CALCULATION OF BOTTOM-HOLE PRESSURE AND SUBMERSIBLE PUMP INTAKE PRESSURE Ildar K Shayhutdnov In ths artcle the desgn procedure of a bottom-hole pressure and ntake pressure of submersble pump under the fact sheet of operaton of well s offered A feature of the algorthm conssts of usng the gven standard feld values of annulus pressure, dynamc level, flow rate and water cut In artcle results of calculatons are compared to actual measured pressure at the level of pump ntake It s demonstrated, that the appled methodology provdes hgh accuracy of calculaton for requred parameters Wth artfcal lft the mportant parameters of the ol producng wells are the bottom-hole pressure as well as the ntake pressure of the submersble pump The defnton accuracy of these parameters s dctated by the necessty to calculate the potental well producton opportuntes when selectng the approprate pumpng equpment and optmzng well performance Fndng BH pressure thru actual well performance data can be dvded n two stages: а) calculaton of pressure dstrbuton n annulus (n tubng) and defnton of pressure at the pump run-n depth; б) defnton of pressure n the well bore at the nterval pump ntake BH and estmate of BH pressure Defnton of pressure at the pump ntake The hardest bt n fndng the BH pressure n the producng well s calculaton of pressure at the pump run-n depth usng actual well performance data Ths artcle consders methodology for calculaton of mentoned pressure based on plottng the curve of pressure dstrbuton n annulus Fg1 shows the dagram for producng well performance usng submersble pump As a rule, the majorty of producng wells for a more relable pump performance are equpped wth s Wth the bgger part of free gas, lberated from crude, under condtons of pump ntake s drected nto annulus Wth absence of (gas anchor / bottom hole separator) on the pump ntake less quantty of free gas s comng nto annulus Gas phase flow process n annulus can be characterzed as gas lft operaton at zero feed/delvery mode Theoretcal and practcal researches of AP Krylov [1] were devoted to t Equaton for lqud-gas mxture flow n ths case s presented the followng way dp a0 = (1) gdl Q a г + Q г - volumetrc gas dscharge/flow n the annulus, m 3 /s; - flud densty n the annulus (presupposng that flud n the annulus s presented by ol), kg/m 3 ; a 0 - rato, consderng geometrcal dmenson of flud passage, m 3 /s; g gravty acceleraton, m/s a0 = 0,785( D d ), () D - producton casng ID, m; d - tubng OD, m 0 1
Calculaton of pressure dstrbuton n annulus s based on numercal calculaton of equaton (1) wth known pressure at the pump run-n depth P At that the teraton procedure s mplemented and actual and calculated pressure at dynamc level P are compared The algorthm for defnton of pressure at the pump run-n depth s the followng 1 The followng ntal data are put n: Q ст - flud flow rate under standard condtons, m 3 /day; ϕ - volume rato of water n producton under standard condtons; P зат - annulus pressure, MPa; Т пл - formaton pressure, K; L c - well depth (vertcal), m; H - pump run-n depth (vertcal), m; h - well dynamc level (vertcal), m; d - tubng ID, m; d - tubng OD, m; D - producton casng ID, m; - densty of degassed ol under standard condtons, kg/m 3 ; µ - dynamc vscosty of degassed ol under standard condtons, mpa s; P ас - Fg1 Dagram, for calculaton bubble pont pressure at formaton temperature, MPa; of ESP performance wth olgas mx condtons, m 3 /m 3 ; го - densty of gas, lberated from G 0 - GOR of ol n place (gas-ol rato) under normal crude at flash lberaton under normal condtons, kg/m 3 ; y a, y м - mole fracton of ntrogen and methane n gas at flash lberaton; - water densty under standard condtons, kg/m 3 Numercal calculaton of equaton (1) s presented as followng P( Qг + 0,785( D d )) = L (3) 0,785( D d ) g P - pressure steppng, Pa; L - length delta, m Pressure steppng taken and the sequental pressure values are dentfed for varous depths For that the general pressure varaton range ( Р Pзат ) s dvded nto several ntervals, e under condton P = 0,05( P Pзат ), (4) where P зат - annular pressure, Pa; Р - assumed pump ntake-level pressure (at frst approxmaton s taken at random), Pa Accordngly recurrence relaton defnes the calculated pressures P = P 3 The temperature dstrbuton n producng well bore s defned [] Wth known formaton temperature the temperature at the pump s run-n depth (calculaton «bottom-up») s calculated thru equaton h t( h) = t пл 1 St (6) d To calculate the temperature dstrbuton above the pump ntake t s necessary to know the wellhead temperature (calculaton «top-down»): N = 1 Р (5)
