.256
4.747
10.420
2.073
1.219
1.449
b
n-C6H14
31
0.530.97
0.955
1.021
1.770
6.195
2.894
12.737
2.931
1.635
1.597
b
n-C7H16
11
0.570.74
0.267
1.676
0.663
2.029
0.698
12.140
0.774
1.773
0.516
a
n-C8H18
12
0.600.98
0.592
1.590
1.797
7.880
5.916
16.758
4.286
1.961
2.248
a
n-C9H20
14
0.500.94
1.622
2.389
2.231
6.213
4.953
15.904
9.213
6.778
6.638
a
n-C10H22
14
0.550.94
0.835
2.362
1.819
6.714
7.428
18.132
3.862
1.928
2.179
a
C2H4
12
0.570.96
0.507
0.658
0.808
4.429
6.197
7.215
1.458
1.189
0.575
a
C3H6
19
0.520.98
0.704
1.487
0.900
5.071
6.612
7.128
2.026
1.482
0.387
a
C7H14
28
0.550.97
0.529
0.788
0.822
5.801
3.802
11.179
2.733
1.229
0.975
b
C2H2
12
0.650.97
1.072
1.496
2.275
6.578
4.192
11.429
3.654
1.248
1.372
a
C6H6
25
0.550.98
0.640
0.908
0.681
5.325
3.166
11.216
2.506
1.167
0.717
a
C6H5CH3
20
0.510.98
1.023
1.339
1.148
5.443
2.447
13.273
2.255
2.557
1.874
a
C3H6O
20
0.590.94
2.434
2.288
1.631
14.051
12.236
22.475
4.176
2.488
2.207
a
CHCl3
14
0.520.99
1.698
3.949
4.290
4.992
6.671
8.114
3.054
4.433
4.665
a
CHClF2
39
0.550.98
0.733
0.596
0.653
6.026
3.029
12.632
2.661
1.084
0.917
b
۱۳۸۳ ﺁﺫﺭﻣﺎﻩ۵ ﺍﻟﯽ۳ ، ﺩﺍﻧﺸﮕﺎﻩ ﻋﻠﻢ ﻭ ﺻﻨﻌﺖ ﺍﻳﺮﺍﻥ،ﻧﻬﻤﻴﻦ ﮐﻨﮕﺮﻩ ﻣﻠﯽ ﻣﻬﻨﺪﺳﯽ ﺷﻴﻤﯽ ﺍﻳﺮﺍﻥ
٤٩٧
ﺗﻌﺎﺩﻝ ﻓﺎﺯﯼ ﻭ ﺗﺮﻣﻮﺩﻳﻨﺎﻣﻴﮏ: ۲ ﻣﺤﻮﺭ ﻋﻠﻤﻲ
IChEC9
C2H5Cl
26
0.530.83
1.307
0.460
1.732
6.508
3.560
14.396
4.216
2.364
3.466
b
C2Cl2F4
29
0.670.96
0.571
0.462
1.045
4.509
4.322
9.019
3.673
0.987
1.227
b
CF4
10
0.570.97
2.067
1.466
1.794
5.516
6.284
7.585
4.475
2.331
2.843
a
CCl4
27
0.500.97
0.331
1.542
0.946
5.568
4.243
10.494
1.782
2.262
0.923
a
CO2
14
0.720.99
1.204
0.669
0.401
5.053
3.879
11.668
4.382
1.389
1.614
a
CO
8
0.720.98
0.646
0.182
0.660
5.169
7.221
6.759
4.872
6.541
5.056
a
Ar
13
0.560.96
0.888
0.316
1.646
3.853
10.330
3.619
2.300
1.580
2.255
a
Br2
14
0.510.96
2.244
1.098
1.800
10.439
16.263
5.067
5.678
6.566
7.245
a
Cl2
19
0.530.97
1.011
1.046
0.470
5.650
4.077
9.449
1.126
2.658
0.996
a
F2
15
0.490.97
1.086
0.445
1.900
4.901
9.481
3.882
2.056
1.294
2.156
a
H2
19
0.420.96
1.423
4.018
7.231
3.942
21.839
9.846
5.124
6.385
12.775
a
He4
25
0.520.98
0.264
4.407
3.447
5.304
19.500
10.705
1.142
6.277
5.237
a
Kr
11
0.550.96
0.449
0.601
1.463
3.741
9.242
3.828
0.546
1.923
2.193
a
N2
13
0.510.95
0.521
0.689
1.191
4.358
9.777
3.461
1.114
1.364
1.486
a
O2
17
0.480.97
0.360
1.593
1.544
4.385
10.598
3.369
0.745
2.196
1.663
a
Ne
9
0.590.95
0.122
1.045
1.546
4.318
13.317
4.193
1.237
6.778
1.119
a
SO2
20
0.530.98
1.001
2.444
2.144
6.524
2.329
12.948
3.423
2.574
1.900
a
Xe
12
0.590.97
0.691
1.095
0.813
4.918
7.204
6.441
0.780
2.527
1.025
a
Total
746
0.859
1.313
1.585
5.825
6.863
9.824
2.792
2.370
2.333
a
R.H. Perry, D.W. Green, Perry’s Chemical Engineers’ Handbook, 6th Edition, McGraw Hill,
[۹] Tokyo, Japan, (1988).
