Absorption Theory Fundamentals

1. Principles of Gas Absorption

Gas absorption is a unit operation in which one or more components of a gas mixture are transferred from the gas phase into a liquid phase by contacting the gas with a suitable solvent. In midstream gas processing, absorption is one of the oldest and most widely practiced methods for recovering natural gas liquids (NGL) from the gas stream and for removing acid gas contaminants (H₂S, CO₂) using chemical solvents.

The driving force for absorption is the deviation from thermodynamic equilibrium between the gas and liquid phases. When a gas containing a target component contacts a liquid in which that component is soluble, molecules transfer from the gas phase into the liquid phase until equilibrium is established. The absorber column is designed to provide intimate contact between the phases under conditions that favor the transfer of specific components from gas to liquid.

Physical Absorption vs. Chemical Absorption

Two fundamentally different absorption mechanisms are employed in gas processing, and the distinction has significant implications for equipment design, operating conditions, and regeneration requirements:

Thermodynamic Basis: Equilibrium Laws

The fundamental thermodynamic relationships that govern gas-liquid equilibrium in absorption systems are described below. These relationships determine the theoretical limits of absorption and establish the minimum solvent circulation rate required for a given recovery target.

Henry's Law applies to dilute systems where the absorbed component is present at low concentrations in the liquid phase. It states that the partial pressure of a solute gas above a solution is directly proportional to the mole fraction of the solute in the liquid:

Where p_i is the partial pressure of component i in the gas phase, H_i is Henry's Law constant (atm or psia), and x_i is the mole fraction of component i in the liquid phase. Henry's Law constants are strong functions of temperature—increasing temperature increases H, which decreases solubility. This is why absorption is favored at low temperatures and stripping (desorption) is favored at high temperatures.

Raoult's Law applies to ideal solutions, where the interactions between solute and solvent molecules are similar to those between like molecules. Raoult's Law states:

Where P_i^sat is the vapor pressure of pure component i at the system temperature. For non-ideal solutions (which includes virtually all real absorption systems), Raoult's Law is modified with an activity coefficient γ_i to account for molecular interactions:

Activity coefficients greater than 1.0 indicate positive deviation from ideality (less soluble than ideal), while values less than 1.0 indicate negative deviation (more soluble than ideal). For hydrocarbon absorption in lean oil, activity coefficients are typically 0.8–1.5, depending on the molecular weight mismatch between the absorbed component and the oil.

Why Absorbers Work: Creating Favorable Conditions

An absorber operates effectively when the equilibrium K-value for the target component is less than 1.0 (K < 1), meaning the component preferentially partitions into the liquid phase under the prevailing conditions. Absorber designers manipulate three process variables to achieve K < 1 for the target components:

• Temperature: Lower temperatures reduce K-values and increase solubility. Lean oil absorbers typically operate at 80–120°F, and inlet gas may be chilled to improve recovery
• Pressure: Higher pressures reduce K-values. Most lean oil absorbers operate at 400–1,000 psig. Increasing pressure is one of the most effective ways to improve absorption, but it increases compression costs
• Solvent selection: Choosing a solvent with high affinity for the target component reduces its activity coefficient and K-value. For NGL recovery, heavier absorption oils (higher molecular weight) generally provide lower K-values for C₃+ components but at the cost of higher viscosity and reduced tray efficiency

2. Vapor-Liquid Equilibrium (VLE)

Vapor-liquid equilibrium (VLE) is the foundation of all absorption column design. The equilibrium relationship between the gas and liquid phases determines the maximum achievable separation, the minimum solvent rate, the number of theoretical stages required, and the sensitivity of the process to changes in operating conditions. Accurate VLE data and reliable K-value correlations are essential for any rigorous absorber design.

K-Value Definition

The equilibrium ratio, or K-value, for any component i is defined as the ratio of the mole fraction in the vapor phase to the mole fraction in the liquid phase at equilibrium:

Where y_i is the mole fraction of component i in the vapor phase and x_i is the mole fraction in the liquid phase, both at thermodynamic equilibrium. The K-value is a dimensionless number that encapsulates the combined effects of temperature, pressure, and composition on the phase distribution of each component. A K-value greater than 1.0 means the component favors the vapor phase; a K-value less than 1.0 means it favors the liquid phase.

