# Vertical transmissibility assessment from pressure transient analysis with integration of core data and its impact on water and miscible water-alternative-gas injections

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## Abstract

The major key uncertainty of complex carbonate reservoirs are the vertical transmissibility across the tight dense (stylolite) layers and areal distribution of high permeability streaks (HKS), which have major impact on reservoir management, well locations, and well completion design in water and miscible water-alternative-gas (miscible WAG) injection process. The present study presents interpretation methodology of vertical transmissibility through assessment of horizontal to vertical permeability ratio (*K*_{v}/*K*_{h}) from various dynamic data. The *K*_{v}/*K*_{h} range assessment was done after integration with whole core data and pressure transient data. The impact of *K*_{v}/*K*_{h} on water and miscible WAG injection processes has also been investigated. The result shows that good vertical communication between the bulk of the porous sub-units and all across stylolite layers except one stylolite layer which acts as field wide barrier. In addition, simulation result of water and miscible WAG injection with higher order of estimated *K*_{v}/*K*_{h} ratio (0.2 to 1 as found in good permeability porous layers of most of the carbonate reservoirs) indicates no major impact on water cut (WCT), gas oil ratio (GOR), water breakthrough (WBT), gas breakthrough (GBT), and expected ultimate recovery (EUR) in homogeneous area, while oil recovery acceleration with lower WCT/GOR and slightly early WBT/GBT time in heterogeneous area due to gravity or viscous effect suppressed by heterogeneity effect. However, the lower order of *K*_{v}/*K*_{h} ratio (~ < 0.05) provide delay in WBT/GBT and lower WCT / GOR production due to viscous dominant flow which results in lower gravity-viscous number.

## Keywords

*K*

_{v}/

*K*

_{h}ratio Anisotropy assessment Pressure transient analysis Miscible WAG Reservoir simulation model Stylolite layer Carbonate reservoir

## Nomenclature

*K*_{v}/*K*_{h}Horizontal to vertical permeability ratio

- OOIP
Original oil-in-place

- EUR
Expected ultimate recovery

- PBU
Pressure build-up test

- PFO
Pressure fall off test

- MRT
MultiMate test

- VIT
Vertical interference test

- RFT
Repeat formation tester

- MDT
Modular formation dynamics tester

*–*Schlumberger- SCAL
Special core analysis

- K
_{v} Vertical permeability

- K
_{h} Horizontal permeability

- PP
Packer probe

- RRT
Reservoir rock type

- Lwe
Effective well length

- REV
Representative element volume

- WAG
Water-alternative gas

- HKS
High permeability streaks

*q*Oil production rate (bbl/day)

- μ
_{o} Oil viscosity (cp)

*M*Mobility ratio (μ

_{o}/μ_{g})*B*_{o}Oil formation volume factor

*L*_{w}Horizontal well length (ft)

*L*Reservoir length

- Φ
Porosity (fraction)

*K*_{x}Horizontal

*p*ermeability (md) in X direction*K*_{y}Horizontal

*p*ermeability (md) in Y direction*K*_{v}Vertical permeability (md) in Z direction

*C*_{t}Formation compressibility (1/psia)

*t*Time (hours)

*t*_{erf}Time at which early radial flow and linear flow intersect

*H*Reservoir thickness (ft)

*H*_{Dw}Well eccentricity (horizontal well dimensionless location ad) = hw/h

*H*_{w}Distance from no-flow boundary from horizontal length position = min (h1, h2)

- h1 and h2
Distances from no flow boundaries to the horizontal well

- D1, D2, D3, D4
*,*and D5 Dense

*l*ayers (stylolite intervals) of reservoir- M1, M2, M3, M4, M5
*,*and M6 Porous layer of reservoir

*M*Mobility ratio (μo/μg)

*V*Vector of Darcy velocity

*D*Dispersion tensor

*c*Concentration

*G*Dimensionless gravity-viscous number

*H*_{t}Heterogeneity number

*D*Symmetric dispersion tensor, [L2t-1]

- Ω
Vorticity, [t-1]

- ∇
Differential operator, [L-1]

*h*_{p}Length of the open zone between two straddle packers in VIT tool

*r*_{w}Wellbore radius

*r*_{sw}Spherical wellbore of radius

*K*_{sp}Permeability in spherical flow regime

*t*_{sp}Time during spherical flow

*t*_{D}Dimensionless time in spherical flow

*P*_{D’}Dimensionless pressure derivative in spherical flow

- (
*t**dp/d)_{sp} Logarithmic derivative in spherical flow

- (
*t**dp/d)_{lr} Logarithmic derivative in late radial flow

## Notes

### Acknowledgements

The authors gratefully acknowledge the management of KOC (Kuwait Oil Company), ZADCO (Zakum Development Company), and IIT-ISM (Indian Institute of Technology-Indian School of Mines) for their support and permission to publish this paper.

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