Reservoir Simulator 1D 2 Phases
Technical Overview and Mathematical Framework
In this section, we develop a comprehensive, fully implicit 1D two-phase reservoir simulator that models the transient, coupled flow of immiscible oil and water through a heterogeneous porous medium. The simulator is designed to capture the complex fluid-fluid and fluid-rock interactions that occur during waterflooding performance.
The mathematical framework couples the physics of multiphase porous media flow with operational engineering constraints.It incorporates highly nonlinear constitutive relationships—including fluid compressibilities, pressure-dependent viscosities, relative permeability curves, and capillary pressure effects—along with dynamic well control logic and an automated adaptive time-stepping engine.
Governing Flow Equations
The core of the simulator is governed by mass conservation equations for each fluid phase: water (\(w\)) and oil (\(o\)). In a 1D horizontal system, assuming Darcy flow, the partial differential equations(PDEs) are expressed as: Water Phase Mass Conservation:
\[\frac{\partial }{\partial x} \left[ \alpha \frac{k \cdot k_ { rw }}{\mu_w B_w} \frac{\partial P_w}{\partial x} \right] \pm q_w = \frac{1}{\beta} \frac{\partial}{\partial t} \left( \frac{\phi S_w}{ B_w} \right)\]
Oil Phase Mass Conservation:
\[\frac{\partial}{\partial x} \left[ \alpha \frac{ k \cdot k_{ ro} }{\mu_o B_o} \frac{\partial P_o} {\partial x} \right] \pm q_o = \frac{ 1} {\beta} \frac{\partial} {\partial t} \left( \frac{\phi S_o} { B_o} \right)\]
Where: \(P_o\) and \(P_w\) are the oil and water phase pressures respectively (\(\text{psi}\)).
\(S_o\) and \(S_w\) are the oil and water phase saturations, satisfying the algebraic constraint: \(S_o + S_w = 1.0\).
\(k\) is the absolute rock permeability(\(\text{md}\)), and \(\phi\) is the rock porosity.
\(\alpha\) (\(1.127 \times 10^{ -3}\)) and \(\beta\) (\(5.615\ \text{ ft}^3/\text{bbl}\)) are conversion constants matching standard field units.
\(q_w, q_o\) represent volumetric source/sink well terms (\(\text{STB/day}\)).
Constitutive and Petrophysical Relationships
To close the system of equations, several empirical and thermodynamic relationships are explicitly modeled as functions of the primary state variables (\(P_o\) and \(S_w\)):
Phase Pressure Coupling (Capillary Pressure) The water phase pressure is dynamically linked to the oil phase pressure via the laboratory-measured imbibition capillary pressure function (\(P_{ cI}\)):
\[P_w = P_o - P_{ cI} (S_w)\]
The capillary pressure curve is scaled using an effective saturation profile(\(S_{ we}\)):
\[S_{ we} = \frac{ S_w - S_{ wr} } { 1 - S_{ wr} -S_{ or} }\]
\[P_{ cI}(S_w) = P_e \cdot \left[ (S_{we})^{ -0.5}-1 \right]\]
where \(P_e\) is the entry capillary pressure, \(S_{ wr}\) is the residual water saturation, and \(S_{ or}\) is the residual oil saturation.
Relative Permeability(Modified Corey-Brooks Model) Multiphase fluid interference inside the pore throat structure is dictated by power-law relative permeability functions:
\[k_{ rw}(S_w) = k_{ rw0} \cdot(S_{ we})^{ n_w}\]
\[k_{ ro}(S_o) = k_{ ro0} \cdot \left(1 - \frac{(1 - S_o) - S_{wr}}{ 1 - S_{ wr} -S_{ or} }\right)^{n_o}\]
Fluid PVT Behavior (Compressibility and Viscosity) Fluid volumes and flows scale dynamically with local pressure fields to model slightly compressible behaviors:
\[B_o(P_o) = B_{ o0} \cdot e^{c_o(2000 - P_o)} \quad \text{and} \quad B_w(P_w) = B_{ w0} \cdot e^{c_w(2500 - P_w)}\]
\[\mu_o(P_o) = \mu_{o0} \cdot e^{b_o(P_o - 2000)} \quad \text{and} \quad \mu_w(P_w) = \mu_{w0} \cdot e^{b_w(P_w - 2500)}\]
Spatial Discretization &Transmissibilities
The continuous governing equations are discretized in space using a block-centered finite volume formulation.For fluid flow between block \(i\) and block \(i+1\), the inter-block absolute permeability is resolved using a harmonic mean:
\[k_{i+1/2} = \text{Harmmean}(k_i, k_{i+1}) = \cfrac{2}{\cfrac{1}{k_i} + \cfrac{1}{k_{i+1}}}\]
To ensure numerical stability and avoid unphysical oscillations across displacement fronts, the phase fluid mobilities (\(k_{r}/(\mu B)\)) are evaluated using Single-Point Upstream Weighting. The properties are chosen entirely from the cell possessing the higher phase pressure:
\[\begin{split}\left(\cfrac{k_{rw}}{\mu_w B_w} \right)_{i+1/2} = \begin{cases}
\left(\cfrac{k_{rw}}{\mu_w B_w} \right)_i & \text{if} P_{w, i} > P_{w,i+1} \\
\left(\cfrac{k_{rw}}{\mu_w B_w} \right)_{i+1} & \text{if} P_{w, i+1} > P_{ w,i}
\end{cases}\end{split}\]
Wellbore Boundary Equations and Operational Controls Wells represent external localized source/sink boundary constraints modeled via a radial inflow Peaceman formulation. The equivalent well block radius (\(r_e\)) and baseline Well Index (\(WI\)) are evaluated as:
\[r_e = 0.14\sqrt{\Delta x^2 + \Delta y^2}\]
\[WI = \frac{2\pi \alpha \cdot k \cdot \Delta z}{\ln(r_e / r_w)}\]
The individual phase flow rates produced or injected in a grid block are functions of the drawdown between the cell pressure and the wellbore’s bottomhole flowing pressure (\(P_{wf}\)):
\[Q_w = WI \cdot \frac{k_{rw}}{\mu_w B_w} \cdot(P_{ wf} - P_w)\]
\[Q_o = WI \cdot \frac{k_{ro}}{\mu_o B_o} \cdot(P_{ wf} - P_o)\]
Dynamic Constraint Swapping
Wells operate on dual-modifier switching scripts. They enforce target surface volume constraints as long as the system remains within safe pressure limits:
Producer: Operates at a target production rate \(Q_{ target}\). If the calculated \(P_{ wf}\) drops below the mechanical limit \(P_{ min}\) (\(1500\ \text{psi}\)), the control loop automatically switches to variable-rate, fixed-BHP mode (\(P_{ wf} = P_{ min}\)).
Injector: Operates at a target injection rate \(Q_{ target}\). If the injection pressure exceeds a formation fracturing threshold \(P_{ max}\) (\(4500\ \text{psi}\)), the solver seamlessly overrides the control variables to fixed-pressure boundaries (\(P_{wf} = P_{max}\)).
Numerical Solution and Post-Processing Applying backward Euler finite differences (Full_Implicit) in time yields a highly non-linear algebraic system of discrete residual equations at each time level (\(n+1\)). The total mathematical system vector is assembled explicitly via a custom packing scheme:
\[\begin{split}\vec{R}(\vec{x}) = \begin{bmatrix} \vec{R_{oil}} \\ \vec{R_{water}} \\ \vec{R_{wellbore-balance}} \\ \vec{R_{operational-controls}} \end{bmatrix} = \vec{0}\end{split}\]
This combined system is solved iteratively using the high-performance Fsolve method, which is part of the Solver class inside SepalSolver—a proprietary scientific computing and mathematical library developed by CypherCrescent. To maximize computational throughput, the simulator pairs SepalSolver’s root-finding capabilities with an automated adaptive time-stepping loop. If the non-linear solver encounters a convergence failure or an operational constraint violation, the engine automatically cuts the time step size (\(\Delta t\)) by \(75\%\) and retries the step. Conversely, when convergence is achieved rapidly (\(\text{Iterations} < 4\)), the engine safely scales up \(\Delta t\) by \(25\%\) for subsequent steps. Finally, the localized state data histories collected are processed dynamically to output diagnostic performance graphs (tracking fractional water cuts, bottomhole pressures, and overall volumetric sweep efficiency) while compiling a high-speed animated GIF visualizing the propagation of the transient water saturation shock front over time.
// =========================================================================
// STAGE 1: GLOBAL SIMULATION PARAMETERS & FIELD CHARACTERISTICS
// =========================================================================
// Set root project repository path for exporting tracking diagnostics/GIFs
//folderpath = "C:\\Users\\lateef.a.kareem\\Documents\\GitHub\\ReservoirSimulation\\";
// Nblocks: Spatial discretization grid cells
// L: Maximum block boundary index for flow limits
// M: Total number of discrete primary variables tracking
// the porous media blocks (2 variables * 25 blocks)
// Nwells: Count of source/sink boundaries active in the system
int Nblocks = 25, L = Nblocks - 1, M = 2*Nblocks, Nwells = 2;
// Thermodynamic properties, initial pressures (psi),
// initial fluid saturation baselines,
// residual saturation limits (Sw_r, So_r),
// and baseline phase viscosities (cp)
double Pinit = 3000, Sinit = 0.2, Sw_r = 0.10, So_r = 0.15,
μw0 = 5.005, μo0 = 2, kro0 = 1.0, krw0 = 0.30, Pe = 2,
co = 2e-5, cw = 4e-6, cr = 1e-5, bo = 2e-5, bw = 4e-10,
Bw0 = 1.005, Bo0 = 1.4, no = 2.5, nw = 3;
// Well operational specifications using named tuples:
// constraints, metrics, and grid block locations
var Producer =
(MinPressure: 1500.0, ProdRate: 0.0,
OilRate: 0.0, WaterRate: 0.0, Index: 0);
var Injector =
(MaxPressure: 4500.0, InjRate: 0.0,
OilRate: 0.0, WaterRate: 0.0, Index: 24);
// =========================================================================
// STAGE 2: DATA STRUCTURE PACKING & UNPACKING (VECTOR TO PHYSICAL FIELDS)
// =========================================================================
// Unpacks a monolithic 1D solver array back into distinct,
// physically meaningful array fields
(double[], double[], double[], double[]) Unpack(double[] x)
{
int indx = 0;
double[] Po = Zeros(Nblocks), Sw = Zeros(Nblocks),
Pwells = Zeros(Nwells), Qwells = Zeros(Nwells);
// Extract interleaved cell variables: [Po_0, Sw_0, Po_1, Sw_1, ...]
for (int i = 0; i < Nblocks; i++)
{
// Extract Oil Pressure
Po[i] = x[indx++];
// Extract Water Saturation
Sw[i] = x[indx++];
}
// Extract interleaved well variables: [Pwf_0, Q_0, Pwf_1, Q_1, ...]
for (int i = 0; i < Nwells; i++)
{
// Extract Well Bottomhole Pressure (BHP)
Pwells[i] = x[indx++];
// Extract Total Well Volumetric Flow Rate
Qwells[i] = x[indx++];
}
return (Po, Sw, Pwells, Qwells);
}
// Packs separate grid-block and well residuals into a single
// consolidated vector for Fsolve
double[] Pack(double[] Ro, double[] Rw, double[] Rwells, double[] Rcontrol)
{
int indx = 0;
double[] R_total = Zeros(M + 2*Nwells);
// Map conservation equations sequentially to match variable indexing
for (int i = 0; i < Nblocks; i++)
{
// Oil mass conservation residual
R_total[indx++] = Ro[i];
// Water mass conservation residual
R_total[indx++] = Rw[i];
}
for (int i = 0; i < Nwells; i++)
{
// Wellbore mass balance residual
R_total[indx++] = Rwells[i];
// Well operating constraint/control residual
R_total[indx++] = Rcontrol[i];
}
return R_total;
}
// =========================================================================
// STAGE 3: CONSTITUTIVE EQUATIONS & PETROPHYSICAL RELATIONS
// =========================================================================
// Normalized and effective water saturations used to
// calculate relative permeabilities and capillary pressures
double Sws(double Sw) => (Sw - Sw_r)/(1 - Sw_r);
double Swe(double Sw) => (Sw - Sw_r)/(1 - Sw_r - So_r);
// Capillary Pressure relationships (Drainage vs Imbibition curves)
double Pc_D(double Sw) => Pe * Pow(Sws(Sw), -0.5);
double Pc_I(double Sw) => Pe * (Pow(Swe(Sw), -0.5) - 1);
// Formation Volume Factors (B-factors) modeling fluid compressibility
double Bo(double Po) => Bo0 * Exp(co*(1500 - Po));
double Bw(double Pw) => Bw0 * Exp(cw*(2500 - Pw));
// Pressure-dependent dynamic fluid viscosities
double μo(double Po) => μo0 * Exp(bo*(Po - 1500));
double μw(double Pw) => μw0 * Exp(bw*(Pw - 2500));
// Modified Corey Brooks models evaluating relative permeability curves
double Krw(double Sw) => krw0 * Pow(Swe(Sw), nw);
double Kro(double So) => kro0 * Pow(1 - Swe(1 - So), no);
// Inter-block transmissibility calculation using the
// harmonic mean of raw cell permeabilities
double Harmmean(double x1, double x2) => 2/(1/x1 + 1/x2);
// Unit conversion coefficients for oilfield standard parameters
// =================================================================
// Transmissibility conversion factor (Darcy to Field Units)
double alpha = 1.127e-3;
// Geometric productivity factor conversion for radial well inflows
double alpha_well = alpha*2*pi;
// Reservoir volume factor (Cubic feet to Stock Tank Barrels)
double beta = 5.615;
// Spatial dimensions (ft), block pore volume (STB),
// and well radius parameters
double dt, Dx = 200, Dy = 1000, Dz = 20, Ax = Dy*Dz,
V = Dx*Dy*Dz/beta, rw = 0.5, re, WI, WIw, WIo;
// Heterogeneous field instantiation using a
// normal distribution for porosity and permeability
// Localized Porosity array
double[] Phi = Randn(Nblocks, 0.2, 0.01);
// Localized Permeability array (md)
double[] K = Randn(Nblocks, 900.0, 300.0);
// Arrays storing baseline values at historical time level (n)
double[] Po_n, Sw_n, Pwells_n, Qwells_n, Pw_n, So_n;
// Tracks operational control mode for each well
// (True = Rate, False = Pressure)
bool[] RateControl = [true, true];
// =========================================================================
// STAGE 4: NONLINEAR RESIDUAL FORMULATION (MASS CONSERVATION & WELL EQUATIONS)
// =========================================================================
double[] Residual(double[] xnp1)
{
double Po_up, Pw_up, So_up, Sw_up, Tr, Tw, To;
// Unpack current iteration guess variables for evaluation
var (Po_np1, Sw_np1, Pwells_np1, Qwells_np1) = Unpack(xnp1);
// Calculate dependent properties using
// capillary pressure and saturation definitions
double[] Pw_np1 = [.. Po_np1.Zip(Sw_np1, (po, sw) => po - Pc_I(sw))],
So_np1 = [.. Sw_np1.Select(sw => 1 - sw)];
double[] Rw = Zeros(Nblocks), Ro = Zeros(Nblocks),
Rwells = Zeros(Nwells), Rcontrol = Zeros(Nwells);
// Grid block mass balance accumulation loop
for (int i = 0; i < Nblocks; i++)
{
// Inter-block inter-flux flux logic (Left neighbor interaction)
if (i > 0)
{
Tr = alpha*Ax*Harmmean(K[i-1], K[i]);
// Single-point upstream weighting for water phase stability
(Pw_up, Sw_up) = Pw_np1[i-1] > Pw_np1[i] ?