[۱۰] b B.D. Smith, R. Srivastava, Thermodynamic data for pure compounds, Elsevier (1986).
۱۳۸۳ ﺁﺫﺭﻣﺎﻩ۵ ﺍﻟﯽ۳ ، ﺩﺍﻧﺸﮕﺎﻩ ﻋﻠﻢ ﻭ ﺻﻨﻌﺖ ﺍﻳﺮﺍﻥ،ﻧﻬﻤﻴﻦ ﮐﻨﮕﺮﻩ ﻣﻠﯽ ﻣﻬﻨﺪﺳﯽ ﺷﻴﻤﯽ ﺍﻳﺮﺍﻥ
٤٩٨
ﺗﻌﺎﺩﻝ ﻓﺎﺯﯼ ﻭ ﺗﺮﻣﻮﺩﻳﻨﺎﻣﻴﮏ: ۲ ﻣﺤﻮﺭ ﻋﻠﻤﻲ
IChEC9
SRK ﻭPR ، ﻣﻘﺎﻳﺴﻪ ﻧﺘﺎﻳﺞ ﺧﻄﺎﻱ ﺁﻧﺘﺎﻟﭙﻲ ﻭ ﺁﻧﺘﺮﻭﭘﻲ ﺗﺒﺨﻴﺮ ﻣﻮﺍﺩ ﺧﺎﻟﺺ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﻣﻌﺎﺩﻟﻪ ﺣﺎﻟﺖ ﺟﺪﻳﺪ-۲-ﺟﺪﻭﻝ
Percent of average absolute deviation (%AAD)
Compound
n
Tr range
Enthalpy of vaporization
Entropy of vaporization
New
PR
SRK
New
PR
SRK
Reference
CH4
19
0.50-0.97
1.472
1.418
2.486
2.311
2.394
3.373
a
C2H6
15
0.52-0.98
1.613
1.794
2.619
1.608
1.804
2.624
a
C3H8
17
0.51-0.95
0.717
1.308
1.048
0.719
1.304
1.050
a
n-C4H10
20
0.54-0.99
1.982
2.083
2.767
1.914
2.015
2.700
a
i-C4H10
17
0.54-0.98
1.477
1.343
1.216
1.452
1.354
1.237
a
n-C5H12
22
0.64-0.97
1.751
1.428
2.200
-
-
-
b
i-C5H12
28
0.53-0.97
1.657
1.768
2.547
-
-
-
b
n-C6H14
31
0.53-0.97
2.685
2.368
2.968
-
-
-
b
n-C7H16
11
0.57-0.74
0.965
0.591
1.194
0.973
0.576
1.203
a
n-C8H18
12
0.60-0.98
4.213
3.269
4.167
4.273
3.294
4.197
a
n-C9H20
14
0.50-0.94
3.742
4.956
5.282
4.059
7.442
7.817
a
n-C10H22
14
0.55-0.94
3.436
1.527
2.306
3.337
1.444
2.213
a
C2H4
12
0.57-0.96
0.804
1.240
1.662
1.187
2.360
2.785
a
C3H6
19
0.52-0.98
1.155
1.691
1.704
1.168
1.699
1.717
a
C7H14
28
0.55-0.97
1.957
1.450
1.813
-
-
-
b
C2H2
12
0.65-0.97
3.740
3.804
4.431
3.690
1.337
4.463
a
C6H6
25
0.55-0.98
1.384
1.317
1.403
2.294
2.354
2.235
a
C6H5CH3
20
0.51-0.98
2.075
2.936
3.268
2.068
2.958
3.240
a
C3H6O
20
