Historical Rate-Time Analysis Methods

Transcription

1 Petroleum Engneerng 648 Pressure Transent Testng Lecture 18 Hstorcal Rate Tme-Rate Relatons for Ol and Gas Flow Hstorcal Rate-Tme Analyss Methods Tom BLASINGAME Texas A&M U. Slde 1

2 Petroleum Engneerng 648 Pressure Transent Testng Lecture 18 Hstorcal Rate Tme-Rate Relatons for Ol and Gas Flow Hstorcal Rate Tme-Rate Relatons for Ol and Gas Flow Orentaton Hstorcal Persectves Ars relatons (exonental, hyerbolc, and harmonc). Dervaton of Ars' exonental declne relaton. Valdaton of Ars' hyerbolc declne relaton. Secalzed Gas Flow Relatons: Fetkovch Gas Flow Relaton. Ansah-Buba-Knowles Gas Flow Relatons. Secalzed Ol Flow Relatons: Fetkovch Ol Flow Relaton. Inflow Performance Relatons (IPR): Early work (for ratonale). Ol IPR and Soluton-Gas Drve IPR. Gas Condensate IPR. Tom BLASINGAME Texas A&M U. Slde

3 Petroleum Engneerng 648 Pressure Transent Testng Gas Producton Rate, MSCFD Gas Producton Rate, MSCFD E+04 1.E+03 1.E+0 1.E+01 Lecture 18 Hstorcal Rate Tme-Rate Relatons for Ol and Gas Flow Orentaton Mosac of Ars' Plots (Barnett Shale (TX)) a. Semlog "Rate-Tme" Plot: Barnett Gas Feld. 0 Sewell Ranch Well No. 1 Barnett Feld (NorthTexas) Gas Flowrate Exonental Rate Model Hyerbolc Rate Model Wellbore Pressure 1.E Producng Tme, days Sewell Ranch Well No. 1 Barnett Feld (NorthTexas) Cumulatve Gas Producton Exonental Model Hyerbolc Model 0 50, , ,000 1,000,000 1,50,000 1,500,000 Cumulatve Gas Producton, MSCF b. Cartesan "Rate-Cumulatve" Plot: Barnett Gas Feld (North Texas) Flowng Tubng Pressure, sg a. b. c. ex( Dt) 1/ (1 bd t) D N ( N N (G-G), MSCF 1.E+07 1.E+06 1.E+05 1.E+04 b 1 b 1 1b ( N N 1b ) (1 b) D b ) (1 b) D 1b Sewell Ranch Well No. 1 Barnett Feld (NorthTexas) (G-G) Data Functon Exonental Model Hyerbolc Model Method s desgned for hyerbolc declne case 1.E+01 1.E+0 1.E+03 1.E+04 Gas Producton Rate, MSCFD (Exonental) (Hyerbolc) (Exonental) (Hyerbolc) (Hyerbolc) c. Log-Log "(G-G )-Rate" Plot: Barnett Gas Feld (North Texas). Tom BLASINGAME t-blasngame@tamu.edu Texas A&M U. Slde 3

4 Petroleum Engneerng 648 Pressure Transent Testng Lecture 18 Hstorcal Rate Tme-Rate Relatons for Ol and Gas Flow Orentaton Mosac of Ars' Plots (Barnett Shale (TX)) 1.E+04 Sewell Ranch Well No. 1 Barnett Feld (NorthTexas) 000 Gas Producton Rate, MSCFD 1.E+03 1.E+0 1.E+01 Gas Flowrate Exonental Rate Model Hyerbolc Rate Model Wellbore Pressure Flowng Tubng Pressure, sg (Exonental) ex( Dt) (Hyerbolc) (1bDt) 1/ b 00 1.E Producng Tme, days 0 Dscusson: Barnett Shale (TX/USA) Semlog "Rate-Tme" Plot: Barnett Gas Feld. Note data scatter and aarent ft of hyerbolc functon. Note behavor of ressure data (ressure ncrease due to curtalment). Tom BLASINGAME t-blasngame@tamu.edu Texas A&M U. Slde 4

