Yijun et al 2022a - Revision history

Rimni: /* 6.3 Distance between multiple downhole throttles */

2022-06-08T13:25:41Z

‎6.3 Distance between multiple downhole throttles

Rimni at 13:24, 8 June 2022

2022-06-08T13:24:45Z

Rimni: /* 6.3 Distance between multiple downhole throttles */

2022-06-08T13:17:48Z

‎6.3 Distance between multiple downhole throttles

Rimni at 13:11, 8 June 2022

2022-06-08T13:11:33Z

Rimni at 12:14, 8 June 2022

2022-06-08T12:14:49Z

Rimni: /* 7. Application */

2022-06-08T12:08:54Z

‎7. Application

Rimni at 12:06, 8 June 2022

2022-06-08T12:06:15Z

Rimni at 12:05, 8 June 2022

2022-06-08T12:05:37Z

Rimni at 12:03, 8 June 2022

2022-06-08T12:03:45Z

Rimni: /* 7. Application */

2022-06-08T12:02:53Z

‎7. Application

@@ Line 179: / Line 179: @@
 {| style="text-align: center; margin:auto;"
 |-
-| <math>{\left. \frac{\partial T\left( {Q}_{g},p,GLR,K\right) }{\partial x}\right| }_{x=\Delta x}=</math><math>G{T}_{wf}</math>
+| <math>{\left. \frac{\partial T\left( {Q}_{g},p,GLR,K\right) }{\partial x}\right| }_{x=\Delta x}=G{T}_{wf}</math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (9)

@@ Line 70: / Line 70: @@
-When the output of natural gas, the temperature and pressure at the upstream inlet of the throttle are known, substituting them into equation (1) and calculating after deformation, the pressure <math display="inline">{p}_{2}</math> after throttling can be determined, the pressure drop can be obtained as <math display="inline">{\Delta p=p}_{1}{-p}_{2}</math>.
+When the output of natural gas, the temperature and pressure at the upstream inlet of the throttle are known, substituting them into Eq.(1) and calculating after deformation, the pressure <math display="inline">{p}_{2}</math> after throttling can be determined, the pressure drop can be obtained as <math display="inline">{\Delta p=p}_{1}{-p}_{2}</math>.
 ===4.2 Gas-liquid two-phase throttle pressure drop===
@@ Line 190: / Line 190: @@
 ===6.4 Calculation method and precedence===
-According to the above proposed theory, the specific calculation method and precedence of multi-stage downhole throttle parameter optimization design are as list follows,
+According to the above proposed theory, the specific calculation method and precedence of multi-stage downhole throttle parameter optimization design are as list follows:
 # The production and bottom hole pressure of gas well are determined according to the reasonable production distribution method of gas well.

@@ Line 172: / Line 172: @@
 ===6.3 Distance between multiple downhole throttles===
-The distance between the throttles uses the well bore temperature field analysis theory, and the temperature after each level of the throttle is used as the starting point, and the node system analysis method is used to analyze the distance [[Image:Draft_Yijun_989359957-image4.png|18px]] when the temperature after the throttles returns to the geothermal gradient as the lowering position of the next-level throttle, namely
+The distance between the throttles uses the well bore temperature field analysis theory, and the temperature after each level of the throttle is used as the starting point, and the node system analysis method is used to analyze the distance <math display="inline"> \Delta x </math> when the temperature after the throttles returns to the geothermal gradient as the lowering position of the next-level throttle, namely
 {| class="formulaSCP" style="width: 100%; text-align: center;"