0.59-0.94
5.776
3.839
4.697
4.013
2.524
4.273
a
CHCl3
14
0.52-0.99
2.404
4.313
4.659
2.299
4.337
4.573
a
CHClF2
39
0.55-0.98
1.548
1.353
1.895
-
-
-
b
C2H5Cl
26
0.53-0.83
3.352
2.057
3.389
-
-
-
b
C2Cl2F4
29
0.67-0.96
2.882
2.003
2.344
-
-
-
b
CF4
10
0.57-0.97
3.366
2.466
3.330
3.626
2.943
3.869
a
CCl4
27
0.50-0.97
1.447
2.079
1.911
1.359
2.002
1.827
a
CO2
14
0.72-0.99
2.869
2.055
2.655
2.924
2.072
2.662
a
CO
8
0.72-0.98
1.750
3.779
3.800
1.952
3.962
4.000
a
Ar
13
0.56-0.96
1.202
1.275
2.563
1.108
1.337
2.620
a
Br2
14
0.51-0.96
5.783
7.285
7.452
5.635
7.333
7.489
a
Cl2
19
0.53-0.97
1.351
3.095
1.897
1.298
3.043
1.891
a
F2
15
0.49-0.97
0.906
1.851
1.986
0.914
1.809
2.184
a
H2
19
0.42-0.96
3.269
5.474
8.815
3.224
5.461
8.786
a
He4
25
0.52-0.98
3.442
8.125
10.058
3.241
8.147
10.192
a
۱۳۸۳ ﺁﺫﺭﻣﺎﻩ۵ ﺍﻟﯽ۳ ، ﺩﺍﻧﺸﮕﺎﻩ ﻋﻠﻢ ﻭ ﺻﻨﻌﺖ ﺍﻳﺮﺍﻥ،ﻧﻬﻤﻴﻦ ﮐﻨﮕﺮﻩ ﻣﻠﯽ ﻣﻬﻨﺪﺳﯽ ﺷﻴﻤﯽ ﺍﻳﺮﺍﻥ
٤٩٩
ﺗﻌﺎﺩﻝ ﻓﺎﺯﯼ ﻭ ﺗﺮﻣﻮﺩﻳﻨﺎﻣﻴﮏ: ۲ ﻣﺤﻮﺭ ﻋﻠﻤﻲ
IChEC9
a
Kr
11
0.55-0.96
0.744
1.882
2.498
0.828
1.933
2.571
a
N2
13
0.51-0.95
0.949
1.697
2.715
0.905
1.663
2.687
a
O2
17
0.48-0.97
0.906
2.126
2.660
0.980
2.137
2.672
a
Ne
9
0.59-0.95
1.333
1.347
2.823
1.307
1.359
2.835
a
SO2
20
0.53-0.98
2.064
1.106
1.160
2.077
1.094
1.138
a
Xe
12
0.59-0.97
0.549
2.497
2.519
0.540
2.469
2.516
a
Total
746
507
2.225
2.485
3.088
2.172
2.827
3.426
R.H. Perry, D.W. Green, Perry’s Chemical Engineers’ Handbook, 6th Edition, McGraw Hill,
[۹] Tokyo, Japan, (1988).
[۱۰] b B.D. Smith, R. Srivastava, Thermodynamic data for pure compounds, Elsevier (1986).