(Pw_np1[i-1], Sw_np1[i-1]) : (Pw_np1[i], Sw_np1[i]);
Tw = Tr*Krw(Sw_up)/(μw(Pw_up)*Bw(Pw_up));
Rw[i] += Tw*(Pw_np1[i-1] - Pw_np1[i])/Dx;
// Single-point upstream weighting for oil phase stability
(Po_up, So_up) = Po_np1[i-1] > Po_np1[i] ?
(Po_np1[i-1], So_np1[i-1]) : (Po_np1[i], So_np1[i]);
To = Tr*Kro(So_up)/(μo(Po_up)*Bo(Po_up));
Ro[i] += To*(Po_np1[i-1] - Po_np1[i])/Dx;
}
// Inter-block inter-flux flux logic (Right neighbor interaction)
if (i < L)
{
Tr = alpha*Ax*Harmmean(K[i], K[i+1]);
// Single-point upstream weighting for water phase stability
(Pw_up, Sw_up) = Pw_np1[i+1] > Pw_np1[i] ?
(Pw_np1[i+1], Sw_np1[i+1]) : (Pw_np1[i], Sw_np1[i]);
Tw = Tr*Krw(Sw_up)/(μw(Pw_up)*Bw(Pw_up));
Rw[i] += Tw*(Pw_np1[i+1] - Pw_np1[i])/Dx;
// Single-point upstream weighting for oil phase stability
(Po_up, So_up) = Po_np1[i+1] > Po_np1[i] ?
(Po_np1[i+1], So_np1[i+1]) : (Po_np1[i], So_np1[i]);
To = Tr*Kro(So_up)/(μo(Po_up)*Bo(Po_up));
Ro[i] += To*(Po_np1[i+1] - Po_np1[i])/Dx;
}
// Time accumulation terms (implicit backward Euler method)
Rw[i] -= V*Phi[i]*(Sw_np1[i]/Bw(Pw_np1[i]) - Sw_n[i]/Bw(Pw_n[i]))/dt;
Ro[i] -= V*Phi[i]*(So_np1[i]/Bo(Po_np1[i]) - So_n[i]/Bo(Po_n[i]))/dt;
}
// Peaceman radius calculation for an isolated wellbore
re = 0.14*Hypot(Dx, Dy);
int idx;
// --- Well Formulation: Producer Section ---
Rwells[0] += Qwells_np1[0];
idx = Producer.Index;
// Base Well Index calculation
WI = alpha_well*K[idx]*Dz/Log(re/rw);
// Water mobility at well
WIw = WI*Krw(Sw_np1[idx])/(μw(Pw_np1[idx])*Bw(Pw_np1[idx]));
// Oil mobility at well
WIo = WI*Kro(So_np1[idx])/(μo(Po_np1[idx])*Bo(Po_np1[idx]));
// Calculate phase flow rates using the wellbore
// pressure and connected grid cell properties
Producer.WaterRate = (Pwells_np1[0] - Pw_np1[Producer.Index])*WIw;
Producer.OilRate = (Pwells_np1[0] - Po_np1[Producer.Index])*WIo;
// Inject sink terms directly back into the connected grid cell
Rw[Producer.Index] += Producer.WaterRate;
Ro[Producer.Index] += Producer.OilRate;
// Well balance check
Rwells[0] -= Producer.WaterRate + Producer.OilRate;
// Evaluate dynamic constraint swapping logic
// (Switch between Target Rate vs Minimum Allowed BHP)
Rcontrol[0] = RateControl[0] ?
Qwells_np1[0] - Producer.ProdRate : Pwells_np1[0] - Producer.MinPressure;
// --- Well Formulation: Injector Section ---
Rwells[1] += Qwells_np1[1];
idx = Injector.Index;
// Base Well Index calculation
WI = alpha_well*K[idx]*Dz/Log(re/rw);
// Injecting pure water phase
WIw = WI*krw0/(μw(Pw_np1[idx])*Bw(Pw_np1[idx]));
// Calculate injection rate using the
// wellbore pressure and connected grid cell properties
Injector.WaterRate = (Pwells_np1[1] - Pw_np1[idx])*WIw;
// Inject source terms directly back into the connected grid cell
Rw[idx] += Injector.WaterRate;
// Well balance check
Rwells[1] -= Injector.WaterRate;
// Evaluate dynamic constraint swapping logic
// (Switch between Target Rate vs Maximum Allowed BHP)
Rcontrol[1] = RateControl[1] ?
Qwells_np1[1] - Injector.InjRate : Pwells_np1[1] - Injector.MaxPressure;
// Consolidate values back into a single vector for solver optimization loops
return Pack(Ro, Rw, Rwells, Rcontrol);
}
// Mathematical mapping and linear interpolation helper utilities
double betweenab(double a, double b, double f) => a + f*(b-a);
double interps(List<double> X, List<double> Y, double x)
{
int i = X.FindIndex(xi => xi>x);
double f = (x-X[i-1])/(X[i]-X[i-1]);
return betweenab(Y[i-1], Y[i], f);
}
double[] interpa(List<double> X, List<double[]> Y, double x)
{
int i = X.FindIndex(xi => xi>x);
double f = (x-X[i-1])/(X[i]-X[i-1]);
return [.. Y[i-1].Zip(Y[i], (a, b) => betweenab(a, b, f))];
}
// chunk writer utility for formatted console output of array values
string Write(double[] data)
{
var chunks = data.Chunk(8);
List<string> sb = [];
foreach (var chunk in chunks)
sb.Add(string.Join(", ", chunk.Select(x => x.ToString("F2"))));
return string.Join(", \n", sb);
}
// =========================================================================
// STAGE 5: RUNTIME EXECUTION MANAGEMENT LOOP & SENSITIVITY DESIGN
// =========================================================================
double EndTime = 10000; // Target simulation duration limit (days)
double delt = EndTime/300; // Time steps for reporting intervals
// Sensitivity loop testing performance metrics across varying injection-production rates
for (int rate = 200; rate <= 500; rate += 100)
{
dt = 0.01; // Reset to a safe initial time step value
// Initialize state vectors for a new sensitivity run
Po_n = Repmat(Pinit, Nblocks); Sw_n = Repmat(Sinit, Nblocks);
Pwells_n = Repmat(Pinit, Nwells); Qwells_n = Zeros(Nwells);
Pw_n = [.. Po_n.Zip(Sw_n, (po, sw) => po - Pc_I(sw))];
So_n = [.. Sw_n.Select(sw => 1 - sw)];
// Initialize historical data tracking containers for plotting and reporting
List<double[]> P = [Po_n], S = [Sw_n];
List<double> Time = [0.0], WaterCut = [0.0], SweepEff = [0.0],
ProdRate = [Qwells_n[0]], InjRate = [Qwells_n[1]],
ProdPwf = [Pwells_n[0]], InjPwf = [Pwells_n[1]];
// Define specific production/injection targets for this scenario run
Producer.ProdRate = -rate;
Injector.InjRate = rate;
// Initialize Plot Subplots for Real-Time Visual Feedback Diagnostics
Subplot(7, 4, [0, 1, 4, 5]);
var Pbhp = Plot([0], [0], "r", 2);
Axis([0, EndTime, 0, Injector.MaxPressure*1.1]);
Title("Producer BHP");
Subplot(7, 4, [8, 9, 12, 13]);
var Prate = Plot([0], [0], "r", 2);
Axis([0, EndTime, 0, Producer.ProdRate*1.1]);
Title("Producer Rate");
Subplot(7, 4, [16, 17, 20, 21]);
var Pbsw = Plot([0], [0], "r", 2);
Axis([0, EndTime, 0, 105]);
Title("Producer WaterCut");
Subplot(7, 4, [2, 3, 6, 7]);
var Ibhp = Plot([0], [0], "b", 2);
Axis([0, EndTime, 0, Injector.MaxPressure*1.1]);
Title("Injector BHP");
Subplot(7, 4, [10, 11, 14, 15]);
var Irate = Plot([0], [0], "b", 2);
Axis([0, EndTime, 0, Injector.InjRate*1.1]);
Title("Injector Rate");
Subplot(7, 4, [18, 19, 22, 23]);
var Iswp = Plot([0], [0], "b", 2);
Axis([0, EndTime, 0, 105]);
Title("Injector Sweep Efficiency");
// Spatial Profile Schematic setup for the moving Water Saturation Front
Subplot(7, 4, [24, 25, 26, 27]);
double[] xpf = [0.3, 0.7], ypf = Linspace(0.3, 0.7, 5);
var (xperf, yperf) = Meshgrid(xpf, ypf);
Rectangle([Producer.Index + 0.45, 0.2, 0.1, 1.6]); HoldOn();
Plot(Producer.Index + xperf, yperf, "k", 2);
Rectangle([Injector.Index + 0.45, 0.2, 0.1, 1.6]);
Plot(Injector.Index + xperf, yperf, "k", 2);
double[] xres = [0, 0, Nblocks, Nblocks], yres = [0, 1, 1, 0];
Fill(xres, yres, [1, 0, 0], 0.5);
xpf = Linspace(0.5, Nblocks - 0.5, Nblocks);
ypf = Repmat(Sinit, Nblocks + 2);
double[] xplot = [0, 0, .. xpf, Nblocks, Nblocks];
double[] yplot = [0, .. ypf, 0];
var Water = Fill(xplot, yplot, [0, 0, 1], 0.5, 0);
Axis([0, Nblocks, 0, 2.5]);
Title("Water Saturation Front");
HoldOff();
// Package the initial state vector and configure the nonlinear solver options
double[] xs = Pack(Po_n, Sw_n, Pwells_n, Qwells_n), xn;
var opts = SolverSet(MaxIter: 10, AbsTol: 1e-6, UseParallel: true);
Console.WriteLine($"""
======================================================================
Starting simulation for Rate = {rate} STB/day
Time:
{0:F2} days
Producer BHP:
{Pinit:F2} psi
Injector BHP:
{Pinit:F2} psi
Pressure:
{Write(Po_n)}
Saturation:
{Write(Sw_n)}
""");
// =========================================================================
// STAGE 6: CORE TIME-STEPPING INTERACTION LOOP (NEWTON RAPHSON + CONTROLS)
// =========================================================================
double[] displaytimes = Linspace(0, EndTime, 21);
double printtime = 0;
while (Time.Last() < EndTime)
{
if (displaytimes.Any(t =>
(Time.Last() - t)*(Time.Last() + dt - t) < 0))
{
opts.Display = true;
printtime = Array.Find(displaytimes,
t => (Time.Last() - t)*(Time.Last() + dt - t) < 0);
}
else
{
opts.Display = false;
}
if (opts.Display)
Console.WriteLine($"""
Time:
{printtime:F2} days
""");
// Call the Newton-Raphson nonlinear solver to
// find the next state solution
xn = [.. Fsolve(Residual, xs, opts)];
// Check convergence. If non-converged,
// chop the time step (time-step cuts) and retry.
