توسعه يك رابطه كاربردي براي تخمين افت فشار در مته حفاري كاجي با استفاده از مدل رئولوژيك بينگهام

Development of an Applied Relationship for Pressure dro‎p Estimation in Tri-Cone Drill Bit Using Bingham Rheological Model

در اﯾﻦ ﻣﻘﺎﻟﻪ، اﻓﺖ ﻓﺸﺎر در ﻣﺘﻪ ﺣﻔﺎري ﺑﺎ ﺷﺒﯿﻪ ﺳﺎزي ﺟﺮﯾﺎن ﺳﯿﺎل ﻏﯿﺮﻧﯿﻮﺗﻨﯽ ﻣﺤﺎﺳﺒﻪ ﺷﺪه اﺳﺖ. ﻣﺘﻪ ﺣﻔﺎري ﮐﺎﺟﯽ ﻧﻮع اف-3 ﺑﺎ اﻧﺪازه 7-7/8 اﯾﻨﭻ ﺑﻮده و داراي ﺳﻪ ﻧﺎزل ﺑﺎ اﻧﺪازه ﯾﮑﺴﺎن ﻣﯽ ﺑﺎﺷﺪ. ﻣﺤﺎﺳﺒﻪ اﻓﺖ ﻓﺸﺎر ﺑﺮاي ﻧﺎزل ﻫﺎﯾﯽ ﺑﺎ اﻧﺪازه ﻫﺎي 10/32 ،9/32 ،7/32و 11/32 اﯾﻨﭻ اﻧﺠﺎم ﺷﺪه اﺳﺖ. ﺗﺤﻠﯿﻞ ﺟﺮﯾﺎن در ﻣﺘﻪ ﺣﻔﺎري ﺑﺮاي ﻫﺸﺖ ﻧﻮع ﮔﻞ ﺣﻔﺎري ﺻﻮرت ﮔﺮﻓﺘﻪ و از ﻣﺪل رﺋﻮﻟﻮژﯾﮏ ﺑﯿﻨﮕﻬﺎم ﺑﺮاي ﺗﻌﯿﯿﻦ ﺧﻮاص رﺋﻮﻟﻮژﯾﮏ ﮔﻞ ﻫﺎي ﺣﻔﺎري اﺳﺘﻔﺎده ﺷﺪه اﺳﺖ. ﺑﺮاي ﺗﻌﯿﯿﻦ ﺿﺮاﯾﺐ ﻣﺪل رﺋﻮﻟﻮژﯾﮏ، ﺧﻮاص رﺋﻮﻟﻮژﯾﮏ ﮔﻞ ﻫﺎي ﺣﻔﺎري ﺑﺎ دﺳﺘﮕﺎه وﯾﺴﮑﻮﻣﺘﺮ ﻓﻦ اﻧﺪازه ﮔﯿﺮي ﺷﺪه اﺳﺖ. اﻓﺖ ﻫﺎي ﻓﺸﺎر ﻣﺤﺎﺳﺒﻪ ﺷﺪه از ﺷﺒﯿﻪ ﺳﺎزي ﺟﺮﯾﺎن، ﺑﺎ ﻧﺘﺎﯾﺞ ﺗﺠﺮﺑﯽ و راﺑﻄﻪ اﯾﮑﻞ- ﺑﻠﺴﺘﯿﻦ ﻣﻘﺎﯾﺴﻪ ﺷﺪه اﺳﺖ. ﻧﺘﺎﯾﺞ ﻧﺸﺎن ﻣﯽ دﻫﺪ، روش ﻋﺪدي، اﻓﺖ ﻓﺸﺎر در ﻣﺘﻪ ﺣﻔﺎري را ﺑﺎ ﻣﺘﻮﺳﻂ ﺧﻄﺎي 9/66 درﺻﺪ ﺗﺨﻤﯿﻦ ﻣﯽ زﻧﺪ؛ در ﺣﺎﻟﯽ ﮐﻪ ﻣﺘﻮﺳﻂ ﺧﻄﺎي راﺑﻄﻪ اﯾﮑﻞ- ﺑﻠﺴﺘﯿﻦ 17/16 درﺻﺪ اﺳﺖ. ﯾﮏ راﺑﻄﻪ ﺟﺪﯾﺪ ﺑﺮاي ﺗﺨﻤﯿﻦ اﻓﺖ ﻓﺸﺎر در ﻣﺘﻪ ﺣﻔﺎري ﮐﺎﺟﯽ ﭘﯿﺸﻨﻬﺎد ﺷﺪه اﺳﺖ، در اﯾﻦ راﺑﻄﻪ ﺗﺎﺛﯿﺮ ﺧﻮاص رﺋﻮﻟﻮژﯾﮏ ﺳﯿﺎل در ﺗﺨﻤﯿﻦ اﻓﺖ ﻓﺸﺎر در ﻧﻈﺮ ﮔﺮﻓﺘﻪ ﻣﯽ ﺷﻮد. اﻓﺖ ﻫﺎي ﻓﺸﺎر ﻣﺤﺎﺳﺒﻪ ﺷﺪه ﺑﺎ راﺑﻄﻪ ﺟﺪﯾﺪ، ﺑﺎ ﻧﺘﺎﯾﺞ ﺗﺠﺮﺑﯽ ﻣﻘﺎﯾﺴﻪ ﺷﺪه اﺳﺖ. ﻧﺘﺎﯾﺞ ﻧﺸﺎن ﻣﯽ دﻫﺪ، راﺑﻄﻪ ﺟﺪﯾﺪ، ﺑﺎ دﻗﺖ ﻣﻨﺎﺳﺒﯽ و ﺑﺎ ﺧﻄﺎي 8/31 درﺻﺪ اﻓﺖ ﻓﺸﺎر در ﻣﺘﻪ ﺣﻔﺎري را ﻣﺤﺎﺳﺒﻪ ﻣﯽ ﮐﻨﺪ.

In this study, non Newtonian fluid flow simulations are obtained through a tri-cone drilling bit. F-3 drill bit of size 7-7/8 inch is used for pressure drop calculations. The drilling bit contains three nozzles of equal size. Nozzle sizes of 7/32, 9/32, 10/32, and 11/32 inch are selected for simulations and each solution considered three nozzles of equal size. Eight drilling fluids of different density and rheological properties are selected and Bingham rheological model is employed in this study. Rheological data were obtained using a Fann 35 viscometer. To validate the results, calculated pressure drops from flow simulations are compared to experimental data and Eckel-Bielstein equation. The results show that flow simulations have predicted the pressure drop for all nozzle sizes with an absolute average percentage error of 9.66, whereas Eckel-Bielstein equation has an absolute average percentage error of 17.16. A new equation is proposed to calculate the pressure drop in the tri-cone bit for Bingham rheological model. The proposed equation considers effects of rheological parameters on the pressure drop. Comparison of results with experimental data revealed that the proposed equation can predict pressure drops with an absolute average percentage error of 8.31.