Enhancing the Material Balance Equation for Shale Gas Reservoirs. Tyler Zymroz April 23, 2015

Transcription

1 Enhancing the Material Balance Equation for Shale Gas Reservoirs Tyler Zymroz April 23, 2015

2 Agenda Personal Background Introduction Research 1. Material Balance Equation 2. Enhancing the MBE 3. Results Project Findings Questions Final Conclusion

3 Personal Background

4 Project Introduction Objective: Increase the effectiveness of the material balance equation (MBE) for shale gas reservoirs. Quick and easy method to evaluate: Initial adsorbed gas in place, G a Initial free gas in place, G f Create an equation that generates a linear-line

5 Work Flow Performed a Literature Analysis Tested method with data set and output results Examined Material Balance Equation practices Created new method to account for desorption Applied current practices to data set to identify problem

6 Material Balance Equation The MBE is an equation based on: Fluid Production = Δreservoir volume due to drive mechanisms Volumetric Gas MBE Underground Removal = Gas Expansion Drive G p B g = G(B g -B gi ) By replacing B g and rearranging: p Z = p i Z i (1- G p G )

7 Volumetric p/z vs. G p A graph can be generated by plotting p/z vs. G p Volumetric Gas Reservoir 2000 p i /Z i (psia) y = x R² = Cumulative Gas Produced (MMMscf) G = G p when p/z = 0, therefore G = (2217/149.8) 14.8 MMMscf

8 p/z vs. G p Error The p/z vs. G p plot is ineffective for shale res. Data displays linear trend initially (blue points) Over time data trends upward (red points) 1800 OGIP Error due to Early Interpretation p/z (psia) y = x R² = G p (MMscf) G p G

9 Adsorption/Desorption Adsorption is the adhesion of gas to the face of the shale. Desorption is the release of gas from the face of the shale. Deviation from trend line during the p/z vs. G p The Langmuir Isotherm

10 Langmuir Isotherm Assumptions: Monolayer of gas on shale surface Equilibrium established between the free gas and adsorbed gas for a given temperature and pressure Reasoning: Mathematically easy to calculate Desorption estimates will be conservative

11 Langmuir Isotherm cont. (1/2)*V L V(p) = V L ( p p + p L ) p L V L is Langmuir s volume, max gas volume at infinite pressure p L is Langmuir s pressure, pressure corresponding to one-half V L V(p) is the volume of gas adsorbed per unit mass (scf/ton)

12 Desorption Gas Desorption 400 Adsorbed Gas (scf/ton) Gas released is equal to V( ) = V( ) = 60 scf/ton Pressure (psi) V(p i - p) = V L ( p i p i + p L - p p + p L )

13 Shale Gas MBE Original Havlena-Odeh Gas MBE G p B g +W p B w = G(B g - B gi )+GB gi S wi c w + c f 1- S wi Dp My approach: Production terms = reservoir drive mechanisms Desorption Nomenclature for drives

14 Desorption Drive Each drive mechanism = reservoir barrels (rb) Starting point: rb (scf/ton) x? Reservoir bbls = desorption (scf/ton) * bulk density (ton/ft 3 ) * bulk volume (ft 3 )*Gas FVF (rb/scf) V L ( p i p i + p L - p p + p L ) r b G a r b G c B g *G a = initial adsorbed gas in place (scf) G c = initial adsorbed gas content (scf/ton)

15 Desorption Drive cont. Reservoir barrels due to desorption: rb = V L ( p i p i + p L - p G ) r a b B g p + p L r b G c In simplified form: rb = G a B g V L G c ( p i p i + p L - p p + p L ) *G a = initial adsorbed gas in place (scf) G c = initial adsorbed gas content (scf/ton)

16 Reservoir Drive Alterations Gas Expansion Drive Changed G to G f G(B g -B gi ) G f (B g -B gi ) Pore Compaction/Water Expansion Drive Changed G to G f for water exp./pore compaction GB gi S wi c w + c f 1- S wi Dp G f B gi S wic w + c f 1- S wi Dp *G f = initial free gas in place (scf)

17 Proposed Shale Gas MBE G p B g +W p B w = G f (B g - B gi )+G f B gi S wi c w + c f 1- S wi Dp + G a B g V L G c ( Reformatted using Havlena-Odeh nomenclature: exp. F = G p B g +W p B w (rb); net production E g = B g -B gi (rb/scf); gas expansion E f,w = (rb/scf); pore & water E d = G f B gi S wi c w + c f 1- S wi Dp V B L p g ( i - G c p i + p L p p + p L ) (rb/scf); desorption p i p i + p L - p p + p L )

18 Proposed Shale Gas MBE cont. The equation can be rewritten in the format: F = G f E g + G f E f,w + G a E d Simplified F = G f (E g +E f,w ) +G a E d Dividing (E g +E f,w ) to create: F E = G a ( d )+G f E g + E f,w E g + E f,w

19 Straight Line Interpretation A straight line can be generated by graphing: F E vs. ( d ) E g + E f,w E g + E f,w F /(E g + E f,w ) scf y = mx + b m = G a b = G f E d /(E g + E f,w ) unitless

20 Coal Bed Methane Analogy Assumptions: Similar Reservoir drive mechanisms Geological characteristics not a factor High water production does not affect analysis Desorption is present in both reservoirs!

21 Example Plot Using CBM data F/(E g +E f,w ) (scf) 5E E+09 4E E+09 3E E+09 2E E+09 1E Plot Using CBM Data y = 12,657,083,257.54x + 69,243, R² = E d /(E g +E f,w ) Graph: G a = 12,657 MMscf and G f = 69,243 Mscf Volumetric: G a = 12,763 MMscf and G f = 37,189 Mscf

22 Project Findings Results Created MBE analysis Was not able to estimate G f Method appropriate for dry and wet gas Increase accuracy of reserve estimates Recommendations Apply method to Marcellus/Utica dry or wet gas reservoir Determine effect of pore compaction/water expansion drive for shale reservoirs Attempt to Generate adsorption isotherm

23 Questions?

24 Conclusion Material Balance Equation Errors Associated with p/z method Adsorption/Desorption New method to estimate reserves Recommendations for moving forward Thank You!

25 Rearranging for p/z Initial: G p B g = G(B g -B gi ) Substitute: G p = G (B g -B gi )/B g G p = G - GpZ i /(p i Z) Multiply Each side by p i /Z i G p p i /Z i =Gp i /Z i Gp/Z Divide out G Final: B g = TZ p G p /Z = p i /Z i (G-G p ) p/z = p i /Z i (1-G p /G) p Z = p i (1- G p Z i G )

26 Approximating Langmuir Volume and Pressure V L and p L Approxima on Methane Adsorp on (scf/ton) V L = b = scf/ton p L = -m = psia y = x R² = V/p (Adsorbed Methane per Pressure, scf/ton/psia)

27 Bulk Volume Calculation Start: G a = Ahρ b G c Where CF = (ton/ft 3 ) per (g/cc) G c = initial adsorbed gas content (scf/ton) ρ b = bulk density (g/cc) = 43560* End: 43560Ah (ft 3 ) = G a /( ρ b G c )

28 BET Isotherm Mathematical equation: V mono C( p ) p V(p) = o (1- p )(1+ C( p )- p ) p o p o p o