Condensate banking vs Geological Heterogeneity who wins? Hamidreza Hamdi Mahmoud Jamiolahmady Patrick Corbett SPE

Transcription

1 Condensate banking vs Geological Heterogeneity who wins? Hamidreza Hamdi Mahmoud Jamiolahmady Patrick Corbett SPE

2 Outline P-T diagram of Gas reservoirs Diffusion equation linearization using gas pseudo pressure Pseudo pressure in gas condensate reservoir Well test signature of the gas condensate reservoir (Analysis procedure) Interfering of geology and fluid Production time Production rate Correlation length Vertical permeability Reservoir stripping of heterogeneities

3 P-T diagram of gas reservoirs GOR>3300 scf/stb to very higher values scf/STB if GOR >50000 small condensation in the reservoir API ~ 40 t0 60 and increases as pressure follows dew point Lightly coloured

4 Linearization of diffusion equation Dry gas reservoir Viscosity =f(p) Compressibility =f(p) Linearization using single phase pseudo pressure The well-test theory can be applied (single phase liquid) m p p pdp = 2 µ z p 0 g g

5 Gas condensate reservoirs Two-phase pseudo pressure m( p) 2 m( p) 2 p ρokro = + po po o p kro = + ρ k g µ µ krg µ z µ z g o o g g rg dp pdp The pseudo-pressure is evaluated based on : Steady state assumption (O Dell and Miller, 1966) : A model composed of a far region P>P dew, and a near wellbore region p<p dew when both fluids flowing Fevang and Whitson assumption (1996) : The existence of an intermediate region where condensate is immobile. Gringarten assumption (2000): The existence of a forth region in immediate vicinity of wellbore (velocity dependent relative permeability) Single-phase pseudo pressure (Al-Hussainy et al. 1966) pdp mp ( ) = 2 µ z p p 0 g g Assuming immobile condensate

6 Two-phase m(p) Two-phase or single phase m(p) Advantages: Remove the fluid heterogeneity effect Disadvantages : Highly dependent on relative permeability data ( a small error in relative permeability data provide higher error than using a singlephase pseudo pressure), relative permeability data as a function of pressure, evaluation of two-phase pseudo pressure function, needs accurate PVT modelling, inaccuracy to model the realistic phenomena, Single phase m(p) Advantages: Easy to apply, the Total skin, Mobility ratio and two-phase skin can be estimated Disadvantages: The assumption of zero-condensate mobility may not be appropriate, the radial composite model may not be seen in short tests Approach: assuming a two-region radial composite model.

7 Gas condensate interpretation method using single phase pseudo-pressure Gas m(p) Outer region stabilization Gas & Oil High WBS and phase segregation Inner region stabilization Sm S2p Horner Time S T S T mp ( ws@1 hr ) mp ( tp ) k out = log m ϕµ outct _ outrw 1 1 R = Sm + 1 ln M M r w or S S m t = + krg S 2 p

8 Geological model and the fluid composition Components Composition % CO C1N C1 88 C C C C C10 12 C C C C Dew Point Pressure (psia) 5341 Maximum liquid drop-out 30 (%PV) WELL-A A realistic pixel-based model of a commingled (i.e. k v =0) multi-facies, high net:gross, braided fluvial reservoir with 86*48*25 cells (each cell: 25m*25m*1.9) We used a real case ten-component rich gas condensate fluid with a maximum liquid dropout of 30 A tuned PR Equation of State was used to model the fluid behaviour.

9 Native pseudo-pressure derivative response: heterogeneous model single-phase fluid 1E+8 Fake WBS Ramp Effect Layered Depletion m(p) & m'(p) 1E+7 1E+6 Ramp m(p) m'(p) 1E+5 1E-5 1E-4 1E-3 1E-2 1E-1 1E+0 1E+1 1E+2 DrawDown Buildup Time, hr Single phase Pseudo pressure test response (geological behaviour) Draw-down and build-up shows a deflection at the late time region (Boundary effect) The early time deflection is due to a Fake Wellbore Storage arrising from the coarse cell penetrated by wellbore The time at the end of FWBS can be estimated as (Blanc 1999) ϕµ c t L 2 t 2.6 k

