Black Liquor Evaporation Efficiency at 75% Solids

How thermodynamic modelling cuts mill energy use by up to 14% and mitigates scaling.

Black liquor evaporation efficiency measures the thermal and mass transfer performance of a multiple-effect evaporator train. As it concentrates weak black liquor to a heavy firing liquor, it targets high-solids operation of 75% dry solids or greater to maximise recovery boiler thermal efficiency. For Kraft pulp mills, the evaporator plant represents one of the largest thermal energy sinks on site. Managing this process requires a deep understanding of complex fluid rheology, multi-component thermodynamic equilibria, and heat-exchanger fouling dynamics.

Pushing liquor concentrations to 75% dry solids and above brings severe operating penalties. These include exponential viscosity growth, massive boiling point rise, and accelerated chemical scaling. Optimising this high-solids regime demands rigorous thermodynamic modelling and systematic process integration.

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The Physics of High-Solids Evaporation and the 75% Dry Solids Threshold

Operating an evaporator train at high concentrations alters the thermodynamic and physical properties of the black liquor. Weak black liquor enters the evaporator island at approximately 15% to 20% dry solids. At this stage, it behaves essentially as a Newtonian fluid with low viscosity. However, as water is driven off, the concentration of inorganic salts and organic lignin fragments increases, causing a non-linear transition in fluid behaviour.

Viscosity and Rheological Behaviour

Once black liquor exceeds 50% dry solids, its viscosity rises exponentially. At concentrations approaching 75% dry solids, the liquor exhibits highly non-Newtonian, pseudoplastic (shear-thinning) behaviour. It can even display viscoelastic properties under specific temperature regimes. This high viscosity suppresses turbulence, shifting the flow profile inside heat exchanger tubes from turbulent to transitional or laminar.

Because the convective heat transfer coefficient depends directly on the Reynolds number ($Re$), this laminar transition severely degrades thermal performance. To maintain flowability and prevent tube pluggage, process engineers must operate the concentrator stage at elevated temperatures, typically between 120°C and 140°C. These high temperatures provide enough thermal energy to disrupt the intermolecular associations of the lignin macromolecular networks, reducing apparent viscosity to manageable operating levels.

Boiling Point Rise and the Temperature Driving Force Penalty

Boiling Point Rise (BPR) represents the increase in the boiling temperature of black liquor compared to pure water at the same pressure. Driven by high concentrations of dissolved inorganic ions, BPR is a strong, non-linear function of dry solids content.

While weak black liquor exhibits a negligible BPR of 1°C to 2°C, the BPR at 75% dry solids typically reaches 15°C to 25°C. This rise directly penalises the available temperature driving force ($\Delta T$) of the entire evaporator train. In a modern 7-effect evaporator system concentrated to 75% dry solids, up to 50% of the total available temperature driving force is consumed by BPR and vapour duct pressure losses. This leaves an average of only 7°C (12°F) of active $\Delta T$ per effect.

The governing equation for heat transfer rate ($Q$) in each evaporator body highlights this constraint:

$$Q=U\cdot A\cdot \Delta T_{active}$$

Where:

• $Q$ is the heat transfer rate in watts (W).
• $U$ is the overall heat transfer coefficient in watts per square metre kelvin (W/m²K).
• $A$ is the heat transfer area in square metres (m²).
• $\Delta T_{active}$ is the active temperature driving force in degrees Celsius (°C), defined as:

$$\Delta T_{active}=\Delta T_{total}-BPR-\Delta T_{losses}$$

Where:

• $\Delta T_{total}$ is the temperature difference between the saturated steam entering the steam chest and the saturation temperature of the vapour leaving the boiling liquor.
• $BPR$ is the boiling point rise of the liquor at local concentration.
• $\Delta T_{losses}$ is the temperature equivalent of pressure drops in the vapour ducting, separator vessels, and hydrostatic head.

Because BPR increases so drastically at 75% solids, $\Delta T_{active}$ is severely compressed. To transfer the required thermal duty ($Q$) without excessively increasing the heat exchanger surface area ($A$), process engineers must maintain high overall heat transfer coefficients ($U$) and closely manage vapour duct pressure drops.

