Heat Pump Buffer Tank, Low-Loss Header & Plate Exchanger Calculator

1. Flow and adiabatic mixing

The equations below are derived here from conservation of mass and energy. The heating-circuit capacity rate is $C_s=Q/\Delta T_s$, and the primary rate is $C_p=\rho c_p\dot V_p$. Direct and series arrangements have one common flow. A low-loss header and an ideal four-pipe buffer share the same steady separator balance.

For the same liquid, let $r=C_p/C_s$. If $r<1$, the secondary supply is $T_{s,out}=T_r+r(T_{p,in}-T_r)$. To maintain the emitter target, the heat pump must therefore supply an extra $\Delta T_{mix}=\max(Q/C_p-\Delta T_s,0)$. If $r>1$, the secondary supply equals the primary supply, while bypass raises the primary return: $T_{p,out}=T_{p,in}-Q/C_p$. Caleffi idronics 15, pp.40–42 gives published supply- and return-mixing examples; both are reference checks here.

Direct and series assessments require both the calculated common operating flow and the entered valve-closed flow to be inside the manufacturer's minimum–maximum window. Separated layouts apply the window to primary flow. The direct annual-energy baseline is flagged as hypothetical if its calculated flow is outside that window. At the illustrative 4.5 kW / 5 K default, common water flow is approximately 0.775 m³/h.

The unchanged-setting result holds secondary return fixed and leaves the heat-pump setting at the original emitter target. It illustrates under-temperature; it is not an emitter or building response simulation.

2. Counterflow plate exchanger

$C_{min}=\min(C_p,C_s)$, $C_r=C_{min}/C_{max}$ and $NTU=UA/C_{min}$. Integrating the two stream energy balances gives

At equal capacity rates use $\varepsilon=NTU/(1+NTU)$. The required hot inlet is $T_r+Q/(\varepsilon C_{min})$. Its excess above emitter supply is the hot-end approach. The cold-end approach is also calculated. As a conservation cross-check, $Q=UA\,LMTD$, using the logarithmic mean of the two end differences. Caleffi idronics 29 section 4 supplies the LMTD method and a published temperature example. UA must come from supplier selection at the actual flows, fluids and fouling condition.

For numerical evaluation, let $D=1-C_r$ and $z=e^{-NTU D}$. The larger end approach is $G=(Q/C_{min})D/(1-z)$ and the smaller is $g=Gz$. The code evaluates $1-z$ with expm1. The hot-end approach is G when the primary is the smaller capacity stream, and g otherwise; the cold end is the other approach. At equal capacity rates both are Q/UA. This avoids subtracting nearly equal inlet/outlet differences. Separate logarithms evaluate the LMTD without overflowing an approach ratio. If the exponential underflows to zero, the LMTD, reconstructed duty and residual are intentionally unavailable, with an explanation, rather than reporting zero duty. The conservation residual is rounded to 12 decimal places only to remove floating-point subtraction noise.

3. COP and seasonal electricity

Fit inverse COP linearly between two same-source data-sheet points:

The extra heat-pump electricity multiplier is $F=COP(T_s)/COP(T_s+\Delta T)$. The default A7/W35 and A7/W55 points are from Vaillant 0020330791_03 p.46, VWL 55/6 A S2. The unused A7/W45 point checks interpolation; the 1.8% discrepancy is documented in that reference case. The interval between the two calibration temperatures is enforced.

For annual useful heat $H$ and baseline seasonal COP $S$, temperature lift adds $(H/S)(F-1)$ electricity. Unrecovered tank heat adds $P_{loss}h_{loss}F/S$; net additional pumps add $P_{pump}h_{pump}$. The sum times the entered tariff gives additional cost. Watts and hours are explicitly converted to kWh. The seasonal ratio is a screening approximation, not a measured or weather-bin seasonal performance factor.

4. Active volume

Using volumetric fluid heat capacity $c_v$:

The governing effective volume is the largest of cycling, defrost and the manufacturer's minimum. Credit existing guaranteed active volume, then divide any shortfall by the usable fraction of the new tank. These constraints are maxima, not additive simultaneous events. Caleffi idronics 17 p.28 distinguishes on/off output from minimum stable modulating output. Manufacturer minimum volume and guaranteed flow remain separate requirements.

• Steady heating, one heat pump and one heating circuit. Water on the secondary side; constant $\rho c_p=4.18$ MJ/(m³·K), approximated from 1,000 kg/m³ and 4.18 kJ/(kg·K). For an isolated primary circuit, enter its own volumetric heat capacity; storage then uses that primary fluid.
• A header or four-pipe buffer has ideal mixing at its connections, no axial conduction, and no dynamic stratification. A series buffer is in the return and has no deliberate supply mixing. Direct and series flow equals heating-circuit flow.
• The two COP points share one source condition and compatible test settings. Actual COP also depends on return temperature, compressor speed, defrost and auxiliaries; those effects are not resolved.
• The baseline seasonal COP is entered separately. The representative fixed-condition electricity multiplier is applied to the entire entered annual space heat. Do not include extra pumps twice if using measured baseline data.
• Run time 10 min, defrost extraction 0.30 kWh, allowable drops 5 K, usable fraction 0.90, extra pump 35 W and tank heat loss 25 W are illustrative design assumptions, not equipment ratings.
• Vaillant defaults illustrate the 2023 VWL 55/6 A S2 manual: 400–860 L/h flow range and 40 L connected volume with the back-up heater deactivated. Replace them for the exact model, back-up-heater setting and installation. Connected volume is conservatively treated as effective volume.
• Fluid isolation and independent-flow requirements are design inputs. The arrangement recommendation assesses the entered minimum and maximum flow limits, and assumes approved layouts, sufficient heat-pump thermal capacity and adequate pump head; these are not calculated.

Use for preliminary hydraulic comparison and active-volume sizing. Installation and commissioning belong to a qualified person following the manufacturer's instructions and applicable local rules.

The COP calculation is restricted to the two entered calibration temperatures. The 2023 manual is an illustrative data source, not a declaration that those requirements apply to newer products. Enter a user tariff in any currency; the default 0.30 per kWh is an illustrative scenario dated 27 October 2026, not a current quoted price.

This steady model omits cycling savings, storage charging temperatures, real tank stratification, pressure-drop selection, control hysteresis details, capacity limits, fouling evolution and dynamic defrost. It gives no extra leaving-temperature lift for primary flow above secondary flow; higher return temperatures can still affect real COP. Fraunhofer ISE WP-QS (2025), p.9, reports that actual storage temperature differences depend on flows, connection arrangement and dynamic operation, supporting this distinction between an ideal balance and field performance.

Count only water accessible during the relevant valve state; secondary water behind a plate exchanger is not automatically available for defrost. Net defrost energy must include concurrent loads and account for auxiliary heat only when guaranteed. Verify the minimum final water temperature, primary flow during defrost and available pump head separately. A non-representable exchanger approach at extreme NTU makes the LMTD cross-check unavailable; use suitable supplier software or higher-precision arithmetic to verify that case.

With two heating circuits, a common-temperature system can be reduced to combined capacity rates, but circuits with different supply temperatures need separate branch balances and mixing controls. This tool does not model them. No domestic hot-water hygiene, refrigerant safety or regulatory compliance sizing is performed.