5 Petroleum Engneerng 648 Pressure Transent Testng Lecture 18 Hstorcal Rate Tme-Rate Relatons for Ol and Gas Flow Orentaton Mosac of Ars' Plots (E.Tx Gas Well (TX)) Gas Producton Rate, MSCFD Gas Producton Rate, MSCFD a. Semlog "Rate-Tme" Plot: SPE 8487 East Texas Gas Well E+05 1.E+04 1.E+03 SPE 8487 East TX Gas Well 1 (Low Permeablty Gas) 1.E Producng Tme, days b. Cartesan "Rate-Cumulatve" Plot: SPE 8487 East Texas Gas Well 1. Tom BLASINGAME t-blasngame@tamu.edu Texas A&M U. Gas Flowrate Exonental Rate Model Hyerbolc Rate Model Wellbore Pressure SPE 8487 East TX Gas Well 1 (Low Permeablty Gas) Cumulatve Gas Producton Exonental Model Hyerbolc Model 0 50, , ,000 1,000,000 1,50,000 1,500,000 Cumulatve Gas Producton, MSCF Flowng Tubng Pressure, sg a. b. c. ex( Dt) 1/ (1 bd t) D N ( N N b 1 b 1 1b ( N N 1b ) (1 b) D (G-G), MSCF b ) (1 b) D 1.E+07 1.E+06 1.E+05 1.E+04 1b SPE 8487 East TX Gas Well 1 (Low Permeablty Gas) 1.E+01 1.E+0 1.E+03 1.E+04 Gas Producton Rate, MSCFD (G-G) Data Functon Exonental Model Hyerbolc Model Method s desgned for hyerbolc declne case (Exonental) (Hyerbolc) (Exonental) (Hyerbolc) (Hyerbolc) c. Log-Log "(G-G )-Rate" Plot: SPE 8487 East Texas Gas Well 1. Slde 5

6 Petroleum Engneerng 648 Pressure Transent Testng Lecture 18 Hstorcal Rate Tme-Rate Relatons for Ol and Gas Flow Orentaton Mosac of Ars' Plots (E.Tx Gas Well (TX)) 1.E+05 SPE 8487 East TX Gas Well 1 (Low Permeablty Gas) 6000 Gas Producton Rate, MSCFD 1.E+04 1.E+03 1.E Producng Tme, days 5500 Gas Flowrate Exonental Rate Model 5000 Hyerbolc Rate Model ex( Dt) Wellbore Pressure Flowng Tubng Pressure, sg (Exonental) (Hyerbolc) (1bDt) 1/ b Dscusson: SPE 8478 Well 1 (East Texas (USA)) Combnaton "Rate-Tme" and "Pressure-Tme" lot. Note ressure buldu (used to check wth PTA). Note behavor of ressure data (ncludng major shut-n). Tom BLASINGAME t-blasngame@tamu.edu Texas A&M U. Slde 6

7 Petroleum Engneerng 648 Pressure Transent Testng Lecture 18 Hstorcal Rate Tme-Rate Relatons for Ol and Gas Flow Hyerbolc Declne Camacho and Raghavan "Proof" Camacho-V., R. G., & Raghavan, R. (1989, November 1). Boundary-Domnated Flow n Solutons-Gas-Drve Reservors. Socety of Petroleum Engneers. do:10.118/1856-pa (Detals of dervaton are omtted, see aer SPE 19009, Camacho and Raghavan (1989)). a. Hyerbolc flowrate relatons for the case of constant ressure roducton from a soluton gas drve reservor (Camacho and Raghavan (1989)). b. Hyerbolc declne tye curve wth data smulaton erformance data suermosed (Camacho and Raghavan (1989)). Dscusson: Ars' Hyerbolc Tme-Rate Relaton Assumes declne arameter based on average moblty/comressblty. Assumes hyerbolc arameter = f[d/dt(average moblty/comressblty)]. Data shows that erformance s not erfectly "hyerbolc." Tom BLASINGAME t-blasngame@tamu.edu Texas A&M U. Slde 7

8 Petroleum Engneerng 648 Pressure Transent Testng Lecture 18 Hstorcal Rate Tme-Rate Relatons for Ol and Gas Flow Gas Relatons Fetkovch Tme-Rate Gas Relaton Gas Materal Balance Relaton: (z=1! (deal gas?)) G G ( z z 1) Gas Pseudosteady-State Flow Relaton: g C g ( ) Fnal Result: (Poor Aroxmaton) n g g 1 (n 1 g 1) G n n 1 t ( 0) Tom BLASINGAME t-blasngame@tamu.edu Texas A&M U. Slde 8