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Thermodynamic Modelling of Multiple-Effect Evaporators

Optimising black liquor evaporation efficiency requires a comprehensive multiple-effect evaporator (MEE) model linking the mass and energy balances across all effects. In an MEE system, vapour generated in one effect acts as the heating medium for the subsequent, lower-pressure effect. This sequential reuse of latent heat allows the system to achieve high thermal efficiency.

Mass and Energy Balances

Each individual effect is modelled as a separate control volume, requiring simultaneous solution of total mass, species (solids and water), and enthalpy balances. The species balance is formulated as:

$${\dot{m}}_{in}\cdot X_{in}={\dot{m}}_{out}\cdot X_{out}$$

Where:

• ${\dot{m}}_{in}$ and ${\dot{m}}_{out}$ are the mass flow rates of liquor entering and exiting the effect (kg/h).
• $X_{in}$ and $X_{out}$ are the respective dry solids mass fractions.

The enthalpy balance balances the heat released by the condensing steam or vapour against the heat required to raise the incoming liquor to its boiling point (sensible heat) plus the heat of vapourisation needed to boil off the water (latent heat), while accounting for the heat of dilution of the black liquor.

Steam Economy and Effect Configurations

Steam economy is the primary performance indicator of an evaporator train. It is defined as the mass of water evaporated per unit mass of live steam supplied to the system:

$$\text{Steam Economy}=\frac{{\dot{m}}_{evap}}{{\dot{m}}_{steam}}$$

Where:

• ${\dot{m}}_{evap}$ is the total water evaporated across all effects (kg/h).
• ${\dot{m}}_{steam}$ is the mass flow rate of live utility steam fed to the first effect and concentrator (kg/h).

Typical target values for steam economy vary by configuration, as shown in the table below. If not optimised, fouling and poor heat integration drastically reduce these performance levels.

To achieve 75% dry solids, mills typically employ a dedicated concentrator stage operating as an auxiliary or split 'Effect 1'. Because the liquor in this stage is highly viscous, forced circulation (FC) or falling film (FF) designs with high recirculation rates are chosen to sustain acceptable heat transfer.

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Fouling Mechanisms and Heat Transfer Degradation

Fouling on heat transfer surfaces is the single greatest operational challenge in high-solids evaporation. It acts as a major bottleneck to maintaining stable black liquor evaporation efficiency. Deposits build up as insulating layers on both the liquor side (scaling) and, occasionally, the condensate side (organic carrying) of the heat exchanger tubes. This fouling degrades the overall heat transfer coefficient ($U$), which typically ranges from 720 to 1,870 W/m²K depending on cleanliness and scaling severity.

Soluble vs. Insoluble Scaling Chemistry

Scaling in black liquor evaporators is categorised into two distinct chemical regimes:

• Insoluble Scaling (Calcium Carbonate): Calcium carbonate ($CaC{O}_3$) scale dominates thermal resistance in the intermediate effects where liquor temperatures exceed 120°C. Calcium in black liquor is bound to organic lignin molecules in weak complexes. As the liquor is heated, these complexes thermally dissociate, releasing free calcium ions ($C{a}^{2+}$) that react with carbonate ions ($C{O}_3^{2-}$) to precipitate $CaC{O}_3$ directly onto hot tube surfaces. This tenacious scale has very low thermal conductivity and cannot be removed with simple water washes, often requiring acid cleaning or mechanical hydro-blating.
• Soluble Scaling (Burkeite and Sodium Salts): This regime is driven primarily by sodium carbonate-sodium sulphate, forming burkeite double salts ($2N{a}_{2}S{O}_4\cdot N{a}_{2}C{O}_3$) and dicarbonate ($2N{a}_{2}C{O}_3\cdot N{a}_{2}S{O}_4$). Unlike calcium carbonate, burkeite precipitation is concentration-driven. It begins to crystallise out of solution when local dry solids exceed approximately 50% to 55%—its solubility limit. Burkeite forms rapid-growing crystalline structures that quickly choke flow channels. Because these salts are water-soluble, operators can manage them via periodic 'boil-outs' using weak black liquor or hot condensate.

