Analysis of production-decline data: Case of geothermal wells as renewable energy

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1 IOSR Journal of Engneerng (IOSRJEN) ISSN (e): , ISSN (p): Vol. 6, Issue 1 (Oct. 216), V3 PP Analyss of producton-declne data: Case of geothermal wells as renewable energy Alfonso Aragón-Agular 1, Rosa M. Barragán 1, Víctor Arellano 1, 1 (Insttuto Naconal de Electrcdad y Energía Lmpas, Reforma 113, Col. Palmra, Cuernavaca, Morelos, Méxco, CP 6249) Abstract: - Geothermal reservors could recover ther condtons after a shut-down perod by ths reason are consdered as renewable energy. In order to optmze the avalablty of ths source, a sustanable explotaton strategy should always be desgned. In contrast wth ol systems whch are practcally solated, geothermal reservors are open systems n whch the flow of recharge due to the pressure drops s possble. Due to depth of geothermal reservors ndrect methods based on montorng data of wells are used to study ther evoluton. In ths work, models wdely used for the analyss of producton declne data n ol wells have been adapted n order to nclude the analyss of geothermal wells. From them, mportant reservor nformaton needed to desgn optmal explotaton strateges s obtaned. The analyss of producton declne n wells s based ether on analytcal methods or on type curves fttng approaches. Wth the declne results of wells and consderng ther economc lmt of producton, the remanng useful lfe and the feasble reserves to be extracted from the source, can also be estmated. In ths work the analyss of producton declne methodology of wells s gven and llustratve examples are dscussed, hghlghtng the renewablty of geothermal systems respect to ol reservors. Keywords: - Producton declne analyss, Producton characterzaton, Economc producton lmt, Renewablty, Recharge entrance. I. INTRODUCTION Geothermal energy has been classfed as a renewable source n the long term snce reservors would fully recover to ther pre-explotaton state after an extended shut-down perod [1]. Besdes, electrcty generaton from geothermal resources reduces damage to the envronment avodng fuels burnng and potental rsks of ther transportaton and storage. Generally, s accepted as beng an envronmentally bengn energy source. Currently, there are 24 countres n the world generatng electrcty from geothermal resources, wth a total nstalled capacty of 1898 MW [2]. In ths work we deal wth both ol and geothermal reservors, whch are natural resources classfed as non-renewable and renewable sources, respectvely. Non-renewable energes cannot be replenshed n a short perod tme. The potental energy to be recovered from these two types of reservors s defned through ther producton capacty. The wells productvty tends to declne dependng on the explotaton tme and reservor propertes and the effcency of wells s measured through ther productvty ndex. The typcal declne of wells s characterzed as a decreasng trend of producton over tme untl a non-sustanable lmt of producton s approached. The producton declne of a well s a functon of both: the petro-physcal propertes of the reservor, the explotaton rate and the recharge water entrance. For ths reason, t s mportant to characterze the wells snce the begnnng and through ther explotaton perod. Assumng that every well, represents a punctual secton of the reservor, the consderaton of varous wells nto the analyss allows the characterzaton of one secton of the reservor. In order to dentfy the productvty declne of wells, the behavor of producton parameters should be nvestgated. In ol wells the varables used to evaluate ther performance are: pressure, flow rates, ol/gas rato, vscosty, densty, etc. In geothermal wells the varables: pressure, flow rates, enthalpy, and water/steam rato, among others are consdered. Durng the commercal explotaton stage, most of the producton wells are ncorporated to the operatve systems, beng dffcult to shut them off, n order to evaluate them. For ths reason, the montorng data consstng of routne measurements n wells taken at the wellhead, are used to study ther performance. Ths technue s sutable snce when the wells operate contnuously they eventually reach a pseudo-steady state. The wells behavor s related wth the effects of explotaton on the reservor. The techncal consderatons that support as representatve of the reservor are: 1) The mass extracted at reservor condtons s the same than that n the surface the only dfference s the steam fracton of fluds; 2) The reservor pressure (p e ) whch s used to obtan formaton propertes could be estmated through well smulaton programs. By correlatng the productvty declne of wells to explotaton, t s possble to forecast wells performance. If n addton, the economc constrants for every well are ncluded n the study, then the useful 32 P a g e

