Panel Analysis f Well Prductin Histry in the Barnett Shale Kenneth Medlck, Likeleli Seitlhek, Gürcan Gülen, Svetlana Iknnikva, and Jhn Brwning fr the study The Rle f Shale Gas in the U.S. Energy Transitin: Recverable Resurces, Prductin Rates, and Implicatins presentatin by Kenneth B Medlck III James A Baker III and Susan G Baker Fellw in Energy and Resurce Ecnmics, and Senir Directr, Center fr Energy Studies, James A Baker III Institute fr Public Plicy Adjunct Prfessr, Department f Ecnmics Rice University Nvember 7, 2012 James A Baker III Institute fr Public Plicy Rice University
Purpse The primary purpse f the empirical analysis is t test the statistical validity f the prpsed methdlgy (REI) fr mdeling well prductin. The REI methd prpses prductin, dented q t,i, can be mdeled as k REI ti, 0.5 The abve equatin can be transfrmed int q where the term ln k REI is well-specific. Mrever, we can test i whether r nt ρ = 0.5. = t ( ) ln q = ln k REI + ρ ln t ( ) ti, i i i i 2
Estimatin Estimatin is dne using lngitudinal mnthly prductin data fr ver 16,500 wells drilled in the Barnett shale cvering 1990 thrugh 2011. We include the well s prductin histry, as well as a set f variables t indicate the gelgical characteristics f the shale at the well s lcatin. We als include variable t indicate the size f the peratr, the year f first prductin, whether r nt the well has been refractured, and the average price f the 12 mnth strip f futures. We estimate the fllwing equatin ln q = u + α ln t + δ ln q + β ln p t, i i i t 1, i NYMEX, t + a prs + a tp + a TM + a TOC + a thick + a θ h + a press + a bg 1 i 2 i 3 i 4 i 5 i 6 i 7 i 8 i + b per + b per + b refrac + b length + b vintage 1 sm, i 2 med, i 3 i 4 i 5 i where u i is a well-specific term that can be mdeled as either fixed r randm. It turns ut that u i is treated as randm, meaning the ther included variables capture the systematic variatin between wells. 3
fr well i Variable Definitins t i dentes the time perid since initial prductin p NYMEX,t is the average f the 12 mnth strip f NYMEX futures prices, prs i dentes the effective prsity f the reservir, tp i dentes the depth t the tp f the shale, TM i dentes thermal maturity f the shale resurce, TOC i dentes ttal rganic carbn, thick i dentes the shale thickness after accunting fr the limestne intrusin, Φh i dentes effective prsity multiplied by thickness, press i is the reservir pressure, length i is the length f the lateral in hrizntal wells bg i dentes the gas frmatin vlume factr, per sm,i and per med,i are indicatr variables denting peratr size, refrac i is an indicatr variable denting a refracture has ccurred, and vintage i dentes the first year f prductin. 4
Estimatin Results Variable Parm Vertical Hrizntal lnt α -0.1570*** -0.1798*** (0.00137) (0.00191) lnq t-i δ 0.6862*** 0.6407*** (0.00128) (0.00129) lnp NYMEX,t β 0.1082*** 0.0305*** (0.00266) (0.00469) prs a 1 13.4287*** 7.6875*** (0.9352) (0.6723) tp a 2-7.1e-05*** -0.00018*** (2.1e-05) (1.4e-05) TM a 3 0.5715*** 0.3225*** (0.0254) (0.0164) TOC a 4 0.0581*** 0.0150*** (0.0051) (0.00411) thick a 5 0.0005*** 0.00144*** (0.0002) (0.00012) Φh a 6-0.00378-0.00502** (0.00269) (0.00219) Variable Parm Vertical Hrizntal press a 7-0.00018*** -0.00041*** (3.9e-05) (2.6e-05) bg a 8-32.9624** -115.093*** (16.4667) (14.8089) per sm,i b 1-0.2182*** -0.0837*** (0.0062) (0.0064) per med,i b 2-0.1447*** -0.0546*** (0.0067) (0.00444) refrac i b 3 0.1532*** 0.0426*** (0.0066) (0.0099) length i b 4 9.6e-05*** 8.6e-05*** (2.0e-05) (1.96e-06) vintage i b 5-0.0079*** 0.00292** (0.0009) (0.00133) R 2 0.807 0.693 Observatins 360,039 405,326 Sample Size 3,839 11,645 Nte: Standard errrs in parentheses, *** p<0.01, ** p<0.05, * p<0.1 5
Implicatins The equatin estimated represents a state-transitin equatin and, accrdingly, the term is interpreted as a shrt run effect. Thus, the prductin prfile f any well is path dependent, and by definitin, depends n prductin in the previus perid. Because f this, we shuld expect autcrrelatin in the residuals if we impse the restrictin δ = 0. By specifying the mdel as such, we want t test the hypthesis that ρ = -0.5, where ρ = α/(1 δ). It turns ut that we cannt reject the hypthesis that ρ = -0.5 in either vertical r hrizntal wells. In fact, we have Hrizntal: ρ = -0.5014 Vertical: ρ = -0.5000 S, the data supprts using the REI measure as a valid descriptin f well perfrmance in the Barnett shale. Nte that the decline prfile s mdeled is apprximated by a hyperblic decline mdel where b can be fit r numerically apprximated. 6
Simulatin Fitted Hrizntal Type Well EUR 2010 = 1.441 bcf Sample Average Values Variables Vertical Hrizntal tp -6365.55-5921.97 TM 1.2835 1.3079 TOC 3.3685 2.9627 thick 291.394 285.121 perfzn 462.73 2293.47 phih 18.6864 17.0353 bg 0.0045 0.0049 press 3662.24 3376.41 prs 0.0641 0.0589 length 427.09 2876.64 price 4.00 4.00 Fitted Vertical Type Well EUR 2010 = 0.528 bcf 7
Marginal Effects f Gelgy and Other Parameters n Prductin Hrizntal Type Well Price Prsity Thermal Maturity Ttal Organic Carbn Perfratin Zne Length Refracture Operatr Size Depth Pressure Φh bg 8
A Nte n Refracs The value f the estimated parameter b 3 indicates that refractures imprve well prductin, in particular because b 3 > 0, meaning prductin will n average be higher after a refracture. Mrever, the degree t which prductin increases will depend n when in the well s life the refracture ccurs, and whether r nt the refracture is in a vertical r hrizntal well. If a refrac ccurs in mnth 12, the effect n prductin is given as: q pst refrac b 12 3 ln = + ρ ln q 1 δ 11 pre refrac where the calculated values fr hrizntal and vertical wells are given as: hrizntal: 1.176 vertical: 1.703 The baseline type curve is 0.502 MMcf/d in a hrizntal well and 0.190 MMcf/d in a vertical well, meaning the prductin increase s estimated is nt large 9
Questins/Cmments 10