Multiple Flow Rate Well Testing with Production Logging in Determining Production Formation Dynamics Parameter

Transcription

1 Multple Flow Rate Well Testng wth Producton Loggng n Determnng Producton Formaton Dynamcs Parameter Song Hong-we 1,2 1 Key Laboratory of Exploraton Technologes for Ol and Gas Resources (Yangtze unversty) Mnstry of Educaton, Hube Wuhan PR Chna 2 Hube Cooperatve nnovaton Center of Unconventonal Ol and Gas, Hube Wuhan PR Chna. e-mal: shwcyu@126.com Yang Guo-feng School of geophyscs and ol resources, Yangtze Unversty, Hube Wuhan , PR Chna e-mal: guofengy_loggng@163.com ABSTRACT Estmaton of effectve well and reservor propertes has been a long standng challenge n developed felds. The conventonal pressure buld up test s the man tool for montorng well productvty (permeablty and skn) and reservor pressure. However, one of the predcaments of tradtonal well testng s the requrement of shuttng-n producng well to conduct a pressure buldup test. Ths deterrent factor s more promnent n prolfc wells due to loss of revenue and problems assocated wth water cross flow or when brngng a well back on producton. Moreover, n case of commngled reservors, conventonal pressure buldup provdes only average values of permeablty, skn factor and layer pressure for the whole producng formaton. Ths paper presents multlayer testng and analyss technques to obtan well and reservor propertes (.e., permeablty, skn factor, layer pressure, and productvty ndex) of mult-layer mxed systems usng pressure data from sequental flow tests acqured wth multrate producton loggng measurements. An ntegrated workflow s shown and a new analyss technque s presented. Based on the well nflow equaton analyses, the relatons between formaton dynamcs parameter and produced lqud rate and the pressure alteraton of bottom hole flowng are studed. An nnovatve method to estmate the ndvdual formaton dynamcs parameter of each producton layer by modulatng the surface flow rate has been proposed. Smultaneously, adaptve genetc algorthm and Levenberg- Marquardt algorthm have been consdered n solvng Darcy s law on an nterval bass to provde formaton characterstcs of each producton layer. The study also hghlghts the potental for the applcaton of ths method to pressure transent, flow rate transent analyss, multlayer test analyss and nterpretaton. Ths transent and flow perod was followed by a producton log survey at ths stablzed rate. Ths technque elmnates the dsadvantage of shuttng-n a well and mantans the producton wth a multple flow rate pattern. It s well suted for montorng near wellbore propertes. KEYWORDS: optmzaton method; producton loggng; reservor parameters

2 Vol. 21 [2016], Bund INTRODUCTION In developed felds, realstc estmates of ol recovery and optmzed reservor management requre good estmates of the reservor parameters. A conventonal well testng s the man tool for montorng well productvty (permeablty and skn) and reservor pressure by conductng a pressure buldup test wth shuttng-n producng well. However, operators are reluctant to perform such a test as t nvolves shuttng-n ther producng well. Another lmtaton of a conventonal well testng s n ts applcaton to commngled reservors where t only provdes a total permeablty-thckness and an average skn value. Usually, permeablty s dstrbuted between dfferent layers based on small-scale permeablty measurements (manly from cores) [1]. In ths case, such a dstrbuton can result n erroneous reservor characterzaton. Durng the development of olfeld, producton loggng provdes a lot of producton performance data whch can help deepen our understandng of the formaton characterstcs and dynamc performance. It can smultaneously detect flowrate, flowng pressure, flud densty and temperature whch reflect developng reservor dynamc performance. It s sgnfcant to estmate dynamc performance wth all producton data lsted above [2]. Actually, producton loggng data s response to producton dynamc of well after steady state flow condtons have prevaled. It does not only reflects drectly the producton status of well, but also reflects the character of producton layers and ts change [3]. As the producton loggng data s obtaned when flud s flowng n the wellbore n order to determne the dynamc parameters of formaton wth the producton loggng data, t must fnd out the response relatonshp between the producton loggng data and the flud flow performance n the reservor, that s to establsh the relatonshp between flud flow n porous meda and the flud flow n the wellbore. In the process of olfeld producton, producton loggng can run many tmes whch does not requre shuttng down the producton n order to obtan producton dynamc nformaton (flowrate, flowng pressure, flud densty, temperature, etc.). The flow profle derved from nterpretaton result of producton loggng test can help acqure flood effcency of each njecton layer and producton status of each producton layer [2]. It s known that the flood effcency of every njecton layer and the productvty of every producton layer are closely related to permeablty of formaton, the dstrbuton of subterranean remanng ol and saturaton [4]. Therefore, the flowrate and flow pressure of each layer provde datum for the purpose of obtanng well and reservor dynamc parameter. Based on producton loggng nformaton and combned wth the steady soluton n the pressure equatons of porous meda and optmzaton mathematcs, ths paper ntroduces a new well testng method named Multple Flowrate well testng wth Producton Loggng (MFPL), by whch the sublayer permeablty, reservor pressure and skn factor of multlayer reservor can be determned n ol/water two-phase and sngle-phase strata wth the zonal producton rate and pressure nformaton extracted from producton loggng. Ths method can provde the dynamc parameters of reservor by mprovng tongung of njecton water and adjustng development project. THEORY AND BACKGROUND A feld may be bured wth one or more reservors. Each reservor conssts of several nterconnected ol-bearng formatons, and therefore t can be seen as an ndependent underground ol storage contaner where effectve reservor porostes are bascally connected wth each other and ol, gas, water can stay or flow.

