Key Takeaways (Plain Language)

• Conductance alone doesn’t uniquely determine capacity, but it sets hard limits. A point can only fall within a narrow feasible region defined by electrolyte and plate constraints.
• Below ~60% conductance ((G_d/G_n < 0.6)), capacity is guaranteed to be <100%, and in practice is very likely <80%.
• Undercharge / soft or hard sulfation can lower capacity while keeping conductance unchanged or slightly higher.
• Electrolyte dry-out tends to reduce conductance first; capacity may remain near-normal initially, then declines as dry-out progresses.
• Use trendlines: a steady decline in (G) at stable float voltage and temperature typically signals progressive dry-out.

Definitions & Normalization

• (G): battery conductance, (g): specific conductivity of the electrolyte.
• (Ah): deliverable capacity at a defined rate/cutoff.
• Subscripts: n = new reference; d = degraded in service.
• We compare batteries by ratios:
  • Normalized conductance: (G_d/G_n)
  • Normalized capacity: (Ah_d/Ah_n)

OCV vs. Acid Concentration (Why float settings limit concentration)

Open-circuit voltage (OCV) rises with sulfuric acid molality (m). A widely used fit (25 °C) is:

$$ OCV = 1.9228 + 0.147519\log(m) + 0.063552\log^2(m) + 0.073772\log^3(m) + 0.033612\log^4(m)\quad \mathrm{V/cell} $$

Because float voltage clamps terminal voltage, it indirectly caps the maximum acid concentration achievable in service.

Electrolyte Conductance Fundamentals (Simplified)

For a uniform electrolyte path of effective length (L), cross-section (A), resistivity (\rho), and specific conductivity (g = 1/\rho):

• Resistance: (R = \rho,L/A)
• Conductance: (G = 1/R = g,A/L)

In porous electrodes (VRLA), the effective area/geometry makes (G) scale with the amount and concentration of electrolyte. A convenient proportional form is:

$$ G \propto g \times \frac{V}{L^2} $$

where (V) is electrolyte volume. When we normalize to the new state and track how concentration (affecting (g)) and quantity (affecting (V)) change, we obtain an electrolyte conductance ratio:

$$ \frac{G_d}{G_n} \approx \left(\frac{g_d}{g_n}\right)\left(\frac{B_d}{B_n}\right)\left(\frac{D_n}{D_d}\right) $$

Here (B) is electrolyte mass and (D) is density; this form captures how losing water or acid shifts both (g) and the total electrolyte present.

Two Mechanisms That Move the Point

1) Undercharge / Sulfation ((m_d < m_n))

• Electrolyte concentration drops (lower (m)), often because the battery is chronically under-floated, cycled shallowly without recovery, or sulfated.
• Capacity falls (active material is poorly utilized), while conductance may stay flat or even rise slightly in mild cases.
• Diagnostic signature: Low (Ah_d/Ah_n) with moderate (G_d/G_n).

2) Electrolyte Dry-Out ((m_d > m_n))

• Water is lost (electrolysis, evaporation, seal leakage), acid becomes more concentrated until float-limited.
• Once the acid reaches a float-limited ceiling (about (m \approx 10.3 ,\mathrm{mol/kg}); density (\approx 1.394,\mathrm{kg/L}) at typical floats), further water loss forces acid removal from solution as PbSO(_4) on plates.
• Diagnostic signature: (G_d/G_n) trends downward over time; capacity may lag, then falls.

Practical Boundaries You Can Use

Upper boundary (what’s physically achievable)

By conserving how much acid and how much water the cell can have relative to new, and by enforcing the float-limited maximum concentration, one obtains an upper envelope: the highest capacity possible for a given conductance ratio. Intuitively:

• Undercharge zone (left branch): capacity can be low even if conductance hasn’t dropped much.
• Dry-out zone (right branch): conductance must decrease as electrolyte is lost; capacity initially declines slowly.

Lower boundary under dry-out (near float-limited concentration)

Once the electrolyte sits at the float-limited concentration, mass-balance links additional water loss to acid precipitation as PbSO(_4) and to a nearly linear relation between the two ratios:

$$ \frac{Ah_d}{Ah_n} \approx k \cdot \frac{G_d}{G_n}\quad\text{(dry-out lower bound)} $$

where (k) is a constant calculated from the new-state density, the float-limited density, and specific conductivities. In practical terms: as conductance drops further in dry-out, capacity must drop proportionally along (or above) this line—never below.

