Alpha. APEX
Reservoir Simulation Module
Multiwell Black Oil Simulator · 3D
IMPES · Finite Difference · Ni×Nj×Nk Layered · Darcy Flow
Idle
STAFF ONLY
3D Layered
IMPES
v2.2
Reservoir 3D
LMB drag · rotate  |  wheel · zoom
Permeability kh (mD)
102000
12×12×4 = 576 cells STOIIP: —
Build 1 · Grid & Structure
Areal grid, layering and datum · drives cell geometry and volumetrics
12×12×4
Parameters
Ni (x-blocks)12
Nj (y-blocks)12
Nk (layers)4
Δx Block (m)120
Δy Block (m)120
Layer Δz (m)8
Top Depth (m SS)2380
Grid Dimensions
Ni × Nj × Nk12×12×4
Active cells576
Cell Δx·Δy·Δz120·120·8 m
Areal extent1.44 km²
Gross thickness32 m
Volumetrics
Bulk volume—
Pore volume—
HCPV—
STOIIP—
STOIIP (MMbbl)—
Vertical Heterogeneity
Kv/Kh0.10
Dykstra-Parsons0.40
k range (layers)—
Avg layer kh200 mD
3D Continuity — Six-Point Stencil (TPFA)
∂(φSₚρₚ)/∂t = ∑[face=x±,y±,z±] Tface·λₚ·(Pₙₑᵢ − Pᵢ) + qₚ
Tz = 2·Kv·Δx·Δy / Δz  ·  Kv = (Kv/Kh)·kh  ·  vertical cross-flow couples layers
Build 2 · Layer Properties
Base rock, per-layer porosity, permeability & net-to-gross · drives 3D heterogeneity
4 layers
Base Rock Parameters
Porosity φ0.22
Perm kh (mD)200
Kv/Kh ratio0.10
Heterogeneity (V_DP)0.4
Layer properties are auto-generated from base rock and the Dykstra-Parsons heterogeneity coefficient, ordered fining-upward. Edit any cell directly — values feed the 3D model and simulation immediately. A high-perm "thief zone" can be created by setting one layer's kh well above the others.
Layer Property Table click values to edit
Permeability Profile vs Depth
Porosity Profile vs Depth
Build 3 · Fluid PVT Properties
Black oil formulation · Standing / Beal correlations · pressure-dependent tables
UndersaturatedPb=190 bar
Fluid Parameters
Pᵢ Init Pres (bar)260
Pb Bubble Pt (bar)190
μₒ Oil Visc (cP)2.2
μw Water Visc (cP)0.5
Bₒ FVF @ Pi1.26
Rₛᵢ Sol GOR90
Black Oil PVT Relations
Bₒ(P)=Bₒb·exp[−cₒ(P−Pb)] for P>Pb · Rₛ(P)=Rₛᵢ(P/Pb)^1.2 for P≤Pb · μₒ(P)=μₒb(Pb/P)^0.6
Oil FVF Bₒ vs P
BₒPb
Solution GOR Rₛ vs P
Rₛ
Oil Viscosity μₒ vs P
μₒ
Gas FVF Bᵍ vs P
Bᵍ
PVT Table
Build 4 · Rock & SCAL
Corey relative permeability · capillary pressure · endpoint saturations
Water-wetCorey
Endpoint Parameters
Swi Connate0.20
Corey Relative Permeability
kᵣₒ=kᵣₒ(Swi)[(1−Sw−Sor)/(1−Swi−Sor)]^nₒ · kᵣw=kᵣw(Sor)[(Sw−Swi)/(1−Swi−Sor)]^nw
Oil-Water Rel Perm
kᵣₒkᵣw
Gas-Oil Rel Perm
kᵣₒgkᵣg
Oil/Water Endpoints
Swi0.20
Sor0.28
kᵣₒ(Swi)0.85
kᵣw(Sor)0.30
nₒ / nw3.0 / 2.5
Gas/Oil Endpoints
Sgc0.05
Slr0.20
kᵣg(Slr)0.75
ng / nog2.0 / 2.5
Compressibility
cr rock4.5e-5 bar⁻¹
cw water4.6e-5 bar⁻¹
ct total~1.5e-4 bar⁻¹
Build 5 · Wells & Completions
Peaceman model · BHP control · per-well parameters · per-layer completions
5 wellsBHP
Field Defaults apply to all non-customised wells · well count regenerates the pattern
Producers3