3 Vol. 21 [2016], Bund When a few njecton and producton wells located n the same reservor workng at the same tme, dynamc analyss of flud flow becomes more complcated because of the nfluence of output and pressure related to connectvty of nternal reservor. The ablty of reservor to provde flud to the wells depends largely on the hydrocarbon reservor type and drvng mechansm such as reservor pressure, permeablty and other varables. As soon as the profle derved from nterpretaton of the results from producton loggng testng s acqured, reservor estmaton can turn from qualtatve way to the quanttatve one. Under these crcumstances, Darcy's law for the radal flow of sngle phase ol can be expressed as[5] Qµ re Pe Pwf = ln 2πKh r (1) w when r = rw then P = Pwf when r = re then P = Pe where K s the permeablty, μ s vscosty, r s the dstance from boundary to wellbore, P s reservor pressure, P wf s the bottom hole flowng pressure, r w s the radus of wellbore, r e s the dranage radus, r s the dstance from boundary to wellbore, P s reservor pressure, and P e s the boundary pressure. When a well s beng drlled t s always necessary to have a postve pressure dfferental actng from the wellbore nto the formaton to prevent nflow of the reservor fluds. Because of ths, some of the drllng mud wll flow nto the formaton and the partcles suspended n the mud can partally plug the pore spaces, reducng the permeablty, and creatng a damaged zone n the vcnty of the wellbore. It mples that the pressure drop wll be larger than normal, or that P wf wll be reduced. Ths addtonal pressure drop close to the well has been descrbed by mechancal skn factor (S), whch s just a dmensonless number. Therefore t s more common to express the pressure drawdown n terms of P nstead of P e P wf, snce, the average pressure wthn the dranage volume, can readly r P wf Pr be determned from a well test. Combnng ths aspect and the mechancal skn factor, the modfed nflow equaton [5] s Qµ re 1 Pr Pwf = (ln + 2πKh r 2 (2) The above analyss shows that when reservor flud s sngle or ol-water bphasc flow, a well drlled through each ndvdual zone of commngled reservors and adjacent sub-layers are separated by non-permeable zone wthout water crossflow or vertcal flow, therefore, the reservor pressure, permeablty, thckness, skn factor and mass producton of each layer satsfes the nflow equaton. MFPL METHOD MFPL s a record of one or more n-stu measurements that descrbe the nature and behavor of fluds n or around the borehole durng producton or njecton n dfferent steady condtons by modulatng the surface flow rate. Ths test mposes varatons of flowrate by changng the choke sze or rod stroke, and the operators perform such a test under stablzed flowng condtons. Lqud output and pressure of each ndvdual layer of commngled reservors can be derved from nterpretaton of the results from producton loggng testng n the stable producton stage wth multple flow rate tests [6]. MFPL s conducted n the producton well n whch the typcal lthology, permeablty and pressure are dstrbuted. It must be conducted three tmes or more wth ndvdual flowrate pattern. w S)

