perforating dynamics and modeling · carlos vega, university of utah john mclennan, university of...
TRANSCRIPT
-
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