Impact on the Heat Transfer Coefficient

Scale deposition introduces an additional thermal resistance term ($R_f$) to the overall heat transfer equation. The relationship between the clean heat transfer coefficient ($U_{clean}$) and the fouled coefficient ($U_{fouled}$) is expressed as:

$$\frac{1}{U_{fouled}}=\frac{1}{U_{clean}}+R_{f,liquor}+R_{f,steam}$$

Where:

• $R_{f,liquor}$ is the fouling resistance on the liquor side (m²K/W).
• $R_{f,steam}$ is the fouling resistance on the steam/condensate side (m²K/W).

As $R_{f,liquor}$ grows due to burkeite or calcium carbonate deposition, $U_{fouled}$ drops from its design baseline of 1,870 W/m²K towards the lower limit of 720 W/m²K. This thermal degradation forces the operator to either accept lower liquor throughput, drop the product dry solids concentration below the 75% target, or increase steam pressure. Raising steam pressure to elevate the temperature driving force, however, accelerates calcium scaling.

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Pinch Analysis and System Heat Integration

Pinch analysis provides a systematic thermodynamic framework for optimising the heat exchanger network (HEN) of the entire pulp mill. It focuses on how the evaporator island integrates with utility systems. In a Kraft mill, the evaporator train is both a massive consumer of high-grade thermal energy (medium and low-pressure steam) and a major producer of low-grade thermal energy (vapour condensate and flash steam).

Identifying the Pinch Point in Recovery Islands

By constructing hot and cold composite curves for the recovery island, process engineers can identify the process 'pinch point'—the temperature level where heat transfer constraints are tightest.

• Above the Pinch: Live steam heat supplied above the pinch temperature must be minimised. This is achieved by maximising process-to-process heat exchange, such as utilising hot process condensates to preheat incoming weak black liquor.
• Below the Pinch: Low-grade heat from the evaporator condensers must be rejected to the cooling tower or utilised for water heating elsewhere in the fibreline.

In a typical non-integrated mill, live steam frequently preheats the weak liquor before it enters the first effect. Pinch analysis demonstrates that this is a thermodynamic error. Preheating should instead utilise secondary flash vapour from the liquor flash tanks or intermediate condensate streams. This reserves high-grade steam exclusively for the high-solids concentrator stage, where elevated temperatures are mandatory to overcome viscosity.

Heat Integration Strategies for the Concentrator Stage

When operating at 75% solids, the thermal demands of the concentrator are high. Implementing pinch-based modifications often reveals opportunities to reconfigure stream layouts:

1. Split-Feed Configurations: Directing a portion of the intermediate-strength liquor to bypass certain effects and feed directly into the concentrator reduces the total volume of high-viscosity fluid pumped through the primary heat exchangers, preserving their heat transfer coefficients.
2. Vapour Recompression Integration: Integrating Mechanical Vapour Recompression (MVR) or Thermal Vapour Recompression (TVR) into the pre-evaporation stages elevates the thermal grade of low-pressure vapours. This allows their reuse within the main evaporator body, substantially reducing fresh utility steam demand.
3. Condensate Heat Recovery: Segmenting condensates into clean, intermediate, and foul fractions allows targeted heat recovery. The hottest, cleanest condensates return directly to the boiler feedwater tank. Lower-temperature, foul condensates undergo steam stripping, with heat from the stripper overheads integrated back into the evaporator preheaters.

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Mill-Wide Optimisation: EnerTherm's 11-Step Process Simulation Methodology

Achieving and maintaining 75% dry solids in an evaporator train while preserving a high steam economy cannot be solved in isolation. It requires a structured, data-driven approach spanning the entire pulp mill. EnerTherm Engineering applies a proprietary 11-step engineering methodology to standardise process optimisation, ensuring that mass and energy balances are fully reconciled against real-world constraints.