2 Analyss of producton-declne data: Case of geothermal wells as renewable energy tme-lfe, the total producton capacty and the remanng reserve of wells can be obtaned. Thus the results of declne studes can sustan explotaton strateges for every well whle the generalzaton to the whole reservor wll support ts development projects. Intally the methodology was desgned to be appled n ol ndustry, then the purpose of ths work s to show that the methodology s also sutable and hence can be extended to study aspects related to the renewablty of geothermal systems. One of the challenges to be faced when dealng wth geothermal systems s to estmate how they behave regardng flud extracton wth respect to the recharge. In other words, the mass balance at reservor, whch conssts n estmatng by one hand the output of the system n terms of produced mass flow rates and by the other hand, the recharge nputs, both of them should nearly eulbrate to avod overexplotaton n the case that the mass extracted s hgher than the nput consttuted by the recharge. When such condton s acheved the system under explotaton becomes a renewable system. The nnovatve contrbutons gven n ths work to the energy resources knowledge are as follows: It s demonstrated that the declne analyss methodology s sutable and can be used n both, ol and geothermal producton wells and reservors. The methodology analyss can help studes on the renewablty of geothermal system. The results of the declne trend allow estmate the reserve whch can be recovered up to acheve the lmt of useful lfe. It s emphaszed n the mportance to know the recharge water entrance n order to determne the approprate explotaton rate for mantan a balance between both. The objectves of ths work are: a) to use the producton declne methodology n wells that have overcome transent effects and, b) to characterze the reservor through estmatng the useful lfe, the total mass wth possblty to be extracted and the remanng reserves. II. BACKGROUND The analyss of declne curves through the use of mathematcal expressons was ntroduced by [3] and up to now, t s used wdely wth vast success. In the analyss [3] establshed the followng types of producton declne: Exponental, hyperbolc and harmonc. [4, 5] extended the use of type curves to the analyss of producton data by combnng n a theoretcal way, the response of a well n a closed reservor wth the classc technue of declne curves. The flow normalzaton technue to the declne analyss of wells based on producton measurements was ntroduced by [6]. Modern methods for the producton declne analyss [7, 8] show the combned use of type curves and the declne analyss concepts. The man dfference between ntals and some actual methods s that these latter take nto account the well bottom pressure together wth the producton mass flow rates. A complete producton analyss technue to be used n mature felds was proposed by [9], whle results of declne analyss focused on reservor characterzaton were presented by [1]. The technues of producton data analyss to predct the behavor of gas wells were developed by [11]. Dfferent methodologes to analyze declne n geothermal reservors were dscussed by [12]. III. THEORETICAL CONCEPTS The methods more wdely used to nvestgate the natural response of reservors to explotaton are based on producton data of wells through declne analyss. The typcal declne of wells s dentfed as a sharp decreasng trend n producton untl a non-sustanable lmt s approached. When such condton s reached the wells are classfed as margnal. Every well represents a porton of a larger area whch corresponds to the reservor. Dependng on the ndvdual behavor of each one of the wells, the producton-declne correlaton represents the general tendency of the reservor. The euatons to obtan the ntal mass flow rate and the declne rate D were proposed by [3]: k h ( p p ) r e B ln.5 o o r wa w f (1) D 2 ( ) k r 2 2 e C ( r r ) ln.5 o t e w a r wa where s the ntal flow rate, k s he permeablty of the formaton, h s the useful producton thckness, p s the ntal pressure, p wf s the well bottom flowng pressure, o s the flud vscosty, B o s the ( 2 ) 33 P a g e

