Solar Swimming Pool Heating - Thermo-Economic Analysis

To follow along with my hand written work or view the code print out, download the Thermo-Economic model here.

This analysis was performed with Engineering Equation Solver (EES), a non-linear equation solver that includes various resources for thermodynamics, heat transfer, unit handling, and economic functions.

Introduction

If you live in a sunny climate that can still be cold, like the high desert of the Rocky Mountain front range, you may have thought about adding solar panels to your home. But what about using solar energy for heat? Can a system be installed to adequately heat your swimming pool to a comfortable temperature throughout the year?

In this analysis, I investigated upgrading a traditional heated pool with solar collector as a method to reduce natural gas water heating costs.

Solar flux collectors, also commonly known as solar thermal collectors, are used for various applications, including heating swimming pools. These systems capture and convert solar energy into heat energy, which is then transferred to a fluid (usually water or a glycol mixture) circulating through the collector. This heated fluid can then be used to heat water in a swimming pool, reducing the dependency on conventional energy sources such as natural gas or electricity.

You can read more about how they work, here.

Baseline System

The unmodified heated pool system consists of the swimming pool itself, a water pump, and a natural gas powered water heater.

A schematic of the baseline system is shown below in Figure 1.

Known Parameters - Baseline

Several parameters are known about the system. The pool water is modeled as an imcompressible fluid and the system is assessed during steady state operation.

The pump curve of the system is defined via the following equations.

EQ 1. ∆P = ∆P_dh*(1-(Vol_dot/Vol_dot_oc))

EQ 2. ∆P_dh = 150 [Pa-min/rev]*N [rev/min]

EQ 3. Vol_dot_oc = 5x10^-7 [m^3-min/s-rev]*N [rev/min]

EQ 4. ∆P_h = 3x10^12 [Pa-s/m^6]*Vol_dot^2

States & Balances - Baseline

State [4-1] - Pool

Mass Balance

In = Out —> m_dot[1] = m_dot[4] = m_dot

During steady state operaiton, the mass flowrate of water into the pool equals the mass flowrate of water leaving the pool.

Energy Balance

m_dot * h[4] = Q_dot_pool + m_dot * h[1]

The energy associated with the mass of the water entering and leaving the system is related to the enthalpy of the water, which is defined by the properties of the water.

Entropy Balance

S_dot_gen_pool = (Q_dot_pool / T_pool) + m_dot * (s[4]-s[1])

Entropy generation inside the pool can be calculated to measure exergy destruction.

State [1] - Pump Inlet

State Properties

T[1] = T_pool = 80 [F]

P[1] = P_o = 14.7 [psi] (Assumption for P[2] == Ambient)

Pump inlet water properties are equal to the properties of the water leaving the pool.

Incompressible Fluid Model

u[1] = c_w * T[1]

h[1] = c_w * T[1] - v_w * P[1]

State [1-2] - Water Pump

Mass Balance

m_dot_2 = m_dot_1 = m_dot = Vol_dot/v_w

Water mass flow rate during steady state operation can also be calculated from the volumetric flowrate of the water, divided by the specific volume of the water (determined by T and P).

Energy Balance

m_dot[1] * h[1] + W_dot_p = m_dot[2] * h[2]

Energy from the pump is added to the water from state 1 to 2.

Entropy Balance

m_dot[1] * s[1] + S_dot_gen_p = m_dot[2] * s[2]

(s[2]-s[1]) = c_w * ln(T[2]/T[1])

Reversible Energy Balance

m_dot[1] * h[1] + W_dot_p_s = m_dot[2] * h_s[2]

h_s[2] = c_w * T[1] + v_w * P[2]

Pump Performance Balance

eta_p = 0.4 = W_dot_p_s / W_dot_p

The water pump is marked with a 40% efficiency compared to a perfectly reversible pump with no entropy generation.

State [2] - Pump Outlet

P[2] = P[1] + ∆P

T[2] = From E-bal, State 1-2

State fixed with Pressure and Temperature

State [2-3] - Piping

P[3] = P[2] (Ignoring pressure loss through pipe resistance / geometry)

T[3] = T[2]

Mass Balance

m_dot[3] = m_dot[2]

Energy Balance

m_dot[3]*h[3] = m_dot[2]*h[2]

State [3] - Water Heater Inlet

T[3] = T[2]

P[3] = P[2]

h[3] = h[2]

u[3] = u[2]

State fixed with Pressure and Temperature

State [3-4] - Water Heater

Energy Balance

m_dot[3] * h[3] + Q_dot_f = m_dot[4]*h[4]

h[4] = c_w * T[4] + v_w * P[4]

Entropy Balance

m_dot[3] * s[3] + (Q_dot_f/T_f) + S_dot_gen,h = m_dot[4] * s[4]

S_dot_gen,h = m_dot(s[4]-s[3]) - Q_dot_f/T_f

(s[4]-s[3]) = c_w * ln(T[4]/T[3])

Heat Exchanger Efficiency

eta_h = 0.95 = Q_dot_f,s / Q_dot_f

Reversible Energy Balance

m_dot[3] * h[3] + Q_dot_f,s = m_dot[4] * h_s[4]

h_s[4] = c_w * T[3] + v * P[4]

State [4] - Heater Outlet

P[4] = P[3] - ∆P_h

∆P_h = 3E12 [Pa-s/m^6] * Vol_dot^2

u[4] = c_w * T[4]

h[4] = solved from Reversible Energy Balance and Heat Exchanger Efficiency

Performance Calculations - Baseline

Pump Curves - Baseline

System Curves - Baseline

Performance Metrics - Baseline

Economic Calculations - Baseline

Solar Modified System

Known Parameters - Modified

States & Balances - Modified

State [2-3] - Solar Flux Collector

State [3] - Solar Collector Outlet

Performance Calculations - Modified

Economic Calculations - Modified

Economic Comparison

The baseline heating system comes with higher operational costs, driven by the inefficiencies of conventional methods. In contrast, the upgraded system introduces smarter solutions like integrating a solar collector, which offsets a significant portion of the heating load. This means less reliance on expensive energy sources and more money saved over time.

For example, the upgraded system reduces water heating costs from $0.4074/hour in the baseline to $0.2384/hour by covering 41.6% of the heating load through solar input. That’s a huge efficiency boost with direct cost savings for every hour the system is in use.

Conclusion

This comparison shows a clear advantage: upgrading the system cuts operational costs, plain and simple. By lowering the amount you’re spending on heat while still meeting the same demand, the upgraded setup pays for itself over time. If saving money is the goal, the numbers make this a no-brainer.