Case Study Five

Case Study 5: Advanced 7×7 Simulator with Fault Barrier

A 7×7 Cartesian grid simulator with a fault-induced zero-transmissibility barrier, custom Gaussian elimination solver, and pressure-constrained well operations. Models compartmentalized flow and injector-producer communication in structurally complex reservoirs.

Client & context

Developed at GSERC as a physics-based numerical simulator for pressure transient analysis and reservoir performance forecasting. Designed as a transparent alternative to commercial black-box software, enabling engineers and students to understand the underlying mathematics governing fluid flow in porous media with structural complexity.

Problem statement

Reservoir simulation in faulted African basins requires tools that can:
• Model compartmentalized flow systems with impermeable barriers
• Maintain numerical stability during long-term simulations
• Accurately propagate pressure fronts between injector and producer wells
• Achieve convergence toward steady-state flow conditions
• Handle pressure-constrained boundary conditions within finite-difference frameworks

Methodology

Step 1 — Grid & properties. Constructed a 7 × 7 Cartesian grid system (49 active grid blocks) covering 1400 ft × 1400 ft with 60 ft thickness. Reservoir properties: permeability 250 mD, porosity 18%, fluid viscosity 1 cP, initial reservoir pressure 4500 psi.

Step 2 — Fault implementation. Incorporated a fault-induced zero-transmissibility barrier, creating a compartmentalized flow system. This introduces a realistic reservoir management challenge by blocking direct pressure communication across the fault.

Step 3 — Finite-difference discretization. Discretized the diffusivity equation using finite-difference methods with transmissibility calculations between all neighboring grid blocks.

Step 4 — Fully implicit formulation. Implemented fully implicit pressure formulation for unconditional numerical stability. Constructed and solved large systems of coupled linear equations representing pressure communication throughout the reservoir.

Step 5 — Custom solver. Developed a custom Gaussian elimination and matrix-solver implementation in Python, providing full transparency into the numerical solution process.

Step 6 — Well modeling. Implemented Peaceman well model with well index computation. Pressure-constrained injection at 6000 psi and pressure-constrained production at 3000 psi. Accounted for wellbore radius, skin effects, and grid geometry.

Step 7 — Time stepping. Developed time-stepping algorithms for transient reservoir-pressure evolution, capturing the progression from initial hydrostatic conditions toward stabilized pressure distribution.

Key parameters

Grid: 7 × 7 (49 blocks)
Area: 1400 × 1400 ft
Thickness: 60 ft
Permeability: 250 mD
Porosity: 18%
Viscosity: 1 cP
Initial pressure: 4500 psi

Well & fault configuration

Injector: 6000 psi (BHP)
Producer: 3000 psi (BHP)
Fault: Zero transmissibility
Model: Peaceman well index
Skin: Included
Solver: Custom Gaussian elimination

[Figure 13: Pressure contour map — early time showing fault barrier effect]

[Figure 14: Pressure contour map — late time showing compartmentalized steady state]

[Figure 15: Injector-producer pressure communication across faulted system]

Results & deliverables

• Transient and steady-state pressure distributions across the faulted reservoir
• Field-wide pressure maps for reservoir surveillance and compartment identification
• Injector-producer pressure communication analysis quantifying fault impact
• Pressure support mechanisms during production in compartmentalized systems
• Convergence validation toward steady-state flow conditions
• Foundation for future multiphase and compositional simulators

Impact

This project demonstrates GSERC’s capacity to develop advanced petroleum-engineering software locally, contributing to technology transfer, engineering education, and computational geoscience innovation across Africa. The simulator provides a foundation for future development of multiphase and compositional reservoir simulators while serving as an immediate training tool for understanding pressure propagation in structurally complex reservoirs.

Project comparison

Attribute	Nechelik	Waterflood	IMPES Gravity	PTA/Well Perf	Fault Barrier
Language	MATLAB	Python	Python	Python	Python
Dimensionality	2D	3D	2D	2D	2D
Phases	Single-phase	Multiphase (black-oil)	Two-phase (oil-water)	Single-phase	Single-phase
Grid	54 × 22	3D Cartesian	2D structured	3 × 3 non-uniform	7 × 7 (49 blocks)
Formulation	Fully implicit	Fully implicit	IMPES	Fully implicit	Fully implicit
Well model	Peaceman	Dynamic BHP	Peaceman + adaptive	Peaceman (mixed)	Peaceman (BHP)
Solver	Sparse inversion	Newton-Raphson	IMPES sequential	Sparse implicit	Custom Gaussian
Validation	Ei-function	Material-balance	Buckley-Leverett	Analytical pressure	Steady-state
Special feature	Real-field data	5-case scenarios	Gravity + capillary	Anisotropy (ky=2kx)	Fault barrier
Forecast	201 days	400+ days	6,169 days	Transient to steady	Transient to steady
Recovery factor	N/A (pressure)	Scenario-dependent	46.27%	N/A (pressure)	N/A (pressure)

Project timeline

Phase 1: Nechelik simulator development

2D implicit simulator built in MATLAB. Real-field geostatistical data integration, Peaceman well model implementation, Ei-function analytical validation.

Phase 2: Waterflood simulator development

3D black-oil simulator built from first principles in Python. Coupled oil-water flow, Newton-Raphson solver with Jacobian assembly, 5-case scenario optimization.

Phase 3: Integration into training curriculum

Both simulators deployed as case studies in GSERC internship and professional training programs. Trainees build, modify, and validate simulators hands-on.

Phase 4: Field deployment & consulting

Simulators adapted for specific African operator projects. Custom grid generation, well configuration, and scenario analysis for field development planning.