@@ Line 55: / Line 55: @@
 |}
-Here, <math display="inline">{q}_{sc}\,</math> is natural gas production (under standard conditions), <math>10^4</math>Nm<sup>3</sup>/d; <math display="inline">{p}_{1}</math> and <math display="inline">{p}_{2}</math> are the the upstream and downstream pressures of the throttle, respectively, MPa;  <math display="inline"> d </math> is the diameter of the orifice, mm; <math display="inline">{T}_{1}</math> is the upstream inlet temperature of the throttle, <math display="inline"> K </math>; <math display="inline">{Z}_{1}</math> is the gas compressibility coefficient at the inlet of the throttle; <math display="inline">{\gamma }_{g}</math> is the relative density of natural gas; <math display="inline">k</math> is the natural gas adiabatic index.
+where, <math display="inline">{q}_{sc}\,</math> is natural gas production (under standard conditions), <math>10^4</math>Nm<sup>3</sup>/d; <math display="inline">{p}_{1}</math> and <math display="inline">{p}_{2}</math> are the the upstream and downstream pressures of the throttle, respectively, MPa;  <math display="inline"> d </math> is the diameter of the orifice, mm; <math display="inline">{T}_{1}</math> is the upstream inlet temperature of the throttle, <math display="inline"> K </math>; <math display="inline">{Z}_{1}</math> is the gas compressibility coefficient at the inlet of the throttle; <math display="inline">{\gamma }_{g}</math> is the relative density of natural gas; <math display="inline">k</math> is the natural gas adiabatic index.
 In the critical flow state, when the critical pressure ratio is calculated according to Eq.(1), the maximum output is
@@ Line 98: / Line 98: @@
 |}
+where, <math display="inline">{F}_{w}</math> is water cut correction coefficient, and <math display="inline">{\gamma }_{w}</math> is the relative density of the composite gas and the other parameters are the same as before.
-Here, <math display="inline">{F}_{w}</math> is water cut correction coefficient, and <math display="inline">{\gamma }_{w}</math> is the relative density of the composite gas and the other parameters are the same as before.
 ===4.3 Downhole throttling temperature drop===
@@ Line 115: / Line 114: @@
 |}
-Here, <math display="inline">{Z}_{1}</math> and <math display="inline">{Z}_{2}</math> are the gas compressibility coefficients at the inlet and outlet conditions of the throttle respectively, and <math display="inline">{T}_{2}</math> is the downstream outlet temperature of the throttle. The phase balance equation before and after gas throttling and the throttling temperature drop model established in literature are used for calculation.
+where, <math display="inline">{Z}_{1}</math> and <math display="inline">{Z}_{2}</math> are the gas compressibility coefficients at the inlet and outlet conditions of the throttle respectively, and <math display="inline">{T}_{2}</math> is the downstream outlet temperature of the throttle. The phase balance equation before and after gas throttling and the throttling temperature drop model established in literature are used for calculation.
 ==5. Analysis of applicable conditions for multistage downhole throttling==
@@ Line 131: / Line 130: @@
 |}
-Here, <math display="inline">{p}_{wf}</math> is the bottom hole pressure under reasonable production allocation of gas wells, MPa; <math display="inline">{p}_{wsmax}</math> is the highest safety gas gathering pressure at the wellhead of gas well, MPa; <math display="inline">{T}_{hp}</math> is the hydrate formation temperature corresponding to the highest safe gas gathering pressure, <math display="inline">^\circ\mbox{C}</math>; <math display="inline">{\Delta p}_{w}</math> is well bore pressure loss, MPa; <math display="inline">{\Delta p}_{ci}</math> is the throttling pressure drop of the downhole throttling device, MPa; <math display="inline">N</math> is the number of downhole throttles. <math display="inline">{T}_{ws}</math> is the wellhead flow temperature after multistage throttling of the well bore, <math display="inline">^\circ\mbox{C}</math>.
+where, <math display="inline">{p}_{wf}</math> is the bottom hole pressure under reasonable production allocation of gas wells, MPa; <math display="inline">{p}_{wsmax}</math> is the highest safety gas gathering pressure at the wellhead of gas well, MPa; <math display="inline">{T}_{hp}</math> is the hydrate formation temperature corresponding to the highest safe gas gathering pressure, <math display="inline">^\circ\mbox{C}</math>; <math display="inline">{\Delta p}_{w}</math> is well bore pressure loss, MPa; <math display="inline">{\Delta p}_{ci}</math> is the throttling pressure drop of the downhole throttling device, MPa; <math display="inline">N</math> is the number of downhole throttles. <math display="inline">{T}_{ws}</math> is the wellhead flow temperature after multistage throttling of the well bore, <math display="inline">^\circ\mbox{C}</math>.
 ==6. Optimization design of downhole multistage throttling parameters==