Field rule of thumb: Below ~60% conductance ((G_d/G_n < 0.6)), the combined electrolyte + plate constraints force (Ah_d/Ah_n < 1.0) (i.e., capacity <100%), and in service datasets it is very often <80%.

Plate Mass Limits (Why plates set additional caps)

Theoretical active material per 1 Ah (before utilization factors):

• ( \mathrm{PbO_2} ): (4.462\ \mathrm{g/Ah}) (effective ~11.155 g/Ah at ~40% utilization)
• ( \mathrm{Pb} ): (3.865\ \mathrm{g/Ah}) (effective ~8.589 g/Ah at ~45% utilization)

Because sulfation consumes active surfaces and blocks pores, plate-limited capacity gives additional upper/lower bounds that can dominate when plate loss or hard sulfate is severe—even if electrolyte looks “acceptable.”

What the Data Say (12 V, 55 Ah VRLA, 61 units, 2-year field)

• Test rate: 4 h at 10.1 A, cutoff 1.8 V/cell (10.8 V/block).
• New references used for normalization: (Ah_n \approx 40.4\ \mathrm{Ah}) at test conditions; (G_n \approx 800\ \mathrm{S}).
• 41 blocks had (G_d/G_n < 0.6) and all delivered <100% capacity; 40/41 were <80%, one was 83% ⇒ 97.5% chance that (G_d/G_n<0.6) implies (Ah<80%) for this population.
• Scatter points fell within the theoretical envelopes, especially close to the linear dry-out lower bound at low conductance—consistent with dry-out being a dominant degradation path.

A Quick Diagnostics Workflow

1. Normalize conductance: measure after adequate rest or float stabilization; compute (G_d/G_n) against a new-battery baseline (from vendor spec or your own acceptance data at the same temperature).
2. If (G_d/G_n < 0.6): capacity is certainly reduced; plan a capacity test and prepare for replacements (very likely <80% in similar fleets).
3. If capacity is low but (G_d/G_n) is moderate/high: suspect undercharge/sulfation. Check float voltage set-point, charger health, OCV, and (if accessible) specific gravity.
4. If (G_d/G_n) trends down slowly with time at stable temperature and float: suspect dry-out; review ambient heat, ventilation, charge voltage, and seal/valve health.
5. Always pair conductance with at least one more indicator (OCV trend, temperature history, or periodic capacity sampling) to avoid misclassification.

Assumptions & Scope (Read Me)

• Focused on flat-plate VRLA geometries; very large tubular or front-access blocks may add metallic path resistance effects that slightly alter conductance readings.
• Float at ~2.25 V/cell sets the practical concentration ceiling.
• Electrolyte-only conductance modeled (metallic paths treated as small).
• Equations and envelopes describe feasible regions, not exact points—manufacturing tolerances and service histories matter.

Core Equations (for reference)

• OCV–molality (25 °C): $$ OCV = 1.9228 + 0.147519\log(m) + 0.063552\log^2(m) + 0.073772\log^3(m) + 0.033612\log^4(m) $$
• Conductance–geometry: $$ R = \rho \frac{L}{A},\quad G=\frac{1}{R}=g\frac{A}{L} $$
• Electrolyte conductance ratio (simplified mass–density form): $$ \frac{G_d}{G_n} \approx \left(\frac{g_d}{g_n}\right)\left(\frac{B_d}{B_n}\right)\left(\frac{D_n}{D_d}\right) $$
• Dry-out lower bound (float-limited concentration): $$ \frac{Ah_d}{Ah_n} \approx k \cdot \frac{G_d}{G_n}\quad\text{with }k\text{ computed from }(g,D,m)\text{ at new and float-limited states.} $$

Conclusion

By separating electrolyte and plate effects and enforcing mass/voltage constraints, we get hard boundaries between normalized conductance and capacity in VRLA batteries. Practically:

• Treat (G_d/G_n < 0.6) as a red flag—capacity is not only below nameplate; in fleet data it’s very likely <80%.
• Distinguish mechanisms: undercharge can devastate capacity with small conductance change; dry-out steadily drags conductance down before capacity collapses.
• Use trends and a second indicator to make confident maintenance decisions.