Injection Well Simulation¶

This document describes the injection well simulation mode in Marlim3 (-s INJETOR / tipoSimulacao_t::poco_injetor). Injection well simulations are steady-state only and model injection flow from the surface down to one or more injection zones.

Key source files:

File	Role
`src/Num4Main.cpp`	Entry point: `SolveTramoSolteiro()`, `permanenteSimples()` dispatching
`src/SisProd.h` / `SisProd.cpp`	`SProd` class: `marchaInjPerm1()`, `buscaInjPfundoPerm1–5()`, `delpInjPerm()`
`src/Leitura.h` / `Leitura.cpp`	`detCondConInjec` structure, `parse_condcont_pocinjec()`
`src/PropFluCol.h` / `PropFluCol.cpp`	`ProFluCol` — injection fluid properties (water, CO₂, compositional)
`src/FonteMas.h` / `FonteMas.cpp`	`IPR` class — injectivity index model

Table of Contents¶

Overview
Boundary Condition Types
JSON Input
Injection Fluid Types
Call Hierarchy
The Marching Method — marchaInjPerm1
Root-Finding and Iterative Methods
buscaInjPfundoPerm1 — CC 1 or 3
buscaInjPfundoPerm2 — CC 0
buscaInjPfundoPerm3 — CC 2
buscaInjPfundoPerm4 — CC 4
buscaInjPfundoPerm5 — CC 5
IPR Model for Injection
Pressure Drop Estimation — delpInjPerm
Injection Network — RedeInj
Compositional Injection
Key Differences from Production
Summary of Key Methods

Overview¶

Injection well simulations model the downward flow of an injection fluid from the surface wellhead to one or more reservoir injection zones. The solver computes pressure, temperature, and flow-rate profiles along the wellbore under steady-state conditions.

For user-defined liquid and saline-water modes, the model is effectively single-phase. For table-based CO₂ and especially compositional injection, the code may also initialize and propagate gas/liquid split information (for example via alfini, betini, and FracMassHidra() in marchaInjPerm1), so the implementation should not be interpreted as strictly single-phase in every injection case.

The fundamental approach is the same shooting method used for production:

Guess an unknown boundary value (surface pressure or injection rate)
March cell-by-cell from surface to bottom, computing pressure and temperature
Evaluate a residual — the mismatch at the bottom boundary (IPR-predicted rate vs. computed rate, or specified vs. computed bottom-hole pressure)
Iterate using Ridder's root-finding method when the selected boundary-condition formulation requires bracketing of a scalar unknown

The key constraint: injection wells are steady-state only (no transient simulation).

Boundary Condition Types¶

The detCondConInjec structure (Leitura.h) defines six BC configurations via the CC flag:

CC	Given	Solved for	Root-finding?
0	Flow rate + IPR at bottom	Surface pressure	Yes (`buscaInjPfundoPerm2`)
1	Injection pressure (surface) + IPR at bottom	Flow rate	Yes (`buscaInjPfundoPerm1`)
2	Bottom-hole pressure + IPR at bottom	Flow rate	Iterative pressure-profile correction (`buscaInjPfundoPerm3`)
3	Injection pressure + bottom-hole pressure	Flow rate	Yes (`buscaInjPfundoPerm1`)
4	Flow rate + injection pressure	Bottom pressure/profile computed directly	No
5	Flow rate + bottom-hole pressure	Surface pressure	Yes (`buscaInjPfundoPerm5`)

`detCondConInjec` members¶

Member	Type	Units	Description
`CC`	`int`	—	BC type (0–5)
`tipoFlui`	`int`	—	Fluid type (0 = user, 1 = water, 2 = CO₂ PVTSim table, 3 = compositional)
`salin`	`double`	g/L	Water salinity (for `tipoFlui == 1`)
`tempinj`	`double`	°C	Injection temperature
`vazinj`	`double`	Sm³/d	Injection flow rate
`presinj`	`double`	kgf/cm²	Surface injection pressure
`presfundo`	`double`	kgf/cm²	Bottom-hole pressure
`pvtsimarqInj`	`string`	—	PVTSim file path for CO₂/compositional fluid

JSON Input¶

Injection well parameters are parsed by parse_condcont_pocinjec() from the "CondicaoContPocInjec" JSON object:

"CondicaoContPocInjec": {
  "ativo": true,
  "condcontorno": 2,
  "tipoFluido": 1,
  "salinidade": 20.0,
  "tempInj": 40.0,
  "vazLiq": 1000.0,
  "presInjec": 33.91,
  "presFundo": 339.0,
  "arquivoPvtsim": "PVTSIM_MARLIM.tab"
}

Conditional field requirements (enforced at parse time):

CC values	Required fields
0, 4, 5	`vazLiq`
1, 3, 4	`presInjec`
2, 3, 5	`presFundo`