@@ Line 280: / Line 280: @@
 ==References==
-[1] Duncan KW, Musaffar AK and Anas MQ (2011) Foam sticks application to increase production and encapsulated inhibitors to mitigate corrosion and scale formation. In SPE/PAPG Annual Technical Conference, Islamabad, Pakistan. Society of Petroleum Engineers, Richardson, TX, USA, paper SPE 156213.
+<div class="auto" style="text-align: left;width: auto; margin-left: auto; margin-right: auto;font-size: 85%;">
-[2] Orta D, Ramanchandran S, Yang J et al. (2007) A novel foamer for deliquification of condensate-loaded wells. In SPE Rocky Mountain Oil & Gas Technology Symposium, Denver, Colorado, U.S.A. Society of Petroleum Engineers, Richardson, TX, USA, paper SPE 107980.
+[1] Duncan K.W., Musaffar A.K.,  Anas M.Q. Foam sticks application to increase production and encapsulated inhibitors to mitigate corrosion and scale formation. In SPE/PAPG Annual Technical Conference, Islamabad, Pakistan. Society of Petroleum Engineers, Richardson, TX, USA, paper SPE 156213, 2011.
-[3] Siddiqui S and Yang J (1999) Successful application of foam for lifting liquids from low-pressure gas wells. In SPE Mid-Continent Operations Symposium, Oklahoma City, Oklahoma. Society of Petroleum Engineers, Richardson, TX, USA, paper SPE 52122.
+[2] Orta D., Ramanchandran S., Yang J. et al. A novel foamer for deliquification of condensate-loaded wells. In SPE Rocky Mountain Oil & Gas Technology Symposium, Denver, Colorado, U.S.A. Society of Petroleum Engineers, Richardson, TX, USA, paper SPE 107980, 2007.
-[4] Wang F, Liang Z, Deng X. (2017) Automation of liquid removal from natural gas wells. Proceedings of Institution of Civil Engineers: Energy '''170(1)''':37-42.
+[3] Siddiqui S.,  Yang J. Successful application of foam for lifting liquids from low-pressure gas wells. In SPE Mid-Continent Operations Symposium, Oklahoma City, Oklahoma. Society of Petroleum Engineers, Richardson, TX, USA, paper SPE 52122, 1999.
-[5] William H (2010) Gas well deliquification. In SPE Abu Dhabi International Petroleum Exhibition and Conference, Abu Dhabi, UAE. Society of Petroleum Engineers, Richardson, TX, USA, paper SPE 138672.
+[4] Wang F., Liang Z., Deng X. Automation of liquid removal from natural gas wells. Proceedings of Institution of Civil Engineers - Energy, 170(1):37-42, 2017.
-[6] Xie C, Liu Y, Li X (2022) A novel comprehensive model for predicting production of downhole choke wells. Fuel '''313''':1-23.
+[5] William H. Gas well deliquification. In SPE Abu Dhabi International Petroleum Exhibition and Conference, Abu Dhabi, UAE. Society of Petroleum Engineers, Richardson, TX, USA, paper SPE 138672, 2010.
-[7] Zheng L, Fei W, Xiong D (2014) A novel technology of combining foam injection and compression to lift liquid in water flooded gas wells. Journal of Natural Gas Science and Engineering '''19(7)''': 147–151.
+[6] Xie C., Liu Y., Li X. A novel comprehensive model for predicting production of downhole choke wells. Fuel, 313:1-23, 2022.