ﻣﻘﺎﻳﺴﻪ ﻧﺘﺎﻳﺞ ﺧﻄﺎﻱ ﻓﺸﺎﺭ ﺣﺒﺎﺏ )ﺗﻌﺎﺩﻟﻲ( ﻭ ﺟﺰﺀ ﻣﻮﻟﻲ ﻓﺎﺯ ﺑﺨﺎﺭ ﻣﺨﻠﻮﻃﻬﺎﻱ ﺩﻭ ﺗﺎﻳﻲ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﻣﻌﺎﺩﻟﻪ-۳-ﺟﺪﻭﻝ
[۱۶-۱۱] . SRK ﻭPR ،ﺣﺎﻟﺖ ﺟﺪﻳﺪ
Percent of average absolute deviation (%AAD)
Systems(1)+(2)
Bubble Pressure
n
Vapor mole fraction
New
PR
SRK
New
PR
SRK
Ethanol+ CHCl3
29
11.460
12.264
16.285
26.092
30.981
29.758
CO2+Ethanol
56
9.857
25.852
22.266
0.562
0.516
0.566
CO2+iso-butanol
31
21.762
36.600
35.191
0.704
0.667
0.692
CO2+iso-pentanol
51
11.274
33.182
31.720
1.192
1.183
1.197
CO2+n-C4H10
38
21.168
17.655
17.674
7.535
17.978
18.411
CO2+CHCl3
30
6.016
16.384
15.096
2.086
1.949
2.034
CO2+Vinyl Acetate
12
7.673
12.307
11.678
-
-
-
CO2+Vinyl Acrylate
18
9.517
22.434
22.090
-
-
-
CO2+Toluene
45
17.976
36.002
35.422
0.424
0.514
0.504
CO2+1,1,1-Trichloroethane
32
9.978
24.735
24.262
0.750
1.318
1.231
C2H6+CO2
14
19.160
22.922
22.777
8.444
25.022
25.178
C6H6+C6H5Cl
7
4.114
3.759
3.343
0.445
2.706
1.659
Methanol+H2O
18
9.763
7.744
7.574
1.632
1.886
1.644
Methanol+2-butanone
10
4.352
6.785
6.964
2.419
3.606
3.727
Methyl acetate+ Methanol
13
0.580
4.928
5.136
1.708
5.226
5.017
N2+CH4
24
8.930
9.506
9.248
4.305
5.434
4.462
Total
426-396
10.849
18.350
17.960
4.164
7.070
6.863
۱۳۸۳ ﺁﺫﺭﻣﺎﻩ۵ ﺍﻟﯽ۳ ، ﺩﺍﻧﺸﮕﺎﻩ ﻋﻠﻢ ﻭ ﺻﻨﻌﺖ ﺍﻳﺮﺍﻥ،ﻧﻬﻤﻴﻦ ﮐﻨﮕﺮﻩ ﻣﻠﯽ ﻣﻬﻨﺪﺳﯽ ﺷﻴﻤﯽ ﺍﻳﺮﺍﻥ
٥٠٠
ﻣﺤﻮﺭ ﻋﻠﻤﻲ : ۲ﺗﻌﺎﺩﻝ ﻓﺎﺯﯼ ﻭ ﺗﺮﻣﻮﺩﻳﻨﺎﻣﻴﮏ
IChEC9
ﺟﺪﻭﻝ -۴-ﻣﺸﺨﺼﺎﺕ ﻳﮏ ﻧﻤﻮﻧﻪ ﻧﻔﺘﻲ ﺍﺯ ﻣﺨﺎﺯﻥ ﺟﻨﻮﺏ ﻏﺮﺑﻲ ﺍﻳﺮﺍﻥ ﺟﻬﺖ ﻣﺤﺎﺳﺒﺎﺕ ﻣﻘﺪﺍﺭ ﺭﺳﻮﺏ ﺁﺳﻔﺎﻟﺘﻴﻦ[۸] .