if (!opts.ans.IsConverged)
{
dt = 0.25*dt;
Console.WriteLine("""
================================================
Rejected (Non-Convergence)
================================================
""");
continue;
}
// Unpack solution values to evaluate operational constraint validations
var (Po_s, Sw_s, Pwells_s, Qwells_s) = Unpack(xn);
// Validate Producer constraints:
// switch to BHP control if pressure falls below minimum limits
if (Pwells_s[0] < Producer.MinPressure)
{
RateControl[0] = Pwells_s[0] > Producer.MinPressure;
Console.WriteLine("""
================================================
Rejected (Minimum Pressure Violated)
================================================
""");
continue;
}
// Validate Injector constraints:
// switch to BHP control if pressure exceeds fracturing limits
if (Pwells_s[1] > Injector.MaxPressure)
{
RateControl[1] = Pwells_s[1] < Injector.MaxPressure;
Console.WriteLine("""
================================================
Rejected (Maximum Pressure Violated)
================================================
""");
continue;
}
// Accept the validated time step and update internal tracking states
(Po_n, Sw_n, Pwells_n, Qwells_n) = (Po_s, Sw_s, Pwells_s, Qwells_s);
Pw_n = [.. Po_n.Zip(Sw_n, (po, sw) => po - Pc_I(sw))];
So_n = [.. Sw_n.Select(sw => 1 - sw)];
// Log verified parameters to performance history arrays
P.Add(Po_n); S.Add(Sw_n);
ProdPwf.Add(Pwells_n[0]); InjPwf.Add(Pwells_n[1]);
ProdRate.Add(Qwells_n[0]); InjRate.Add(Qwells_n[1]);
WaterCut.Add(Producer.WaterRate*100/(Producer.WaterRate + Producer.OilRate));
SweepEff.Add((Sw_n.Sum()/Nblocks - Sinit)*100/(1 - Sinit));
Time.Add(Time.Last() + dt);
// Adaptive Time-Stepping Logic:
// scale dt up if convergence is fast, scale down if slow
if (opts.ans.Iter < 4) dt = 1.25*dt;
if (opts.ans.Iter > 8) dt = 0.5*dt;
if (dt < 1e-5) throw new Exception("time step is too small");
// Set current solution vector as the next time step initialization guess (xs)
xs = [.. xn];
if (opts.Display)
{
Console.WriteLine($"""
Producer BHP:
{interps(Time, ProdPwf, printtime):F2} psi
Injector BHP:
{interps(Time, InjPwf, printtime):F2} psi
Pressure:
{Write(interpa(Time, P, printtime))}
Saturation:
{Write(interpa(Time, S, printtime))}
""");
}
}
// =========================================================================
// STAGE 7: POST-PROCESSING VISUALIZATION & ANIMATION EXPORT
// =========================================================================
// Dynamic closure map function mapping raw state histories
// directly onto figure frames
byte[] Animfun(int i)
{
// Sync time dimensions to interpolation index targets
Pbhp.Xdata = Vcart(Pbhp.Xdata, i*delt);
Pbhp.Ydata = Vcart(Pbhp.Ydata, interps(Time, ProdPwf, i*delt));
Prate.Xdata = Pbhp.Xdata;
Prate.Ydata = Vcart(Prate.Ydata, interps(Time, ProdRate, i*delt));
Pbsw.Xdata = Pbhp.Xdata;
Pbsw.Ydata = Vcart(Pbsw.Ydata, interps(Time, WaterCut, i*delt));
Ibhp.Xdata = Pbhp.Xdata;
Ibhp.Ydata = Vcart(Ibhp.Ydata, interps(Time, InjPwf, i*delt));
Irate.Xdata = Pbhp.Xdata;
Irate.Ydata = Vcart(Irate.Ydata, interps(Time, InjRate, i*delt));
Iswp.Xdata = Pbhp.Xdata;
Iswp.Ydata = Vcart(Iswp.Ydata, interps(Time, SweepEff, i*delt));
// Generate spatial mapping visualization showing fluid front changes over time
Sw_n = interpa(Time, S, i*delt);
yplot = [0, Sw_n.First(), .. Sw_n, Sw_n.Last(), 0];
Water.Ydata = yplot;
// Capture rendered visual asset frame dimensions
return GetFrame(800, 1000);
}
// Compile and output the processed timeline visualization to an animated GIF
Console.WriteLine(DateTime.Now);
AnimationMaker(Animfun, $"1D_WaterFlooding_{rate}.gif", 30, 300);
Console.WriteLine(DateTime.Now);
// Clean up graphics devices to free memory hooks for the next loop run
CloseFig();
}
Ouput
======================================================================
Starting simulation for Rate = 200 STB/day
Time:
0.00 days
Producer BHP:
3000.00 psi
Injector BHP:
3000.00 psi
Pressure:
3000.00, 3000.00, 3000.00, 3000.00, 3000.00, 3000.00, 3000.00, 3000.00,
3000.00, 3000.00, 3000.00, 3000.00, 3000.00, 3000.00, 3000.00, 3000.00,
3000.00, 3000.00, 3000.00, 3000.00, 3000.00, 3000.00, 3000.00, 3000.00,
3000.00
Saturation:
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20
Time:
500.00 days
Iteration Func-count f(x) Norm of Step
0 1 194.152 start
1 56 0.00241 5.58969
2 57 1.983e-006 6.541e-004
3 58 3.308e-009 1.087e-007
4 59 6.067e-011 2.084e-010
Producer BHP:
2260.02 psi
Injector BHP:
2598.57 psi
Pressure:
2308.29, 2317.00, 2324.20, 2331.08, 2337.38, 2345.53, 2353.09, 2361.06,
2369.62, 2375.85, 2382.58, 2390.64, 2397.20, 2402.45, 2408.11, 2413.16,
2419.42, 2426.86, 2434.75, 2445.40, 2455.81, 2466.09, 2476.06, 2490.40,
2524.26
Saturation:
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.39,
0.69
Time:
1000.00 days
Iteration Func-count f(x) Norm of Step
0 1 185.256 start
1 56 0.00284 5.94753
2 57 2.153e-006 5.671e-004
3 58 5.347e-009 1.406e-007
4 59 7.539e-011 5.701e-010
Producer BHP:
1612.46 psi
Injector BHP:
2014.64 psi
Pressure:
1660.83, 1669.55, 1676.76, 1683.64, 1689.93, 1698.06, 1705.61, 1713.55,
1722.07, 1728.27, 1734.96, 1742.97, 1749.48, 1754.67, 1760.28, 1765.28,
1771.46, 1778.80, 1786.58, 1797.07, 1807.31, 1817.80, 1855.19, 1908.96,
1940.04
Saturation:
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.20, 0.20, 0.20, 0.21, 0.49, 0.71,
0.76
================================================
Rejected (Minimum Pressure Violated)
================================================
Time:
1500.00 days
Iteration Func-count f(x) Norm of Step
0 1 162.271 start
1 56 0.00251 0.44495
2 57 2.112e-006 1.955e-004
3 58 1.997e-009 3.134e-007
4 59 5.937e-011 1.661e-010
Producer BHP:
1500.00 psi
Injector BHP:
1945.54 psi
Pressure:
1534.80, 1541.15, 1546.45, 1551.58, 1556.33, 1562.54, 1568.38, 1574.60,
1581.37, 1586.35, 1591.81, 1598.42, 1603.86, 1608.27, 1613.09, 1617.45,
1622.90, 1629.49, 1636.58, 1646.29, 1656.99, 1711.73, 1793.03, 1842.08,
1870.88
Saturation:
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.20, 0.20, 0.23, 0.56, 0.72, 0.76,
0.79
Time:
2000.00 days
Iteration Func-count f(x) Norm of Step
0 1 150.500 start
1 56 0.00205 0.49140
2 57 5.543e-006 1.311e-004
3 58 4.823e-009 2.543e-007
4 59 4.746e-011 2.258e-010
Producer BHP:
1500.00 psi
Injector BHP:
2028.16 psi
Pressure:
1534.78, 1541.12, 1546.43, 1551.55, 1556.29, 1562.50, 1568.34, 1574.56,
1581.33, 1586.31, 1591.76, 1598.36, 1603.81, 1608.22, 1613.03, 1617.39,
1622.85, 1629.43, 1636.53, 1649.34, 1720.46, 1803.26, 1879.39, 1925.85,
1953.51
Saturation:
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.20, 0.27, 0.62, 0.73, 0.76, 0.78,
0.80
Time:
2500.00 days
Iteration Func-count f(x) Norm of Step
0 1 165.942 start
1 56 0.00319 0.26278
2 57 1.291e-005 1.730e-004
3 58 1.140e-008 6.328e-007
4 59 7.083e-011 7.808e-010
Producer BHP:
1500.00 psi
Injector BHP:
2104.88 psi
Pressure:
1534.86, 1541.22, 1546.54, 1551.67, 1556.42, 1562.65, 1568.50, 1574.73,
1581.51, 1586.50, 1591.96, 1598.59, 1604.04, 1608.46, 1613.28, 1617.65,
1623.12, 1629.74, 1642.70, 1725.20, 1807.29, 1885.58, 1958.44, 2003.31,
2030.24
Saturation:
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.34, 0.67, 0.73, 0.76, 0.77, 0.79,
0.81
Time:
3000.00 days
Iteration Func-count f(x) Norm of Step
0 1 177.315 start
1 56 0.00591 0.26287
2 57 2.493e-005 3.406e-004
3 58 1.283e-008 1.725e-006
4 59 4.944e-011 6.795e-010
Producer BHP:
1500.00 psi
Injector BHP:
2151.99 psi
Pressure:
1534.88, 1541.24, 1546.57, 1551.70, 1556.46, 1562.68, 1568.54, 1574.77,
1581.56, 1586.55, 1592.01, 1598.64, 1604.10, 1608.52, 1613.34, 1617.71,
1623.24, 1639.51, 1701.08, 1783.10, 1861.18, 1936.53, 2007.18, 2050.93,
2077.36
Saturation:
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.40, 0.69, 0.74, 0.76, 0.77, 0.78, 0.80,
0.81
Time:
3500.00 days
Iteration Func-count f(x) Norm of Step
0 1 174.593 start
1 56 0.00680 0.30776
2 57 2.788e-005 3.986e-004
3 58 6.532e-009 2.032e-006
4 59 4.046e-011 3.993e-010
Producer BHP:
1500.00 psi
Injector BHP:
2192.07 psi
Pressure:
1534.86, 1541.22, 1546.53, 1551.66, 1556.42, 1562.64, 1568.49, 1574.72,
1581.50, 1586.48, 1591.95, 1598.56, 1604.02, 1608.43, 1613.25, 1617.74,
1635.30, 1692.68, 1752.21, 1830.74, 1906.20, 1979.47, 2048.49, 2091.40,
2117.45
Saturation:
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.21,
0.45, 0.69, 0.74, 0.76, 0.77, 0.78, 0.79, 0.80,
0.81
Time:
4000.00 days
Iteration Func-count f(x) Norm of Step
0 1 161.595 start
1 56 0.00679 0.38220
2 57 2.040e-005 3.400e-004
3 58 6.846e-009 1.631e-006
4 59 4.417e-011 2.938e-010
Producer BHP:
1500.00 psi
Injector BHP:
2226.06 psi
Pressure:
1534.82, 1541.17, 1546.48, 1551.60, 1556.35, 1562.56, 1568.41, 1574.63,
1581.40, 1586.38, 1591.84, 1598.45, 1603.89, 1608.30, 1613.50, 1634.10,
1681.63, 1736.90, 1794.16, 1870.38, 1943.98, 2015.69, 2083.44, 2125.70,
2151.44
Saturation:
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.22, 0.53,
0.70, 0.74, 0.76, 0.77, 0.78, 0.78, 0.79, 0.80,
0.82
Time:
4500.00 days
Iteration Func-count f(x) Norm of Step
0 1 146.772 start
1 56 0.00349 0.46385
2 57 6.673e-006 7.976e-005
3 58 1.003e-008 1.771e-007
4 59 4.947e-011 3.340e-010
Producer BHP:
1500.00 psi
Injector BHP:
2259.72 psi