9 Petroleum Engneerng 648 Pressure Transent Testng Lecture 18 Hstorcal Rate Tme-Rate Relatons for Ol and Gas Flow Gas Relatons Fetkovch Tme-Rate Gas Relaton Dscusson: Fetkovch "Analytcal" Gas Declne Tye Curve ( = 0) Cheated (z=1)... ths s not a vald soluton (Fetkovch, 1973). Good ntentons... wanted to develo a "smle" gas soluton. Curve shaes "look" correct, but do not conform to gas well erformance. Tom BLASINGAME t-blasngame@tamu.edu Texas A&M U. Slde 9

10 Petroleum Engneerng 648 Pressure Transent Testng Lecture 18 Hstorcal Rate Tme-Rate Relatons for Ol and Gas Flow Gas Relatons Knowles Tme-Rate Gas Relaton "Knowles" rate-tme relaton for gas flow: Models declne of gas flowrate versus tme. Better reresentaton of rate-tme behavor than the "Ars" hyerbolc declne relatons. gdd 1 wd 1 ex( wdtdd ) g 1 wd wd 1 g (1 wd ) 1 wd 1 ex( wdtdd ) 1 wd t Dd 1 wd g / z / z / z / z G t Dscusson: Knowles Gas Tme-Rate Relaton (assumton) Volumetrc, dry gas reservor. (assumton) < 6000 sa [( g c t )/( g c g ) vs. (/z)/( /z ) lnear behavor]. (assumton) Assumes = constant. Tom BLASINGAME t-blasngame@tamu.edu Texas A&M U. Slde 10

11 Petroleum Engneerng 648 Pressure Transent Testng Lecture 18 Hstorcal Rate Tme-Rate Relatons for Ol and Gas Flow Gas Relatons Knowles-Buba Rate-Cumulatve Gas Relaton Ths work resents an analyss and nterretaton seuence for the estmaton of reserves n a volumetrc dry-gas reservor. Ths s based on the "Knowles" rate-cumulatve roducton relaton for seudosteady-state gas flow gven as: g g 1 g / z / z G G 1 g / z / z G G Dscusson: Knowles-Buba Gas Rate-Cumulatve Relaton (assumton) Volumetrc, dry gas reservor. (assumton) < 6000 sa [( g c t )/( g c g ) vs. (/z)/( /z ) lnear behavor]. (assumton) Assumes = constant. Tom BLASINGAME t-blasngame@tamu.edu Texas A&M U. Slde 11

12 Petroleum Engneerng 648 Pressure Transent Testng Lecture 18 Hstorcal Rate Tme-Rate Relatons for Ol and Gas Flow Gas Relatons Valdaton of Knowles Tme-Rate Gas Relaton b. Smulated Performance Case: G versus t ( = 5000 sa, =1000 sa, G uad =4.0 BSCF). a. Smulated Performance Case: g versus t ( = 5000 sa, =1000 sa, G uad =4.0 BSCF). Tom BLASINGAME t-blasngame@tamu.edu Texas A&M U. g vs. t and G vs. t: Base lots verfy models by Ansah, et. al Comaratve trends of 0.9 g, g and 1.1 g. Comarson aled to all analyss lots. Very good match on both lots, accuracy verfes model. Slde 1

13 Petroleum Engneerng 648 Pressure Transent Testng Lecture 18 Hstorcal Rate Tme-Rate Relatons for Ol and Gas Flow Gas Relatons Valdaton of Knowles-Buba Rate-Cumulatve Gas Relaton D Dscusson: Valdaton of the "Knowles-Buba" Relatons Usng Smulaton = 5000 sa, =1000 sa, G uad =4.0 BSCF. Data functon matches well wth uadratc model functon. The "uadratc root" s somewhat confusng to ractcng engneers. Tom BLASINGAME t-blasngame@tamu.edu Texas A&M U. 1 g / z / z G g g D G 1 D G G Slde 13

14 Petroleum Engneerng 648 Pressure Transent Testng Lecture 18 Hstorcal Rate Tme-Rate Relatons for Ol and Gas Flow Ol Relatons Fetkovch Tme-Rate Ol Relaton Ol Materal Balance Relaton: ( formulaton!) ( ) ( ) ( ) Ol Pseudosteady-State Flow Relaton: (Fetkovch) Fnal Result: (Poor Aroxmaton) N N o J o ( ) n o o n o t N 1 ( 0) Tom BLASINGAME t-blasngame@tamu.edu Texas A&M U. Slde 14