Mole%
Component
0
C1-C3
0.05
iC4
0.64
nC4
1.69
iC5
2.21
nC5
4.23
nC6
91.18
C7+
Oil Specification
11%
Asphaltene content
200
Molecular weight of oil
211.82
C 7 + Molecular weight of
0.8778
C 7 + Specific gravity of
ﺟﺪﻭﻝ -۵-ﻣﻘﺎﺩﻳﺮ ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ ﺗﻨﻈﻴﻤﻲ ﻣﺪﻝ ﺑﻬﺒﻮﺩ ﻳﺎﻓﺘﻪ ﻓﻠﻮﺭﻱ-ﻫﺎﮔﻴﻨﺰ ﺩﺭ ﻣﺪﻝ ﺍﺭﺍﺋﻪ ﺷﺪﻩ ﺟﺪﻳﺪ
c
b
a
Solvent
0.009979 0.00023
nC5
0.004945 3.45222 9.24*10-5
nC6
0.000937 2.95935
nC7
-0.49289
ﻧﻬﻤﻴﻦ ﮐﻨﮕﺮﻩ ﻣﻠﯽ ﻣﻬﻨﺪﺳﯽ ﺷﻴﻤﯽ ﺍﻳﺮﺍﻥ ،ﺩﺍﻧﺸﮕﺎﻩ ﻋﻠﻢ ﻭ ﺻﻨﻌﺖ ﺍﻳﺮﺍﻥ ۳ ،ﺍﻟﯽ ۵ﺁﺫﺭﻣﺎﻩ ۱۳۸۳
٥٠١
ﻣﺤﻮﺭ ﻋﻠﻤﻲ : ۲ﺗﻌﺎﺩﻝ ﻓﺎﺯﯼ ﻭ ﺗﺮﻣﻮﺩﻳﻨﺎﻣﻴﮏ
IChEC9
ﺟﺪﻭﻝ -۶-ﻧﺘﺎﻳﺞ ﻣﺤﺎﺳﺒﺎﺕ ﻣﺪﻝ ﺑﺮﺍﻱ ﺣﻼﻝ ﻧﺮﻣﺎﻝ ﭘﻨﺘﺎﻥ[۸] .
Δ
δA
SR
1.20
1.37
2.7
16.3
1
1.60
1.62
2.8
16.2
1.2
2.05
1.81
3
16.0
1.4
2.60
2.18
3.2
15.8
1.9
3.10
2.57
3.4
15.60
2.5
3.80
3.52
3.5
15.55
3
)Wt(cal) Wt(exp
ﺟﺪﻭﻝ -۷-ﻧﺘﺎﻳﺞ ﻣﺤﺎﺳﺒﺎﺕ ﻣﺪﻝ ﺑﺮﺍﻱ ﺣﻼﻝ ﻧﺮﻣﺎﻝ ﻫﮕﺰﺍﻥ[۸] .
Δ
)Wt(cal) Wt(exp
δA
SR
0.7
0.64
16.6 2.4
1.00
1.24
1.2 16.4 2.6
1.1
1.61
1.4 16.3 2.7
1.40
1.76
1.5 16.3 2.7
1.45
1.89
1.6 16.3 2.7
1.60
2.1
1.8 16.2 2.8
1.95
2.28
2.25
2.67
16.1 2.9
3
1
2
2.5 16.0
2.55
3.04
15.9 3.1
3
2.55
3.74
15.8 3.2
4
ﺟﺪﻭﻝ -۸-ﻧﺘﺎﻳﺞ ﻣﺤﺎﺳﺒﺎﺕ ﻣﺪﻝ ﺑﺮﺍﻱ ﺣﻼﻝ ﻧﺮﻣﺎﻝ ﻫﭙﺘﺎﻥ[۸] .
