Recent Decline Models for Resource Plays. John Lee University of Houston 25 January 2012

Transcription

1 Recent Decline Models for Resource Plays John Lee University of Houston 25 January 2012

2 We Have a Problem Forecasting methods we use in conventional reservoirs may not work well in Tight gas Gas shales Unconventional gas resources generally

3 Decline Curves: Approaches Major categories Arps empirical model As originally proposed 10 With terminal exponential decline imposed Theoretical/semi-theoretical models Long-duration linear flow Recent empirical models Valkó Power-Law model Duong model Rate, STB/mo Exponential Hyperbolic Harmonic Time, months

4 Critique of Arps Model Requires stabilized (not transient) flow for 1600 Exponential validity 1400 Hyperbolic Harmonic q = q 1000 i (1/ b) 800 (1 + bd t) i 400 Transient flow likely for most, possibly all, Time, months life of well in ultra-low permeability reservoirs Best-fit b values almost always >1 Hyperbolic decline equation derived assuming b constant (explicit in Arps original paper) Extrapolation to economic limit with high b value can lead to unrealistically large reserves estimates Cum Prod, MSTB

5 Arps: Keeping Reserves Estimates Reasonable Common method: Use best-fit b until predetermined minimum decline rate reached; then impose exponential decline Problems Extrapolation with best-fit b problematic apparent best b decreases continually with time Appropriate minimum decline rate based on observed long-term behavior in appropriate analogy usually unavailable in resource plays

6 Valkó Decline Model -- Stretched Exponential (SEDM) Empirical model q = q i t exp τ Validated for wells with both transient and stabilized flow in Barnett Shale (horizontal, multi-stage fractures, Carthage Cotton Valley (vertical, layered, some depleted), others n

7 Validation of SEDM

8 SPE Rushing-Blasingame Study: 42 Simulated Cases

9 Base Case Stretched-Exponential Model (based on 5-yr production history) Out[930]= Q, mmcf Stretched exp model n:0.25, :25.4 days qi:11.7 mmcf d days 0.5 q, mmcf d Stretched exp model n:0.25, :25.4 days qi:11.7 mmcf d days

10 Base Case Arps Model (based on 5-yr production history) Just as good a fit Q, mmcf Arps model b:1.5, D: days qi:4.823 mmcf d days 0.5 q, mmcf d Arps model b:1.5, D: days qi:4.823 mmcf d days

11 Comparison: 50- Year Forecasts Based on 5- Year Production History n 0.25 Red: Arps b 1.5, Blue: Stretched exp Q, mmcf Conclusion: While the limited span of data can be described equally well with the traditional and the new model, the extrapolation to 50 yrs yields different results (the new model being more conservative and nearer to the actual value known in this case.) yrs

12 Forecasting Ability of SEDM Model Much Better Years of History Matched Best Fit, Arps b Arps: Error in Remaining Reserves, % SEDM: Error in Remaining Reserves, %

13 Long-Duration Linear Flow Model Reasonable expectation in formation with hydraulic fracture(s) in communication with wellbore Characterized by slope = -(1/2) on log q log t plot, b = 2 in Arps model Linear flow possibly followed by boundarydominated flow, 0 <b <0.5 in Arps model, when boundaries of Stimulated Reservoir Volume (SRV) felt Linear flow may then reappear as flow from beyond SRV develops

14 Linear Flow, Boundary-Dominated Flow Observed in Denton County Well Group (234 Wells)

15 Upper Bound of EUR for Denton County Well Group: Immediate Resumption of Linear Flow

16 Lower Bound of EUR for Denton County Well Group: Well Declines Exponentially for Remaining Life b = 2 b = 0 30 yr EUR = BSCF

17 Duong Method (SPE , June 2011 SPEREE)

18 Duong Method Applied to Shale Well

19 Barnett Shale Denton County

20 Barnett Shale Denton County

21 Fayetteville Shale Conway County

22 Fayetteville Shale Conway County

23 Critique of Duong Method Duong method easily applied to forecast future production and reserves for lowpermeability wells Method appears to be reliable for both horizontal and vertical wells, but verification for shales not possible without long-term performance data for comparison Method currently unproved for wells with transitions from linear (or bilinear) flow to boundary dominated flow

24 Conclusions Forecasting in resource plays uncertain Understanding of basic physics incomplete Ability to model hypothesized controls on production limited by incomplete data, difficulty in validating models due to limited duration well histories

25 Conclusions Arps production decline model inappropriate without empirical modifications Minimum final (exponential) decline? Other models arguably more appropriate for resource play evaluations more complete validation desirable Valkó (SEDM) Long-duration linear flow Duong

26 Recent Decline Models for Resource Plays John Lee University of Houston 25 January 2012