@@ Line 210: / Line 210: @@
 <div id='tab-1'></div>
-{| class="wikitable" style="margin: 1em auto 0.1em auto;border-collapse: collapse;font-size:85%;width:85%;"
+{| class="wikitable" style="margin: 1em auto 0.1em auto;border-collapse: collapse;font-size:85%;width:auto;"
 |-style="text-align:center"
 ! No. !! Production <br> (10<sup>4</sup>m<sup>3</sup>/d) !! Mean annual temperature<br>  (℃) !! Choke series !! Choke depth<br> (m) !! Pressure before choke<br> (MPa) !! Temperature before choke<br> (℃) !! Pressure  after choke <br> (MPa) !!Temperature  after choke <br> (℃) !! Hydrate formation temperature <br> (℃)

@@ Line 225: / Line 225: @@
 |  style="text-align: center;"|22.23
 |-
-|  style="text-align: center;"|2<sup>ed</sup> level
+|  style="text-align: center;"|2<sup>nd</sup> level
 |  style="text-align: center;"|1999
 |  style="text-align: center;"|10.93
@@ Line 244: / Line 244: @@
 |  style="text-align: center;"|21.34
 |-
-|  style="text-align: center;"|2<sup>ed</sup> level
+|  style="text-align: center;"|2<sup>nd</sup> level
 |  style="text-align: center;"|2005
 |  style="text-align: center;"|9.43
@@ Line 263: / Line 263: @@
 |  style="text-align: center;"|22.20
 |-
-|  style="text-align: center;"|2<sup>ed</sup> level
+|  style="text-align: center;"|2<sup>nd</sup> level
 |  style="text-align: center;"|2008
 |  style="text-align: center;"|10.97