10 Native pseudo-pressure derivative response: homogenous model, two-phase fluid system 1E+7 m(p) m(p) & m'(p) 1E+6 Kg=73md Condensat e Total Skin Condensat e m'(p) K=172md 1E+5 1E-5 1E-4 1E-3 1E-2 1E-1 1E+0 1E+1 1E+2 1E+3 Drawdown Build-up Time, hr A) When two stabilizations present S t =S m +S 2p 1. First stabilization S m 2. Second Stabilization S t B) When only one stabilization (second) presents (e.g. due to WBS) S t =S m +S 2p 1. Second Stabilization S t 2. Correlation S 2p

11 Native pseudo-pressure derivative response: homogenous model, two-phase fluid system Buildup vs Drawdown weighting function 0.14 Kernel function (Build-up explanation) Weighting time π r D r D r D tdgr ( D, td) = 0.5 exp W1/2,1/2 td 2tD td Distance index Sensitivity coefficients (Drawdown Explaination) Pw( t) Pw( t, k1, k2,..., km + δ km,..., kn) Pw( t, k1, k2,..., km,..., kn) = k δ k m m The logarithm of well pressure sensitivity with respect to local permeability field at the early time (left) and at the late time (right).

12 Analytical-Numerical combination: WT history matching Create a model with Log-normal distr. x= y=10ft. ( 2000ft*2000ft*25ft^3) Follow the methodology described here Calculate the analytical Kinst (Feitosa 1994) Plot both kinst (Numerical and Analytical) Results: Can be used in well test history matching to skip simulation A ring ln K = A ln K ring i i i Layer 1: 1 1 = Wjt, k () t k inst disk = j ringj 1 1 = Wjt, Layer 2: k () t k inst j ringj Time ti ri ri+1 rn W rj+ 1 rj disk j, t = i rn r0 Kernel _ Function(, t r) Kernel _ Function(, t r) DP Total: K () t = Power _ Average _ of ( k ()) t inst Time inslayerk

13 Sensitivity Coefficients Pw( t) Pw( t, k1, k2,..., km + δ km,..., kn) Pw( t, k1, k2,..., km,..., kn) = k δ k m m tn xl+ 1/2 d( i, i, i, n) c 1 d(, m, n, ) nd(, m, n, n ) = m n kx µ x x ( t ) 0 xl 1/2 n s P x y z t P xy z s P xy z t s y z dsdx The wellbore pressure always remains sensitive to any potential permeability changes in near wellbore area

14 Interfering effect of the geological and the production parameters: combined geology vs. fluid signatures : Effect of Production Rate on drawdown & subsequent build-up N. m(p) & N. m'(p) 1E+6 1E+5 Fluid+FWBS Fluid & geology Layerd Corr_Length =250m Drawdow time =4 Days Fluid > Geology Fluid < Geology Geology Fluid ~ Geology Ramp Ramp m(p) m'(p) Fluid effect 1E+4 1E-5 1E-4 1E-3 1E-2 1E-1 1E+0 1E+1 1E+2 Time, hr BU with rate 5MMscf/d BU with rate 30MMscf/d 1E+7 N. m(p) & N. m'(p) 1E+6 1E+5 Rate=20MMscf/d Corr.Length=250 m Drawdown Time= 4 Day P>P dew Liquid drop-out effect m(p) m'(p) 1E+4 1E-5 1E-4 1E-3 1E-2 1E-1 1E+0 1E+1 1E+2 Time, hr DD with rate 30MMscf/d DD with rate 5MMscf/d

15 Interfering effect of the geological and the production parameters: combined geology vs. fluid signatures : Effect of Production Time on Subsequent Build-up 1E+8 Fluid+FWBS Fluid & geology Layerd PSS m(p) m(p) & m'(p) 1E+7 1E+6 Fluid effect m'(p) 1E+5 1E-5 1E-4 1E-3 1E-2 1E-1 1E+0 1E+1 1E+2 Time, hr 4 Days of DD 8 Days of DD 12 Days of DD

16 Interfering effect of the geological and the production parameters: combined geology vs. fluid signatures : Effect of Correlation length m(p) & m'(p) 1E+8 1E+7 1E+6 1E+5 Fluid+FWBS Geology Layerd PSS Rate=20MMscf/d Corr_Length =750m Drawdown Time= 4 Days Geology Fluid effect m(p) m'(p) 1E-5 1E-4 1E-3 1E-2 1E-1 1E+0 1E+1 1E+2 Time, hr Drawdown Build-up m(p) & m'(p) 1E+8 1E+7 1E+6 1E+5 Fluid+FWBS Fluid & Geology Layerd PSS Rate=20MMscf/d Corr_Length =25m Fluid effect m(p) m'(p) 1E-5 1E-4 1E-3 1E-2 1E-1 1E+0 1E+1 1E+2 Drawdown Build-up Time, hr