3 Analyss of producton-declne data: Case of geothermal wells as renewable energy volume factor of the flud, r e s the reservor dranage radus and r wa s the apparent rad of the well. The classc expresson for declne analyss proposed by [3, 13, 14] s: e D where s the flow rate, D s the declne constant and t s tme. By changng varables (D = b) n (3), t stands that for b = the declne s exponental type, for b = 1 declne s harmonc type beng these the lmts of the type curves. For the cases where < b < 1 the declne s hyperbolc type. In order to estmate the accumulated producton of the wells the followng euaton proposed by [14] s used: N p lo g lo g ( 4 ) D It s possble to represent (4) by a straght lne n logarthmc scale by plottng the accumulated mass flow rate produced n the log scale. Due to that transton snce steady-state to pseudo steady state s practcally mmedate; a natural extenson of the declne type curves s combnng these declnatons n one graph. The declne durng transent perods depends manly on the near-well formaton characterstcs. Thus t s mportant to notce that the apparent radus of the well (r wa ) s used to obtan the formaton propertes. In addton, the declne type curves are sutable for wells wth ether postve or negatve damage factor. The expressons for the non-dmensonal parameters whch are used n the declne analyss wth type curves are: For non-dmensonal mass flow: Dd ( t) For non-dmensonal tme: t D t ( 6 ) D d The euatons to obtan the reservor propertes from non-dmensonal mass flow and tme are as follows. By usng the dmensonless mass flow ( D ), the permeablty (k) can be obtaned: D B o o o kh( p p ) w f And by usng the dmensonless tme, the porosty () s obtaned: t D kt 2 cr t w a The frst analyss methods usng type curves appled to reservors were those, for transent pressure test [15, 16]. By usng the same analogy, the superposton method [17] follows a smlar procedure than that of the (log-log) type curves fttng, used to analyze pressure data for constant mass flow rate. It s advsable to make a general dagnoss of the behavor of the producton hstory prevous to perform the analyss. It s possble to ft data to an euaton for extrapolatng behavor to the future and make predctons on the producton of the well for example to 1, 2, 5, 1 or more years.. By plottng the flow rate vs tme, t s seen that the flow rate declnes as the explotaton tme ncreases. The varatons of both producton and pressures of the wells depend on the orfce dameter. In addton, when the producton data of a well are plotted vs the cumulatve producton of extracted mass (Np) t s observed that the part of the curve that declnes becomes to a straght lne. From ths lne, extrapolatons to estmate future behavors can be made, so t s possble to dentfy two stages of declnng evoluton: The transent (n the ntal stage of explotaton) and the pseudo stable trends of declne. IV. PRACTICAL CASES In order to llustrate the applcaton of the declnng analyss theory, some cases are presented usng data of ol and geothermal wells. IV.1. Ol well An ol well produces n a low-permeablty zone of a reservor wth a bottom hole flowng pressure of 8 psa (55.16 E 5 Pa). Fg. 1 shows the mass flow rate declnng of the well. By usng the well data and results of a transent pressure test, the followng determnatons are gven: 1) The declne model of the producton n the well, by extrapolatng to the pont n whch the flow reaches 1 b/d (1.592 m 3 /d) as the crtc lmt. 2) Through the use of declne data o and D are calculated. Subseuently, by usng the declne rate shown n Fg. 1, s obtaned. ( 3 ) ( 5 ) (7 ) ( 8 ) 34 P a g e

