A Course on Hydrophilic-Lipophilic Deviation (HLD/HLDN)

2.1 The Multivariable HLD Equation

The core quantitative tool developed through extensive experimental studies is the Hydrophilic-Lipophilic Deviation (HLD) equation. This equation emerged from quantifying the conditions required to achieve optimum formulation (Winsor's R=1 equivalent) in surfactant-oil-water systems.⁴ The HLD equation is fundamentally semi-empirical, representing a linear correlation derived from observing systematic phase behavior transitions during formulation scans.

Recognizing that different types of surfactants respond differently to formulation variables, distinct forms of the HLD equation were initially proposed. These equations represent the specific condition where HLD = 0 (optimum formulation)¹⁴. Hover over the terms for brief explanations:

These equations linearly combine the effects of the major variables influencing the hydrophilic-lipophilic balance. The remarkable success of these linear equations across a wide range of experimental conditions, despite representing a first-order approximation of potentially more complex relationships,⁷ underscores their practical utility. Decades of experimental validation supported this linear framework as robust for modeling and predicting SOW system behavior.¹ While potential deviations, particularly with complex mixtures,⁷ were acknowledged, the evidence supported the linear HLD equation as a powerful tool for formulation tasks.¹⁴

2.3 The Surfactant Parameter: SCP and PACN

Central to the HLDN equation is the **Surfactant Contribution Parameter (SCP)**.¹¹ This single term encapsulates the overall contribution of the surfactant's molecular structure (both head and tail) to the hydrophilic-lipophilic balance. It replaces parameters like σ, β, Cc from earlier formulations and always carries a coefficient of +1 in the HLDN equation.¹²

It's crucial to understand that SCP is not an intrinsic constant of the surfactant molecule alone.⁷ Its numerical value depends on integration constants and the specific reference conditions chosen for other variables (T_ref, reference salinity, etc.).

To provide a more tangible measure, the concept of **Preferred Alkane Carbon Number (PACN)** was introduced.¹¹ PACN is the experimentally determined SCP value under standardized reference conditions (e.g., T=25°C, pure water or 1 wt% NaCl, WOR=1). Operationally, PACN is the ACN of the n-alkane oil that results in optimum formulation (HLDN=0) with the surfactant under these reference conditions, often found via an ACN scan.¹¹ PACN serves as a standardized, experimentally accessible descriptor of a surfactant's effective hydrophilicity/lipophilicity.

PACN (and thus SCP) is directly related to the surfactant's molecular structure⁷:

• Tail Length (SAT): Increasing hydrophobic tail length increases lipophilicity, thus increasing PACN. For linear alkyl tails, an approximate relationship is: PACN ≈ PACN₀ + 2.25 * SAT, where PACN₀ depends on the head group.¹²
• Head Group Hydrophilicity: Making the head group more polar or larger (e.g., increasing Ethylene Oxide Number, EON; changing head group type) increases hydrophilicity, thus decreasing PACN.⁷

The introduction of PACN bridges the gap between the abstract SCP term and concrete experimental measurement, providing a practical way to characterize surfactants for HLDN calculations.¹²

Table 2.3: Experimentally Determined PACN Values (Illustrative)

*Note: PACN values for ionic surfactants are highly sensitive to reference salinity.

2.5 Variable Effects: Salinity (S), Temperature (T), Alcohol (f(A)), Pressure (P)

The HLDN equation explicitly quantifies how different formulation variables shift the hydrophilic-lipophilic balance. Understanding these effects is key to manipulating formulations:

• Salinity (S): Primarily influences ionic surfactants. Increasing electrolyte concentration (e.g., wt% NaCl) screens head group repulsion, reducing hydration. Surfactant behaves more lipophilic (HLDN increases). Effect often modeled with kS*Ln(S).¹¹ Nonionics are much less sensitive (small linear effect kS'*S sometimes included).¹¹
• Temperature (T): Most significant for nonionic ethoxylates (C_iE_j). Increasing T disrupts hydrogen bonding between EO groups and water, reducing hydration. Surfactant behaves more lipophilic (HLDN increases). Effect usually modeled linearly kT*(T-Tref).¹¹ Ionic surfactants generally show much lower temperature sensitivity.
• Alcohol (f(A)): Effect depends on alcohol chain length and concentration.¹¹
  • Short-chain (C2-C4): Often partition to interface/water, increase effective head group area, making system more hydrophilic (HLDN decreases).
  • Longer-chain (C5+): Partition more to oil/interface tail region, act as lipophilic linkers, making system more lipophilic (HLDN increases).
  Effect captured by kA*f(A) term.^{4, 47}
• Pressure (P): Generally smaller effect, relevant at high pressures (e.g., EOR). Increasing P can enhance water structure/hydration, making surfactants slightly more hydrophilic (HLDN decreases).¹¹ Represented by kP*(P-Pref) term.¹¹

The Compensation Principle

A fundamental concept arising from these relationships is **compensation**. Because multiple variables influence HLDN, a change in one variable shifting the system away from optimum (HLDN=0) can often be counteracted by adjusting another variable.¹

Example: If salinity increases (making an ionic system more lipophilic, HLDN > 0), balance (HLDN=0) can be restored by using a more lipophilic oil (increasing ACN) or a more hydrophilic surfactant (decreasing SCP).¹

The HLDN equation provides the quantitative basis for predicting these compensations.