17 Interfering effect of the geological and the production parameters: combined geology vs. fluid signatures : Effect of Vertical Permeability m(p) & m'(p) m(p) & m'(p) 1E+8 1E+7 1E+6 1E+8 1E+7 1E+6 1E+5 Fluid+FWBS Geology Layerd PSS Rate=20MMscf/d Corr_Length =25m Drawdown Time= 4 Days Kv=Kh 1E-5 1E-4 1E-3 1E-2 1E-1 1E+0 1E+1 1E+2 Drawdown Fluid+FWBS Geology Layerd PSS Rate=20MMscf/d Corr_Length =750m Drawdown Time= 4 Days Kv=Kh Build-up Time, hr Geology m'(p) m(p) m'(p) m(p) The sensitivity of the derivative response with respect to the correlation length decreases in the cases with high vertical permeability. Increasing the vertical flow communication between the reservoir layers causes the ramp effect to disappear 1E+5 1E-5 1E-4 1E-3 1E-2 1E-1 1E+0 1E+1 1E+2 Time, hr Drawdown Build-up

18 Interfering effect of the geological and the production parameters: combined geology vs. fluid signatures : Stepwise homogenization 1E+8 m(p) & m'(p) 1E+7 1E+6 (2) (1) (3) (5) (4) 1E+5 1E-5 1E-4 1E-3 1E-2 1E-1 1E+0 1E+1 1E+2 1E+3 Time,hr Fluid Effcet (1) Heterogeneous (2) Heterogeneous (Shale->Homogeneous) (3) Heterogeneous (shale & fine sand->homogeneous) (4) Heterogeneous(Shale & Fine Sand & Sand->Homogeneous) (5) Homogeneous Geology Effcet

19 Conclusions The two-phase pseudo pressure function can theoretically eliminate the fluid heterogeneity effect, however the higher degree of uncertainty in the relative permeability data leads to use the single phase pseudo pressure The condensate drop-out has different signature on build-up and drwadown The averaging Kernel function and the single phase sensitivity coefficients explain this different signature

20 Conclusions The production rate has a significant effect on the subsequent build-up response. This complicate the well test response in presence of geological heterogeneity (Ramp) The test response has less order of sensitivity than the production rate The shorter the correlation length, the higher the condensate signature on the test response The higher correlation length compensate the effect of vertical permeability.

21 Acknowledgements Alaa Sarikouzel (BP) Schlumberger (E300, PVTi, E100, FloGrid) Kappa (Ecrin) Weatherford (PanSystem ) Total E&P UK ltd

22 References Al-Hussainy, R., Ramey, H. J., and Crawford, P. B.: The flow of real gases through porous media, JPT, May 1966, p Blanc, G., Ding, D.Y., Estebenet, T. And Rahon, D. : Transient productivity index for numerical well test simulations, in Schatzinger, R. and Jordan, J., eds.: Reservoir charactrization: recent advances, AAPG Memoir 71, 1999, pp Fevang, O. and Whitson, C. H.: Modeling gas-condensate well deliverability, SPERE, November 1996, p Gringarten, A. C., Al-Lamki, A., Daungkaew, S., Mott, R. And Whittle, T. M.: Well test analysis in gas condensate reservoirs, Paper SPE 62920, Presented at SPE Annual Technical Conference and Exhibition, Dallas, Texas,1-4 October He, N.: Three dimensional reservoir description by inverse theory using well-test pressure and geostatistical data, PhD thesis, University of Tulsa, O Dell, H. G. and Miller, R. N.: Successfully cycling a low permeability, highyield gas condensate reservoir, Paper SPE 1495, Presented at the SPE 41 st Annual Fall Meeting, Dallas, Texas, October Oliver, D. S.: The averaging process in permeability estimation from well-test data, Paper SPE 19845, SPE Formation Evaluation, 5(3), September Raghavan, R.: Testing under multi-phase flow conditions, in Kamal, M.M. (eds) : Transient Well Testing,, Society of Petroleum Engineers, 2009, pp