4 (b/d) Analyss of producton-declne data: Case of geothermal wells as renewable energy 3) Comparson s made between calculated o and D of the step 2 and these obtaned through (1) and (2) by usng the results of the pressure tests. In order to obtan a complete characterzaton of the test, a mass flow vs tme graph (Fg. 1) s used as a base for a general dagnoss. After havng a general conceptual understandng of the test, the more convenent model of flow declnng s dentfed by usng two graphcal methods: 1) Log flow rate versus log tme and, 2) Log flow rate versus tme t (day) Fgure 1. Graph of behavor of the volumetrc flow vs tme n an ol well. By fttng data to a straght lne, the slope and the ntercepton to the orgn are obtaned. The orgn ntercept allows to be obtaned whle the declnng rate s gven by the slope D. The fttng of data provdes a straght lne defned by (3) from whch, and D are: = 675 b/d (17.46 m 3 /d) D = (b/d)/month [.254 (m 3 /d)/month] As no measurements of hstorcal producton are avalable, the parameters of (3) can also be determned from reservor data. Wth (1) and (2) and data from transent pressure tests and D are obtaned. By substtutng values n (1) and (2) both the ntal flow rate ( ) and the declne (D) can be calculated. o (1 2 1)( ) b m d d (.4 6 )1.3 6 ln D 2 ( ) ( 3 6 ) (.4 6 )(1. 9 (1 ))( ) ln D = (b/d)/month [.243 (m 3 /d)/month] As can be seen and D values calculated wth Arps euaton [3], compare farly well wth the values obtaned from euatons proposed by [13]. The mportant ssue s that ths methodology provdes crtera on the nterval of the parameters nvolved n the declne of the well. By usng the producton data, the economc lmt of producton (Fg. 2) and the cumulatve producton volume (Fg. 3) of the well are obtaned. From Fg. 2, t s also nferred that for the same declnng rate, the crtcal lmt for the flow (1 b/d) s beng attaned n approxmately 5 days. In order to have a more precse 35 P a g e

5 (b/d) Analyss of producton-declne data: Case of geothermal wells as renewable energy estmaton of ths tme perod, t s advsable to use the hstory of producton of the well and the analytcal method. Accordng ths approach, the extrapolated values are ftted to an euaton and rearrangng varables, the tme (t) s calculated as follows: t ( d a y s ) ( m o n th s ) t (days) Fgure 2. Log of the flow rate vs log of tme for the analyzed well [18] used for determnng the useful lfe of the well at the economc lmt of producton. The estmated cumulatve producton n the well was barrels (79544 m 3 ); whle assumng an economc lmt of producton for the well of 1 (b/d) [1.592 (m 3 /d)], the maxmum producton volume can be extrapolated from the graph n Fg. 3. Thus, for ths case results slghtly above 525 barrels (8358 m 3 ) are seen, whch could be assumed as the total reserve of the well. Therefore, the well has declned approxmately 95.2 % n 2 88 days. The maxmum recoverable producton whch s also related to total reserve can be estmated by usng the cumulatve produced volume together wth the volumetrc flow of the well. Ths graph can be used for estmatng the reserve whch could be extracted before the well reaches the economc lmt of the producton. Fg. 4 shows the superposton of the producton values, flow and tme n a log-log scale, on the type curve [3]. In order to dentfy whch of the type curves better fts the measured data both graphs should have the same scale. IV.2. Geothermal well In order to llustrate the use of the declne analyss technues n geothermal wells, the producton data of a Mexcan geothermal well s gven n Fg. 5 [19]. In ths fgure the producton hstory of the well over 34 months s shown along wth the wellhead pressure and the dscharge orfce dameter over tme. Fg. 5 s useful to make a general dagnostc of the data and ther possble use for declne analyss; t s seen that between months 16 and 2 the well s shut n, whch causes an abrupt ncrease n wellhead pressure even reachng that measured at statc condtons. However, when the well s reopened usng an orfce dameter smlar to that has operated before be shut off, t was found that the mass flow rate s slghtly hgher (about 5%) than that recorded prevously. Ths evdences that the shuttng caused a small recovery of the well, although t mantaned ts declne tendency, after reopenng. 36 P a g e

6 (b/d) (b/d) Analyss of producton-declne data: Case of geothermal wells as renewable energy 1 1.E+ 2.E+5 4.E+5 6.E+5 Np (b) Fgure 3. Log of volumetrc flow () vs cumulatve produced volume of the well (Np) t (days) Fgure 4. Comparson and fttng the producton data wth the declnng type curve. Fg. 6 shows the producton data vs tme of the well. One of the nterestng uses of ths graph s to estmate the tme wll take for the well to reach ts economc producton lmt by consderng the declne tendency. The economc producton lmt for geothermal wells s taken as 1 (t/h) and 7 bar (7E 5 Pa) of pressure, such condtons are consdered to be enough to generate at least 1 MW of electrcty. Thus, accordng to ths nformaton and by extrapolatng n Fg. 6 t s seen that ths tme approxmately s 495 months. 37 P a g e

