Video summary

Balance de Energía. Calculo de la temperatura en un intercambiador de calor con excel

Main summary

Key takeaways

Educational

Main ideas / lessons

  • The video walks through how to perform an energy balance on a heat exchanger to compute the outlet temperature of a process stream (brine).
  • It emphasizes that before doing the energy balance, you should do a degrees of freedom (DoF) analysis to determine whether the system is coupled or uncoupled.
  • The method uses:
    • Material balance (described as simple in the example).
    • Energy balance using temperature-dependent heat capacity via a (c_p) polynomial (and reference-state selection).
    • Excel (including the Solver add-in) to solve for the unknown outlet temperature, even when the resulting equation is higher-order and has multiple roots.

Step-by-step methodology (as presented)

1) Define the problem and assumptions

  • Goal: Calculate the outlet temperature of the brine in a heat exchanger.
  • Given / assumed:
    • Brine (process fluid), pressure = 1 bar, inlet temperature = 50°C
    • Pressure assumed constant
    • Heating fluid (“auxiliary service”):
      • A saturated liquid at 10 kPa (as stated)
      • Flow rate = 100 kg/h
      • Outlet conditions: constant pressure and 75°C
    • Relationship between flow rates:
      • Brine flow rate is twice the liquid flow rate
    • Brine composition is not provided, so properties are treated as brine/water using water/brine approximations.

2) Do degrees of freedom analysis (coupled vs. uncoupled)

  • Concept: A system is coupled or uncoupled depending on the number of degrees of freedom.
  • Rules given:
    • DoF = 0 → system is uncoupled in the sense that balances can be solved sequentially
      • In this case: solve material balance first, then energy balance
    • DoF = 1 → system is coupled
      • Then: solve material + energy balances simultaneously
  • For the shown example: It states DoF is zero, so it proceeds with solving the energy balance after a simple material balance.

3) Set up the energy balance using (c_p) (ideal method)

  • Energy balance structure: Because each stream has one inlet and one outlet, you use a relationship of the form:
    • ( \text{heat flow} \propto \dot{m} \, (h_{out}-h_{in}) )
  • Equivalently, the video describes using heat capacities and temperature integration approximated by a polynomial.
  • The method uses an ideal method relying on heat capacities and a (c_p) polynomial.

4) Choose reference states and obtain polynomial constants

  • Key concept: Pick reference states (starting points) for enthalpy/entropy calculations.
  • Video’s specific choice:
    • For both brine and water, use the inlet conditions as reference.
    • Those inlet conditions are treated as a saturated liquid, so steam tables are used:
      • The corresponding saturation temperature found in steam tables is 179.88°C (noted as dependent on which steam-table source is used).
  • In the spreadsheet:
    • The reference-state temperature is set as 0 for the “center/day 0” reference (intended meaning: the reference enthalpy/entropy baseline).

5) Convert units to match the (c_p) polynomial basis

  • The (c_p) polynomial is in units of:
    • kg-moles per °C (molar form: “kilograms per mole per degree Celsius” per the description)
  • Flow rates are given in:
    • kg/h
  • Therefore you must:
    • Convert so polynomial evaluation basis (molar) matches mass-flow inputs (kg/h).
  • The video highlights the need for molecular weight for the conversion.

6) Compute the service (water) heat flow and infer heating/cooling direction

  • Using the polynomial for water and the inlet/outlet temperatures, the video obtains:

    • Heat flow for the water service as approximately 43,900 and 33.06 (subtitles appear garbled; it describes a computed negative heat rate)

  • It interprets the sign:

    • Since the heat flow is negative, the water is losing heat, so its associated temperature decreases.
  • Energy-transfer direction is then framed as:
    • brine is gaining energy (energy-receiving side).

7) Use an entropy-based relation with (c_p) polynomial to solve for brine outlet temperature

  • The video introduces an equation involving:
    • (c_p) polynomial coefficients (or derived parameters),
    • entropy changes, and
    • the known heat flow on the water side.
  • It states key quantities used:
    • An intermediate numerical result for the brine side after substituting known values:
      • around 19.66, then converted to a molar basis as 3.95.
  • Equation form depends on how many polynomial parameters are used:
    • If only a limited number of polynomial parameters are used (e.g., only one coefficient like “a”): the final equation can become algebraic.
    • With more polynomial coefficients: the equation becomes higher-order (second-, third-, up to fourth-order) and may have multiple roots.

8) Solve the outlet temperature in Excel

Option A: Direct algebraic solution (when only one parameter/coefficient is effectively used)

  • Substitute known polynomial pieces into the algebraic equation.
  • Computed brine outlet temperature: 102.44°C

Option B: Use Excel Solver for numerical solution (when not directly solvable)

  • Workflow shown:
    1. Prepare a cell for an estimated brine outlet temperature.
    2. Compute (q) (heat flow) and/or an entropy-based equality using the (c_p) polynomial.
    3. Enforce that computed values match the “known values” equality condition.
  • Solver setup:
    • Go to Data tab → Solver.
    • If Solver is missing:
      • File → Options → Add-ins
      • in Excel Add-ins: click Go
      • enable Solver and accept.
  • In Solver:
    • Unknown variable: temperature
    • Objective/constraint: matching entropy (or a heat/entropy-based target)
  • Output:
    • Solver finds 102.44°C, matching the algebraic result.

9) Handling multiple roots / numerical methods

  • Because a fuller (c_p) polynomial can yield higher-order equations:
    • There may be more than one mathematical root.
  • Suggested approach:
    • Use the method to locate the desired root, or apply a numerical method if needed.

Speakers or sources featured

  • Speaker: Not explicitly identified by name.
  • Sources mentioned:
    • Steam tables (reference values depend on “the literature you use”).
    • A (c_p) polynomial from literature for water (and used similarly for brine/water properties), including mention of:
      • molecular weight, and
      • polynomial units.
    • Excel Solver (software feature/add-in instructions).

Original video