PERFORATING DYNAMICS AND MODELING
Numerical simulation for near borehole fluid dynamics
at perforation tunnel
2019-NAPS-XXAUTHORS: Carlos Vega, University of UtahJohn McLennan, University of UtahIan Walton, Energy and Geoscience Institute
DALLAS - FORT WORTH. AUGUST 5-6, 2019.
OBJECTIVE
2019-NAPS-XX Numerical simulation for near borehole fluid dynamics at perforation tunnel
The proposed numerical simulation is a mathematical solution and visualization tool that can be implemented for the analysis of real case scenarios of fluid dynamics in perforations
AGENDA
Outline
2019-NAPS-XX Numerical simulation for near borehole fluid dynamics at perforation tunnel
Wellbore perforations Formation and perforation simulator Mass Balance Equation Numerical Method Description Fluid mechanics at perforation tunnel Results Conclusions
1. WELLBORE PERFORATIONSTunnel Description
2019-NAPS-XX Numerical simulation for near borehole fluid dynamics at perforation tunnel
• Hydraulic communication between borehole and formation
• Industry standards as per API 19B
Schematics of the perforating geometry:
1. Perforating Charge2. Perforating Gun3. Perforation jet4. Casing5. Cement6. Reservoir rock 7. Perforation tunnel length 8. Entrance Hole Diameter 9. Crushed zone 10. Crushed Zone Thickness
(Grove, et al. 2012)
2. FORMATION SIMULATION
Petrophysical properties of the rock
2019-NAPS-XX Numerical simulation for near borehole fluid dynamics at perforation tunnel
Each cell with unique properties simulating rock texture:
PorosityPermeability
Grid block size: 70x70 cellsGrid block dimensions: 16 x 16 in
Assumptions:
- All processes are isothermal
- Fluids are incompressible and non-reactive.
- No gravity effects on fluid segregation
- Perforation tunnel is considered as high permeability packed bed with spherical particles.
- Crushed zone permeability and porosity are reduced by a fraction of original values.
- Grid block and dimensions kept at low figures for low computational load.
- Convergence analysis to be done
3. PERFORATION SIMULATION
Petrophysical properties in the perforation tunnel
2019-NAPS-XX Numerical simulation for near borehole fluid dynamics at perforation tunnel
Perforation properties:Gun type: 2” HSD, 6 spfPenetration: 11.5 inEntrance Hole: 0.25 inCrushed Zone Thickness: 0.5 inCrushed zone ratios:
K: 0.3f: 0.3Sw: 0.3
4. Material Balance Equations
At every grid cell (control volume)
2019-NAPS-XX Numerical simulation for near borehole fluid dynamics at perforation tunnel
Mass Balance:
𝑚𝑖𝑛 − 𝑚𝑜𝑢𝑡 + 𝑚𝑠𝑖𝑛𝑘/𝑠𝑜𝑢𝑟𝑐𝑒 = 𝑚𝑎𝑐𝑐
−𝜕
𝜕𝑖𝜌𝑢𝑖𝐴𝑖 𝛥𝑖 +
𝑞𝑚𝑎𝑐
=𝑉𝑏𝑎𝑐
𝜕
𝜕𝑡𝜙𝜌
Differential equation form:
i= cartesian coordinates x, y, z.
4. Material Balance Equations
At every grid cell (control volume)
2019-NAPS-XX Numerical simulation for near borehole fluid dynamics at perforation tunnel
𝑎𝑐 =𝑉𝑏ϕ𝑜𝐶𝑓
α𝑐 Δ𝑡
−𝜕
𝜕𝑥𝜌𝑢𝑥𝐴𝑥 𝛥𝑥 −
𝜕
𝜕𝑦𝜌𝑢𝑦𝐴𝑦 𝛥𝑦 −
𝜕
𝜕𝑧𝜌𝑢𝑧𝐴𝑧 𝛥𝑧 +
𝑞𝑚𝑎𝑐
=𝑉𝑏𝑎𝑐
𝜕
𝜕𝑡𝜙𝜌
𝑢𝑥 = −𝛽𝑐𝑘𝑥𝜇
𝜕𝑃
𝜕𝑥
𝜕
𝜕𝑥𝛽𝑐𝐾𝑥𝐴𝑥
𝐾𝑟𝑜𝜇𝑜𝐵𝑜
𝜕𝑃𝑜𝜕𝑥
∆𝑥 +𝜕
𝜕𝑦𝛽𝑐𝐾𝑦𝐴𝑦
𝐾𝑟𝑜𝜇𝑜𝐵𝑜
𝜕𝑃𝑜𝜕𝑦
∆𝑦=𝑉𝑏𝑎𝑐
𝜕
𝜕𝑡
𝜙 𝑆𝑜𝐵𝑜
− 𝑞𝑜𝑠𝑐
From material balance equation:
From Darcy equation:
Reservoir Engineering form of mass balance equation:
PermeabilityRelative PermeabilityPorosity
PressureControl volume dimensionsTime Steps Dt
Sink/Source FlowForm Vol FactorFluid Viscosity
Variables:
5. Fluid mechanics at perforation tunnel
Equations developed for mass transfer in porous media
2019-NAPS-XX Numerical simulation for near borehole fluid dynamics at perforation tunnel
∆𝑷 =𝟏𝟓𝟎𝝁𝑳
𝑫𝒑𝟐
𝟏 − 𝝓 𝟐
𝝓𝟑𝒗𝒔 +
𝟏. 𝟕𝟓𝑳𝝆
𝑫𝒑
𝟏 − 𝝓
𝝓𝟑𝒗𝒔 𝒗𝒔
Based on Ergun equation (Ergun 1952)
Application of pipe packed with spherical beads (Jamiolahmady, et al. 2006).
