Case Study Four

Case Study 4: Indigenous 2D PTA & Well Performance Simulator
A fully implicit 2D non-uniform grid simulator for pressure transient analysis and well performance forecasting in anisotropic heterogeneous reservoirs. Implements Peaceman well modeling with mixed boundary conditions and gravity-aware initialization.
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Client & context
Developed at GSERC as a transparent alternative to commercial black-box simulators, allowing engineers and students to understand the governing physics and numerical methods behind subsurface flow processes. Serves as both a research tool and an educational platform.
Problem statement
African petroleum engineers need accessible simulation tools that can:
• Model heterogeneous and anisotropic reservoirs with realistic property distributions
• Handle mixed well constraints (rate-controlled and BHP-controlled) simultaneously
• Capture gravity effects in structurally complex reservoirs
• Provide transparent, modifiable code for learning and research
Methodology

Step 1 — Grid & properties. Built a 3 × 3 non-uniform 2D heterogeneous Cartesian grid covering 1200 ft × 600 ft with 200 ft thickness. Permeability varies between 1000 and 2500 mD; porosity ranges from 18% to 26%. Anisotropic flow behavior modeled with k_y = 2k_x.

Step 2 — Finite-difference discretization. Discretized the pressure diffusivity equation using finite-difference methods with harmonic averaging for inter-block transmissibility calculations.

Step 3 — Fully implicit formulation. Implemented fully implicit pressure formulation for numerical robustness and unconditional stability. Assembled sparse matrices for efficient linear equation solution.

Step 4 — Gravity-aware initialization. Computed gravity potential calculations to capture flow behavior in reservoirs with variable depth and structural dip.

Step 5 — Well modeling. Implemented two operating strategies: (1) constant-rate producing well at (600 ft, 300 ft) with 10,000 scf/day constraint, and (2) constant BHP well at (1000 ft, 500 ft) operating at 1500 psi. Used Peaceman’s productivity index formulation accounting for wellbore radius, skin effects, effective permeability, grid geometry, and anisotropy corrections.

Step 6 — Sparse computation. Developed entirely in Python using sparse matrix techniques and scientific computing libraries for efficient large-system solution.

Key parameters
Grid: 3 × 3 non-uniform
Area: 1200 × 600 ft
Thickness: 200 ft
Permeability: 1000 – 2500 mD
Porosity: 18% – 26%
Anisotropy: k_y = 2k_x
Wells: 1 rate + 1 BHP
Well configuration
Producer: (600, 300) ft
Rate: 10,000 scf/day
BHP well: (1000, 500) ft
BHP: 1500 psi
Model: Peaceman PI
Skin: Included

[Figure 10: Pressure contour map — early production time]

[Figure 11: Pressure contour map — late production time showing steady state]

[Figure 12: Well flow-rate evolution and BHP trends]

Results & deliverables
• Pressure contour maps at early, intermediate, and late production times
• Spatial visualization of pressure diffusion throughout the reservoir
• Well flow-rate evolution with time for rate-controlled producer
• Bottom-hole pressure trends for BHP-constrained well
• Pressure support and depletion zone identification
• Impact of heterogeneity, gravity, and well placement on reservoir performance
Impact
This simulator provides a powerful educational platform for training students and industry professionals in reservoir engineering, numerical methods, and computational geosciences. It demonstrates GSERC’s capacity to design and implement advanced petroleum engineering software using locally developed expertise, combining reservoir engineering, scientific computing, applied mathematics, and computational geosciences into a single integrated modeling framework.