t у t( H ) = (7) H 1 St d In equatons (6) and (7) t пл, t у - formaton and wellhead temperatures accordngly, о С; h - vertcal depth, measured from bottom-hole, m; H - vertcal depth, measured from wellhead, m; St - non-dmensonal Stanton number Dependence of Stanton number on mass well flow rate s represented as: 4 1,763 10 4 St = 0,0 10, (8) ln( q + 40) where q - mass well flow rate, t/day If wellhead temperature data s not avalable the calculaton of temperature dstrbuton above the pump ntake can be done usng the equaton (6), takng as base for measurng the temperature at the pump-settng depth In ths case the value of wellhead temperature s the requred parameter and s defned for h = L c H But, n case the well s operated usng centrfugal, cavty/screw or daphragm pump the heatng of lqud gas mx passng the submersble motor wll not be consdered Thus we are gettng the temperature dstrbuton n producng well bore 4 Usng the data of flud propertes we fnd the physcal propertes of ol, gas, water or water-ol mx under correspondng thermo dynamc condtons P, T ) [1,] ( 5 The volumetrc gas-lqud flow parameters Q and Q г are defned n condtons of pump ntake [] To defne gas volume, gong nto annulus, we need to set the gas separaton rato For that we recommend to use the followng equatons, obtaned from theoretcal and expermental researches []: at the level of flowng lft shoe σ 0 σ = ; (9) at the sucker-rod pump ntake ш ф Q 1 + 0,7 w F 0 σ 0 = Q 1+1,05 w F 0 эк эк σ ; (10) at the electrcal submersble pump ntake σ 0 σ ц =, (11) Q 1+ 0,75 w0 f з ' where σ 0 - free gas separaton rato wth zero feed/delvery mode d σ 0 = 1 (1) D Here Q - volumetrc flud flow under condtons of pump ntake, m 3 /s; w 0 - relatve velocty of gas bubbles, m/s Relatve velocty of gas bubbles depends on the water volume rato n producton: at ϕ 0,5 w0 = 0,0 м / с ; ϕ > 0,5 w0 = 0,17 м / с ; F эк - cross sectonal area of producton casng, m ; f з ' - area of crcular clearance between producton casng and submersble pump, m After calculaton of separaton rato the volume Q of gas flow gong nto annulus s defned In case of well operatng wth ESP the volume of gas flow s calculated the followng way: Q = Q σ (13) г з г ц г з 3
If the centrfugal s avalable at the ESP s ntake the separaton rato s varyng wthn range 0,6-0,8 (t s recommended to take t as 0, 7 ) If the gas anchor / bottom hole separator s avalable at the SRP s ntake the separaton rato s varyng wthn range 0,4-0,6 (t s recommended to take t as 0, 5 ) 6 Values of Q г = Qг з and = assumng there s ol-gas mx above the pump ntake, values set n equaton (3) and the well depth delta L1 s found Hence, at the depth h1 = H L1 we are havng the pressure P1 = P Р 7 From equatons (6)-(8) the temperature T 1 s defned at the depth of h 1 Usng equaton (5) we calculate the sequental pressure step P = P 1 P The followng calculatons are done for the average pressure between P 1 and P : Р1 + Р Р ср = and for the temperature T 1 Here you can see that at numercal ntegraton of equaton (1) the mplemented calculatons are one step behnd n temperature But t appears that calculaton error wth such approxmaton s very mnor The volume of gas flow gong nto annulus s calculated for taken Р : z PT Q г = Qг з, (14) z PT where Q г з - volume of gas flow n annulus under pump ntake condtons, m 3 /s; P, T - taken pump ntake pressure and calculated temperature correspondngly; z, z - correspondngly the supercompressblty ratos for the pump ntake condtons and set Р When calculatng the densty of three-phase mx n the annulus addtonal complcatons occur due to necessty to account for dssolved gas lberatng from crude If we presuppose there s no mass exchange/transfer between the flud n the annulus and the flud gong to the pump ntake, then the presence of free gas phase n the annulus wll be determned only by the separaton at the pump s ntake Then flud densty n equaton (3) wll be equal to ol densty at set Р In realty there s a constant mass transfer/exchange