Factors Affecting K-Values

K-values are functions of three fundamental variables—temperature, pressure, and composition—and the sensitivity to each varies by component and system:

K-Value Methods and Correlations

Several methods are used in industry to determine K-values for absorber design. The choice depends on the complexity of the system, the accuracy required, and the available computational resources:

• DePriester charts: Graphical correlations of K-values as functions of temperature and pressure for individual hydrocarbon components. These charts, originally published in the 1950s and updated in GPSA Ch. 25, remain valuable for quick estimates and hand calculations. They assume the K-value is independent of composition (valid for light hydrocarbons at moderate pressures)
• Wilson equation: A simplified analytical correlation for K-values based on critical properties and acentric factor. The Wilson equation provides reasonable accuracy for hydrocarbon systems at pressures below 50% of the convergence pressure and is commonly used in preliminary design calculations
• Equation of state (EOS) methods: The Soave-Redlich-Kwong (SRK) and Peng-Robinson (PR) cubic equations of state provide rigorous K-value calculations that account for composition effects, non-ideal behavior, and high-pressure conditions. These are the standard methods used in commercial process simulators (HYSYS, ProMax, Pro/II) for final absorber design

Wilson Equation for K-Value Estimation

The Wilson correlation provides a convenient analytical expression for estimating K-values of hydrocarbon components:

Where P_ci is the critical pressure of component i, P is the system pressure, ω_i is the acentric factor, T_ci is the critical temperature, and T is the system temperature (absolute units). This equation is adequate for preliminary absorber sizing but should be replaced with rigorous EOS methods for final design, particularly at pressures above 500 psig or in systems with significant non-hydrocarbon components.

Relative Volatility

The relative volatility α_ij between two components i and j is the ratio of their K-values and provides a direct measure of how easily they can be separated by absorption or distillation:

For lean oil absorption, the relative volatility between the light key (typically methane or ethane, which should pass through the absorber) and the heavy key (typically propane, which should be absorbed) determines the fundamental separability. Higher relative volatility means fewer stages are needed for a given separation. In a lean oil absorber operating at 600 psig and 100°F, the relative volatility of methane to propane is typically 8–15, indicating that the separation is thermodynamically favorable.

Convergence Pressure Concept

At very high pressures, the K-values of all components in a mixture approach 1.0 as the mixture approaches its critical point. The convergence pressure is the pressure at which all K-values converge to unity for a given temperature and mixture composition. This concept is important because:

• Simple K-value correlations (DePriester charts, Wilson equation) lose accuracy as the system pressure approaches the convergence pressure
• Operating near the convergence pressure reduces relative volatility and dramatically increases the number of stages required for separation
• For typical lean oil absorber conditions (600–1,000 psig, 80–120°F), the convergence pressure is usually well above the operating pressure (3,000–5,000 psia), so simple correlations remain reasonably accurate

Phase Diagrams

Understanding the phase behavior of the gas-oil system is essential for absorber design. The key phase diagram features relevant to absorption include the bubble point curve (below which the system is entirely liquid), the dew point curve (above which the system is entirely vapor), and the two-phase envelope between them. The absorber operates in the two-phase region, where vapor and liquid coexist and mass transfer occurs across the phase boundary.

3. Equilibrium Stage Concept

The equilibrium stage (also called a theoretical stage or theoretical tray) is the fundamental design unit for absorption columns. A theoretical stage is defined as a contacting device in which the gas and liquid streams leaving the stage are in thermodynamic equilibrium with each other. While no real tray or packing section achieves perfect equilibrium between the exiting phases, the theoretical stage concept provides a powerful framework for column design by separating the thermodynamic analysis (how many theoretical stages are needed) from the mass transfer analysis (how much real tray area or packing height is required to achieve one theoretical stage).