)Wt(exp
)Wt(cal
Δ
δA
SR
1.05
1.05
2.5
16.5
1.2
1.40
1.47
2.6
16.4
1.4
1.57
1.64
2.7
16.3
1.5
1.60
1.78
2.8
16.2
1.6
1.70
1.91
2.8
16.2
1.7
1.95
2.02
2.8
16.2
1.8
2.15
2.21
2.9
16.1
2
2.55
2.60
3.1
15.9
2.5
3.45
3.64
3.3
15.7
4
3.55
4.48
3.5
15.5
4.0
ﻧﻬﻤﻴﻦ ﮐﻨﮕﺮﻩ ﻣﻠﯽ ﻣﻬﻨﺪﺳﯽ ﺷﻴﻤﯽ ﺍﻳﺮﺍﻥ ،ﺩﺍﻧﺸﮕﺎﻩ ﻋﻠﻢ ﻭ ﺻﻨﻌﺖ ﺍﻳﺮﺍﻥ ۳ ،ﺍﻟﯽ ۵ﺁﺫﺭﻣﺎﻩ ۱۳۸۳
٥٠٢
ﻣﺤﻮﺭ ﻋﻠﻤﻲ : ۲ﺗﻌﺎﺩﻝ ﻓﺎﺯﯼ ﻭ ﺗﺮﻣﻮﺩﻳﻨﺎﻣﻴﮏ
IChEC9
2.5
CH4
2.0
C2H6
C3H8
1.5
nC4H10
1.0
C3H6
Xe
0.5
N2
%Dev
0.0
-0.5
-1.0
-1.5
-2.0
-2.5
1.0
0.9
0.8
0.7
0.6
0.5
0.4
Tr
ﺷﮑﻞ -۱-ﺩﺭﺻﺪ ﺍﻧﺤﺮﺍﻑ ﻓﺸﺎﺭﺑﺨﺎﺭ ﭘﻴﺶ ﺑﻴﻨﻲ ﺷﺪﻩ ﺗﻮﺳﻂ ﻣﻌﺎﺩﻟﻪ ﺍﺯ ﺩﺍﺩﻩ ﻫﺎﻱ ﺗﺠﺮﺑﻲ ﺑﺮﺍﻱ ۷ﻣﺎﺩﻩ ﺧﺎﻟﺺ ][۹
0.050
CH4
C2H4
O2
Predicted
0.040
0.020
)Density(mol/cm3
0.030
0.010
1.00
0.90
0.80
0.70
0.60
0.50
0.000
0.40
Tr
ﺷﮑﻞ -۲-ﻣﻘﺎﺩﻳﺮ ﺗﺠﺮﺑﻲ ﻭ ﭘﻴﺶ ﺑﻴﻨﻲ ﻣﻌﺎﺩﻟﻪ ﺣﺎﻟﺖ ﺟﺪﻳﺪ ﺑﺮﺍﻱ ﺩﺍﻧﺴﻴﺘﻪ ﻓﺎﺯ ﻣﺎﻳﻊ ۳ﻣﺎﺩﻩ ﺧﺎﻟﺺ ][۹
ﻧﻬﻤﻴﻦ ﮐﻨﮕﺮﻩ ﻣﻠﯽ ﻣﻬﻨﺪﺳﯽ ﺷﻴﻤﯽ ﺍﻳﺮﺍﻥ ،ﺩﺍﻧﺸﮕﺎﻩ ﻋﻠﻢ ﻭ ﺻﻨﻌﺖ ﺍﻳﺮﺍﻥ ۳ ،ﺍﻟﯽ ۵ﺁﺫﺭﻣﺎﻩ ۱۳۸۳
٥٠٣
ﻣﺤﻮﺭ ﻋﻠﻤﻲ : ۲ﺗﻌﺎﺩﻝ ﻓﺎﺯﯼ ﻭ ﺗﺮﻣﻮﺩﻳﻨﺎﻣﻴﮏ
IChEC9
450.00
n-C7H16