process between the flud n the annulus and the flud gong to the pump ntake Accountng for flud densty change n the annulus due to dssolved gas lberatng from crude s done usng the followng correlaton: = ϕ + гс ( 1 ϕ ), (15) where - ol densty n the annulus flud at Р, kg/m 3 ; гс - gas lqud mx densty from crude and gas lberated from t as part of the annulus flud at Р, kg/m 3 ; ϕ - volume rato of ol degassed at Р (wthout consderaton for free gas phase lberated n condtons of pump ntake) It s easy to see that = ( 1 ϕ ) + ϕ, (16) гс 0 ( G ( P, T ) G ) z( P, T ) + 1 P0 T ( G0 м ( P, T ) G0 м ) z( P, T ) PT 0 ϕ =, (17) P T 0 м 0 м PT 0 г р PT 0 = (18) z( P, T ) P0 T Here ϕ - volume rato of gas, lberated at Р (wthout consderaton for free gas phase lberated n condtons of pump ntake); - densty of gas addtonally lberated from crude at Р, kg/m 3 ; G 0 м - specfc volume of gas lberated n condtons of pump 4
ntake, modfed to normal condtons, m 3 /t; G0 м ( P, T ) - specfc volume of gas lberated at Р, modfed to normal condtons, m 3 /t; г р - densty of gas dssolved n crude n condtons of pump ntake, modfed to normal condtons, kg/m 3 Note: when determnng the densty no free gas accounted lberated n condtons of pump ntake Determnng гс ϕ parameter presents a hard task Based on actual data processng we receved the followng emprcal dependence: 0,5587 Q Qг з ϕ =, (19) Qгс where Q г з - volumetrc gas flow n the annulus n condtons of pump ntake, m 3 /day; Q - volumetrc ol flow n condtons of pump ntake, m 3 /day; Q гс - volumetrc gas lqud mx flow n condtons of pump ntake, m 3 /day Acqured values Q г and are placed n equaton (3) and delta s determned L Value h = h1 L s calculated wth P Р + Р3 Sequental pressure step s taken P 3 = P P, Р ср 3 = etc Thus the sequental/step-by-step calculaton s mplemented tll the vertcal depth h s decreases or equalzes the value of well dynamc level h, e h h Pressure P at the last calculaton sequence/step s defned for certan depth h, and not р for h To determne pressure P drectly at the dynamc level we are usng the followng correlaton р ( h h )( P 1 P ) P = P 1 (0) h 1 h 8 Pressure P at dynamc level s calculated assumng the pump ntake pressure s equal р Р, taken at random at frst approxmaton Pressure р on comparson of calculated P and actual Actual pressure Р at the pump ntake s corrected based Ф P pressures at dynamc level Ф P at dynamc level s determned by known barometrc equaton [1]: 0,03415h Ф P = Pзат е, (1) where Т ср - average temperature n the nterval from the wellhead to dynamc level; z - supercompressblty rato at P зат pressure ср temperature To correct the pump ntake pressure the followng procedure s used: P P f 100% 5% and P ф < P, then the pump ntake pressure taken at frst P approxmaton Р s excessve, and t has to be lowered, for example, take t equal to Р = 0, 95Р ; P P f 100% 5% and P ф > P, then the pump ntake pressure taken at frst P approxmaton Р underrated, and t has to be ncreased, for example, up to value of Р = 1, 05Р P P 9 Calculaton thru ponts -8 s repeated tll condton 100% 5% s ф P fulflled г ср zt 5
Durng the mplementaton of teraton procedure the stuaton mght occur when as a result of numercal ntegraton of equaton (1), at the depth sgnfcantly lower than dynamc level the calculated value of pressure appears to be close to atmospherc and lower It happens when ntally settng the overrated pressure value Р at the pump ntake level In ths case the assumed ntal pump ntake pressure s lowered Note: f settng ncorrect ntal data the proposed teraton procedure doesn t always match Hence t s recommended to use the closest soluton of equaton gvng the mnmal accuracy error Also keep n mnd that the algorthm proposed to determne the pump ntake pressure doesn t consder the foamng leadng to data corrupton of measurng the dynamc level n annulus Calculaton examples Thru proposed calculaton algorthm for submersble pump ntake level pressure usng Vsual С++ Borland the software has been created called Well analyst Intal data for calculatons are gven n tables 1 and Calculaton results are gven n table 3 Physcal propertes of ol-n-place and degassed crude Table 1 Feld, Ol n place Degassed crude and sngle degassng gas formaton Т f, К Р f, MPa Р b, MPa G, m 3 /t b o µ пл, пл, 0, µ 0, г0, N, % mpa*s kg/m 3 kg/m 3 mpa*s kg/m 3 Varyogan, formaton БВ 8 345 1,4 15,6 175,1 1,49 0,5 785 83 4,1 1,168 1,4 formaton АВ 1 1 333 17,1 11,8 97,8 1,7 1,5 755 844 5,0 0,86 0, formaton АВ 1-333 16,5 9,4 76 1,18 1,4 735 844 5,0 0,86 0, formaton БВ 8 349 1,19 13,5 135 1,6 1,15 735 843 7,0 1,13 3,84 formaton ЮВ 1 349 4,4 11 119 1,4 1,03 735 844 6,6 0,955 3, VKY, formaton ЮВ 1 349 5 0,6 36 1,45 0,4 808 83 5 0,85 0,75 6