15 Petroleum Engneerng 648 Pressure Transent Testng Lecture 18 Hstorcal Rate Tme-Rate Relatons for Ol and Gas Flow Ol Relatons Fetkovch Tme-Rate Ol Relaton Dscusson: Fetkovch "Analytcal" Ol Declne Tye Curve ( = 0) Cheated ( )... ths s not a vald soluton (Fetkovch, 1973). Agan, good ntentons... wanted to develo a "smle" ol soluton. Curve shaes "look" correct, but do not conform to ol well erformance. Tom BLASINGAME t-blasngame@tamu.edu Texas A&M U. Slde 15

16 Petroleum Engneerng 648 Pressure Transent Testng Lecture 18 Hstorcal Rate Tme-Rate Relatons for Ol and Gas Flow Inflow Performance Relatonshs (IPR) Early Performance Relatons From: Back-Pressure Data on Natural-Gas Wells and Ther Alcaton to Producton Practces Rawlns and Schellhardt (USBM Monograh, 1935). Early "Gas Delverablty Plot," note the straght-lne trends for the data (crca 1935). Early "Gas IPR Plot," note the uadratc relatonsh between well-head ressure and flowrate (crca 1935). Dscusson: Early Performance Relatons Early erformance correlatons. Interret ast-erformance and redct future behavor. Catures unue character of the ressure-rate relatonsh. Tom BLASINGAME Texas A&M U. Slde 16

17 Petroleum Engneerng 648 Pressure Transent Testng Lecture 18 Hstorcal Rate Tme-Rate Relatons for Ol and Gas Flow Inflow Performance Relatonshs (IPR) Early Performance Relatons Back-Pressure Data on Natural-Gas Wells and Ther Alcaton to Producton Practces Rawlns and Schellhardt (USBM Monograh, 1935). Gas Well Delverablty: The orgnal well delverablty relaton was derved from observatons: n g C( ) The "nflow erformance relatonsh" (or IPR) for ths case s: (assumng n=1) g g,max C g g,max ( C( ) ( 0) 1 ) Tom BLASINGAME t-blasngame@tamu.edu Texas A&M U. Slde 17

18 Petroleum Engneerng 648 Pressure Transent Testng Soluton-Gas Drve Systems Vogel IPR Lecture 18 Hstorcal Rate Tme-Rate Relatons for Ol and Gas Flow Vogel Correlaton: (Statstcal) o, max o IPR behavor s deendent on the deleton stage (.e., the level of reservor deleton). It s very lkely that no sngle correlaton of IPR behavor s ossble. The Vogel IPR correlaton and ts varatons are well establshed as the rmary erformance redcton relatons for roducton engneerng alcatons. The orgnal correlaton s derved from reservor smulaton. Dscusson: Vogel IPR Correlaton Soluton Gas-Drve Behavor Derved as a statstcal correlaton from smulaton cases. No "theoretcal" bass "ntutve" correlaton ( o,max and avg ). Vogel correlaton s "ntutve," an aroxmate general roof can be shown. Tom BLASINGAME t-blasngame@tamu.edu Texas A&M U. Slde 18

19 Petroleum Engneerng 648 Pressure Transent Testng Lecture 18 Hstorcal Rate Tme-Rate Relatons for Ol and Gas Flow Soluton-Gas Drve Systems Other Aroaches Fetkovch IPR: (Sem-Emrcal) 1 o, max o n Rchardson, et al. IPR: (Emrcal) x, max x 1 ν x (1 ν x ) (x = hase (e.g., ol, gas, water)) Dscusson: Other IPR Correlatons Fetkovch: Derved assumng lnear moblty-ressure relatonsh. Rchardson, et al.: Emrcal, generalzed correlaton. All correlatons assume a fxed form for moblty, or an emrcal correlaton. Tom BLASINGAME t-blasngame@tamu.edu Texas A&M U. Slde 19

20 Petroleum Engneerng 648 Pressure Transent Testng Lecture 18 Hstorcal Rate Tme-Rate Relatons for Ol and Gas Flow Soluton-Gas Drve Systems Other IPR Correlatons Wggns, et al. IPR: (Sem-Rgorous) o o, max 1 a a a... Dscusson: Other IPR Correlatons Wggns, et al.: Used a olynomal exanson of the moblty functon n order to yeld a sem-rgorous IPR formulaton. Coeffcents (a 1, a ) are determned based on the moblty functon and ts dervatves taken at the average reservor ressure. Tom BLASINGAME t-blasngame@tamu.edu Texas A&M U. Slde 0