Injection Fluid Types¶

The injection fluid is modeled by ProFluCol, dispatched via injPoc:

`tipoFlui`	`injPoc`	Fluid model	Properties source
0	0	User-defined liquid	ASTM viscosity, constant Cp, constant conductivity, compressibility model
1	2	Saline water	Built-in correlations: \(\rho = f(P, T, \text{salinity})\), Arrhenius \(\mu\), polynomial \(C_p\) and \(k\)
2	3	CO₂-rich gas (supercritical)	Bilinear interpolation from PVTSim 2D (P × T) tables for \(\rho\), \(\mu\), \(k\), \(C_p\)
3	—	Compositional	Full cubic EOS flash via Fortran compositional library

For CO₂ injection (tipoFlui == 2), property tables are loaded from a PVTSim .tab file and stored as 2D arrays (RhoInj[][], ViscInj[][], CondInj[][], CpInj[][], DrhoDtInj[][]). The interpolaVarInj() method performs bilinear interpolation on these arrays after first clamping pressure and temperature to the table bounds; therefore, out-of-range states are clipped to the nearest tabulated boundary rather than extrapolated.

Call Hierarchy¶

main()
 └─ SolveTramoSolteiro(sistem1)                         [Num4Main.cpp]
     ├─ (compositional) Switch to black-oil mode, run permanenteSimples
     ├─ (compositional) Restore compositional, use black-oil as initial guess
     └─ permanenteSimples(sistem1)                       [Num4Main.cpp]
         └─ Detect pocinjec != 0, dispatch by CC:
             ├─ CC 1 or 3 → buscaInjPfundoPerm1(chute)  [SisProd.cpp]
             ├─ CC 0      → buscaInjPfundoPerm2(chute)
             ├─ CC 2      → buscaInjPfundoPerm3(chute)
             ├─ CC 4      → buscaInjPfundoPerm4()
             └─ CC 5      → buscaInjPfundoPerm5(chute)
                             │
                             └─ marchaInjPerm1(x)        [SisProd.cpp]
                                 ├─ Set initial T from injection source
                                 ├─ Handle surface choke ΔP
                                 └─ March cell-by-cell (i=1 to ncel):
                                     ├─ RenovaPresPermMon(i)
                                     ├─ RenovaMassPerm(i)
                                     ├─ RenovaTempPerm(i)
                                     ├─ RenovaPresPermJus(i)
                                     └─ RenovaTransMassPerm(i-1)

The Marching Method — marchaInjPerm1¶

SProd::marchaInjPerm1(double chute) (SisProd.cpp) is the core marching function for injection wells.

Input interpretation¶

The meaning of chute depends on the BC type:

CC	`chute` represents
1, 2, 3	Flow rate (Sm³/d) — sets `injl.QLiq` or `injg.QGas`
0, 5	Surface pressure (kgf/cm²) — sets `pGSup`

Algorithm¶

Set initial temperature from the injection source (injl.temp or injg.temp)
If surface choke is active (opening < 0.6): compute ΔP across choke
For compositional gas: compute initial phase fractions (\(\alpha_{ini}\), \(\beta_{ini}\))

Cell-by-cell march from surface (i=1) to bottom (i=ncel):

while i ≤ ncel AND P ≥ 1 kgf/cm² AND mass_balance ≥ 0:
    RenovaPresPermMon(i)       — pressure: center → upstream face
    RenovaMassPerm(i)          — mass balance (including IPR sources)
    RenovaTempPerm(i)          — energy equation
    RenovaPresPermJus(i)       — pressure: upstream face → center
    RenovaTransMassPerm(i-1)   — interphase mass transfer
    Accumulate mass sources from IPR zones

Return the objective function value:
For CC ≠ 3, 5: net mass flow at bottom (masfim). Zero means mass balance is satisfied.
For CC = 3, 5: \(P_{\text{bottom,specified}} - P_{\text{bottom,computed}}\). Zero means pressure match.

Error conditions¶

\(P < 1\) kgf/cm² — pressure dropped below physical minimum
\(P_{\text{reservoir}} > P_{\text{bottom}}\) — well would produce instead of inject
Net mass at bottom < 0 — flow direction inconsistency

Root-Finding and Iterative Methods¶

The injection-well solution methods fall into two groups:

Bracketed scalar solves using zriddr (Ridder's method)
Direct or iterative profile construction without Ridder bracketing

buscaInjPfundoPerm1 — CC 1 or 3¶

Given: injection pressure (or both pressures for CC 3)
Unknown: flow rate
Initial guess: hydrostatic pressure walk from the surface combined with cumulative IPR-based injection-rate accumulation along the well, including density correction for tipoFlui ≥ 2
Bracketing: multiplies guess by 0.9 / 1.1 until sign change in marchaInjPerm1
Root-finding: zriddr(chuteNeg, chutePos)

buscaInjPfundoPerm2 — CC 0¶

Given: injection flow rate + IPR at bottom
Unknown: surface pressure
Initial guess: reverse pressure estimate from the bottom condition using explicit hydrostatic and friction terms evaluated along the wellbore
Bracketing: multiplies by 0.9 / 1.1
Root-finding: zriddr

buscaInjPfundoPerm3 — CC 2¶

Given: bottom-hole pressure + IPR
Unknown: flow rate
Method type: iterative pressure-profile correction, not a Ridder/bracketed root solve
Algorithm: sets celula[ncel].pres = presfundo, estimates flow rate from the terminal IPR, reconstructs the pressure profile upward, then remarches from the surface and repeats until the computed bottom-hole pressure matches the specified value
Pressure update: uses delpInjPerm() during the reverse pressure reconstruction step
Convergence: \(|P_{\text{computed}} - P_{\text{specified}}| / P_{\text{specified}} < 0.01\%\)

buscaInjPfundoPerm4 — CC 4¶

Given: flow rate + injection pressure
Method type: direct march
Algorithm: performs a forward march with the prescribed inlet condition and computes the resulting bottom pressure/profile as an output
Returns net mass flow at bottom for diagnostics

buscaInjPfundoPerm5 — CC 5¶

Given: flow rate + bottom-hole pressure
Unknown: surface pressure
Initial guess: reverse pressure estimate from the bottom condition using explicit hydrostatic and friction terms evaluated along the wellbore
Root-finding: zriddr

IPR Model for Injection¶

Injection zones use a linear injectivity index model. At each cell with acsr.tipo == 3:

\[Q_{\text{inj}} = -II \cdot (P_{\text{res}} - P_{\text{bottom}})\]

where: - \(II\) = injectivity index (celula[i].acsr.ipr.ij) - \(P_{\text{res}}\) = reservoir pressure (celula[i].acsr.ipr.Pres)

Since \(P_{\text{bottom}} > P_{\text{res}}\) for injection, the term \((P_{\text{res}} - P_{\text{bottom}})\) is negative, making \(Q_{\text{inj}}\) positive (fluid flows into the reservoir).

For tabulated fluids (tipoFlui ≥ 2), the IPR is corrected for in-situ density:

\[Q_{\text{inj,std}} = -\frac{II \cdot \rho(P,T)}{\rho_{\text{std}}} \cdot (P_{\text{res}} - P_{\text{bottom}})\]

Multiple injection zones along the wellbore are supported — each cell can independently host an IPR accessory.

Pressure Drop Estimation — delpInjPerm¶

SProd::delpInjPerm(int i) estimates the pressure drop across the interface between cells \(i-1\) and \(i\) using a two-half-cell evaluation: one contribution from the right half of cell \(i-1\) / left connection, and another from the left half of cell \(i\). In each half-step, the code reevaluates local geometry, temperature, density, viscosity, Reynolds number, and friction factor.

A compact conceptual representation of the implemented model is:

\[ \Delta P \approx \frac{f \rho |v| v S_i \Delta x /(2A) + \rho g \sin\theta \Delta x}{98066.5} \]

where \(f\) is the friction factor, \(\rho\) is the fluid density from fluicol, and the result is in kgf/cm². In the actual implementation, this expression is applied separately over two half-cell segments, and the user-specified correction factors dPdLFric and dPdLHidro are applied to the friction and hydrostatic contributions respectively.

This method is used mainly in reverse pressure reconstruction and pressure-guess support routines such as buscaInjPfundoPerm3() and hidroreversoInj().

Injection Network — RedeInj¶

When the simulation type is REDE and the network is tagged as injection (arqRede.injec == 1), the RedeInj() function (Num4Main.cpp) manages the network-level solve.

Algorithm¶

Construct all tramo SProd objects from JSON files
Tag each tramo: noextremo (end of network / leaf), noinicial (start / root)
Initial pressure guess via chutePresRedeInj(): walks the network tree from collectors to leaves, distributing flow proportionally by pipe area and estimating node pressures via hidroreversoInj()

\[Q_{\text{tramo}} = Q_{\text{total}} \cdot \frac{A_{\text{tramo}}}{A_{\text{total}}}\]

Iterative convergence loop (cicloRedeInj):
Solve leaf tramos first (no upstream dependencies) using buscaInjPfundoPerm1 or buscaInjPfundoPerm5
Then solve collector tramos once all upstream tributaries converge
At collectors: mix temperatures and flow rates from upstream tributaries
Update inter-tramo boundary conditions (upstream pressure → downstream injection pressure)
Convergence criterion: norma < 0.001 * relax
If a tramo fails convergence, mark it inactive and propagate to downstream collectors

hidroreversoInj¶

hidroreversoInj(double hol, double vaz) estimates pressures in reverse direction (bottom to surface). Starting from the bottom-hole pressure (or IPR-estimated pressure), it marches upward using delpInjPerm to compute the surface pressure. Used to provide initial pressure guesses for network nodes.