McCabe-Thiele Method Applied to Absorption

The McCabe-Thiele graphical method, originally developed for distillation, can be applied to absorption by plotting the operating line and equilibrium curve on a y-x diagram (mole fraction of the absorbed component in the vapor phase vs. mole fraction in the liquid phase). The number of theoretical stages is determined by stepping between the operating line and the equilibrium curve.

For absorption, the construction proceeds as follows:

• Equilibrium curve: Plot y = K · x for the key absorbed component. For systems where K is approximately constant (dilute solutions), this is a straight line through the origin with slope K
• Operating line: Plot the material balance relationship between the vapor and liquid compositions at each stage. For a simple absorber with no heat effects, the operating line is straight with slope L/V (molar liquid-to-vapor ratio)
• Stage stepping: Starting from the top of the column (lean end), step between the operating line and equilibrium curve to count the number of theoretical stages required to reach the desired bottom composition (rich end)

Operating Line and Equilibrium Curve

The overall material balance for a component being absorbed, written around the top of the column down to any stage n, gives the operating line equation:

Where y_n+1 is the vapor composition entering stage n from below, x_n is the liquid composition leaving stage n, L is the molar liquid flow rate, V is the molar vapor flow rate, y₁ is the vapor composition leaving the top of the column (residue gas), and x₀ is the lean oil composition entering the top of the column.

For absorption to be feasible, the operating line must lie above the equilibrium curve on the y-x diagram. The vertical distance between the operating line and the equilibrium curve at any point represents the driving force for mass transfer at that location in the column. The wider this gap, the fewer stages are needed but the more solvent is required.

Minimum Solvent Rate (L/G Ratio)

The minimum liquid-to-gas ratio (L/V)_min is the solvent rate at which the operating line just touches the equilibrium curve, creating a pinch point where infinite stages would be required. For a component with constant K-value, the minimum L/V ratio for complete absorption is:

In practice, the actual L/V ratio is set at 1.2 to 2.0 times the minimum to provide a reasonable number of stages and adequate operating margin. The economic optimum L/V ratio balances the cost of additional solvent circulation (pumping, cooling, regeneration) against the cost of additional column stages (height, trays, or packing).

Stage Efficiency

Real trays do not achieve equilibrium between the exiting vapor and liquid streams. The degree to which a real tray approaches equilibrium is quantified by the tray efficiency, which is used to convert theoretical stages to actual trays:

Where y_n is the actual vapor composition leaving tray n, y_n+1 is the vapor composition entering tray n from below, and y_n* is the vapor composition that would be in equilibrium with the liquid leaving tray n.

Factors Affecting Tray Efficiency in Absorption

Tray efficiency in absorption service is generally lower than in distillation service because of several factors inherent to the absorption process:

• High liquid viscosity: Absorption oils (MW 120–250) are significantly more viscous than typical distillation liquids. Higher viscosity reduces liquid-phase mass transfer coefficients, which is often the controlling resistance in absorption. Typical lean oil viscosity at absorber conditions is 1.5–4.0 cSt
• Large molecular weight difference: The absorbed components (C₃–C₅, MW 44–72) are much lighter than the solvent (MW 120–250), creating non-equimolar transfer effects that reduce efficiency
• Foaming tendency: Absorption oils contaminated with corrosion products, treating chemicals, or degradation products are prone to foaming, which reduces effective tray capacity and efficiency
• Temperature effects: Heat of absorption raises the liquid temperature on each tray, which increases K-values and reduces the local driving force. This thermal effect can reduce apparent efficiency by 5–15%

For lean oil absorbers, overall column efficiencies of 25–40% are typical for heavy oils (MW > 180), while lighter oils (MW 120–160) may achieve 35–50% overall efficiency.

4. Absorption Factor Method (Kremser-Brown)

The absorption factor method, also known as the Kremser-Brown-Souders method, provides an analytical shortcut for calculating the number of theoretical stages required for a specified component recovery (or conversely, calculating the recovery achievable with a given number of stages). This method is the standard tool for preliminary absorber design and is widely used in the gas processing industry per GPSA Ch. 16.

