Class TransientWellModel

java.lang.Object
neqsim.process.fielddevelopment.reservoir.TransientWellModel
All Implemented Interfaces:
Serializable
public class TransientWellModel extends Object implements Serializable
Transient well model with time-dependent IPR.

This class models transient pressure behavior in production and injection wells, including:

  • Pressure Buildup: Shut-in pressure recovery analysis
  • Pressure Drawdown: Flowing pressure decline during production
  • Superposition: Effect of multiple rate changes
  • Radius of Investigation: Time-dependent drainage area
  • Boundary Effects: Transition from infinite-acting to boundary-dominated

Mathematical Basis

The line-source solution for radial flow in an infinite-acting reservoir:

ΔP = (q·μ)/(4πkh) × Ei(-r²/(4·η·t))

where η = k/(φ·μ·ct) is the hydraulic diffusivity. For the wellbore (r=rw), using the logarithmic approximation:

P_wf = P_i - (q·μ)/(4πkh) × [ln(4·η·t/r_w²) - γ + 2S]

Superposition Principle

For multiple rate changes at times t₁, t₂, ... tₙ with rates q₁, q₂, ... qₙ:

ΔP(t) = Σ (qᵢ - qᵢ₋₁) × P_D(t - tᵢ)

This allows modeling complex production histories including shut-ins and rate changes.

Usage Example - Drawdown Analysis

TransientWellModel well = new TransientWellModel();
well.setReservoirPressure(250.0, "bara");
well.setPermeability(100.0, "mD");
well.setFormationThickness(30.0, "m");
well.setPorosity(0.20);
well.setTotalCompressibility(1.5e-4, "1/bar");
well.setFluidViscosity(0.5, "cP");
well.setWellboreRadius(0.1, "m");
well.setSkinFactor(2.0);

// Calculate flowing pressure after 10 hours at 1000 Sm3/day
DrawdownResult result = well.calculateDrawdown(1000.0, 10.0);
System.out.println("Pwf after 10 hours: " + result.flowingPressure + " bara");

Usage Example - Buildup Analysis (Horner Method)

// Well flowed at 1500 Sm3/day for 100 hours before shut-in
well.addRateChange(0.0, 1500.0); // Start production
well.addRateChange(100.0, 0.0); // Shut-in

BuildupResult buildup = well.calculateBuildup(24.0); // After 24 hrs shut-in
System.out.println("Pws: " + buildup.shutInPressure + " bara");
System.out.println("Permeability from slope: " + buildup.permeabilityFromSlope + " mD");
System.out.println("Skin from intercept: " + buildup.skinFromIntercept);
Version:
1.0
Author:
ESOL
See Also:

  • Field Details

    • serialVersionUID

      private static final long serialVersionUID
      See Also:

    • EULER_GAMMA

      private static final double EULER_GAMMA
      See Also:

    • PI

      private static final double PI
      See Also:

    • wellType

      private TransientWellModel.WellType wellType

    • boundaryType

      private TransientWellModel.BoundaryType boundaryType

    • initialPressure

      private double initialPressure

    • currentPressure

      private double currentPressure

    • permeability

      private double permeability

    • formationThickness

      private double formationThickness

    • porosity

      private double porosity

    • totalCompressibility

      private double totalCompressibility

    • drainageRadius

      private double drainageRadius

    • reservoirTemperature

      private double reservoirTemperature

    • wellboreRadius

      private double wellboreRadius

    • skinFactor

      private double skinFactor

    • wellboreStorage

      private double wellboreStorage

    • fluidViscosity

      private double fluidViscosity

    • fluidDensity

      private double fluidDensity

    • formationVolumeFactor

      private double formationVolumeFactor

    • rateHistory

      private List<TransientWellModel.RateChange> rateHistory

    • hydraulicDiffusivity

      private double hydraulicDiffusivity

    • transmissibility

      private double transmissibility

  • Constructor Details

    • TransientWellModel

      public TransientWellModel()
      Creates a new transient well model with default parameters.

