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Cross Sections

A cross section defines the radial structure of the pipe: the flow area where fluid moves, the inner wall where friction acts, and the concentric layers through which heat is conducted between fluid and environment.

Cross-Section Identity

Each cross section has an integer identifier. Pipe segments reference the cross section they use via this ID, allowing multiple pipe segments to share the same radial geometry.

JSON key: crossSection (EN) · secaoTransversal (PT) — top-level array Each element: id — integer identifier

Flow Area and Hydraulic Resistance

The 1D axial equations require a flow area and a friction surface to compute velocities and pressure losses. Two properties define this:

Internal Diameter

The inner diameter always defines the hydraulic inner boundary of the flow region:

  • For non-annular flow (annular = false): it is the pipe internal diameter used in $A = \pi d^2 / 4$.
  • For annular flow (annular = true): it is the smallest annular-flow diameter.

All hydraulic calculations (Reynolds number, friction factor, holdup geometry) depend on this dimension.

JSON key: innerDiameter (EN) · diametroInterno (PT) — unit: m

Outer Diameter (Annular Flow)

For annular flow, the simulator needs both annulus boundaries. outerDiameter defines the largest diameter of the annular flow area.

JSON key: outerDiameter (EN) · diametroExterno (PT) — unit: m, valid when annular = true

Wall Roughness

Absolute roughness of the inner pipe surface, entering the Colebrook (or Moody) friction-factor correlation. Typical values range from 1.5×10⁻⁶ m (polished tubing) to 4.6×10⁻⁴ m (corroded old pipe).

JSON key: roughness (EN) · rugosidade (PT) — unit: m

Annular Flow Geometry

Some well configurations have production occurring in the annulus between tubing and casing rather than inside the tubing. When annular geometry is indicated, hydraulic calculations use annular geometry built from:

  • innerDiameter = smallest annulus-flow diameter
  • outerDiameter = largest annulus-flow diameter

JSON key: annular (EN) · anular (PT) — default false

Concentric Layers (Thermal Structure)

Heat transfer between the flowing fluid and the external environment passes through concentric solid (or fluid) layers surrounding the flow area. Each cross section defines these layers from the inner wall outward:

┌─────────────── External boundary (formation, seawater, or atmosphere)
│  Layer N  ← cement, rock contact, or concrete coating
│  Layer 2  ← insulation (PU foam, polypropylene, etc.)
│  Layer 1  ← pipe wall (steel)
│  ═════════  Inner surface (roughness applies here)
│  Fluid flow area (innerDiameter)
└─────────────── Pipe center

Each layer is defined by its geometric extent, radial discretization, and material reference.

JSON key: layers (EN) · camadas (PT) — array inside each cross-section object

Layer Geometric Definition

Two ways to specify layer size:

  • By thickness — the radial thickness of the layer, building outward from the previous boundary.
  • By diameter — the diameter from pipe center to the outer circumference of the layer.

JSON key: layerMeasurementType (EN) · tipoMedicaoCamada (PT) Values: "THICKNESS" (EN) / "ESPESSURA" (PT) or "DIAMETER" (EN) / "DIAMETRO" (PT)

Thickness: thickness (EN) · espessura (PT) — unit: m Diameter mode key: diameter (EN) · diametro (PT) — unit: m

If layerMeasurementType is omitted, default is diameter mode.

Radial Discretization

Each layer is subdivided into radial nodes for the heat-conduction calculation. More nodes provide better resolution of temperature gradients within the layer, at the cost of additional computation.

JSON key: discretization (EN) · discretizacao (PT) — default 1

Material Reference

Each layer references a material entry (by integer ID) that provides the thermal properties (conductivity, specific heat, density) for heat-conduction calculations.

JSON key: materialId (EN) · idMaterial (PT)

Annulus, Gas Line, and Thermal Coupling

Cross-section annularity and pipe thermal coupling are related but distinct concepts:

  • Cross section (crossSection): defines geometry (annular, innerDiameter, outerDiameter, layers).
  • Pipe segment (productionPipe): defines whether that segment is thermally coupled to service line via thermalCoupling / acoplamentoTermico.

Practical implications:

  • Setting annular = true changes hydraulic geometry; it does not by itself activate thermal coupling.
  • Thermal coupling is configured at pipe-segment level and requires a service line (gasLine / linhaGas enabled).
  • In coupled segments, production and service pipes should be coincident in position, length, and discretization for consistent exchange.

JSON keys:

  • Service-line enable: initialConfig.gasLine (EN) · configuracaoInicial.linhaGas (PT)
  • Segment coupling flag (pipe-level key): thermalCoupling (EN) · acoplamentoTermico (PT)

Practical Guidance

  • Layer consistency: Layers nest concentrically. When using thickness mode, the outer radius of each layer is computed cumulatively from the inner diameter outward.
  • Annular consistency: For annular sections, ensure outerDiameter > innerDiameter and both represent annulus-flow boundaries (not wall-layer diameters).
  • Roughness calibration: If pressure-drop predictions deviate from field data, roughness is often the first parameter to calibrate (especially in old or scaled pipes).
  • Multiple cross sections: Use different cross-section IDs for different pipe segments (e.g., one for the riser with thick insulation, another for the subsea flowline with concrete coating).
  • Annular wells: When annular geometry is active, ensure the layer structure reflects the casing/tubing arrangement correctly.
  • Coupled annulus/column cases: Configure thermal coupling in productionPipe, not in the cross-section object.

Example: Simple Pipeline (Steel + Insulation)

{
  "crossSection": [
    {
      "id": 0,
      "active": true,
      "annular": false,
      "innerDiameter": 0.15,
      "roughness": 5e-5,
      "layers": [
        {
          "layerMeasurementType": "THICKNESS",
          "thickness": 0.012,
          "discretization": 1,
          "materialId": 0
        },
        {
          "layerMeasurementType": "THICKNESS",
          "thickness": 0.050,
          "discretization": 3,
          "materialId": 1
        }
      ]
    }
  ]
}

Example: Well Completion (Tubing + Annular Fluid + Casing + Cement)

{
  "crossSection": [
    {
      "id": 1,
      "active": true,
      "annular": true,
      "innerDiameter": 0.10,
      "outerDiameter": 0.18,
      "roughness": 1.83e-4,
      "layers": [
        {
          "layerMeasurementType": "THICKNESS",
          "thickness": 0.008,
          "discretization": 1,
          "materialId": 0
        },
        {
          "layerMeasurementType": "THICKNESS",
          "thickness": 0.020,
          "discretization": 2,
          "materialId": 1
        },
        {
          "layerMeasurementType": "THICKNESS",
          "thickness": 0.010,
          "discretization": 1,
          "materialId": 0
        },
        {
          "layerMeasurementType": "THICKNESS",
          "thickness": 0.040,
          "discretization": 2,
          "materialId": 2
        }
      ]
    }
  ]
}

Where material IDs map to: 0 = steel, 1 = completion fluid (type 2), 2 = cement.

Tip

Start with 1 node per layer for steady-state validation, then increase to 2–3 in insulation/cement layers for transient cooldown studies where radial resolution matters.