CF4
C6H6
n-C6H14
n-C10H22
Predicted
400.00
350.00
300.00
200.00
)h(KJ/kg
250.00
150.00
100.00
50.00
0.80
1.00
0.00
0.40
0.60
Tr
ﺷﮑﻞ -۳-ﺩﺍﺩﻩ ﻫﺎﻱ ﺗﺠﺮﺑﻲ ﺁﻧﺘﺎﻟﭙﻲ ﺗﺒﺨﻴﺮ ﺑﺮﺣﺴﺐ ﺩﻣﺎﻱ ﮐﺎﻫﻴﺪﻩ ﻭ ﻧﺘﺎﻳﺞ ﻣﻌﺎﺩﻟﻪ ﺣﺎﻟﺖ ﺟﺪﻳﺪ ﺑﺮﺍﻱ ﺑﺮﺧﻲ ﻣﻮﺍﺩ
ﺧﺎﻟﺺ ][۹
3.5
nC4H10
nC8H18
3
C3H6
O2
2.5
Predicted
1.5
)s (KJ/kg.K
2
1
0.5
0
1.1
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
Tr
ﺷﮑﻞ -۴-ﺩﺍﺩﻩ ﻫﺎﻱ ﺗﺠﺮﺑﻲ ﺁﻧﺘﺮﻭﭘﻲ ﺗﺒﺨﻴﺮ ﺑﺮﺣﺴﺐ ﺩﻣﺎﻱ ﮐﺎﻫﻴﺪﻩ ﻭ ﻧﺘﺎﻳﺞ ﻣﻌﺎﺩﻟﻪ ﺣﺎﻟﺖ ﺟﺪﻳﺪ ﺑﺮﺍﻱ ﺑﺮﺧﻲ ﻣﻮﺍﺩ
ﺧﺎﻟﺺ ] ۹ﻭ [۱۰
ﻧﻬﻤﻴﻦ ﮐﻨﮕﺮﻩ ﻣﻠﯽ ﻣﻬﻨﺪﺳﯽ ﺷﻴﻤﯽ ﺍﻳﺮﺍﻥ ،ﺩﺍﻧﺸﮕﺎﻩ ﻋﻠﻢ ﻭ ﺻﻨﻌﺖ ﺍﻳﺮﺍﻥ ۳ ،ﺍﻟﯽ ۵ﺁﺫﺭﻣﺎﻩ ۱۳۸۳
٥٠٤
ﻣﺤﻮﺭ ﻋﻠﻤﻲ : ۲ﺗﻌﺎﺩﻝ ﻓﺎﺯﯼ ﻭ ﺗﺮﻣﻮﺩﻳﻨﺎﻣﻴﮏ
IChEC9
4
3.8
3.6
3.4
Delta
3.2
3
2.8
2.6
2.4
7
5
6
3
4
1
2
0
SR
ﺷﮑﻞ -۵-ﺗﻐﻴﻴﺮﺍﺕ ﺍﺧﺘﻼﻑ ﭘﺎﺭﺍﻣﺘﺮ ﺣﻼﻟﻴﺖ ﺁﺳﻔﺎﻟﺘﻴﻦ ﻭ ﻧﻔﺖ ﻧﺴﺒﺖ ﺑﻪ ﻣﻘﺪﺍﺭ ﺯﺳﻮﺏ ﺩﻫﻨﺪﻩ ﺑﺮﺍﻱ ﻧﺮﻣﺎﻝ ﭘﻨﺘﺎﻥ
3.8
3.6
3.4
3.2
3
Delta
2.8
2.6
2.4
2.2
2
12
10
8
6
4
2
0
SR
ﺷﮑﻞ -۶-ﺗﻐﻴﻴﺮﺍﺕ ﺍﺧﺘﻼﻑ ﭘﺎﺭﺍﻣﺘﺮ ﺣﻼﻟﻴﺖ ﺁﺳﻔﺎﻟﺘﻴﻦ ﻭ ﻧﻔﺖ ﻧﺴﺒﺖ ﺑﻪ ﻣﻘﺪﺍﺭ ﺯﺳﻮﺏ ﺩﻫﻨﺪﻩ ﺑﺮﺍﻱ ﻧﺮﻣﺎﻝ ﻫﮕﺰﺍﻥ