  • Method Details

    • updateDerivedProperties

      private void updateDerivedProperties()
      Updates derived properties from input parameters.

    • calculateDrawdown

      public TransientWellModel.DrawdownResult calculateDrawdown(double rate, double timeHours)
      Calculates drawdown pressure at a given time.
      Parameters:
      rate - production rate (Sm³/day)
      timeHours - time since start of production (hours)
      Returns:
      drawdown result

    • calculateBuildup

      public TransientWellModel.BuildupResult calculateBuildup(double shutInTimeHours)
      Calculates buildup pressure after shut-in.
      Parameters:
      shutInTimeHours - time since shut-in (hours)
      Returns:
      buildup result

    • calculatePressureWithSuperposition

      public double calculatePressureWithSuperposition(double timeHours)
      Calculates pressure at a given time using superposition of all rate changes.
      Parameters:
      timeHours - time (hours)
      Returns:
      pressure (bara)

    • generatePressureProfile

      public List<TransientWellModel.PressurePoint> generatePressureProfile(double[] timePointsHours)
      Generates a transient pressure profile.
      Parameters:
      timePointsHours - array of time points (hours)
      Returns:
      list of pressure points

    • generateLogTimePoints

      public double[] generateLogTimePoints(double startHours, double endHours, int numPoints)
      Generates logarithmically spaced time points for analysis.
      Parameters:
      startHours - start time (hours)
      endHours - end time (hours)
      numPoints - number of points
      Returns:
      array of time points

    • calculatePressureDrop

      private double calculatePressureDrop(double rate, double timeSec)
      Calculates pressure drop using line-source solution.

      Uses the dimensionless pressure function with logarithmic approximation for late time:

      p_D = 0.5 × [ln(t_D) + 0.80907 + 2S] for t_D greater than 25

      Or the exponential integral for early time:

      p_D = -0.5 × Ei(-1/(4t_D)) + S for t_D ≤ 25

      The dimensional pressure drop is then:

      ΔP = q_res / (2πT) × p_D

      where T = kh/μ is the transmissibility.

      Parameters:
      rate - rate (Sm³/day)
      timeSec - time (seconds)
      Returns:
      pressure drop (bar)

    • dimensionlessTime

      private double dimensionlessTime(double timeSec)
      Calculates dimensionless time.

      Dimensionless time is defined as:

      t_D = η·t / r_w² = (k·t) / (φ·μ·c_t·r_w²)

      where η is the hydraulic diffusivity. This parameter controls the rate of pressure propagation through the reservoir.

      Parameters:
      timeSec - time (seconds)
      Returns:
      dimensionless time t_D (dimensionless)

    • calculateRadiusOfInvestigation

      private double calculateRadiusOfInvestigation(double timeSec)
      Calculates radius of investigation.

      The radius of investigation represents how far the pressure transient has propagated:

      r_inv = √(4·η·t)

      This is based on the distance at which the pressure disturbance is approximately 1% of the wellbore value. When r_inv approaches the drainage radius, the well transitions from infinite-acting to boundary-dominated flow.

      Parameters:
      timeSec - time (seconds)
      Returns:
      radius of investigation (m)

    • exponentialIntegral

      private double exponentialIntegral(double x)
      Exponential integral function Ei(-x).

      The exponential integral is defined as:

      Ei(x) = ∫_{-∞}^{x} (e^t / t) dt

      For negative arguments (transient flow), this is computed using:

      • Small |x| (less than 1): Series expansion: Ei(-x) = -γ - ln(x) + x - x²/(2·2!) + x³/(3·3!) - ...
      • Large |x| (≥ 1): Asymptotic expansion: Ei(-x) ≈ -(e^(-x)/x) × [1 - 1/x + 2!/x² - ...]

      where γ = 0.5772... is the Euler-Mascheroni constant.