The first term is the Carman-Kozeny equation: Laminar fluids.
The second term: Correction for intermediate to turbulent flow regime
6. Results
Scenarios created for demonstration of Simulator Capabilities
2019-NAPS-XX Numerical simulation for near borehole fluid dynamics at perforation tunnel
Scenario 1Homogeneous grid
Scenario 2Horizontal Lamination
Scenario 3Damaged vs Improved
Injection Scheme
Driving Force: Constant Injection Flow Rate: 7 BPMElapsed time: 100 s
6. Results
Constant Injection Rate in Homogeneous Formation
2019-NAPS-XX Numerical simulation for near borehole fluid dynamics at perforation tunnel
t = 10 st = 20 st = 40 st = 60 st = 80 st = 100 s
Perforation and Crushed Zone 2D Pressure Distribution
Elapsed time
6. Results
Constant Injection Rate in Homogeneous Formation
2019-NAPS-XX Numerical simulation for near borehole fluid dynamics at perforation tunnel
Pressure Profile at tunnel
Pressure Profile at Crushed ZonePressure Profile at vertical section
Gridblock simulation
6. Results
Constant Injection Rate in Low Permeability Laminated Formation
2019-NAPS-XX Numerical simulation for near borehole fluid dynamics at perforation tunnel
t = 10 st = 20 st = 40 st = 60 st = 80 st = 100 s
Perforation and Crushed Zone 2D Pressure Distribution
Elapsed time
6. Results
High Damage vs Low Damage Crushed Zone
2019-NAPS-XX Numerical simulation for near borehole fluid dynamics at perforation tunnel
High-Damage Crushed ZonePermeability K = 0.3 KoPorosity f = 0.3 fo
Low Damage Crushed ZonePermeability K = 0.8 KoPorosity f = 0.8 fo
6. Results
Dynamic Underbalance Perforation
2019-NAPS-XX Numerical simulation for near borehole fluid dynamics at perforation tunnel
Technique to create a temporary pressure drawdown in the gun casing and create a surge in the perforation tunnelIntended to clean out the debris inside the tunnel and reduce the damage in the crushed zone
Simulated Pressure Profile Driving Force: Dynamic UnderbalanceElapsed time: 1 sec
6. Results
Dynamic Underbalance Perforation
2019-NAPS-XX Numerical simulation for near borehole fluid dynamics at perforation tunnel
t = 0 st = 0.1 st = 0.2 st = 0.4 st = 0.6 st = 0.8 st = 1.0 s
Elapsed time DUB Pressure Profile 2D Pressure Distribution
Velocity Vector Field
6. Results
Two Perforations through a Conductive Fracture
2019-NAPS-XX Numerical simulation for near borehole fluid dynamics at perforation tunnel
t = 0 st = 50 st = 100 st = 200 st = 300 st = 400 st = 500 s
6. Results
Two Perforations through a Conductive Fracture
2019-NAPS-XX Numerical simulation for near borehole fluid dynamics at perforation tunnel
Pressure Mapping @ = 500 s
7. Convergence Analysis
Matrix size and computing time
2019-NAPS-XX Numerical simulation for near borehole fluid dynamics at perforation tunnel
Calculated Pressure at Tip of Tunnel
50 x 50 grid
Calculated Pressure at Tip of Tunnel
35 x 35 grid
Matrix size: 35x35
Matrix size: 50x50
7. Conclusions
2019-NAPS-XX Numerical simulation for near borehole fluid dynamics at perforation tunnel
The proposed fluid mechanics perforation simulator in the near borehole region is a powerful tool to visualize and evaluate the pressure transient at the perforation tunnel, crushed zone and nearby region.
The simulator is flexible enough to process a wide range of variables. Pressure transient or pumping schedule Perforation parameters Rock texture and Reservoir fluid characteristics
Initial development of the mathematical solution is a single plane, and it is not a realistic representative of the entire model.
Simulation results must be compared to experimental data for validation.
2019-NAPS-XXCarlos Vega, University of UtahJohn McLennan, University of UtahIan Walton, Energy and Geoscience Institute
DALLAS - FORT WORTH. AUGUST 5-6, 2019. QUESTIONS? THANK YOU