Pressure:
1534.77, 1541.10, 1546.40, 1551.52, 1556.26, 1562.46, 1568.29, 1574.50,
1581.27, 1586.24, 1591.69, 1598.29, 1603.73, 1609.23, 1641.72, 1679.42,
1725.03, 1778.29, 1834.03, 1908.56, 1980.70, 2051.16, 2117.89, 2159.61,
2185.11
Saturation:
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.20, 0.20, 0.20, 0.26, 0.60, 0.72,
0.74, 0.76, 0.77, 0.78, 0.78, 0.79, 0.80, 0.81,
0.82
Time:
5000.00 days
Iteration Func-count f(x) Norm of Step
0 1 160.233 start
1 56 0.00419 0.27692
2 57 2.034e-005 1.657e-004
3 58 2.740e-008 7.436e-007
4 59 4.834e-011 1.546e-009
Producer BHP:
1500.00 psi
Injector BHP:
2293.89 psi
Pressure:
1534.84, 1541.19, 1546.51, 1551.63, 1556.38, 1562.60, 1568.44, 1574.67,
1581.44, 1586.43, 1591.89, 1598.52, 1607.72, 1644.16, 1685.60, 1721.86,
1766.07, 1818.12, 1872.82, 1946.14, 2017.22, 2086.74, 2152.68, 2193.98,
2219.28
Saturation:
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.20, 0.20, 0.33, 0.66, 0.72, 0.75,
0.76, 0.77, 0.77, 0.78, 0.79, 0.79, 0.80, 0.81,
0.82
Time:
5500.00 days
Iteration Func-count f(x) Norm of Step
0 1 169.980 start
1 56 0.00636 0.38401
2 57 3.039e-005 3.656e-004
3 58 1.408e-008 2.041e-006
4 59 3.257e-011 6.924e-010
Producer BHP:
1500.00 psi
Injector BHP:
2331.47 psi
Pressure:
1534.79, 1541.13, 1546.43, 1551.55, 1556.29, 1562.50, 1568.33, 1574.55,
1581.31, 1586.29, 1591.79, 1607.56, 1654.29, 1691.74, 1731.52, 1766.70,
1809.85, 1860.88, 1914.67, 1986.88, 2056.97, 2125.62, 2190.83, 2231.75,
2256.87
Saturation:
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.20, 0.40, 0.68, 0.73, 0.75, 0.76,
0.77, 0.77, 0.78, 0.78, 0.79, 0.80, 0.80, 0.81,
0.82
Time:
6000.00 days
Iteration Func-count f(x) Norm of Step
0 1 170.981 start
1 56 0.00759 0.45631
2 57 3.314e-005 4.633e-004
3 58 2.794e-009 2.551e-006
4 59 4.742e-011 1.806e-010
Producer BHP:
1500.00 psi
Injector BHP:
2377.34 psi
Pressure:
1534.75, 1541.08, 1546.38, 1551.49, 1556.23, 1562.42, 1568.25, 1574.45,
1581.21, 1586.35, 1605.81, 1663.25, 1709.31, 1745.45, 1784.17, 1818.59,
1860.96, 1911.18, 1964.20, 2035.46, 2104.71, 2172.61, 2237.19, 2277.78,
2302.75
Saturation:
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.21, 0.47, 0.70, 0.74, 0.75, 0.76, 0.77,
0.77, 0.78, 0.78, 0.79, 0.79, 0.80, 0.81, 0.82,
0.82
Time:
6500.00 days
Iteration Func-count f(x) Norm of Step
0 1 157.546 start
1 56 0.00588 0.56858
2 57 1.344e-005 2.955e-004
3 58 9.603e-009 1.244e-006
4 59 4.264e-011 5.135e-010
Producer BHP:
1500.00 psi
Injector BHP:
2415.44 psi
Pressure:
1534.68, 1541.00, 1546.28, 1551.38, 1556.11, 1562.29, 1568.10, 1574.30,
1581.73, 1607.70, 1654.95, 1710.38, 1754.88, 1790.17, 1828.10, 1861.93,
1903.65, 1953.17, 2005.52, 2075.96, 2144.46, 2211.70, 2275.73, 2316.03,
2340.87
Saturation:
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.23, 0.54, 0.71, 0.74, 0.75, 0.76, 0.77, 0.77,
0.78, 0.78, 0.79, 0.79, 0.80, 0.80, 0.81, 0.82,
0.83
Time:
7000.00 days
Iteration Func-count f(x) Norm of Step
0 1 144.796 start
1 56 0.00302 0.78223
2 57 8.047e-006 1.439e-004
3 58 8.396e-009 3.255e-007
4 59 5.576e-011 2.920e-010
Producer BHP:
1500.00 psi
Injector BHP:
2462.59 psi
Pressure:
1534.54, 1540.83, 1546.10, 1551.17, 1555.88, 1562.04, 1567.84, 1575.66,
1623.65, 1666.46, 1711.82, 1765.46, 1808.88, 1843.47, 1880.74, 1914.03,
1955.15, 2004.01, 2055.73, 2125.37, 2193.17, 2259.78, 2323.29, 2363.31,
2388.02
Saturation:
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.26,
0.61, 0.72, 0.74, 0.75, 0.76, 0.77, 0.77, 0.78,
0.78, 0.78, 0.79, 0.79, 0.80, 0.80, 0.81, 0.82,
0.83
Time:
7500.00 days
Iteration Func-count f(x) Norm of Step
0 1 154.694 start
1 56 0.00336 0.50085
2 57 1.551e-005 1.821e-004
3 58 3.578e-008 5.215e-007
4 59 4.506e-011 1.587e-009
Producer BHP:
1500.00 psi
Injector BHP:
2510.37 psi
Pressure:
1534.69, 1541.01, 1546.29, 1551.39, 1556.12, 1562.32, 1571.39, 1621.68,
1679.73, 1721.12, 1765.42, 1818.18, 1861.04, 1895.25, 1932.15, 1965.14,
2005.89, 2054.35, 2105.67, 2174.79, 2242.11, 2308.28, 2371.40, 2411.21,
2435.82
Saturation:
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.31, 0.65,
0.72, 0.74, 0.75, 0.76, 0.77, 0.77, 0.77, 0.78,
0.78, 0.79, 0.79, 0.80, 0.80, 0.81, 0.81, 0.82,
0.83
Time:
8000.00 days
Iteration Func-count f(x) Norm of Step
0 1 164.236 start
1 56 0.00487 0.41397
2 57 2.348e-005 2.285e-004
3 58 7.834e-009 1.300e-006
4 59 4.547e-011 3.172e-010
Producer BHP:
1500.00 psi
Injector BHP:
2550.28 psi
Pressure:
1534.73, 1541.06, 1546.35, 1551.46, 1556.22, 1568.53, 1617.77, 1670.82,
1726.89, 1767.30, 1810.84, 1862.87, 1905.21, 1939.05, 1975.58, 2008.26,
2048.66, 2096.72, 2147.63, 2216.25, 2283.10, 2348.84, 2411.60, 2451.22,
2475.74
Saturation:
0.20, 0.20, 0.20, 0.20, 0.20, 0.36, 0.67, 0.73,
0.75, 0.75, 0.76, 0.77, 0.77, 0.77, 0.78, 0.78,
0.79, 0.79, 0.79, 0.80, 0.80, 0.81, 0.81, 0.82,
0.83
Time:
8500.00 days
Iteration Func-count f(x) Norm of Step
0 1 170.770 start
1 56 0.00658 0.36491
2 57 3.273e-005 3.143e-004
3 58 2.032e-008 1.990e-006
4 59 4.540e-011 1.080e-009
Producer BHP:
1500.00 psi
Injector BHP:
2591.05 psi
Pressure:
1534.76, 1541.09, 1546.38, 1551.57, 1564.41, 1618.04, 1667.72, 1719.07,
1773.91, 1813.65, 1856.61, 1908.03, 1949.92, 1983.43, 2019.63, 2052.02,
2092.09, 2139.77, 2190.31, 2258.45, 2324.87, 2390.23, 2452.65, 2492.09,
2516.52
Saturation:
0.20, 0.20, 0.20, 0.21, 0.42, 0.69, 0.73, 0.75,
0.76, 0.76, 0.77, 0.77, 0.77, 0.78, 0.78, 0.78,
0.79, 0.79, 0.80, 0.80, 0.81, 0.81, 0.82, 0.82,
0.83
Time:
9000.00 days
Iteration Func-count f(x) Norm of Step
0 1 169.230 start
1 56 0.00692 0.47287
2 57 2.837e-005 4.474e-004
3 58 7.624e-009 2.508e-006
4 59 4.803e-011 6.843e-010
Producer BHP:
1500.00 psi
Injector BHP:
2622.54 psi
Pressure:
1534.68, 1541.00, 1546.51, 1565.68, 1606.77, 1659.27, 1707.32, 1757.53,
1811.42, 1850.58, 1892.99, 1943.82, 1985.27, 2018.45, 2054.31, 2086.42,
2126.14, 2173.46, 2223.63, 2291.30, 2357.30, 2422.28, 2484.39, 2523.66,
2548.02
Saturation:
0.20, 0.20, 0.21, 0.48, 0.70, 0.73, 0.75, 0.76,
0.76, 0.77, 0.77, 0.77, 0.78, 0.78, 0.78, 0.79,
0.79, 0.79, 0.80, 0.80, 0.81, 0.81, 0.82, 0.82,
0.83
Time:
9500.00 days
Iteration Func-count f(x) Norm of Step
0 1 152.731 start
1 56 0.00551 0.70290
2 57 1.048e-005 2.756e-004
3 58 5.831e-009 1.267e-006
4 59 5.274e-011 1.938e-010
Producer BHP:
1500.00 psi
Injector BHP:
2659.23 psi
Pressure:
1534.53, 1541.54, 1570.28, 1614.49, 1654.24, 1705.03, 1751.95, 1801.23,
1854.28, 1892.89, 1934.76, 1984.98, 2025.97, 2058.80, 2094.30, 2126.10,
2165.48, 2212.40, 2262.18, 2329.37, 2394.94, 2459.54, 2521.33, 2560.43,
2584.72
Saturation:
0.20, 0.23, 0.55, 0.71, 0.74, 0.75, 0.76, 0.76,
0.77, 0.77, 0.77, 0.78, 0.78, 0.78, 0.79, 0.79,
0.79, 0.80, 0.80, 0.80, 0.81, 0.81, 0.82, 0.82,
0.83
Time:
10000.00 days
Iteration Func-count f(x) Norm of Step
0 1 142.935 start
1 56 0.00277 1.22419
2 57 8.548e-006 3.077e-004
3 58 2.942e-009 9.610e-007
4 59 5.723e-011 4.208e-010
Producer BHP:
1500.00 psi
Injector BHP:
2708.87 psi
Pressure:
1544.00, 1589.36, 1634.53, 1676.87, 1715.23, 1764.65, 1810.53, 1858.86,
1910.98, 1948.98, 1990.21, 2039.72, 2080.17, 2112.59, 2147.67, 2179.12,
2218.09, 2264.55, 2313.89, 2380.54, 2445.62, 2509.80, 2571.24, 2610.17,
2634.37
Saturation:
0.26, 0.61, 0.72, 0.74, 0.75, 0.76, 0.76, 0.77,
0.77, 0.77, 0.78, 0.78, 0.78, 0.79, 0.79, 0.79,
0.79, 0.80, 0.80, 0.81, 0.81, 0.81, 0.82, 0.83,
0.83
5/16/2026 9:37:24 PM
5/16/2026 9:39:17 PM
======================================================================
Starting simulation for Rate = 300 STB/day
Time:
0.00 days
Producer BHP:
3000.00 psi
Injector BHP:
3000.00 psi
Pressure:
3000.00, 3000.00, 3000.00, 3000.00, 3000.00, 3000.00, 3000.00, 3000.00,
3000.00, 3000.00, 3000.00, 3000.00, 3000.00, 3000.00, 3000.00, 3000.00,
3000.00, 3000.00, 3000.00, 3000.00, 3000.00, 3000.00, 3000.00, 3000.00,
3000.00
Saturation:
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20
Time:
500.00 days
Iteration Func-count f(x) Norm of Step
0 1 240.531 start
1 56 0.00308 0.36140
2 57 8.068e-006 1.725e-004
3 58 4.540e-009 3.511e-007
4 59 8.280e-011 1.764e-010
Producer BHP:
1500.00 psi
Injector BHP:
1996.79 psi
Pressure:
1552.39, 1561.95, 1569.94, 1577.66, 1584.81, 1594.16, 1602.96, 1612.33,
1622.52, 1630.03, 1638.24, 1648.19, 1656.40, 1663.04, 1670.29, 1676.85,
1685.07, 1695.00, 1705.68, 1720.30, 1734.77, 1749.29, 1767.46, 1836.37,
1884.82
Saturation:
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.26, 0.62,
0.75
Time:
1000.00 days
Iteration Func-count f(x) Norm of Step
0 1 246.014 start
1 56 0.00585 0.79923
2 57 6.583e-006 4.444e-004
3 58 6.834e-009 8.442e-007
4 59 7.248e-011 5.129e-010
Producer BHP:
1500.00 psi
Injector BHP:
2165.87 psi
Pressure:
1552.14, 1561.65, 1569.61, 1577.28, 1584.40, 1593.70, 1602.46, 1611.78,
1621.92, 1629.38, 1637.56, 1647.46, 1655.62, 1662.23, 1669.44, 1675.97,
1684.14, 1694.01, 1704.63, 1719.17, 1735.08, 1815.96, 1937.74, 2010.96,
2053.91
Saturation:
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.20, 0.20, 0.23, 0.56, 0.72, 0.76,
0.79
Time:
1500.00 days
Iteration Func-count f(x) Norm of Step
0 1 257.654 start
1 56 0.00823 0.77618
2 57 2.206e-005 7.175e-004
3 58 7.537e-009 2.248e-006
4 59 7.738e-011 6.150e-010
Producer BHP:
1500.00 psi
Injector BHP:
2339.56 psi
Pressure:
1552.09, 1561.59, 1569.54, 1577.20, 1584.31, 1593.61, 1602.35, 1611.66,
1621.79, 1629.24, 1637.40, 1647.29, 1655.44, 1662.04, 1669.24, 1675.76,
1683.92, 1693.77, 1704.78, 1762.31, 1887.94, 2007.95, 2118.91, 2186.95,
2227.66
Saturation:
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.21, 0.49, 0.70, 0.74, 0.77, 0.78,
0.80
Time:
2000.00 days
Iteration Func-count f(x) Norm of Step
0 1 266.160 start
1 56 0.00530 0.28985
2 57 1.665e-005 2.695e-004
3 58 2.018e-009 9.255e-007
4 59 6.778e-011 6.940e-011
Producer BHP:
1500.00 psi
Injector BHP:
2476.06 psi
Pressure:
1552.31, 1561.85, 1569.83, 1577.53, 1584.67, 1594.00, 1602.78, 1612.13,
1622.31, 1629.79, 1637.99, 1647.92, 1656.11, 1662.74, 1669.97, 1676.52,
1684.81, 1708.53, 1801.09, 1924.01, 2040.93, 2153.66, 2259.30, 2324.71,
2364.21
Saturation:
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.40, 0.69, 0.74, 0.76, 0.77, 0.78, 0.80,
0.81
Time:
2500.00 days
Iteration Func-count f(x) Norm of Step
0 1 227.371 start
1 56 0.00278 0.37700
2 57 9.576e-006 1.151e-004
3 58 1.308e-008 2.152e-007
4 59 6.603e-011 3.543e-010
Producer BHP:
1500.00 psi
Injector BHP:
2567.17 psi
Pressure:
1552.18, 1561.69, 1569.65, 1577.33, 1584.45, 1593.76, 1602.52, 1611.84,
1622.00, 1629.47, 1637.64, 1647.56, 1655.73, 1662.34, 1669.57, 1679.19,
1743.43, 1828.32, 1915.55, 2031.18, 2142.55, 2250.86, 2353.02, 2416.65,
2455.35
Saturation:
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.29,
0.63, 0.73, 0.75, 0.76, 0.77, 0.78, 0.79, 0.80,
0.82
Time:
3000.00 days
Iteration Func-count f(x) Norm of Step
0 1 221.165 start
1 56 0.00344 0.54727
2 57 3.243e-006 7.372e-005
3 58 4.675e-009 6.600e-008
4 59 1.091e-010 9.823e-011
Producer BHP:
1500.00 psi
Injector BHP:
2635.49 psi
Pressure:
1552.01, 1561.50, 1569.43, 1577.08, 1584.18, 1593.46, 1602.19, 1611.48,
1621.60, 1629.05, 1637.20, 1647.07, 1655.22, 1663.25, 1711.13, 1767.63,
1835.86, 1915.53, 1998.87, 2110.30, 2218.15, 2323.47, 2423.20, 2485.57,
2523.70
Saturation:
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.20, 0.20, 0.20, 0.25, 0.59, 0.72,
0.74, 0.76, 0.77, 0.78, 0.78, 0.79, 0.80, 0.81,
0.82
Time:
3500.00 days
Iteration Func-count f(x) Norm of Step
0 1 240.465 start
1 56 0.00554 0.64990
2 57 9.153e-006 2.727e-004
3 58 6.175e-009 7.328e-007
4 59 8.312e-011 3.217e-010
Producer BHP:
1500.00 psi
Injector BHP:
2709.95 psi
Pressure:
1551.90, 1561.36, 1569.27, 1576.91, 1583.99, 1593.25, 1601.95, 1611.22,
1621.32, 1628.74, 1636.87, 1647.66, 1690.53, 1747.60, 1808.04, 1861.23,
1926.32, 2003.17, 2084.09, 2192.66, 2298.01, 2401.15, 2499.07, 2560.49,
2598.19
Saturation:
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.20, 0.22, 0.54, 0.71, 0.74, 0.75,
0.76, 0.77, 0.78, 0.78, 0.79, 0.80, 0.80, 0.81,
0.82
Time:
4000.00 days
Iteration Func-count f(x) Norm of Step
0 1 258.795 start
1 56 0.00693 0.48042
2 57 2.333e-005 3.635e-004
3 58 2.944e-009 1.414e-006
4 59 8.382e-011 1.470e-010
Producer BHP:
1500.00 psi
Injector BHP:
2810.91 psi
Pressure:
1552.02, 1561.50, 1569.44, 1577.09, 1584.18, 1593.46, 1602.19, 1611.48,
1621.60, 1629.24, 1656.65, 1742.81, 1811.79, 1865.90, 1923.82, 1975.32,
2038.69, 2113.79, 2193.08, 2299.62, 2403.15, 2504.65, 2601.18, 2661.85,
2699.19
Saturation:
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.21, 0.46, 0.70, 0.74, 0.75, 0.76, 0.77,
0.77, 0.78, 0.78, 0.79, 0.79, 0.80, 0.81, 0.82,
0.83
Time:
4500.00 days
Iteration Func-count f(x) Norm of Step
0 1 249.846 start
1 56 0.00533 0.46039
2 57 1.933e-005 2.637e-004
3 58 2.719e-009 1.009e-006
4 59 5.892e-011 8.707e-011
Producer BHP:
1500.00 psi
Injector BHP:
2897.81 psi
Pressure:
1551.99, 1561.46, 1569.39, 1577.04, 1584.13, 1593.40, 1602.12, 1611.47,
1633.33, 1696.92, 1766.56, 1848.30, 1914.20, 1966.57, 2022.93, 2073.21,
2135.25, 2208.91, 2286.81, 2391.62, 2493.58, 2593.68, 2689.03, 2749.08,
2786.13
Saturation:
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.38, 0.67, 0.73, 0.75, 0.76, 0.76, 0.77, 0.77,
0.78, 0.78, 0.79, 0.79, 0.80, 0.80, 0.81, 0.82,
0.83
Time:
5000.00 days
Iteration Func-count f(x) Norm of Step
0 1 226.957 start
1 56 0.00272 0.65915
2 57 8.990e-006 1.331e-004
3 58 1.154e-008 2.580e-007
4 59 8.270e-011 4.149e-010
Producer BHP:
1500.00 psi
Injector BHP:
3006.48 psi
Pressure:
1551.73, 1561.15, 1569.04, 1576.65, 1583.70, 1592.95, 1605.70, 1679.78,
1766.52, 1828.29, 1894.38, 1973.07, 2037.00, 2088.02, 2143.05, 2192.26,
2253.06, 2325.37, 2401.94, 2505.10, 2605.58, 2704.36, 2798.60, 2858.07,
2894.85
Saturation:
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.29, 0.64,
0.72, 0.74, 0.75, 0.76, 0.77, 0.77, 0.78, 0.78,
0.78, 0.79, 0.79, 0.80, 0.80, 0.81, 0.81, 0.82,
0.83
Time:
5500.00 days
Iteration Func-count f(x) Norm of Step
0 1 227.851 start
1 56 0.00444 0.84171
2 57 4.518e-006 1.967e-004
3 58 4.181e-009 4.454e-007
4 59 1.141e-010 2.343e-010
Producer BHP:
1500.00 psi
Injector BHP:
3094.43 psi
Pressure:
1551.48, 1560.86, 1568.71, 1576.29, 1584.20, 1637.83, 1713.05, 1790.40,
1872.61, 1932.07, 1996.27, 2073.08, 2135.66, 2185.72, 2239.79, 2288.19,
2348.06, 2419.34, 2494.90, 2596.80, 2696.12, 2793.88, 2887.26, 2946.26,
2982.83
Saturation:
0.20, 0.20, 0.20, 0.20, 0.23, 0.56, 0.71, 0.74,
0.75, 0.76, 0.76, 0.77, 0.77, 0.78, 0.78, 0.78,
0.79, 0.79, 0.80, 0.80, 0.81, 0.81, 0.82, 0.82,
0.83
Time:
6000.00 days
Iteration Func-count f(x) Norm of Step
0 1 257.875 start
1 56 0.00635 0.47281
2 57 2.081e-005 3.476e-004
3 58 3.715e-009 1.437e-006
4 59 8.715e-011 2.567e-010
Producer BHP:
1500.00 psi
Injector BHP:
3175.20 psi
Pressure:
1551.89, 1561.34, 1569.48, 1595.16, 1656.81, 1735.49, 1807.42, 1882.53,
1963.13, 2021.69, 2085.08, 2161.05, 2223.00, 2272.58, 2326.15, 2374.13,
2433.48, 2504.16, 2579.10, 2680.19, 2778.76, 2875.81, 2968.58, 3027.23,
3063.63
Saturation:
0.20, 0.20, 0.21, 0.46, 0.70, 0.73, 0.75, 0.76,
0.76, 0.77, 0.77, 0.77, 0.78, 0.78, 0.78, 0.79,
0.79, 0.80, 0.80, 0.80, 0.81, 0.81, 0.82, 0.82,
0.83
Time:
6500.00 days
Iteration Func-count f(x) Norm of Step
0 1 247.363 start
1 56 0.00527 0.57899
2 57 2.001e-005 2.935e-004
3 58 2.065e-008 1.536e-006
4 59 7.655e-011 1.383e-009
Producer BHP:
1500.00 psi
Injector BHP:
3260.03 psi
Pressure:
1552.06, 1572.25, 1639.69, 1705.01, 1763.72, 1839.00, 1908.70, 1981.98,
2060.88, 2118.34, 2180.64, 2255.37, 2316.38, 2365.24, 2418.08, 2465.42,
2524.04, 2593.89, 2668.01, 2768.07, 2865.71, 2961.93, 3053.99, 3112.28,
3148.50
Saturation:
0.20, 0.38, 0.67, 0.73, 0.75, 0.75, 0.76, 0.76,
0.77, 0.77, 0.78, 0.78, 0.78, 0.79, 0.79, 0.79,
0.79, 0.80, 0.80, 0.81, 0.81, 0.81, 0.82, 0.83,
0.83
Time:
7000.00 days
Iteration Func-count f(x) Norm of Step
0 1 136.263 start
1 56 0.00973 10.2235
2 57 3.186e-006 0.00492
3 58 2.205e-009 7.107e-007
4 59 3.484e-011 9.105e-010
Producer BHP:
1500.00 psi
Injector BHP:
3529.79 psi
Pressure:
1860.32, 1934.50, 1994.88, 2052.11, 2104.51, 2172.46, 2235.88, 2303.02,
2375.71, 2428.90, 2486.85, 2556.69, 2613.96, 2660.03, 2710.05, 2755.06,
2811.01, 2878.00, 2949.41, 3046.21, 3141.06, 3234.93, 3325.15, 3382.54,
3418.38
Saturation:
0.62, 0.72, 0.74, 0.75, 0.76, 0.76, 0.77, 0.77,
0.77, 0.78, 0.78, 0.78, 0.79, 0.79, 0.79, 0.79,
0.80, 0.80, 0.81, 0.81, 0.81, 0.82, 0.82, 0.83,
0.83
Time:
7500.00 days
Iteration Func-count f(x) Norm of Step
0 1 13.1525 start
1 56 0.00118 2.79237
2 57 1.776e-006 0.00180
3 58 5.228e-010 8.463e-007
4 59 9.832e-012 4.094e-010
Producer BHP:
1500.00 psi
Injector BHP:
3680.69 psi
Pressure:
1944.85, 2023.84, 2088.82, 2150.65, 2207.27, 2280.55, 2348.73, 2420.62,
2498.15, 2554.66, 2615.95, 2689.50, 2749.55, 2797.65, 2849.66, 2896.26,
2953.95, 3022.71, 3095.68, 3194.21, 3290.37, 3385.19, 3475.97, 3533.52,
3569.34
Saturation:
0.74, 0.75, 0.76, 0.76, 0.77, 0.77, 0.77, 0.78,
0.78, 0.78, 0.78, 0.79, 0.79, 0.79, 0.79, 0.80,
0.80, 0.80, 0.81, 0.81, 0.81, 0.82, 0.82, 0.83,
0.84
Time:
8000.00 days
Iteration Func-count f(x) Norm of Step
0 1 6.33665 start
1 56 9.250e-004 5.33505
2 57 1.730e-006 0.00340
3 58 1.060e-009 1.504e-006
4 59 8.001e-012 1.947e-009
Producer BHP:
1500.00 psi
Injector BHP:
3648.19 psi
Pressure:
1927.74, 2004.62, 2068.22, 2128.96, 2184.72, 2257.00, 2324.34, 2395.41,
2472.12, 2528.05, 2588.77, 2661.66, 2721.20, 2768.91, 2820.52, 2866.79,
2924.10, 2992.43, 3064.99, 3163.01, 3258.73, 3353.17, 3443.65, 3501.06,
3536.83
Saturation:
0.75, 0.76, 0.76, 0.77, 0.77, 0.77, 0.78, 0.78,
0.78, 0.78, 0.79, 0.79, 0.79, 0.79, 0.80, 0.80,
0.80, 0.81, 0.81, 0.81, 0.82, 0.82, 0.82, 0.83,
0.84
Time:
8500.00 days
Iteration Func-count f(x) Norm of Step
0 1 4.59297 start
1 56 5.860e-004 5.76652
2 57 1.068e-006 0.00357
3 58 6.772e-010 1.648e-006
4 59 7.605e-012 1.740e-009
Producer BHP:
1500.00 psi
Injector BHP:
3626.91 psi
Pressure:
1918.74, 1994.32, 2056.98, 2116.93, 2172.03, 2243.52, 2310.17, 2380.57,
2456.58, 2512.03, 2572.25, 2644.57, 2703.67, 2751.04, 2802.31, 2848.28,
2905.25, 2973.20, 3045.38, 3142.94, 3238.25, 3332.34, 3422.54, 3479.81,
3515.54
Saturation:
0.76, 0.77, 0.77, 0.77, 0.77, 0.78, 0.78, 0.78,
0.78, 0.79, 0.79, 0.79, 0.79, 0.80, 0.80, 0.80,
0.80, 0.81, 0.81, 0.81, 0.82, 0.82, 0.82, 0.83,
0.84
Time:
9000.00 days
Iteration Func-count f(x) Norm of Step
0 1 3.77489 start
1 56 5.870e-004 7.14045
2 57 1.306e-006 0.00533
3 58 9.834e-010 3.174e-006
4 59 6.283e-012 3.795e-009
Producer BHP:
1500.00 psi
Injector BHP:
3610.54 psi
Pressure:
1912.71, 1987.34, 2049.29, 2108.61, 2163.17, 2234.01, 2300.09, 2369.91,
2445.32, 2500.36, 2560.15, 2631.97, 2690.68, 2737.76, 2788.72, 2834.43,
2891.09, 2958.69, 3030.55, 3127.68, 3222.63, 3316.40, 3406.34, 3463.49,
3499.16
Saturation:
0.77, 0.77, 0.77, 0.77, 0.78, 0.78, 0.78, 0.78,
0.79, 0.79, 0.79, 0.79, 0.80, 0.80, 0.80, 0.80,
0.81, 0.81, 0.81, 0.81, 0.82, 0.82, 0.83, 0.83,
0.84
Time:
9500.00 days
Iteration Func-count f(x) Norm of Step
0 1 3.22257 start
1 56 4.587e-004 7.45612
2 57 1.069e-006 0.00533
3 58 7.483e-010 3.471e-006
4 59 1.018e-011 3.388e-009
Producer BHP:
1500.00 psi
Injector BHP:
3596.81 psi
Pressure:
1908.08, 1981.94, 2043.31, 2102.09, 2156.20, 2226.47, 2292.05, 2361.36,
2436.24, 2490.91, 2550.30, 2621.68, 2680.04, 2726.85, 2777.53, 2823.00,
2879.38, 2946.68, 3018.22, 3114.98, 3209.59, 3303.06, 3392.77, 3449.80,
3485.43
Saturation:
0.77, 0.77, 0.78, 0.78, 0.78, 0.78, 0.78, 0.79,
0.79, 0.79, 0.79, 0.79, 0.80, 0.80, 0.80, 0.80,
0.81, 0.81, 0.81, 0.82, 0.82, 0.82, 0.83, 0.83,
0.84
Time:
10000.00 days
Iteration Func-count f(x) Norm of Step
0 1 2.90897 start
1 56 4.615e-004 8.30673
2 57 1.221e-006 0.00635
3 58 9.174e-010 4.727e-006
4 59 8.053e-012 5.021e-009
Producer BHP:
1500.00 psi
Injector BHP:
3584.81 psi
Pressure:
1904.25, 1977.47, 2038.33, 2096.66, 2150.36, 2220.13, 2285.25, 2354.10,
2428.50, 2482.83, 2541.88, 2612.85, 2670.88, 2717.45, 2767.87, 2813.13,
2869.25, 2936.26, 3007.52, 3103.93, 3198.22, 3291.42, 3380.91, 3437.83,
3473.42
Saturation:
0.77, 0.78, 0.78, 0.78, 0.78, 0.78, 0.79, 0.79,
0.79, 0.79, 0.79, 0.80, 0.80, 0.80, 0.80, 0.81,
0.81, 0.81, 0.81, 0.82, 0.82, 0.82, 0.83, 0.83,
0.84
5/16/2026 9:40:24 PM
5/16/2026 9:42:13 PM
======================================================================
Starting simulation for Rate = 400 STB/day
Time:
0.00 days
Producer BHP:
3000.00 psi
Injector BHP:
3000.00 psi
Pressure:
3000.00, 3000.00, 3000.00, 3000.00, 3000.00, 3000.00, 3000.00, 3000.00,
3000.00, 3000.00, 3000.00, 3000.00, 3000.00, 3000.00, 3000.00, 3000.00,
3000.00, 3000.00, 3000.00, 3000.00, 3000.00, 3000.00, 3000.00, 3000.00,
3000.00
Saturation:
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20
Time:
500.00 days
Iteration Func-count f(x) Norm of Step
0 1 367.849 start
1 56 0.00818 0.64568
2 57 1.427e-005 6.347e-004
3 58 5.668e-009 1.218e-006
4 59 1.036e-010 3.903e-010
Producer BHP:
1500.00 psi
Injector BHP:
2219.88 psi
Pressure:
1569.78, 1582.50, 1593.15, 1603.42, 1612.94, 1625.40, 1637.11, 1649.58,
1663.16, 1673.14, 1684.08, 1697.32, 1708.24, 1717.08, 1726.72, 1735.46,
1746.39, 1759.59, 1773.79, 1793.24, 1812.48, 1832.41, 1903.48, 2009.39,
2070.62
Saturation:
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.20, 0.20, 0.20, 0.21, 0.48, 0.71,
0.77
Time:
1000.00 days
Iteration Func-count f(x) Norm of Step
0 1 300.611 start
1 56 0.00314 0.84495
2 57 4.782e-006 1.630e-004
3 58 4.482e-009 1.812e-007
4 59 8.990e-011 1.736e-010
Producer BHP:
1500.00 psi
Injector BHP:
2550.10 psi
Pressure:
1569.27, 1581.90, 1592.48, 1602.67, 1612.13, 1624.50, 1636.12, 1648.51,
1661.99, 1671.91, 1682.77, 1695.93, 1706.78, 1715.57, 1725.15, 1733.84,
1744.71, 1757.83, 1771.97, 1796.94, 1937.42, 2102.36, 2253.72, 2346.02,
2400.98
Saturation:
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.20, 0.26, 0.61, 0.73, 0.76, 0.78,
0.80
Time:
1500.00 days
Iteration Func-count f(x) Norm of Step
0 1 354.612 start
1 56 0.00522 0.32440
2 57 1.344e-005 2.407e-004
3 58 1.204e-009 6.396e-007
4 59 1.045e-010 7.037e-011
Producer BHP:
1500.00 psi
Injector BHP:
2799.49 psi
Pressure:
1569.72, 1582.43, 1593.07, 1603.33, 1612.85, 1625.29, 1636.99, 1649.45,
1663.02, 1673.00, 1683.92, 1697.16, 1708.08, 1716.91, 1726.55, 1735.29,
1746.32, 1777.31, 1900.77, 2064.54, 2220.23, 2370.30, 2510.90, 2597.93,
2650.51
Saturation:
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.39, 0.69, 0.74, 0.76, 0.77, 0.78, 0.80,
0.81
Time:
2000.00 days
Iteration Func-count f(x) Norm of Step
0 1 330.612 start
1 56 0.00668 0.45511
2 57 1.409e-005 2.783e-004
3 58 5.025e-009 7.599e-007
4 59 1.384e-010 2.001e-010
Producer BHP:
1500.00 psi
Injector BHP:
2944.84 psi
Pressure:
1569.53, 1582.21, 1592.82, 1603.05, 1612.54, 1624.95, 1636.61, 1649.04,
1662.56, 1672.51, 1683.40, 1696.59, 1707.47, 1716.27, 1726.46, 1765.38,
1860.48, 1970.75, 2084.86, 2236.68, 2383.19, 2525.88, 2660.65, 2744.71,
2795.94
Saturation:
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.22, 0.51,
0.70, 0.74, 0.76, 0.77, 0.78, 0.79, 0.79, 0.81,
0.82
Time:
2500.00 days
Iteration Func-count f(x) Norm of Step
0 1 313.980 start
1 56 0.00338 0.41566
2 57 9.969e-006 1.200e-004
3 58 7.016e-009 2.678e-007
4 59 1.529e-010 2.504e-010
Producer BHP:
1500.00 psi
Injector BHP:
3078.97 psi
Pressure:
1569.39, 1582.04, 1592.63, 1602.84, 1612.31, 1624.70, 1636.34, 1648.75,
1662.25, 1672.19, 1683.07, 1696.28, 1713.37, 1785.90, 1868.58, 1940.82,
2028.82, 2132.40, 2241.23, 2387.05, 2528.39, 2666.60, 2797.68, 2879.80,
2930.14
Saturation:
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.20, 0.20, 0.31, 0.65, 0.72, 0.75,
0.76, 0.77, 0.77, 0.78, 0.79, 0.79, 0.80, 0.81,
0.82
Time:
3000.00 days
Iteration Func-count f(x) Norm of Step
0 1 346.394 start
1 56 0.00683 0.51698
2 57 1.937e-005 3.189e-004
3 58 3.244e-009 9.885e-007
4 59 9.900e-011 1.488e-010
Producer BHP:
1500.00 psi
Injector BHP:
3241.89 psi
Pressure:
1569.24, 1581.86, 1592.42, 1602.61, 1612.05, 1624.40, 1636.02, 1648.39,
1661.85, 1671.98, 1706.52, 1821.26, 1913.10, 1985.08, 2062.14, 2130.63,
2214.91, 2314.78, 2420.21, 2561.89, 2699.53, 2834.48, 2962.82, 3043.49,
3093.15
Saturation:
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.21, 0.45, 0.69, 0.73, 0.75, 0.76, 0.77,
0.77, 0.78, 0.78, 0.79, 0.79, 0.80, 0.81, 0.82,
0.83
Time:
3500.00 days
Iteration Func-count f(x) Norm of Step
0 1 290.459 start
1 56 0.00357 1.03968
2 57 1.598e-006 1.169e-004
3 58 9.340e-010 9.579e-008
4 59 1.705e-010 5.284e-011
Producer BHP:
1500.00 psi
Injector BHP:
3399.99 psi
Pressure:
1568.24, 1580.68, 1591.09, 1601.13, 1610.44, 1622.62, 1634.07, 1648.53,
1736.94, 1821.84, 1911.61, 2017.70, 2103.58, 2171.99, 2245.73, 2311.63,
2393.02, 2489.80, 2592.27, 2730.30, 2864.71, 2996.81, 3122.80, 3202.24,
3251.34
Saturation:
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.24,
0.59, 0.71, 0.74, 0.75, 0.76, 0.77, 0.77, 0.78,
0.78, 0.79, 0.79, 0.80, 0.80, 0.81, 0.81, 0.82,
0.83
Time:
4000.00 days
Iteration Func-count f(x) Norm of Step
0 1 315.477 start
1 56 0.00351 0.64397
2 57 1.006e-005 1.393e-004
3 58 3.648e-009 3.573e-007
4 59 1.567e-010 1.778e-010
Producer BHP:
1500.00 psi
Injector BHP:
3577.65 psi
Pressure:
1568.80, 1581.35, 1591.84, 1601.96, 1611.38, 1632.39, 1728.70, 1834.17,
1945.36, 2025.44, 2111.67, 2214.68, 2298.51, 2365.51, 2437.84, 2502.54,
2582.55, 2677.75, 2778.62, 2914.58, 3047.07, 3177.40, 3301.84, 3380.43,
3429.11
Saturation:
0.20, 0.20, 0.20, 0.20, 0.20, 0.33, 0.66, 0.73,
0.75, 0.76, 0.76, 0.77, 0.77, 0.78, 0.78, 0.78,
0.79, 0.79, 0.80, 0.80, 0.80, 0.81, 0.82, 0.82,
0.83
Time:
4500.00 days
Iteration Func-count f(x) Norm of Step
0 1 345.477 start
1 56 0.00614 0.49837
2 57 1.731e-005 2.891e-004
3 58 1.970e-009 9.682e-007
4 59 1.600e-010 1.036e-010
Producer BHP:
1500.00 psi
Injector BHP:
3722.86 psi
Pressure:
1569.01, 1581.59, 1592.34, 1623.08, 1705.15, 1809.94, 1905.65, 2005.53,
2112.67, 2190.49, 2274.72, 2375.64, 2457.94, 2523.79, 2594.95, 2658.67,
2737.50, 2831.38, 2930.91, 3065.17, 3196.07, 3324.96, 3448.15, 3526.05,
3574.40
Saturation:
0.20, 0.20, 0.21, 0.44, 0.69, 0.73, 0.75, 0.76,
0.76, 0.77, 0.77, 0.77, 0.78, 0.78, 0.79, 0.79,
0.79, 0.80, 0.80, 0.80, 0.81, 0.81, 0.82, 0.82,
0.83
Time:
5000.00 days
Iteration Func-count f(x) Norm of Step
0 1 289.336 start
1 56 0.00395 1.28089
2 57 1.398e-006 2.113e-004
3 58 1.644e-009 3.751e-007
4 59 1.182e-010 9.829e-011
Producer BHP:
1500.00 psi
Injector BHP:
3872.39 psi
Pressure:
1577.63, 1655.61, 1745.23, 1829.05, 1904.92, 2002.61, 2093.28, 2188.81,
2291.82, 2366.93, 2448.45, 2546.36, 2626.36, 2690.50, 2759.91, 2822.16,
2899.30, 2991.30, 3089.02, 3221.03, 3349.95, 3477.09, 3598.84, 3676.00,
3724.01
Saturation:
0.24, 0.58, 0.71, 0.74, 0.75, 0.76, 0.76, 0.77,
0.77, 0.77, 0.78, 0.78, 0.78, 0.79, 0.79, 0.79,
0.80, 0.80, 0.80, 0.81, 0.81, 0.82, 0.82, 0.83,
0.83
Time:
5500.00 days
Iteration Func-count f(x) Norm of Step
0 1 32.0807 start
1 56 0.00156 1.64194
2 57 1.535e-006 0.00134
3 58 2.678e-010 3.768e-007
4 59 1.793e-011 2.006e-010
Producer BHP:
1500.00 psi
Injector BHP:
4396.25 psi
Pressure:
2100.00, 2205.40, 2291.67, 2373.53, 2448.36, 2545.11, 2635.08, 2729.92,
2832.17, 2906.70, 2987.55, 3084.59, 3163.83, 3227.32, 3295.99, 3357.54,
3433.77, 3524.66, 3621.15, 3751.48, 3878.73, 4004.25, 4124.47, 4200.70,
4248.19
Saturation:
0.72, 0.74, 0.75, 0.76, 0.76, 0.77, 0.77, 0.78,
0.78, 0.78, 0.78, 0.79, 0.79, 0.79, 0.79, 0.80,
0.80, 0.80, 0.81, 0.81, 0.81, 0.82, 0.82, 0.83,
0.84
Time:
6000.00 days
Iteration Func-count f(x) Norm of Step
0 1 8.44017 start
1 56 9.607e-004 6.30685
2 57 1.470e-006 0.00286
3 58 7.491e-010 8.475e-007
4 59 9.901e-012 9.891e-010
Producer BHP:
1500.00 psi
Injector BHP:
4357.12 psi
Pressure:
2070.96, 2173.49, 2258.27, 2339.19, 2413.43, 2509.64, 2599.23, 2693.77,
2795.76, 2870.12, 2950.82, 3047.67, 3126.77, 3190.14, 3258.68, 3320.12,
3396.20, 3486.90, 3583.19, 3713.23, 3840.22, 3965.47, 4085.46, 4161.58,
4209.03
Saturation:
0.75, 0.76, 0.76, 0.77, 0.77, 0.77, 0.78, 0.78,
0.78, 0.78, 0.79, 0.79, 0.79, 0.80, 0.80, 0.80,
0.80, 0.81, 0.81, 0.81, 0.82, 0.82, 0.82, 0.83,
0.84
Time:
6500.00 days
Iteration Func-count f(x) Norm of Step
0 1 5.59715 start
1 56 6.543e-004 7.60969
2 57 1.084e-006 0.00394
3 58 6.651e-010 1.350e-006
4 59 1.249e-011 1.500e-009
Producer BHP:
1500.00 psi
Injector BHP:
4320.01 psi
Pressure:
2055.08, 2155.30, 2238.41, 2317.91, 2390.99, 2485.80, 2574.19, 2667.53,
2768.31, 2841.83, 2921.66, 3017.53, 3095.86, 3158.66, 3226.61, 3287.54,
3363.04, 3453.10, 3548.77, 3678.05, 3804.37, 3929.06, 4048.61, 4124.52,
4171.90
Saturation:
0.76, 0.77, 0.77, 0.77, 0.78, 0.78, 0.78, 0.78,
0.79, 0.79, 0.79, 0.79, 0.79, 0.80, 0.80, 0.80,
0.80, 0.81, 0.81, 0.81, 0.82, 0.82, 0.83, 0.83,
0.84
Time:
7000.00 days
Iteration Func-count f(x) Norm of Step
0 1 4.47727 start
1 56 5.895e-004 9.09020
2 57 1.166e-006 0.00548
3 58 7.983e-010 2.421e-006
4 59 9.351e-012 2.650e-009
Producer BHP:
1500.00 psi
Injector BHP:
4293.47 psi
Pressure:
2045.43, 2144.10, 2226.04, 2304.51, 2376.70, 2470.43, 2557.86, 2650.25,
2750.04, 2822.87, 2901.98, 2997.04, 3074.73, 3137.04, 3204.48, 3264.99,
3339.99, 3429.49, 3524.62, 3653.24, 3778.98, 3903.16, 4022.31, 4098.03,
4145.34
Saturation:
0.77, 0.77, 0.77, 0.78, 0.78, 0.78, 0.78, 0.79,
0.79, 0.79, 0.79, 0.79, 0.80, 0.80, 0.80, 0.80,
0.81, 0.81, 0.81, 0.82, 0.82, 0.82, 0.83, 0.83,
0.84
Time:
7500.00 days
Iteration Func-count f(x) Norm of Step
0 1 3.77821 start
1 56 4.496e-004 9.36462
2 57 9.354e-007 0.00540
3 58 5.896e-010 2.634e-006
Producer BHP:
1500.00 psi
Injector BHP:
4271.90 psi
Pressure:
2038.29, 2135.77, 2216.78, 2294.40, 2365.85, 2458.67, 2545.29, 2636.86,
2735.80, 2808.03, 2886.53, 2980.86, 3057.99, 3119.87, 3186.87, 3247.00,
3321.55, 3410.57, 3505.21, 3633.24, 3758.44, 3882.17, 4000.96, 4076.51,
4123.76
Saturation:
0.77, 0.78, 0.78, 0.78, 0.78, 0.78, 0.79, 0.79,
0.79, 0.79, 0.79, 0.80, 0.80, 0.80, 0.80, 0.81,
0.81, 0.81, 0.81, 0.82, 0.82, 0.82, 0.83, 0.83,
0.84
Time:
8000.00 days
Iteration Func-count f(x) Norm of Step
0 1 3.29347 start
1 56 4.039e-004 10.0561
2 57 9.301e-007 0.00586
3 58 5.920e-010 3.202e-006
Producer BHP:
1500.00 psi
Injector BHP:
4253.40 psi
Pressure:
2032.50, 2128.99, 2209.22, 2286.12, 2356.94, 2448.97, 2534.88, 2625.72,
2723.91, 2795.61, 2873.55, 2967.24, 3043.87, 3105.37, 3171.97, 3231.75,
3305.91, 3394.48, 3488.69, 3616.17, 3740.90, 3864.21, 3982.67, 4058.06,
4105.24
Saturation:
0.78, 0.78, 0.78, 0.78, 0.78, 0.79, 0.79, 0.79,
0.79, 0.79, 0.80, 0.80, 0.80, 0.80, 0.80, 0.81,
0.81, 0.81, 0.82, 0.82, 0.82, 0.82, 0.83, 0.83,
0.84
Time:
8500.00 days
Iteration Func-count f(x) Norm of Step
0 1 2.96804 start
1 56 4.205e-004 11.2203
2 57 1.105e-006 0.00698
3 58 7.810e-010 4.310e-006
4 59 9.991e-012 4.234e-009
Producer BHP:
1500.00 psi
Injector BHP:
4237.09 psi
Pressure:
2027.59, 2123.22, 2202.77, 2279.04, 2349.30, 2440.62, 2525.90, 2616.10,
2713.61, 2784.84, 2862.27, 2955.39, 3031.56, 3092.71, 3158.94, 3218.42,
3292.21, 3380.37, 3474.19, 3601.18, 3725.46, 3848.40, 3966.56, 4041.80,
4088.92
Saturation:
0.78, 0.78, 0.78, 0.79, 0.79, 0.79, 0.79, 0.79,
0.79, 0.80, 0.80, 0.80, 0.80, 0.80, 0.81, 0.81,
0.81, 0.81, 0.82, 0.82, 0.82, 0.83, 0.83, 0.83,
0.84
Time:
9000.00 days
Iteration Func-count f(x) Norm of Step
0 1 2.66946 start
1 56 4.435e-004 12.5130
2 57 1.313e-006 0.00824
3 58 1.056e-009 5.556e-006
4 59 7.014e-012 6.775e-009
Producer BHP:
1500.00 psi
Injector BHP:
4222.46 psi
Pressure:
2023.28, 2118.17, 2197.11, 2272.82, 2342.57, 2433.27, 2517.97, 2607.58,
2704.48, 2775.28, 2852.26, 2944.85, 3020.60, 3081.43, 3147.34, 3206.53,
3279.99, 3367.78, 3461.23, 3587.77, 3711.65, 3834.24, 3952.11, 4027.22,
4074.29
Saturation:
0.78, 0.78, 0.79, 0.79, 0.79, 0.79, 0.79, 0.79,
0.80, 0.80, 0.80, 0.80, 0.80, 0.81, 0.81, 0.81,
0.81, 0.81, 0.82, 0.82, 0.82, 0.83, 0.83, 0.83,
0.84
Time:
9500.00 days
Iteration Func-count f(x) Norm of Step
0 1 2.44607 start
1 56 5.066e-004 14.2331
2 57 1.696e-006 0.01027
3 58 1.642e-009 7.344e-006
4 59 1.593e-011 1.241e-008
Producer BHP:
1500.00 psi
Injector BHP:
4209.20 psi
Pressure:
2019.44, 2113.65, 2192.05, 2267.25, 2336.55, 2426.67, 2510.85, 2599.93,
2696.27, 2766.67, 2843.23, 2935.34, 3010.72, 3071.25, 3136.85, 3195.79,
3268.94, 3356.39, 3449.50, 3575.62, 3699.13, 3821.40, 3939.02, 4013.99,
4061.01
Saturation:
0.78, 0.79, 0.79, 0.79, 0.79, 0.79, 0.79, 0.80,
0.80, 0.80, 0.80, 0.80, 0.80, 0.81, 0.81, 0.81,
0.81, 0.82, 0.82, 0.82, 0.82, 0.83, 0.83, 0.83,
0.84
Time:
10000.00 days
Iteration Func-count f(x) Norm of Step
0 1 2.26765 start
1 56 4.047e-004 13.1882
2 57 1.231e-006 0.00820
3 58 1.068e-009 5.429e-006
4 59 1.261e-011 7.639e-009
Producer BHP:
1500.00 psi
Injector BHP:
4197.05 psi
Pressure:
2015.97, 2109.57, 2187.46, 2262.20, 2331.09, 2420.68, 2504.39, 2592.97,
2688.80, 2758.83, 2835.02, 2926.68, 3001.70, 3061.97, 3127.29, 3185.98,
3258.85, 3345.98, 3438.79, 3564.52, 3687.69, 3809.65, 3927.03, 4001.89,
4048.86
Saturation:
0.79, 0.79, 0.79, 0.79, 0.79, 0.79, 0.80, 0.80,
0.80, 0.80, 0.80, 0.80, 0.81, 0.81, 0.81, 0.81,
0.81, 0.82, 0.82, 0.82, 0.82, 0.83, 0.83, 0.83,
0.84
5/16/2026 9:43:36 PM
5/16/2026 9:45:29 PM
======================================================================
Starting simulation for Rate = 500 STB/day
Time:
0.00 days
Producer BHP:
3000.00 psi
Injector BHP:
3000.00 psi
Pressure:
3000.00, 3000.00, 3000.00, 3000.00, 3000.00, 3000.00, 3000.00, 3000.00,
3000.00, 3000.00, 3000.00, 3000.00, 3000.00, 3000.00, 3000.00, 3000.00,
3000.00, 3000.00, 3000.00, 3000.00, 3000.00, 3000.00, 3000.00, 3000.00,
3000.00
Saturation:
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20
Time:
500.00 days
Iteration Func-count f(x) Norm of Step
0 1 416.818 start
1 56 0.00760 0.67298
2 57 2.593e-005 4.326e-004
3 58 1.315e-008 1.174e-006
4 59 1.374e-010 7.409e-010
Producer BHP:
1500.00 psi
Injector BHP:
2516.64 psi
Pressure:
1587.15, 1603.05, 1616.35, 1629.18, 1641.08, 1656.64, 1671.27, 1686.85,
1703.82, 1716.30, 1729.97, 1746.53, 1760.18, 1771.23, 1783.30, 1794.22,
1807.90, 1824.42, 1842.20, 1866.53, 1890.69, 1930.98, 2129.64, 2256.61,
2330.21
Saturation:
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.20, 0.20, 0.20, 0.32, 0.66, 0.74,
0.78
Time:
1000.00 days
Iteration Func-count f(x) Norm of Step
0 1 409.496 start
1 56 0.00820 0.77942
2 57 3.093e-005 3.856e-004
3 58 2.019e-008 1.199e-006
4 59 1.347e-010 9.171e-010
Producer BHP:
1500.00 psi
Injector BHP:
3002.57 psi
Pressure:
1586.69, 1602.50, 1615.73, 1628.49, 1640.33, 1655.81, 1670.37, 1685.87,
1702.76, 1715.18, 1728.78, 1745.26, 1758.86, 1769.86, 1781.87, 1792.75,
1806.38, 1822.87, 1853.50, 2058.77, 2263.13, 2457.61, 2638.38, 2749.64,
2816.46
Saturation:
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.33, 0.66, 0.73, 0.76, 0.77, 0.79,
0.81
Time:
1500.00 days
Iteration Func-count f(x) Norm of Step
0 1 375.196 start
1 56 0.00509 0.73625
2 57 1.686e-005 1.804e-004
3 58 2.007e-008 3.495e-007
4 59 1.093e-010 4.690e-010
Producer BHP:
1500.00 psi
Injector BHP:
3270.00 psi
Pressure:
1586.65, 1602.45, 1615.67, 1628.42, 1640.25, 1655.72, 1670.27, 1685.76,
1702.63, 1715.03, 1728.62, 1745.09, 1758.66, 1769.65, 1781.66, 1797.07,
1902.66, 2043.75, 2188.56, 2380.42, 2565.18, 2744.84, 2914.29, 3019.84,
3084.07
Saturation:
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.29,
0.63, 0.72, 0.75, 0.76, 0.77, 0.78, 0.79, 0.80,
0.82
Time:
2000.00 days
Iteration Func-count f(x) Norm of Step
0 1 387.934 start
1 56 0.00629 0.68848
2 57 2.301e-005 2.284e-004
3 58 2.232e-008 5.922e-007
4 59 1.187e-010 7.582e-010
Producer BHP:
1500.00 psi
Injector BHP:
3468.03 psi
Pressure:
1586.53, 1602.31, 1615.51, 1628.25, 1640.05, 1655.50, 1670.03, 1685.50,
1702.35, 1714.74, 1728.31, 1744.78, 1765.53, 1855.54, 1958.72, 2048.82,
2158.56, 2287.69, 2423.38, 2605.17, 2781.36, 2953.67, 3117.08, 3219.47,
3282.25
Saturation:
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.20, 0.20, 0.20, 0.30, 0.65, 0.72, 0.75,
0.76, 0.77, 0.77, 0.78, 0.79, 0.79, 0.80, 0.81,
0.82
Time:
2500.00 days
Iteration Func-count f(x) Norm of Step
0 1 373.863 start
1 56 0.00530 0.99242
2 57 1.824e-005 2.038e-004
3 58 2.099e-008 4.171e-007
4 59 1.047e-010 5.645e-010
Producer BHP:
1500.00 psi
Injector BHP:
3721.99 psi
Pressure:
1585.92, 1601.59, 1614.69, 1627.34, 1639.07, 1654.41, 1668.83, 1684.19,
1700.95, 1718.69, 1825.61, 1966.30, 2078.23, 2166.50, 2261.22, 2345.57,
2449.48, 2572.74, 2702.99, 2878.15, 3048.44, 3215.54, 3374.60, 3474.69,
3536.39
Saturation:
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.20,
0.20, 0.29, 0.64, 0.72, 0.74, 0.76, 0.76, 0.77,
0.77, 0.78, 0.79, 0.79, 0.80, 0.80, 0.81, 0.82,
0.83
Time:
3000.00 days
Iteration Func-count f(x) Norm of Step
0 1 364.674 start
1 56 0.00466 1.31284
2 57 1.293e-005 1.895e-004
3 58 1.290e-008 3.258e-007
4 59 1.239e-010 3.493e-010
Producer BHP:
1500.00 psi
Injector BHP:
3981.03 psi
Pressure:
1585.20, 1600.74, 1613.74, 1626.28, 1637.90, 1653.13, 1672.31, 1789.52,
1932.81, 2034.72, 2143.68, 2273.36, 2378.71, 2462.82, 2553.56, 2634.72,