7 W (t/h) W (t/h) P wh (bar) Analyss of producton-declne data: Case of geothermal wells as renewable energy W (t/h) P wh (bar) Orf dam (n) t (month) Fgure 5. Graph of mass producton, wellhead pressure and dameter of the dscharge orfce vs tme, taken from [19] Economc lmt t (month) Fgure 6. Graph of mass flow rate vs tme, used to determne the economc lmt of the well. 38 P a g e

8 Analyss of producton-declne data: Case of geothermal wells as renewable energy By fttng the declne data for the last secton (from the month 21) of the plot n Fg. 6, the followng expresson was obtaned: W = (t) From ths extrapolaton, the calculated tme for W = 1 (t/h) s 492 months. The ntal volumetrc flow ( ) and the ntal declne (D ) are estmated by substtutng the obtaned values n (5) and (6): 4 t = = h t.7 9 t h and D = = h m o n th Smlar graph to that of Fg.3 (W vs Np) s used for determnng the remanng reserve. The ft of the last part of declne data provdes n terms of Np and W the followng expresson: -6 W = E (N ) p For determnng the Np value as W functon the expresson s: N p = W E Usng W=1 n the last euaton, N p = E 6 (t). Ths represents the total reserve of the well. As a summary, the results obtaned from the analyss developed, provde support for desgnng explotaton strateges of the wells and makng predctons on ther future behavor. The varables obtaned from the analyss allow an understandng of the well performance and ts productvty whle results from every well can be nterpreted together to understand the reservor behavor. Table 1 gves a summary of the results and ther mpact on feld explotaton strateges. V. CONCLUSION The producton declne analyss consttutes a useful tool to characterze both ol and geothermal reservors. Although the methodology of analyss declne was developed for ol systems, n ths work s shown that also can be used for geothermal systems. The analyzed geothermal well recovered ts condton to ts preexplotaton state after a shut-down perod, ths behavor sustans the scenaro that geothermal energy to be a renewable resource. The adeuate combnaton of mass flow, accumulated producton and the tme are a techncal support for extrapolatng the wells behavor, determne ther economc useful lfe, the remanng reserves of the resource and projects development for feld expanson. By establshng the producton economc lmts of wells, and of the reservor, t s possble to predct ts useful lfe. Table 1. Summary of data obtaned from the producton declne analyses whch are useful to ndvdual characterzaton of wells. Intal flow rate D Declne rate Total reserve Useful lfe Remanng reserve Ol well (brl/d) (m 3 /d) (b/d)/month (m 3 /d)/month (b) (m 3 ) (month) (b) (m 3 ) Geothermal W (t/h) (t/h)/month 1 6 (t) (month) 1 6 (t) well Where s the volumetrc flow and W the mass flow, both of them for the tme t =, D s the ntal declne rate. VI. ACKNOWLEDGEMENTS Ths work was developed under support of the project IIE/14454 Técncas y métodos de análss, al estado del arte de declnacón de la produccón en sstemas geotérmcos mexcanos y sus efectos predctvos, The authors express ther grattude by the support to authortes of INEEL (Insttuto Naconal de Electrcdad y Energías Lmpas-Méxco). REFERENCES [1] M O Sullvan, M. Yeh, and W. Mannngton, Renewablty of geothermal resources, Geothermcs, 39(4), 21, [2] R Bertan, Geothermal power generaton n the world update report, Geothermcs, 41, 212, [3] J. J. Arps, Analyss of declne curves, Transactons of the Amercan Insttute of Mnnng, Metallurgcal and Petroleum Engneers, 16, 1945, P a g e

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