Flow Model

Background

Understanding flow characterization is essential for predicting and assessing the corrosivity of systems. Over time, significant progress has been made in studying the relationship between flow dynamics and corrosion. To support these efforts, various flow models have been developed, each tailored to specific conditions. Among them, the single-phase flow model stands out for its simplicity and well-defined structure, making it a fundamental tool in flow characterization studies.

However, multiphase flow—commonly encountered in the petroleum, chemical, and nuclear industries—is significantly more complex due to the challenges associated with characterizing phase distribution and flow patterns. To address this complexity, numerous multiphase flow models have been developed. Some of these models are based on mechanistic approaches, while others rely on empirical correlations derived from laboratory experiments or field data.¹ -⁹

Empirical models often prove inadequate because they are limited to the range of data on which they were developed and, generally, cannot be used with confidence across all fluid types and conditions encountered in oil and gas fields. ¹⁰ Furthermore, many such models exhibit large discontinuities at flow pattern transitions, leading to convergence problems when these models are used for the simultaneous simulation of petroleum reservoirs and associated production facilities.¹¹ Additionally, some models are limited to specific piping configurations, creating discontinuities when switching between models. An ideal flow model should cover the full range of piping inclinations and output key flow parameters, such as flow regime, liquid holdup, pressure drop, and wall shear stress – parameters that are critical for corrosivity assessment. Moreover, such a model should be validated with both laboratory and field data. Two well-known unified models are Barnea and Petalas-Aziz.^{10 ,12}

Single-phase flow refers to the movement of a single fluid phase and can be classified into three categories: laminar flow, transitional flow, and turbulent flow .

• Laminar Flow: This is a smooth, orderly, and stable flow regime that occurs at low flow velocities, characterized by a Reynolds number (Re) below 2,100. It involves minimal turbulence.
• Transition Flow: This regime lies between laminar and turbulent flow, occurring at Reynolds numbers between approximately 2,100 and 4,000. It exhibits characteristics of both laminar and turbulent flows, resulting in intermittent and unstable behavior.
• Turbulent Flow: This chaotic and irregular flow regime occurs at high velocities, typically with a Reynolds number above 4,000. Turbulent flow is marked by random and multidirectional fluid particle movement, strong mixing, and enhanced mass transport. It plays a significant role in corrosion processes due to its ability to influence wall shear stress and protective film stability.

Multiphase flow refers to the simultaneous movement of two or more distinct phases, such as gas, liquid, or solid, within a conduit or environment. The behavior of multiphase flows can vary significantly based on factors such as piping configuration (e.g., size and orientation) and the specific conditions of the flow system.

In horizontal two-phase gas-liquid flow systems, common flow patterns include stratified flow (smooth and wavy), intermittent flow (slug and elongated bubble flow), annular-mist flow, and dispersed bubble flow – please refer to Figure 1 and Figure 2:

• Stratified Flow: Occurs at low gas and liquid velocities, where the liquid flows at the bottom of the pipe and the gas flows long on the top. Stratified smooth flow has smooth interface between the gas and liquid, with minimal turbulence or wave formation. On the other hand, stratified wavy is with wavy interface due to increased velocities.

• Intermittent Flow: Characterized by the liquid bridging the gas-liquid interface and the top of the pipe. The difference between slug and elongated bubble flow depends on the degree of agitation of the bridge.¹³

• Annular Flow: Characterized by a central gas core at high velocity with a thin liquid film lining the pipe walls and fine liquid droplets are usually entrained in the gas flow.

• Dispersed Bubble Flow: Gas is distributed as small bubbles within a continuous liquid phase, commonly observed at relatively low gas flow rates and moderate-to-high liquid flow rates, where the gas phase does not form larger structures like slugs or Taylor bubbles.

In vertical two-phase gas-liquid flow systems, flow is commonly classified into bubble flow, slug flow, churn flow, and annular flow – please refer to Figure 3:

• Bubble Flow: Characterized by small gas bubbles dispersed within the continuous liquid phase. It occurs at low gas rates and is typically in liquid-dominated system.

• Slug Flow: Develops at higher gas rates, where gas bubbles occupy most of the pipe’s cross-section, with liquid slugs between them.

• Churn Flow: Represents chaotic movement with distorted gas pockets and liquid slugs, forming as slug flow breaks down.¹⁴

• Annular Flow: occurs when gas forms a continuous core in the center of the pipe, while liquid forms a film along the walls. It is common at very high gas flow rates and low liquid flow rates.

The multiphase flow model used herein is based on Petalas-Aziz.¹⁰ This model covers the entire range of piping inclinations and has been refined and validated with 20,000 laboratory measurements and approximately 1,800 measurements from actual wells.

Flow and corrosion

Proper flow characterization – including flow patterns, wall shear stress, and other key parameters – is essential for corrosion prediction and assessment. Flow restrictions like elbow, tee, weld protrusion or excessive flow turbulence usually will increase the corrosion rate in both single and multiphase systems.^{14 15}

The majority of corrosion damage mechanisms are influenced by the flow regime, particularly those governed by electrochemical corrosion occurring at low temperatures. Carbon steel corrosion by acids, such as sulfuric or hydrofluoric acid, during the alkylation process is a prominent example. Concentrated sulfuric acid is virtually non-corrosive to carbon steel, provided the flow velocity remains below 1 m/s.¹⁶ However, this threshold can be significantly reduced at elevated temperatures. Therefore, knowledge of acid velocity or Wall Shear Stress is critical for predicting the corrosion behavior of carbon steel and corrosion-resistant alloys in concentrated acids.

Alkaline sour water corrosion (or ammonium bisulfide corrosion) is another prominent example of how the flow regime can influence fluid corrosivity. This is particularly important in hydroprocessing REAC systems (Reactor Effluent Air Cooler), where high turbulence in two-phase flow can lead to rapid metal degradation, even under theoretically “safe” and “non-corroding” conditions. The generic rule of thumb regarding flow velocity—for example, a maximum of 6.1 m/s (20 fps) for REAC tubes and inlets—may prove overly optimistic and insufficiently conservative, especially when the concentration of NH₄HS exceeds 2 wt.%, H₂S partial pressure is high, and cyanides are present. The API normative document governing REAC design explicitly emphasizes that simple velocity rules are inadequate for REAC design and for establishing Integrity Operating Windows (IOWs).¹⁷

To address these challenges, the flow model provided with the subscription offers a highly valuable tool for accurately assessing flow regimes, velocities, and Wall Shear Stress in complex environments like REAC systems. By leveraging this tool, users can better estimate corrosion risks and optimize designs to ensure long-term system integrity and reliability.

Calculator

The screenshots below display the interface of a flow model, showcasing both input parameters and computed results.

The input section includes fields for key variables such as flow rate (for gas, water, and oil), pressure, temperature, and pipe configuration. Users can specify conditions to accurately model the flow behavior under different operational scenarios.

The results section presents computed values, including flow velocities for both gas and liquid phases, Wall Shear Stress, pressure drop, and other relevant hydraulic properties. These outputs provide insights into fluid dynamics, helping users assess flow characteristics, identify potential inefficiencies, and optimize system performance.

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References

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