2735.04, 2854.39, 2980.83, 3151.24, 3317.25, 3480.53, 3636.36, 3734.73,
3795.62
Saturation:
0.20, 0.20, 0.20, 0.20, 0.20, 0.20, 0.27, 0.63,
0.72, 0.74, 0.75, 0.76, 0.77, 0.77, 0.78, 0.78,
0.78, 0.79, 0.79, 0.80, 0.80, 0.81, 0.81, 0.82,
0.83
Time:
3500.00 days
Iteration Func-count f(x) Norm of Step
0 1 366.356 start
1 56 0.00669 1.11217
2 57 2.824e-006 1.719e-004
3 58 3.058e-009 2.102e-007
4 59 1.207e-010 2.336e-010
Producer BHP:
1500.00 psi
Injector BHP:
4223.56 psi
Pressure:
1585.41, 1600.98, 1614.01, 1628.73, 1704.46, 1837.11, 1957.46, 2082.41,
2216.13, 2313.16, 2418.13, 2543.86, 2646.38, 2728.43, 2817.09, 2896.49,
2994.75, 3111.77, 3235.87, 3403.27, 3566.52, 3727.25, 3880.88, 3978.03,
4038.33
Saturation:
0.20, 0.20, 0.20, 0.24, 0.59, 0.71, 0.74, 0.75,
0.76, 0.77, 0.77, 0.77, 0.78, 0.78, 0.78, 0.79,
0.79, 0.80, 0.80, 0.80, 0.81, 0.81, 0.82, 0.82,
0.83
Time:
4000.00 days
Iteration Func-count f(x) Norm of Step
0 1 371.992 start
1 56 0.00947 1.78336
2 57 1.103e-005 4.990e-004
3 58 1.183e-008 1.437e-006
4 59 1.147e-010 6.451e-010
Producer BHP:
1500.00 psi
Injector BHP:
4443.27 psi
Pressure:
1593.22, 1681.85, 1793.68, 1898.25, 1992.82, 2114.55, 2227.51, 2346.50,
2474.81, 2568.35, 2669.88, 2791.81, 2891.44, 2971.31, 3057.75, 3135.27,
3231.33, 3345.90, 3467.59, 3631.96, 3792.48, 3950.77, 4102.35, 4198.41,
4258.19
Saturation:
0.23, 0.56, 0.71, 0.74, 0.75, 0.76, 0.76, 0.77,
0.77, 0.77, 0.78, 0.78, 0.78, 0.79, 0.79, 0.79,
0.80, 0.80, 0.80, 0.81, 0.81, 0.82, 0.82, 0.83,
0.83
================================================
Rejected (Maximum Pressure Violated)
================================================
Time:
4500.00 days
Iteration Func-count f(x) Norm of Step
0 1 25.2465 start
1 56 0.00134 1.07872
2 57 1.764e-006 0.00128
3 58 1.499e-010 1.200e-006
4 59 1.566e-011 2.910e-011
Producer BHP:
1500.00 psi
Injector BHP:
4500.00 psi
Pressure:
2119.04, 2228.21, 2317.71, 2402.72, 2480.45, 2580.96, 2674.42, 2772.94,
2879.15, 2956.54, 3040.49, 3141.22, 3223.46, 3289.33, 3360.56, 3424.39,
3503.43, 3597.65, 3697.66, 3832.72, 3964.59, 4094.64, 4219.19, 4298.14,
4347.31
Saturation:
0.73, 0.75, 0.76, 0.76, 0.77, 0.77, 0.77, 0.78,
0.78, 0.78, 0.78, 0.79, 0.79, 0.79, 0.79, 0.80,
0.80, 0.80, 0.81, 0.81, 0.81, 0.82, 0.82, 0.83,
0.83
Time:
5000.00 days
Iteration Func-count f(x) Norm of Step
0 1 8.16290 start
1 56 9.290e-004 1.77232
2 57 1.631e-006 0.00225
3 58 5.434e-010 2.621e-006
4 59 8.419e-012 6.713e-010
Producer BHP:
1500.00 psi
Injector BHP:
4500.00 psi
Pressure:
2096.40, 2203.65, 2292.38, 2377.12, 2454.91, 2555.75, 2649.70, 2748.87,
2855.89, 2933.95, 3018.68, 3120.41, 3203.52, 3270.14, 3342.21, 3406.83,
3486.89, 3582.37, 3683.80, 3820.85, 3954.74, 4086.86, 4213.50, 4293.87,
4343.98
Saturation:
0.76, 0.76, 0.77, 0.77, 0.77, 0.77, 0.78, 0.78,
0.78, 0.79, 0.79, 0.79, 0.79, 0.80, 0.80, 0.80,
0.80, 0.81, 0.81, 0.81, 0.82, 0.82, 0.82, 0.83,
0.84
Time:
5500.00 days
Iteration Func-count f(x) Norm of Step
0 1 5.67888 start
1 56 5.769e-004 1.58259
2 57 9.336e-007 0.00186
3 58 2.362e-010 2.134e-006
Producer BHP:
1500.00 psi
Injector BHP:
4500.00 psi
Pressure:
2088.46, 2194.77, 2282.97, 2367.37, 2444.97, 2545.68, 2639.59, 2738.80,
2845.93, 2924.11, 3009.02, 3111.01, 3194.37, 3261.21, 3333.56, 3398.45,
3478.89, 3574.87, 3676.88, 3814.78, 3949.57, 4082.66, 4210.32, 4291.41,
4342.03
Saturation:
0.77, 0.77, 0.77, 0.77, 0.78, 0.78, 0.78, 0.78,
0.79, 0.79, 0.79, 0.79, 0.80, 0.80, 0.80, 0.80,
0.80, 0.81, 0.81, 0.81, 0.82, 0.82, 0.83, 0.83,
0.84
Time:
6000.00 days
Iteration Func-count f(x) Norm of Step
0 1 4.58689 start
1 56 6.452e-004 1.76283
2 57 1.231e-006 0.00250
3 58 2.982e-010 3.621e-006
4 59 8.743e-012 7.221e-010
Producer BHP:
1500.00 psi
Injector BHP:
4500.00 psi
Pressure:
2084.11, 2189.83, 2277.64, 2361.75, 2439.15, 2539.67, 2633.45, 2732.58,
2839.67, 2917.85, 3002.78, 3104.85, 3188.30, 3255.24, 3327.72, 3392.76,
3473.40, 3569.66, 3672.02, 3810.45, 3945.82, 4079.56, 4207.92, 4289.52,
4340.52
Saturation:
0.77, 0.77, 0.78, 0.78, 0.78, 0.78, 0.78, 0.79,
0.79, 0.79, 0.79, 0.80, 0.80, 0.80, 0.80, 0.80,
0.81, 0.81, 0.81, 0.82, 0.82, 0.82, 0.83, 0.83,
0.84
Time:
6500.00 days
Iteration Func-count f(x) Norm of Step
0 1 3.93908 start
1 56 6.102e-004 1.76914
2 57 1.169e-006 0.00252
3 58 2.503e-010 3.834e-006
4 59 1.104e-011 6.923e-010
Producer BHP:
1500.00 psi
Injector BHP:
4500.00 psi
Pressure:
2081.16, 2186.43, 2273.94, 2357.80, 2435.02, 2535.35, 2628.99, 2728.00,
2835.00, 2913.14, 2998.06, 3100.14, 3183.62, 3250.61, 3323.16, 3388.28,
3469.05, 3565.51, 3668.12, 3806.94, 3942.75, 4076.99, 4205.92, 4287.94,
4339.24
Saturation:
0.78, 0.78, 0.78, 0.78, 0.78, 0.79, 0.79, 0.79,
0.79, 0.79, 0.80, 0.80, 0.80, 0.80, 0.80, 0.81,
0.81, 0.81, 0.81, 0.82, 0.82, 0.82, 0.83, 0.83,
0.84
Time:
7000.00 days
Iteration Func-count f(x) Norm of Step
0 1 3.46691 start
1 56 6.471e-004 1.87001
2 57 1.301e-006 0.00280
3 58 2.743e-010 4.636e-006
4 59 7.827e-012 8.552e-010
Producer BHP:
1500.00 psi
Injector BHP:
4500.00 psi
Pressure:
2078.90, 2183.82, 2271.08, 2354.73, 2431.78, 2531.93, 2625.43, 2724.31,
2831.21, 2909.29, 2994.17, 3096.24, 3179.72, 3246.74, 3319.33, 3384.52,
3465.39, 3562.00, 3664.80, 3803.94, 3940.11, 4074.77, 4204.17, 4286.55,
4338.12
Saturation:
0.78, 0.78, 0.78, 0.78, 0.79, 0.79, 0.79, 0.79,
0.79, 0.80, 0.80, 0.80, 0.80, 0.80, 0.81, 0.81,
0.81, 0.81, 0.82, 0.82, 0.82, 0.82, 0.83, 0.83,
0.84
Time:
7500.00 days
Iteration Func-count f(x) Norm of Step
0 1 3.09245 start
1 56 7.305e-004 2.03606
2 57 1.574e-006 0.00329
3 58 3.556e-010 5.990e-006
4 59 1.179e-011 1.238e-009
Producer BHP:
1500.00 psi
Injector BHP:
4500.00 psi
Pressure:
2077.06, 2181.68, 2268.72, 2352.18, 2429.08, 2529.05, 2622.42, 2721.19,
2827.98, 2906.00, 2990.84, 3092.87, 3176.35, 3243.38, 3316.00, 3381.23,
3462.18, 3558.91, 3661.88, 3801.28, 3937.76, 4072.79, 4202.61, 4285.30,
4337.11
Saturation:
0.78, 0.78, 0.78, 0.79, 0.79, 0.79, 0.79, 0.79,
0.80, 0.80, 0.80, 0.80, 0.80, 0.81, 0.81, 0.81,
0.81, 0.81, 0.82, 0.82, 0.82, 0.83, 0.83, 0.83,
0.84
Time:
8000.00 days
Iteration Func-count f(x) Norm of Step
0 1 2.78474 start
1 56 5.540e-004 1.81652
2 57 1.018e-006 0.00246
3 58 1.887e-010 3.884e-006
4 59 9.614e-012 6.210e-010
Producer BHP:
1500.00 psi
Injector BHP:
4500.00 psi
Pressure:
2075.48, 2179.84, 2266.68, 2349.98, 2426.75, 2526.56, 2619.79, 2718.45,
2825.14, 2903.10, 2987.89, 3089.88, 3173.35, 3240.39, 3313.04, 3378.30,
3459.31, 3556.14, 3659.25, 3798.89, 3935.64, 4071.00, 4201.19, 4284.17,
4336.19
Saturation:
0.78, 0.79, 0.79, 0.79, 0.79, 0.79, 0.79, 0.80,
0.80, 0.80, 0.80, 0.80, 0.80, 0.81, 0.81, 0.81,
0.81, 0.82, 0.82, 0.82, 0.82, 0.83, 0.83, 0.83,
0.84
Time:
8500.00 days
Iteration Func-count f(x) Norm of Step
0 1 2.57347 start
1 56 7.028e-004 2.08354
2 57 1.462e-006 0.00323
3 58 3.303e-010 5.862e-006
4 59 8.614e-012 1.218e-009
Producer BHP:
1500.00 psi
Injector BHP:
4500.00 psi
Pressure:
2074.09, 2178.22, 2264.89, 2348.03, 2424.67, 2524.34, 2617.45, 2716.00,
2822.59, 2900.49, 2985.23, 3087.19, 3170.65, 3237.68, 3310.35, 3375.64,
3456.70, 3553.62, 3656.85, 3796.71, 3933.71, 4069.36, 4199.89, 4283.12,
4335.34
Saturation:
0.79, 0.79, 0.79, 0.79, 0.79, 0.79, 0.80, 0.80,
0.80, 0.80, 0.80, 0.80, 0.81, 0.81, 0.81, 0.81,
0.81, 0.82, 0.82, 0.82, 0.82, 0.83, 0.83, 0.83,
0.84
Time:
9000.00 days
Iteration Func-count f(x) Norm of Step
0 1 2.33929 start
1 56 5.544e-004 1.89412
2 57 1.004e-006 0.00251
3 58 1.970e-010 4.020e-006
4 59 1.233e-011 6.985e-010
Producer BHP:
1500.00 psi
Injector BHP:
4500.00 psi
Pressure:
2072.84, 2176.77, 2263.27, 2346.28, 2422.80, 2522.33, 2615.33, 2713.77,
2820.27, 2898.12, 2982.81, 3084.73, 3168.17, 3235.21, 3307.88, 3373.19,
3454.31, 3551.31, 3654.65, 3794.70, 3931.92, 4067.84, 4198.68, 4282.16,
4334.56
Saturation:
0.79, 0.79, 0.79, 0.79, 0.79, 0.80, 0.80, 0.80,
0.80, 0.80, 0.80, 0.81, 0.81, 0.81, 0.81, 0.81,
0.81, 0.82, 0.82, 0.82, 0.82, 0.83, 0.83, 0.83,
0.84
Time:
9500.00 days
Iteration Func-count f(x) Norm of Step
0 1 2.18783 start
1 56 7.304e-004 2.20910
2 57 1.518e-006 0.00341
3 58 3.815e-010 6.328e-006
4 59 8.166e-012 1.482e-009
Producer BHP:
1500.00 psi
Injector BHP:
4500.00 psi
Pressure:
2071.70, 2175.44, 2261.80, 2344.68, 2421.09, 2520.49, 2613.39, 2711.73,
2818.15, 2895.94, 2980.59, 3082.47, 3165.89, 3232.92, 3305.61, 3370.94,
3452.09, 3549.17, 3652.62, 3792.84, 3930.27, 4066.44, 4197.57, 4281.26,
4333.83
Saturation:
0.79, 0.79, 0.79, 0.79, 0.80, 0.80, 0.80, 0.80,
0.80, 0.80, 0.81, 0.81, 0.81, 0.81, 0.81, 0.81,
0.82, 0.82, 0.82, 0.82, 0.83, 0.83, 0.83, 0.83,
0.84
Time:
10000.00 days
Iteration Func-count f(x) Norm of Step
0 1 2.00448 start
1 56 5.918e-004 2.03238
2 57 1.086e-006 0.00273
3 58 2.458e-010 4.519e-006
4 59 1.515e-011 9.231e-010
Producer BHP:
1500.00 psi
Injector BHP:
4500.00 psi
Pressure:
2070.66, 2174.22, 2260.44, 2343.20, 2419.51, 2518.79, 2611.59, 2709.85,
2816.17, 2893.92, 2978.52, 3080.37, 3163.77, 3230.80, 3303.50, 3368.85,
3450.04, 3547.18, 3650.72, 3791.10, 3928.73, 4065.12, 4196.52, 4280.43,
4333.15
Saturation:
0.79, 0.79, 0.79, 0.80, 0.80, 0.80, 0.80, 0.80,
0.80, 0.80, 0.81, 0.81, 0.81, 0.81, 0.81, 0.81,
0.82, 0.82, 0.82, 0.82, 0.83, 0.83, 0.83, 0.84,
0.84
5/16/2026 9:46:37 PM
5/16/2026 9:48:29 PM