@@ Line 214: / Line 214: @@
 ! No. !! Production <br> (10<sup>4</sup>m<sup>3</sup>/d) !! Mean annual temperature<br>  (℃) !! Choke series !! Choke depth<br> (m) !! Pressure before choke<br> (MPa) !! Temperature before choke<br> (℃) !! Pressure after choke <br> (MPa) !!Temperature after choke <br> (℃) !! Hydrate formation temperature <br> (℃)
 |-
-|  rowspan='2' style="border-top: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">SuX1</span>
+|  rowspan='2' style="text-align: center;"|SuX1
-|  rowspan='2' style="border-top: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">7.00 </span>
+|  rowspan='2' style="text-align: center;"|7.00
-|  rowspan='2' style="border-top: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">8</span>
+|  rowspan='2' style="text-align: center;"|8
-|  style="border-top: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">1<sup>st</sup> level</span>
+|  style="text-align: center;"|1<sup>st</sup> level
-|  style="border-top: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">2501 </span>
+|  style="text-align: center;"|2501
-|  style="border-top: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">20.88 </span>
+|  style="text-align: center;"|20.88
-|  style="border-top: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">89.45 </span>
+|  style="text-align: center;"|89.45
-|  style="border-top: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">11.40 </span>
+|  style="text-align: center;"|11.40
-|  style="border-top: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">42.21 </span>
+|  style="text-align: center;"|42.21
-|  style="border-top: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">22.23 </span>
+|  style="text-align: center;"|22.23
 |-
-|  style="border-bottom: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">2<sup>ed</sup> level</span>
+|  style="text-align: center;"|2<sup>ed</sup> level
-|  style="border-bottom: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">1999 </span>
+|  style="text-align: center;"|1999
-|  style="border-bottom: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">10.93 </span>
+|  style="text-align: center;"|10.93
-|  style="border-bottom: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">74.89 </span>
+|  style="text-align: center;"|74.89
-|  style="border-bottom: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">5.97 </span>
+|  style="text-align: center;"|5.97
-|  style="border-bottom: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">29.55 </span>
+|  style="text-align: center;"|29.55
-|  style="border-bottom: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">18.34 </span>
+|  style="text-align: center;"|18.34
 |-
-|  rowspan='2' style="border-top: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">SuX2</span>
+|  rowspan='2' style="text-align: center;"|SuX2
-|  rowspan='2' style="border-top: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">6.00 </span>
+|  rowspan='2' style="text-align: center;"|6.00
-|  rowspan='2' style="border-top: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">8</span>
+|  rowspan='2' style="text-align: center;"|8
-|  style="border-top: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">1<sup>st</sup> level</span>
+|  style="text-align: center;"|1<sup>st</sup> level
-|  style="border-top: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">2500 </span>
+|  style="text-align: center;"|2500
-|  style="border-top: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">17.99 </span>
+|  style="text-align: center;"|17.99
-|  style="border-top: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">87.72 </span>
+|  style="text-align: center;"|87.72
-|  style="border-top: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">9.82 </span>
+|  style="text-align: center;"|9.82
-|  style="border-top: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">40.70 </span>
+|  style="text-align: center;"|40.70
-|  style="border-top: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">21.34 </span>
+|  style="text-align: center;"|21.34
 |-
-|  style="border-bottom: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">2<sup>ed</sup> level</span>
+|  style="text-align: center;"|2<sup>ed</sup> level
-|  style="border-bottom: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">2005 </span>
+|  style="text-align: center;"|2005
-|  style="border-bottom: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">9.43 </span>
+|  style="text-align: center;"|9.43
-|  style="border-bottom: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">73.36 </span>
+|  style="text-align: center;"|73.36
-|  style="border-bottom: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">5.15 </span>
+|  style="text-align: center;"|5.15
-|  style="border-bottom: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">28.22 </span>
+|  style="text-align: center;"|28.22
-|  style="border-bottom: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">17.45 </span>
+|  style="text-align: center;"|17.45
 |-
-|  rowspan='2' style="border-top: 1pt solid black;border-bottom: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">SuX3</span>
+|  rowspan='2' style="text-align: center;"|SuX3
-|  rowspan='2' style="border-top: 1pt solid black;border-bottom: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">10.00 </span>
+|  rowspan='2' style="text-align: center;"|10.00
-|  rowspan='2' style="border-top: 1pt solid black;border-bottom: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">8</span>
+|  rowspan='2' style="text-align: center;"|8
-|  style="border-top: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">1<sup>st</sup> level</span>
+|  style="text-align: center;"|1<sup>st</sup> level
-|  style="border-top: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">2408 </span>
+|  style="text-align: center;"|2408
-|  style="border-top: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">20.77 </span>
+|  style="text-align: center;"|20.77
-|  style="border-top: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">90.24 </span>
+|  style="text-align: center;"|90.24
-|  style="border-top: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">11.34 </span>
+|  style="text-align: center;"|11.34
-|  style="border-top: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">42.90 </span>
+|  style="text-align: center;"|42.90
-|  style="border-top: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">22.20 </span>
+|  style="text-align: center;"|22.20
 |-
-|  style="border-bottom: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">2<sup>ed</sup> level</span>
+|  style="text-align: center;"|2<sup>ed</sup> level
-|  style="border-bottom: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">2008 </span>
+|  style="text-align: center;"|2008
-|  style="border-bottom: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">10.97 </span>
+|  style="text-align: center;"|10.97
-|  style="border-bottom: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">78.64 </span>
+|  style="text-align: center;"|78.64
-|  style="border-bottom: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">5.99 </span>
+|  style="text-align: center;"|5.99
-|  style="border-bottom: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">32.81 </span>
+|  style="text-align: center;"|32.81
-|  style="border-bottom: 1pt solid black;text-align: center;"|<span style="text-align: center; font-size: 75%;">18.37 </span>
+|  style="text-align: center;"|18.37
 |}