ﻧﻬﻤﻴﻦ ﮐﻨﮕﺮﻩ ﻣﻠﯽ ﻣﻬﻨﺪﺳﯽ ﺷﻴﻤﯽ ﺍﻳﺮﺍﻥ ،ﺩﺍﻧﺸﮕﺎﻩ ﻋﻠﻢ ﻭ ﺻﻨﻌﺖ ﺍﻳﺮﺍﻥ ۳ ،ﺍﻟﯽ ۵ﺁﺫﺭﻣﺎﻩ ۱۳۸۳
٥٠٥
ﻣﺤﻮﺭ ﻋﻠﻤﻲ : ۲ﺗﻌﺎﺩﻝ ﻓﺎﺯﯼ ﻭ ﺗﺮﻣﻮﺩﻳﻨﺎﻣﻴﮏ
IChEC9
3.8
3.6
3.4
3.2
3
Delta
2.8
2.6
2.4
2.2
2
7
8
5
6
3
4
1
2
0
SR
ﺷﮑﻞ -۷-ﺗﻐﻴﻴﺮﺍﺕ ﺍﺧﺘﻼﻑ ﭘﺎﺭﺍﻣﺘﺮ ﺣﻼﻟﻴﺖ ﺁﺳﻔﺎﻟﺘﻴﻦ ﻭ ﻧﻔﺖ ﻧﺴﺒﺖ ﺑﻪ ﻣﻘﺪﺍﺭ ﺯﺳﻮﺏ ﺩﻫﻨﺪﻩ ﺑﺮﺍﻱ ﻧﺮﻣﺎﻝ ﻫﭙﺘﺎﻥ
4.5
4
3.5
3
2.5
Wt
2
1.5
1
0.5
0
4
3.8
3.6
3.4
3
3.2
2.8
2.6
2.4
2.2
Delta
ﺷﮑﻞ -۸-ﺗﻐﻴﻴﺮﺍﺕ ﻣﻘﺪﺍﺭ ﺭﺳﻮﺏ ﻧﺴﺒﺖ ﺑﻪ ﺍﺧﺘﻼﻑ ﭘﺎﺭﺍﻣﺘﺮ ﺣﻼﻟﻴﺖ ﺁﺳﻔﺎﻟﺘﻴﻦ ﻭ ﻧﻔﺖ ﺑﺮﺍﻱ ﻧﺮﻣﺎﻝ ﭘﻨﺘﺎﻥ
ﻧﻬﻤﻴﻦ ﮐﻨﮕﺮﻩ ﻣﻠﯽ ﻣﻬﻨﺪﺳﯽ ﺷﻴﻤﯽ ﺍﻳﺮﺍﻥ ،ﺩﺍﻧﺸﮕﺎﻩ ﻋﻠﻢ ﻭ ﺻﻨﻌﺖ ﺍﻳﺮﺍﻥ ۳ ،ﺍﻟﯽ ۵ﺁﺫﺭﻣﺎﻩ ۱۳۸۳
٥٠٦
ﻣﺤﻮﺭ ﻋﻠﻤﻲ : ۲ﺗﻌﺎﺩﻝ ﻓﺎﺯﯼ ﻭ ﺗﺮﻣﻮﺩﻳﻨﺎﻣﻴﮏ
IChEC9
4.5
4
3.5
3
2.5
Wt
2
1.5
1
0.5
0
3.6
3.8
3.4
3.2
2.8
3
2.6
2.4
2
2.2
Delta
ﺷﮑﻞ -۹-ﺗﻐﻴﻴﺮﺍﺕ ﻣﻘﺪﺍﺭ ﺭﺳﻮﺏ ﻧﺴﺒﺖ ﺑﻪ ﺍﺧﺘﻼﻑ ﭘﺎﺭﺍﻣﺘﺮ ﺣﻼﻟﻴﺖ ﺁﺳﻔﺎﻟﺘﻴﻦ ﻭ ﻧﻔﺖ ﺑﺮﺍﻱ ﻧﺮﻣﺎﻝ ﻫﮕﺰﺍﻥ
6
5
4
Wt
3
2
1
0
3.8
3.6
3.4
3.2
2.8
3
2.6
2.4
2.2
2
Delta
ﺷﮑﻞ -۱۰-ﺗﻐﻴﻴﺮﺍﺕ ﻣﻘﺪﺍﺭ ﺭﺳﻮﺏ ﻧﺴﺒﺖ ﺑﻪ ﺍﺧﺘﻼﻑ ﭘﺎﺭﺍﻣﺘﺮ ﺣﻼﻟﻴﺖ ﺁﺳﻔﺎﻟﺘﻴﻦ ﻭ ﻧﻔﺖ ﺑﺮﺍﻱ ﻧﺮﻣﺎﻝ ﻫﭙﺘﺎﻥ
ﻧﻬﻤﻴﻦ ﮐﻨﮕﺮﻩ ﻣﻠﯽ ﻣﻬﻨﺪﺳﯽ ﺷﻴﻤﯽ ﺍﻳﺮﺍﻥ ،ﺩﺍﻧﺸﮕﺎﻩ ﻋﻠﻢ ﻭ ﺻﻨﻌﺖ ﺍﻳﺮﺍﻥ ۳ ،ﺍﻟﯽ ۵ﺁﺫﺭﻣﺎﻩ ۱۳۸۳