      Parameters:
      x - argument (should be negative for transient flow)
      Returns:
      Ei(x) value

    • getRateAtTime

      private double getRateAtTime(double timeHours)
      Gets rate at a given time from rate history.
      Parameters:
      timeHours - time (hours)
      Returns:
      rate (Sm³/day)

    • addRateChange

      public TransientWellModel addRateChange(double timeHours, double rate)
      Adds a rate change to the history.
      Parameters:
      timeHours - time of change (hours)
      rate - rate after change (Sm³/day)
      Returns:
      this for chaining

    • clearRateHistory

      public TransientWellModel clearRateHistory()
      Clears the rate history.
      Returns:
      this for chaining

    • setReservoirPressure

      public TransientWellModel setReservoirPressure(double pressure, String unit)
      Sets reservoir initial pressure.
      Parameters:
      pressure - pressure
      unit - unit (bara, psia)
      Returns:
      this for chaining

    • setPermeability

      public TransientWellModel setPermeability(double permeability, String unit)
      Sets formation permeability.
      Parameters:
      permeability - permeability
      unit - unit (mD, D)
      Returns:
      this for chaining

    • setFormationThickness

      public TransientWellModel setFormationThickness(double thickness, String unit)
      Sets formation thickness.
      Parameters:
      thickness - thickness
      unit - unit (m, ft)
      Returns:
      this for chaining

    • setPorosity

      public TransientWellModel setPorosity(double porosity)
      Sets porosity.
      Parameters:
      porosity - porosity (fraction 0-1)
      Returns:
      this for chaining

    • setTotalCompressibility

      public TransientWellModel setTotalCompressibility(double compressibility, String unit)
      Sets total compressibility.
      Parameters:
      compressibility - compressibility
      unit - unit (1/bar, 1/psi)
      Returns:
      this for chaining

    • setFluidViscosity

      public TransientWellModel setFluidViscosity(double viscosity, String unit)
      Sets fluid viscosity.
      Parameters:
      viscosity - viscosity
      unit - unit (cP, mPa.s)
      Returns:
      this for chaining

    • setWellboreRadius

      public TransientWellModel setWellboreRadius(double radius, String unit)
      Sets wellbore radius.
      Parameters:
      radius - radius
      unit - unit (m, ft, in)
      Returns:
      this for chaining

    • setSkinFactor

      public TransientWellModel setSkinFactor(double skin)
      Sets skin factor.
      Parameters:
      skin - skin factor (dimensionless)
      Returns:
      this for chaining

    • setFormationVolumeFactor

      public TransientWellModel setFormationVolumeFactor(double bFactor)
      Sets formation volume factor.
      Parameters:
      bFactor - B (reservoir volume / surface volume)
      Returns:
      this for chaining

    • setDrainageRadius

      public TransientWellModel setDrainageRadius(double radius, String unit)
      Sets drainage radius.
      Parameters:
      radius - radius
      unit - unit (m, ft)
      Returns:
      this for chaining

    • setWellType

      public TransientWellModel setWellType(TransientWellModel.WellType type)
      Sets well type.
      Parameters:
      type - well type
      Returns:
      this for chaining

    • setBoundaryType

      public TransientWellModel setBoundaryType(TransientWellModel.BoundaryType type)
      Sets boundary type.
      Parameters:
      type - boundary type
      Returns:
      this for chaining

    • getHydraulicDiffusivity

      public double getHydraulicDiffusivity()
      Gets the hydraulic diffusivity.
      Returns:
      diffusivity (m²/s)

    • getTransmissibility

      public double getTransmissibility()
      Gets the transmissibility.
      Returns:
      transmissibility (m³/(bar·s))

    • getRateHistory

      public List<TransientWellModel.RateChange> getRateHistory()
      Gets the rate history.
      Returns:
      list of rate changes

    • getInitialPressure

      public double getInitialPressure()
      Gets the initial reservoir pressure.
      Returns:
      pressure (bara)