Injectors2
Pwf Producers (bar)90
Pwf Injectors (bar)360
rw Radius (m)0.11
Skin S3
Peaceman Well Model (per perforated layer)
qₚ = WI·(kᵣₚ/μₚBₚ)·(Pblock−Pwf) · WI=2π·kh·Δz/(ln(r₀/rw)+S) · r₀=0.28√(Δx²+Δy²)/2
Field Map click select · drag move · snaps to cell
Well Inspector
Well Register click a row to edit · ◆ = customised
Inflow Parameters
rw0.11 m
Skin S3.0
Peaceman r₀—
CompletionsPer-layer
Constraints
Prod BHP min90 bar
Inj BHP max360 bar
ControlBHP
Build 6 · Aquifer Model
Analytical influx · Fetkovich / Carter-Tracy · bottom & edge water
Fetkovich
Aquifer Parameters
Aquifer Model
Aquifer Strength1.0
Fetkovich Aquifer
dWe/dt=Jaq·(Paq−Pr) · Paq=Pᵢ(1−We/Wei) · strength multiplier scales Jaq and Wei
Aquifer Influx We vs Time
We cumulative
Aquifer Parameters
ModelFetkovich
Strength ×1.0
DriveEdge + bottom
Connects toLowest layer
Build 7 · Numerical Solver
IMPES · 3D seven-diagonal pressure system · explicit saturation update
IMPES—
Solver & Schedule Parameters
Solver
Δt (days)30
Horizon (yr)12
IMPES Sequence
1. Assemble 3D pressure matrix (7-diag) → solve P implicitly (Gauss-Seidel)
2. Update Sw, Sg explicitly per cell from inter-block fluxes
3. CFL: Δt ≤ φΔx²cₜμ/(2k) · ΔSmax ≤ 0.05 per step
Configuration
MethodIMPES
Pressure solverGauss-Seidel
Tolerance1e-5 bar
Max sweeps200
Timestepping
Δt30 d
Horizon12 yr
Est. steps~146
Status
StateIdle
Steps done0
CPU time—
Simulation Log
Awaiting run command…
Simulation Results
Production forecast · pressure depletion · well performance · 3D saturation evolution is on Mission Control
No results — run simulation
Cum Oil Np
—
10³ m³ SC
Cum Water Wp
—
10³ m³ SC
Avg Res P
—
bar
Final WOR
—
m³/m³
Recovery
—
% STOIIP
Field Rates vs Timem³/d SC
QₒQw
Avg Reservoir Pressurebar
P̄Pb
Cumulative Production10³ m³
NpWp
WOR & GOR vs Time
WORGOR×0.1
Ensemble P10 / P50 / P90
Monte Carlo uncertainty · stochastic realizations around the current model · SPE exceedance convention: P10 high · P90 low
No ensemble — run one
Each realization re-runs the full 3D IMPES engine with parameters sampled around the current base case: layer kh × lognormal(σ=0.35), porosity ± 8%, Kv/Kh × lognormal(σ=0.40), aquifer strength × lognormal(σ=0.50), skin ± 2. The seed makes an ensemble reproducible — same seed and base case give the same percentiles. P10 is the optimistic high case (exceeded with 10% probability), P90 the conservative low case.
Ensemble Control
Realizations25
Idle — uses the current base case
Np P90 · Low
—
10³ m³ SC
Np P50 · Mid
—
10³ m³ SC
Np P10 · High
—
10³ m³ SC
RF P90/P50/P10
—
% STOIIP
P10 / P90 Ratio
—
uncertainty spread
Oil Rate Fanm³/d SC
P50P90–P10 bandBase case
Cumulative Oil Np Fan10³ m³
P50P90–P10 bandBase case
Avg Reservoir Pressure Fanbar
P50P90–P10 bandBase case
Final Np Distribution10³ m³
P90P50P10