Data Reconciliation and Simulation Platforms

To evaluate the multi-component equilibrium of black liquor, simulation teams employ advanced process simulation platforms such as Aspen Plus, HYSYS, or DWSIM. These tools enable the execution of complex flash calculations, multi-phase phase equilibria, and property estimations for highly concentrated non-Newtonian mixtures.

The 11-step engineering methodology proceeds as follows:

1. Data Acquisition: Gathering historical plant DCS logs, piping and instrumentation diagrams (P&IDs), pump curves, and seasonal operational data.
2. Process Mapping and Boundary Definition: Defining the exact thermodynamic boundaries of the recovery island, including the evaporator train, recovery boiler, and recausticising loop.
3. Physical Property Method Selection: Configuring the simulation platform with specialised thermodynamic packages (such as electrolytic NRTL or specialised black liquor property correlations) capable of handling high salt concentrations and polymer-like lignin behaviours.
4. Species-Level Mass Balance Formulation: Constructing detailed mass balances tracking water, organic solids, active alkali, sodium, sulphur, and non-process elements (NPEs) like calcium, potassium, and chloride.
5. Thermodynamic Energy Balance Reconciliation: Resolving heat balances, heat of dilution effects, and latent heat exchanges across all evaporator bodies.
6. Steady-State Process Simulation Development: Constructing the base model in Aspen Plus, HYSYS, or DWSIM to replicate baseline operation.
7. Dynamic Model Calibration: Adjusting heat transfer coefficients and fouling resistance factor ($R_f$) profiles against historical operating curves to capture transient behaviours, such as during boil-out cycles.
8. Pinch-Point Evaluation and Utility Targeting: Applying pinch analysis to identify energy pinch points, heat-exchanger area bottlenecks, and optimal flash steam utilisation routes.
9. Safety, Quality, and Regulatory Constraint Checking: Ensuring all proposed changes comply with pressure vessel safety codes, emission regulations, and pulp quality targets.
10. Single-Source-of-Truth Process Flow Diagram (PFD) Generation: Delivering a verified PFD with embedded stream tables, detailing flows, temperatures, pressures, dry solids percentages, and enthalpies for every process line.
11. Capital Investment Planning: Formulating an actionable execution roadmap with prioritised modifications, cost-benefit analyses, and procurement schedules.

Single-Source-of-Truth Process Flow Diagrams

Developing a 'single-source-of-truth' PFD is a key output of this methodology. In many mills, the recovery island, fibreline, and utility areas operate with disconnected mass and energy data. Reconciling these streams into a single, validated model allows process engineers to predict accurately how a change in the evaporator area—such as increasing product solids from 65% to 75%—will propagate through the rest of the mill.

For example, raising the solids content to 75% increases the net heating value of the black liquor. This allows the recovery boiler to operate with higher thermal efficiency, generating more high-pressure steam and reducing auxiliary fuel usage. However, it also increases the viscosity and temperature of the feed liquor, altering the piping thermal profile and demanding tighter control of recausticising and washing parameters.

Operational and Environmental Paybacks

Applying this systematic thermodynamic optimisation strategy yields measurable financial and ecological benefits. Integrating the 11-step methodology across Kraft pulp mills consistently achieves:

• An average mill-wide energy reduction of 14%.
• An average project payback period of 1.8 years.
• An annual carbon dioxide (${\text{CO}}_2$) emissions reduction of 2,800 tonnes.

Under environmental frameworks like the UK Industrial Decarbonisation Strategy (2021) and the European Union's Best Available Techniques (BAT) Reference Document for the Production of Pulp, Paper and Board (2015 BREF), mills face strict legal mandates to curb specific energy use and lower carbon footprints. Optimising the multiple-effect evaporator train to hit 75% dry solids efficiently is a highly effective pathway to satisfying these regulatory demands, ensuring both compliance and long-term economic competitiveness.

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This article reflects the independent analysis and editorial opinion of EnerTherm Engineering. Product names, trademarks, and brands mentioned belong to their respective owners. EnerTherm Engineering is not affiliated with, endorsed by, or a licensee of any third-party software or product mentioned unless explicitly stated.