Compositional Injection¶

For compositional injection (tipoFlui == 3, flashCompleto == 2), SolveTramoSolteiro applies the same two-pass strategy as production:

Temporarily set flashCompleto = 3 (marks "injection compositional in black-oil pre-solve phase")
Run permanenteSimples in black-oil mode to get an initial guess
Restore flashCompleto = 2 and run permanenteSimples again with the black-oil solution as initial guess
Optionally build dynamic PVT tables via preparaTabDin()

This avoids expensive flash calculations during the initial bracket search.

Sensitivity Analysis¶

When analiseSens.listaV.vpocinj == 1, injection parameters (presfundo, temp, vaz) can be swept parametrically for sensitivity analysis.

Key Differences from Production¶

Aspect	Production	Injection
Flow direction	Reservoir → Surface	Surface → Reservoir
Pressure profile	Decreases upward	Increases downward
IPR sign convention	\(P_{\text{res}} > P_{\text{bottom}}\) (inflow)	\(P_{\text{bottom}} > P_{\text{res}}\) (outflow into reservoir)
Fluid model	Black-oil multiphase (`ProFlu`)	Injection-fluid model centered on `ProFluCol` for user liquid / water / table-based CO₂, with compositional handling available in injection mode
Gas-lift line	Supported	Not applicable
Transient	Supported	Not supported (steady-state only)
Choke model	At outlet (surface separator)	At inlet (surface, restricts injection)
BCS / ESP pumps	Supported (production aids)	Not applicable
Network solver	`solveRedeProd()` / `SolveRedeTrans()`	Separate `RedeInj()` solver
Marcha method	`marchaProdPerm1()` / `marchaProdPerm2()`	`marchaInjPerm1()`
Busca methods	`buscaProdPfundoPerm()` / `buscaProdPfundoPerm2()`	`buscaInjPfundoPerm1()` – `buscaInjPfundoPerm5()`

Summary of Key Methods¶

Method	Location	Description
`marchaInjPerm1(chute)`	`SisProd.cpp`	Cell-by-cell march for injection; returns residual
`buscaInjPfundoPerm1(chute)`	`SisProd.cpp`	Root-finding for CC 1 or 3: given pressure, find flow rate
`buscaInjPfundoPerm2(chute)`	`SisProd.cpp`	Root-finding for CC 0: given flow rate + IPR, find surface pressure
`buscaInjPfundoPerm3(chute)`	`SisProd.cpp`	Iterative solve for CC 2: given BHP + IPR, find flow rate
`buscaInjPfundoPerm4()`	`SisProd.cpp`	Direct march for CC 4: fully determined (no root-finding)
`buscaInjPfundoPerm5(chute)`	`SisProd.cpp`	Root-finding for CC 5: given flow rate + BHP, find surface pressure
`delpInjPerm(i)`	`SisProd.cpp`	Two-half-cell single-phase-like \(\Delta P\) estimate used in reverse pressure reconstruction
`hidroreversoInj(hol, vaz)`	`SisProd.cpp`	Reverse walk for pressure estimation (bottom → surface)
`RedeInj()`	`Num4Main.cpp`	Injection network solver
`chutePresRedeInj()`	`Num4Main.cpp`	Initial pressure guess for injection network
`parse_condcont_pocinjec()`	`Leitura.cpp`	JSON parsing for injection well parameters
`interpolaVarInj(P, T, Var)`	`PropFluCol.cpp`	Bilinear interpolation with pressure/temperature clamping to PVTSim table bounds

Injection Well Simulation¶

Table of Contents¶

Overview¶

Boundary Condition Types¶

detCondConInjec members¶

JSON Input¶

Injection Fluid Types¶

Call Hierarchy¶

The Marching Method — marchaInjPerm1¶

Input interpretation¶

Algorithm¶

Error conditions¶

Root-Finding and Iterative Methods¶

buscaInjPfundoPerm1 — CC 1 or 3¶

buscaInjPfundoPerm2 — CC 0¶

buscaInjPfundoPerm3 — CC 2¶

buscaInjPfundoPerm4 — CC 4¶

buscaInjPfundoPerm5 — CC 5¶

IPR Model for Injection¶

Pressure Drop Estimation — delpInjPerm¶

Injection Network — RedeInj¶

Algorithm¶

hidroreversoInj¶

Compositional Injection¶

Sensitivity Analysis¶

Key Differences from Production¶

Summary of Key Methods¶

`detCondConInjec` members¶