Absorption Factor Definition

The absorption factor A for any component i is defined as the ratio of the molar liquid rate to the product of the K-value and the molar vapor rate:

Where L is the molar liquid flow rate (lean oil), K_i is the equilibrium K-value for component i at the average column temperature and pressure, and V is the molar vapor flow rate (inlet gas). The absorption factor has a direct physical interpretation:

• A > 1: The liquid has excess capacity to absorb the component. The operating line lies above the equilibrium curve, and high recovery is achievable with a finite number of stages
• A = 1: The liquid flow is exactly sufficient to absorb the component at equilibrium. Infinite stages would be needed for complete recovery
• A < 1: The liquid flow is insufficient for complete absorption. Recovery is limited regardless of the number of stages, and the maximum fractional recovery approaches A^N as N becomes large

Kremser Equation

For a system with constant K-values, constant L and V, and negligible heat effects, the Kremser equation relates the fractional recovery of any component to the absorption factor and the number of theoretical stages:

Where φ_i is the fractional recovery of component i (fraction of the component in the inlet gas that is absorbed into the liquid), A_i is the absorption factor for component i, and N is the number of theoretical stages (trays).

Rearranging to solve for the number of stages required for a specified recovery:

For A = 1 (a special case), the recovery simplifies to:

Effective Absorption Factor for Multicomponent Systems

In a real absorber processing multicomponent natural gas, K-values and flow rates vary from tray to tray because of temperature changes (heat of absorption), pressure drop, and composition changes as components are absorbed. The effective absorption factor accounts for these variations by using a geometric mean of the top and bottom stage conditions:

Where A_top = L₀ / (K_top · V₁) uses lean oil and residue gas conditions, and A_bottom = L_N / (K_bottom · V_N+1) uses rich oil and inlet gas conditions. The effective absorption factor is then substituted into the Kremser equation to calculate component recovery. This approach, recommended by GPSA, provides adequate accuracy for preliminary design when column temperature and pressure profiles are reasonably estimated.

Design Procedure Using the Absorption Factor Method

The standard design procedure for a lean oil absorber using the Kremser-Brown method follows these steps:

1. Specify recovery target: Define the desired recovery of the key component (typically C₃ at 70–95% recovery for lean oil plants)
2. Determine K-values: Calculate or look up K-values for all components at the estimated average column temperature and pressure
3. Calculate minimum absorption factor: For the key component, determine the minimum A needed for the specified recovery as a function of the number of stages
4. Select design absorption factor: Choose a practical absorption factor for the key component, typically A = 1.2–2.0 (higher A means fewer stages but more oil circulation)
5. Calculate oil rate: From A = L / (K · V), calculate L = A · K · V for the key component
6. Determine number of stages: Using the Kremser equation, calculate N for the key component at the selected A value
7. Calculate recovery of all components: With N and L fixed, calculate the absorption factor and recovery for every other component in the gas
8. Iterate: Adjust the temperature profile, oil rate, and number of stages to optimize the overall design against economic criteria

Practical Range of Absorption Factors

Stripping Factor: The Inverse Problem

The stripping factor S is the inverse of the absorption factor and is used to analyze the regeneration (stripping) side of the absorption loop, including the rich-oil demethanizer and the oil purification still:

The Kremser equation applies identically to stripping when the stripping factor is substituted for the absorption factor. A stripping factor S > 1 is required for effective stripping, and the same practical range of 1.2–2.0 applies. The still and demethanizer are designed using the stripping factor method to determine the lean oil quality (residual NGL content) and the NGL product recovery.

5. Lean Oil Plant Design Application

Lean oil absorption plants apply the theoretical principles discussed in the preceding sections to recover NGL from natural gas streams. The design of a lean oil plant integrates absorber column sizing, oil selection, heat exchange optimization, and downstream fractionation into a complete processing system. This section addresses the practical engineering decisions that connect absorption theory to field installations.