4 Vol. 21 [2016], Bund The stablzaton tme requred for the flowng passes sometmes s a problem [7]. If the surface flow rate of the test well was modulated, the transent and flow perod whch lasted for perod of tme was then followed by a producton log survey at the stablzed flow rate. For each work pattern of producton well, the maxmum stable tme smlar to reachng nfnte actng radal flow perod of the pressure buldup test can be estmated, as [5] 2 Φµ Ctre max tm = (3) 14.4Kmax where t m s maxmum stable tme(s), Φ s average porosty of reservors, µ s average vscosty of reservors (mpa s), C s effectve compressblty rock (MPa -1 t ), r emax s maxmum dranage radus of 2 reservors (m) and K max s permeablty cutoff of reservors ( µm ). INTERPRETATION METHOD TO DETERMINE PARAMETERS OF FORMATION (IMDPF) Instead of attemptng to drectly compute formaton parameters from well nflow equaton under steady state usng producton loggng data, IMDPF uses an nverse soluton scheme. Frst, pressure and flowrate estmate are made for each of the producton loggng test. Then, the program works to solve a mnmzaton objectve functon that consst of well nflow equaton and nterpretaton results of the producton loggng testng. The purpose of MFPL s to analyze delverablty and evaluate the parameter varable trend of reservors and the effect on producton well. In ths case, the ndvdual lqud output and pressure of each layer of commngled reservors s derved from nterpretaton of the results from producton loggng testng wth the pseudo steady-state delverablty equaton as ther basc theory. The soluton s that: Frstly, based on producton loggng nformaton and combned wth the Darcy s law, ol reservors take the producton formaton dynamc parameters (permeablty, skn factor, and reservor pressure) as ndependent varables X (Pe,K,S) to establsh response pressure equatons of well flud. Secondly, buld the object functon whch combnes theoretcal value of pressure and measured value of pressure accordng to the prncple of nonlnear least square method and error theory. Then, constantly adjust unknown varables X (Pe,K,S) by the optmzaton method for the purpose of approxmatng theoretcal value of pressure to measure the value of pressure n each workng system. Once they approxmate perfecton, as the objectve functon value reached the mnmum, the ndependent varables X (Pe,K,S) used to calculate theoretcal value of pressure are the producton formaton dynamc parameters, that are also optmzaton nterpretaton result X*. Fgure 1 gves an overvew of how IMDPF works.

5 Vol. 21 [2016], Bund Producton loggng datum tested n dfferent flow regme Interpretaton result of njecton profle loggng data Lqud output and pressure of each ndvdual producton zone Interpretaton result of output profle loggng data The optmzaton objectve functon constantly adjust unknown varables X No Whether or not approxmate Yes Output the result of optmzaton Fgure 1: Flow chart of IMDPF Accordng to equaton (9), flud pressure n well derved from producton loggng s consdered as response values (=1, 2 N), where N s measurement numbers. Combned wth theoretcal value of pressure whch derved from the response pressure equatons of well flud ncludng tentatve permeablty, skn factor, and reservor pressure, a mnmzaton objectve functon s bult, as N 2 [ M T ( X )] mn F( X, M ) = mn 2 2 = 1 s + t s.t. g j ( X ) 0 ( j = 1,2,, m) h ( X ) = 0 ( k = 1,2,, q) k (4) where σ s measure error; τ s the error of nonlnear response equaton; F(X, M) s objectve functon of optmzaton nterpretaton; T (X) s approxmatng theoretcal log values of pressure; g j (x) s nequalty constrants for varables X and h k (x) s equalty constrants for varables X. In the course of solvng objectve functon wth the optmzaton method, we must study constrants for varables X, and approxmate the theoretcal log values T (X) to the practcal measured values for the purpose of obtanng reasonable nterpretaton results. For constraned problems, n addton to the exstence of local mnmum soluton, the man factors that affect optmal performance should also be ncluded. Usually, these predcaments can be solved by convertng constraned optmzaton problem nto sequence unconstraned optmzaton problem. In the case of Eq. 4, penalty functons were used as constrants, the optmal mathematcal model can be wrtten as mn F( X, M ) = mn N 2 m 2 [ M T ( X )] g j ( X ) = 1 σ + τ j= 1 τ (5)