Well # 163 883 7476б 9866 61503 9970 1109 61803 51118 594 550 Intal data for calculaton of pump ntake pressure and actual values Table Pump set Dynamc Watercut, Pump type depth, m level, m % Feld, formaton Varyogan, formaton БВ 8 formaton АВ 1 1 formaton АВ 1- formaton БВ 8 formaton БВ 8 formaton БВ 8 formaton БВ 8 formaton Annular pressure, Mpa Flud flow rate, m 3 /day Borehole devaton, degrees Pump ntake pressure, Mpa 1587 350 0,9 144,0 80,0 30 8,4 1587 785,3 144,0 80,0 30 7,1 1587 84,45 144,0 80,0 30 6,8 1610 106,5 0,84 8,4 0,0 9 5,8 УЭЦНМ5А- 160-1750 УЭЦНМ5А- 160-1750 УЭЦНМ5А- 160-1750 УЭЦНММ5А- 80-1700 wth 100 530 0,8 33,0 0,0 0 4,8 УШГН 100 344 0,66 36,0 0,0 0 6,5 УШГН 158 166 1,6 58 8 0,9 1683 403, 5 0 11,9 011 633 1, 81 5 0 9,7 09 564 1,4 114 5 0 9,5 1808 701 1,8 440 5 0 5, ЮВ 1 1987 1513 1,4 36 5 0 3,4 formaton ЮВ 1 18 1313 1,6 36 10 0 6,7 VKY, formaton ЮВ 1 VKY, formaton ЮВ 1 00 70 1,4 6 5 0 6,1 030 135 0,8 146 48 0 6 УЭЦН5-30- 1800 wth gas separator УЭЦНМ5А- 400-150 УЭЦНА-5-60- 1700 wth gas separator УЭЦН5А- 160-1750 wth УЭЦН5А- 500-150 wth УЭЦН5-50- 000 wth gas separator УЭЦН5-50- 000 wth gas separator DN-1750 wth DN-1300 wth Well Actual pressure, MPa Calculated pressure, MPa Absolute dvergence, MPa Comparson of calculated and actual pressures for revewed wells Table 3 Calculated pressure (MPa) and dvergence from actual (%) at Р ф пр (MPa) 163 883 7476б 9866 61503 9970 1109 61803 51118 594 550 8,4 7,1 6,8 5,8 4,8 6,5,9 11,9 9,7 9,5 5, 3,4 6,7 6,1 6 8,8 7,7 7,04 5,69 4,68 5,89 3,41 1,03 9,69 8,96 5,36 4,16 6,87 6,19 6,43 0,1-0,17-0,4 0,11 0,1 0,61-0,51-0,13 0,01 0,54-0,16-0,76-0,17-0,09-0,43 7
As seen from results, gven n table 3, dvergence of calculated from actual pressures does not exceed 0,76 MPa, t shows relatvely hgh accuracy of proposed methodology Besdes the degree of relablty of ndvdual ntal datum leaves much to be desred Applcaton of Well analyst software allows to mplement a farly correct estmate of well potental when selectng the downhole equpment, as well as usng the more correct calculated BH pressure values when adaptng 3D hydrodynamc models Bottom-hole pressure calculaton Let s now revew the peculartes of calculatng the pressure dstrbuton wthn the nterval pump ntake bottom-hole, as well as BH pressure Calculaton methodology s based on numercal calculaton of the followng dfferental equaton for gas lqud mx flow, assumng the neglgbly small nertal loss, dp dp = см g +, (1) dh dh тр dp where - summarzed (total) pressure gradent durng flow of gas lqud mx n lft, Pa/m; dh см - densty of gas lqud mx, kg/m 3 dp ; - frctonal loss gradent, Pa/m dh тр Numercal calculaton of equaton (1) s not presentng extra complexty from methodology pont of vew and s mplemented thru one of the methods shown n detals [1,] The necessary correlatons stated above are to be consdered as well Concluson The proposed algorthm for determnaton of BH pressure and pump ntake level pressure has the most applcable degree of accuracy comparng wth exstng approaches The pecularty of gven calculaton algorthm for determnaton of BH pressure and pump ntake level pressure s that for ts mplementaton suffcent are the relable data for actual well operaton, content and propertes of produced flud Ths, partcularly, wll allow, when adaptng 3D reservor models, a more qualfed applcaton of prevous multple meterng data for dynamc levels and other well parameters Ths aspect partcularly, for the most part, predetermned the statement of correspondng researches Lterature 1 «Reference gude to desgn the development and operaton of ol felds», edton by ShK Gmatutdnov, Moscow, «Nedra», 1983 Mschenko IT, «Calculatons n ol producton», Moscow, «Nedra», 1989 3 Mchael Lssuk, «Analyss of exstng methodology for determnaton of annular pressure wth ESP well operaton», journal «Technque and process of ol producton»,, 000 Author/Credts Ildar K Shayhutdnov E-mal: ldar79@malru 8