flow

    Note

    Either boun or flow are required for a flow problem.

    Flow data. Source and sink parameters are input and may be used to apply boundary conditions. Note that the alternative definitions for isothermal models apply when flow is used in conjunction with control statement **airwater **(See Control statement airwater or air (optional)).

    Input Variable Format Default Description
    Non-Isothermal model      
    SKD real
    		Heat and mass source strength (kg/s), heat only (MJ/s). Negative value indicates injection into the rock mass.
    EFLOW real
    		Enthalpy of fluid injected (MJ/kg). If the fluid is flowing from the rock mass, then the in-place enthalpy is used.
          If EFLOW < 0, then ABS(EFLOW) is interpreted as a temperature (oC) and the enthalpy (assuming water only) calculated accordingly. In heat only problems with EFLOW < 0, the node is in contact with a large heat pipe that supplies heat to the node through an impedance AIPED so as to maintain its temperature near ABS (EFLOW). Large values (approximately 1000) of AIPED are recommended.
    AIPED real
    		Impedance parameter. If AIPED is nonzero, the code interprets SKD as a flowing wellbore pressure (MPa) with an impedance ABS(AIPED). If AIPED < 0, flow is only allowed out of the well. For heat only, AIPED is the thermal resistance. If AIPED = 0, SKD is flow rate. If AIPED ≠ 0 and SKD = 0 the initial value of pressure will be used for the flowing pressure.

    Note

    If the porosity of the node is zero, then there is only a temperature solution, and the code forms a source proportional to the enthalpy difference. The source term is given by \(Q = AIPED \cdot (E - EFLOW)\), where E is the in-place enthalpy and EFLOW is a specified enthalpy.

    Isothermal model
    Case 1: AIPED = 0 (Constant Mass Rate, 1- or 2-Phase Source or Sink)
    SKD real
    		Mass source strength (kg/s). Negative value indicates injection into the rock mass.
    EFLOW real
    a) EFLOW ≥ 0, EFLOW is the source liquid saturation,
    * \(Q_w = SKD \cdot EFLOW\) (kg/s)
    * \(Q_a = SKD \cdot (1 - EFLOW)\) (kg/s)
         
    b) EFLOW < 0, ABS(EFLOW) is the source air pressure (MPa)
    * \(Q_w = SKD\) (kg/s)
    * \(Q_a = 1.0 \cdot (P_a - ABS(EEFLOW))\) (kg/s)
    AIPED     Used only as flag to indicatee Constant Mass Rate

    In the above and following relations, \(Q_w\) is the source term for water, \(Q_a\) is the source term for air, and \(P_a\) is the in-place air pressure. The second case works well in situations where inflow is specified and it is desired to hold the air pressure at a constant value.

    Case 2: AIPED > 0 (Constant Pressure, Constant Liquid Saturation Source or Sink)
    SKD real
    		Specified source pressure (MPa).
    EFLOW real
    a) EFLOW < 0, air only source.
    * \(Q_a = AIPED \cdot (P_a - SKD)\) (kg/s)

    b) 0 < EFLOW < 1, EFLOW is specified source liquid saturation,
    for SKD ≥ 0, 2-phase source,
    * \(Q_a = AIPED \cdot (P_a - SKD)\) (kg/s)
    * \(Q_w = AIPED \cdot (S_l - EEFLOW) \cdot P_0\) (kg/s)
    when SKD < 0, water only source \(Q_a = 0\).

    c) EFLOW = 1, water only source.
    * \(Q_w = AIPED \cdot (P_l - SKD)\) kg/s
    AIPED real  
    Impedance parameter. A large value is recommended (102 - 106) in order to create a flow
    term large enough to maintain constant pressure.
    Case 3: AIPED < 0 (Outflow only, if \(P_l > SKD\))
    SKD real
    		Pressure above which outflow occurs (MPa)
    EFLOW real
    		Not used.
    AIPED real
    		Impedance parameter.
    \(Q_w = ABS(AIPED) \cdot R_l / \mu_l(P_l - SKD)\) (kg/s)

    where \(R_l\) is the water relative peremeability and \(\mu_l\) is the water viscosity.

      PARAMETER SKD EFLOW
    Physics Model AIPED* \(\ge 0\) \(< 0\) \(\ge 0\) \(< 0\)
    Non-isothermal \(> 0\) Flowing wellbore pressure (MPa) Flowing wellbore pressure (MPa) - injection into rock mass Enthalpy (MJ/kg) Temperature (C)
    \(= 0\)
    Flow rate (kg/s)
    Heat only (MJ/s)
    Flow rate (kg/s)
    Heat only (MJ/s) - injection into rock mass
    \(< 0\) Flowing wellbore pressure (MPa) - outflow only N/A
    Isothermal \(> 0\) Specified source pressure (MPa) Specified source pressure (MPa) - Water only source Source liquid saturation Air only source (used as flag)
    \(= 0\) Mass source strength (kg/s) Mass source strength (kg/s) - injection into rock mass Source liquid saturation Source air pressure (MPa)
    \(< 0\) Pressure above which outflow occurs (MPa) N/A N/A N/A
    * Impedance parametere

    The following are examples of flow. In the first example, at node 88, a mass flow of 0.05 kg/s at 25 C is being withdrawn from the model. Because fluid is being withdrawn the in-place temperature will actually be used. For every 14th node from node 14 to 140, the pressure and temperature are being held constant at 3.6 MPa and 160 C, respectively. This represents a constant temperature recharge along one of the problem boundaries.

    flow        
    88 88 1 0.050 -25.0
    14 140 14 3.600 -160.0

    In the second example, the corresponding input for airwater, is included, indicating an isothermal air-water two-phase simulation is being run with a reference temperature for property evaluation of 20 C and a reference pressure of 0.1 MPa. At nodes 26 and 52, water saturation is 100% and water is being injected at 2.e-3 kg/s. At nodes 1 and 27, there is an air only source, with a specified pressure of 0.1 MPa, and the air is being injected at the rate of 100*(Pa - 0.1) kg/s.

    airwater        
    2        
    20.0 0.1      
    flow        
    26 52 26 -2.e-3 1.0
    1 27 26 0.1 -0.2
             

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