6 Vol. 21 [2016], Bund JOINT INVERSION OF FORMATION DYNAMIC PARAMETERS BY AGA AND LEVENBERG-MARQUARDT (LM) ALGORITHM In order to enhance the results of the mnmzaton objectve functon above, Gauss Newton algorthm (G-N), Levenberg-Marquardt algorthm and adaptve genetc algorthm are compared below. The numercal methods for solvng the nonlnear least squares problem are manly Gauss Newton algorthm (G-N), modfed Gauss Newton algorthm and Levenberg-Marquardt algo-rthm (L-M). L- M algorthm s an teratve computng method for objectve functon dfferental calculus, whch become normal method for solvng systems of nonlnear least square problems and was regarded as the combnaton of a gradent descent method and the G-N method [8]. When the teratve answer keeps away from the genune soluton, L-M algorthm s close to the gradent descent method. When the teratve answer s close to the genune soluton, L-M algorthm s close to the Gauss Newton algorthm. In addton, f the objectve functon s strongly nonlnear system, the answer s local soluton; so, L-M algorthm s local search optmzaton method, whose retreval result s affected by ntal models and senstve to the ntal estmate value. In order to mprove the nverson accuracy, n ths paper a hybrd method based on adaptve genetc algorthm (AGA) and Levenberg-Marquardt algorthm (L-M), whch are used prmarly for obtanng formaton parameters, s presented. In such case, the adaptve genetc algorthm s more effcent n fndng global optmal soluton and Levenberg-Marquardt algorthm s the powerful localoptmzaton algorthm. We adopted the combnaton of adaptve genetc algorthm and Levenberg- Marquardt algorthm to the nverson of formaton parameters. Usng varable global results obtaned by the nverson wth AGA as ntal parameters, we agan carry out addtonal local search based on the L-M algorthm for approachng to the optmal soluton. Fgure 2 gves an overvew of how t works.

7 Vol. 21 [2016], Bund Start Practcal problems parameter set (Input practcal measured values, doman of parameters, populaton scale and the number of teraton k max ) Intalzaton,generate the ntal populaton Code genes of chromosome Calculate ftness of populaton (k+1)-th generaton k-th Selecton Crossover Mutaton (k+1)-th generaton populaton No Convergence crteron? Yes Swtch to L-M algorthm Dsadvantage Qualty control Advantag Output the result of optmzaton nterpretaton Fgure 2: Flow chart of Jont nverson of formaton dynamc parameters by AGA and Levenberg-Marquardt (LM) algorthm A survey of 3-9 well feld applcaton and example An MFPL test was conducted on a pumpng well n block SHENG 3 n whch fve producton zones s commnglng, producng nterval s from m. In order to conduct MFPL, three rod strokes was modulated by changng band wheel, workng rod strokes are three cycles per mnute, two cycles per mnute even to one cycle per mnute. In the process of steady producton under each workng system, producton stack loggng tool s used to run n hole for the purpose of obtanng the ndvdual output, water holdup, temperature and pressure of each layer. The profle derved from nterpretaton of the result n producton loggng tests are shown n the fgure 3 and table 1. End

8 Vol. 21 [2016], Bund (one cycle per mnute) (two cycles per mnute) (three cycles per mnute) Fgure 3: T Interpretaton chart of 3-9 well Layer full zone Thckness (m) 3 S1 2.1 S2 2.5 S3 1 S4 2 S5 5.6 Table 1: Interpretaton results of 3-9well rod Ol stroke Output Water (cycle (m 3 output /d) cut(%) (m 3 /d) / m) Water output (m 3 /d) Pressure (MPa) \ 0 0 \ 2 0 \ 0 0 \ 1 0 \ 0 0 \ 3 0 \ 0 0 \ 2 0 \ 0 0 \ 1 0 \ 0 0 \ \ 0 0 \ 2 0 \ 0 0 \ 1 0 \ 0 0 \

9 Vol. 21 [2016], Bund Optmzaton of calculaton results The ndvdual output and pressure of each producton zone tested n dfferent flow regme have been used as response values. Combnng Eq. 2 and Eq. 5 wth these response values ncluded, the mnmzaton objectve functon s bult. Informaton derved from MFPL of 3-9 well have been used to calculate formaton dynamcs parameter of each producton zone by the jont nverson method of AGA and L-M algorthm. The average parameters for the set of producng layers (S3 and S4) are calculated and compared to the parameters obtaned for the entre zone, as ndcated n Table 2. The weghted average permeablty, for example, s estmated regardng the layer thcknesses usng the formula for the parallel or seres layers. Layer Thckness (m) Table 2: Interpretaton result formaton parameters of 3-9 well Productvt y ndex measured Calculated Permea- Error (m3/d/ pressure pressure blty (%) MPa) (MPa) (MPa) (md) Reservor pressure (MPa) Skn factor for reservor Full zone 3 S3 1 S Analyss of the Results The tradtonal testng method can only deal wth all the mddle layers as a producton layer dervng mean value of formaton parameters. Therefore, t cannot be more ratonally evaluate the ndvdual formaton propertes of each layer. The results of the flow profle and IMDPF show that, there are fve perforated ntervals n the whole well nterval, but only two perforated ntervals gave output. S1, S2 and S5 zone are not producng. When the workng rod stroke was modulated from three cycles per mnute to two cycles per mnute even to one cycle per mnute, the total lqud producton rate and the lqud producton rate of S3 zone and S4 zone are reduced accordngly. Reservor pressure of ndvdual layer s also ncreased correspondngly and the results are consstent wth the theory. Reservor pressure of the thrd layer s MPa. Ths layer s prorty pay zone and water cut s more than 95%, the maxmum rate, whch resulted from tongung of njecton water. Whle productvty ndex and permeablty of the fourth layer s the mnmum, ths shows that ts producton capacty s poor.