Selecting the Absorption Oil

The choice of absorption oil is one of the most critical design decisions in a lean oil plant. The oil must provide adequate NGL solubility while maintaining acceptable physical properties for pumping, heat exchange, and long-term thermal stability. The key selection criteria are:

Common absorption oils include light kerosene (MW 140–170), heavy kerosene (MW 170–200), and light gas oil (MW 200–260). The oil selection involves an economic optimization: heavier oils give better NGL absorption (lower K-values) but suffer from higher viscosity (lower tray efficiency, higher pumping costs) and require higher still temperatures for regeneration (greater degradation risk).

Oil Circulation Rate

The oil circulation rate is determined from the absorption factor for the key component (typically propane). For a specified number of stages N and desired propane recovery φ_C3, the required absorption factor A_C3 is calculated from the Kremser equation, and the oil rate follows from:

Typical oil circulation rates for lean oil plants range from 2 to 8 gallons of oil per Mcf of inlet gas, depending on the gas composition, NGL content, operating pressure, and target recovery. Higher circulation rates improve NGL recovery but increase pumping, cooling, and regeneration costs. The economic optimum circulation rate is found by balancing incremental NGL revenue against incremental operating costs.

Absorber Temperature Profile

The absorber column is not isothermal. As NGL components are absorbed into the lean oil, the heat of absorption raises the liquid temperature. This temperature rise increases K-values on the lower trays, reducing the driving force for absorption and degrading performance. Managing the temperature profile is essential for achieving high NGL recovery:

• Lean oil cooling: The lean oil entering the top of the absorber is typically cooled to 80–110°F (or lower in refrigerated plants) to maximize absorption capacity on the top trays, where the highest recovery of lighter components occurs
• Intercooling: In some high-recovery designs, side-draw intercoolers remove heat from the oil at intermediate points in the column, reducing the temperature rise and maintaining lower K-values through the column. Intercooling can improve propane recovery by 5–15% compared to an adiabatic absorber
• Temperature bulge: The maximum temperature in the absorber (the "temperature bulge") occurs several trays below the lean oil inlet, where the rate of NGL absorption and heat release is highest. The location and magnitude of the bulge depend on the inlet gas richness and the oil rate

Rich Oil Loading and Gas-Oil Ratio

The rich oil leaving the absorber bottom contains the absorbed NGL components dissolved in the lean oil carrier. The NGL loading in the rich oil is characterized by the gas-oil ratio (GOR), expressed as standard cubic feet of absorbed gas per gallon of lean oil:

Integration with Downstream Processing

The lean oil absorption plant operates as an integrated system with the following key equipment in the regeneration loop:

• Lean/rich oil heat exchanger: Transfers heat from the hot lean oil (leaving the still) to the cold rich oil (leaving the absorber). This is the most important heat integration in the plant, typically recovering 60–80% of the regeneration heat and significantly reducing reboiler duty. Approach temperature of 20–40°F is typical
• Rich-oil demethanizer: Removes dissolved methane and ethane from the rich oil before it enters the still. This prevents light ends from contaminating the NGL product and reduces the still overhead condenser load
• Oil purification still: Strips the absorbed C₃+ NGL from the rich oil using heat (reboiler) and/or steam stripping. The still produces lean oil for recirculation and raw NGL product
• NGL fractionation: Separates the mixed NGL into individual products (propane, butane, natural gasoline) for sale or pipeline delivery as Y-grade NGL per GPA 2140 specifications

Lean Oil Absorption vs. Cryogenic Processing

The choice between lean oil absorption and cryogenic (turboexpander) processing for NGL recovery involves multiple technical and economic considerations:

Lean oil absorption remains competitive for applications where moderate NGL recovery (70–90% propane) is acceptable, where inlet gas pressure is too low for effective turboexpander operation, or where the simplicity and operational flexibility of absorption systems are valued. Many existing lean oil plants continue to operate economically, and the absorption theory presented in this guide forms the engineering basis for their design, operation, and optimization.

References

1. GPSA, Chapter 16 — Hydrocarbon Recovery
2. GPSA, Chapter 25 — Equilibrium Ratio (K-Value) Data
3. GPA Standard 2140 — Liquefied Petroleum Gas Specifications
4. GPA Standard 2145 — Table of Physical Constants of Paraffin Hydrocarbons