10 Vol. 21 [2016], Bund The calculated pressure data match well wth test data for synthetc as well as feld examples of multlayer transent tests, so t s proved that the calculaton results are correct. CONCLUSIONS A new well testng method called MFPL and an nterpretaton method to determne parameters of formaton have been ntroduced and developed. Based upon the results of ths research, the followng conclusons are drawn: (1)A new approach and workflow for the nterpretaton of multlayer tests has been developed whch uses a mathematcs optmzaton technque. The jont nverson method of AGA and L-M algorthm has been successfully appled to modfy model parameters to match smulaton model pressure data wth test data. The scheme and ts assocated algorthms have been fully descrbed and ts successful applcaton has been llustrated wth feld examples. (2) The multrate producton log can be used to characterze many of the formaton and well completon propertes n a multlayer commngled system usng transent producton output of well measurements. Ths technque provdes formaton dynamc parameters for each layer whch cannot be obtaned from a conventonal pressure buldup analyss. It does not requre shuttng n of the well whch mght damage the near wellbore by asphaltne deposts or by water crossflow or brng a well back on producton. (3) Ths method makes full use of producton loggng datum, pressure data whch has normally used n a qualtatve way and to compute the n-stu flow propertes and locate zones of flud entry nto a well has gotten mportant applcatons, and so, ths technque s a further use of the producton loggng data. In addton, t can reduce the use of standard pressure buldup testng and ncrease the well producton. (4) Ths method manly studes on ol and water lnear radal flow equaton not for the well producng gas. ACKNOWLEDGEMENTS The research s supported by Educatonal Commsson of Hube Provnce of Chna (D ) and Natonal Natural Scence Foundaton of Chna( ). REFERENCES 1. Da Ja-ca. Method Research of Determnng Producton Layer Parameters by Producton Loggng Data of Olfeld [D]. Bejng: Chna Unversty of Geoscences, Ba Jan-png, Tan Zhong-yuan. Estmaton of Dynamc Permeablty from Data of Well Test and Producton Well Logs [J]. Well Testng, 2007, 16(1):1~3. 3. Guo Ha-mn. Introducton of Producton Loggng [M]. Bejng: Petroleum Industry Press, 2003: 21~ Geng Quan-x, Zhong Xng-shu. Producton Loggng Technology of Olfeld [M]. Shandong: Chna Unversty of Petroleum Press, 1992: 302~309.

11 Vol. 21 [2016], Bund L.P. Dake: fundamentals of reservor engneerng, Elsever Scence B.V. Netherlands 1998, Chap.6, Zhao Zhong-jan, He Zh-xang, L Zh-png. New test methods for Parameters of Indvdual pay zones n a Mult-zone Reservor: Research and Practce [J]. Journal of Geomechancs, 2006,12(1) :71~ J. Rochon, V. Jaffrezc, J. L. Boutaud de La Combe, M. Azar, S. Roy, D. Dorffer, A. Webb and J. Snger: Method and Applcaton of Cyclc Well Testng wth Producton Loggng, paper SPE presented at the 2008 SPE Annual Techncal Conference and Exhbton held n Denver, Colorado, USA, September We You-hua, Guo Ke, Chen Lng, et al. The applcaton of data fuson n the research of physc parameters of complcated ol-gas reservor[j]. Progress In Geophyscs, 2008,23(1) :153~ ejge Edtor s note. Ths paper may be referred to, n other artcles, as: Song Hong-we and Yang Guo-feng: Multple Flow Rate Well Testng wth Producton Loggng n Determnng Producton Formaton Dynamcs Parameter Electronc Journal of Geotechncal Engneerng, 2016 (21.23), pp Avalable at ejge.com.