Slip Velocity
Slip velocity in multiphase flow through pipes and wellbores is the difference between the average in-situ velocities of two or more fluid phases flowing simultaneously through the same conduit, arising because the phases have different densities and therefore different buoyant forces acting on them under gravity, with the lighter phase (gas in gas-liquid flow, or light oil in oil-water flow) tending to move faster than the heavier phase in vertical upward flow as buoyancy accelerates the light phase relative to the heavier continuous phase, while in horizontal flow the phases segregate by gravity with the lighter phase occupying the upper portion of the pipe cross-section; slip velocity is a fundamental parameter in multiphase flow modeling because it determines the in-situ holdup of each phase (the fraction of the pipe cross-section occupied by each fluid at any point along the pipe) which differs from the input volume fraction at the surface due to slip, and the holdup difference between a no-slip (homogeneous) model and the actual slipping flow determines the hydrostatic pressure drop correction in wellbore flow calculations, the gas void fraction in separator design, and the liquid loading threshold velocity below which liquids accumulate in a gas well and cause production decline.
Key Takeaways
- The slip velocity magnitude in vertical gas-liquid flow depends on the flow regime (bubble flow, slug flow, churn flow, or annular flow), the physical properties of the gas and liquid (density, viscosity, surface tension), and the pipe diameter: in bubble flow (dispersed small bubbles rising through a continuous liquid phase), each bubble's rise velocity relative to the liquid is given by the drift-flux relationship, with the terminal rise velocity of a single small bubble in a quiescent liquid approximated by the Turner-Brown-Dukler correlation; in slug flow (alternating large Taylor bubbles and liquid slugs that dominate vertical gas-liquid pipe flow at intermediate gas fractions), the Taylor bubble rise velocity is approximately 0.35 times the square root of the pipe diameter times gravitational acceleration (Vs = 0.35 * sqrt(g * D)), a result derived from potential flow theory for the shape of a Taylor bubble rising in a vertical pipe, giving rise velocities of 0.4 to 0.8 m/s for typical well tubing diameters of 2 to 4 inches; in annular flow (gas flowing as a continuous core with liquid as an annular film on the pipe wall), the slip between the gas core and the liquid film is described by the annular flow film thickness and entrainment fraction rather than by a single slip velocity, with the Turner critical velocity being the minimum gas velocity required to prevent liquid film reversal and liquid loading in gas wells.
- Liquid holdup (the fraction of pipe cross-sectional area occupied by liquid at any location in a multiphase system) differs from the liquid input fraction (the volumetric flow rate fraction of liquid at the surface or separator conditions) because of slip: in upward flow, the slower-moving liquid phase occupies more cross-sectional area than its input fraction would suggest (liquid holdup greater than input fraction, gas holdup less than input gas fraction), meaning the actual in-situ gas velocity is higher than the superficial gas velocity (total gas flow rate divided by total pipe area) and the actual in-situ liquid velocity is lower than the superficial liquid velocity; the Griffith-Wallis, Duns-Ros, Orkiszewski, and Beggs-Brill correlations for vertical multiphase pipe flow all use different approaches to computing liquid holdup from the slip velocity or drift flux, and the accuracy of the wellbore pressure drop calculation depends critically on correctly predicting the holdup; the practical consequence of liquid holdup in a gas well is that the hydrostatic pressure head exerted by the liquid-rich mixture in the tubing is higher than would be computed from the gas density alone, increasing the flowing bottomhole pressure and reducing the production rate compared to the no-slip ideal.
- The Turner critical velocity is the minimum gas velocity required to continuously lift all produced liquids (water and condensate) out of a gas well to surface, derived by Turner, Hubbard, and Dukler in 1969 from a force balance on the largest liquid droplet entrained in the gas stream in annular-mist flow: the critical velocity equals approximately 5.62 times the fourth root of the ratio (sigma times (rho_liquid minus rho_gas) divided by rho_gas squared), where sigma is liquid surface tension, rho_liquid and rho_gas are the liquid and gas densities at downhole conditions; when the actual gas velocity in the tubing falls below the Turner critical velocity (which happens as reservoir pressure declines, gas rate decreases, and the larger liquid droplets can no longer be entrained and lifted), the liquids begin to accumulate at the bottom of the well, increasing the hydrostatic backpressure on the formation, further reducing gas influx, and initiating the positive-feedback liquid loading cycle that eventually kills production in many dry and wet gas wells; the solution to liquid loading (reducing tubing size to increase gas velocity at lower rates, installing plunger lift or intermittent gas lift to periodically unload accumulated liquids, or installing a compression unit to reduce wellhead pressure and increase the available differential) directly addresses the slip velocity physics of liquid droplet entrainment.
- In horizontal and near-horizontal multiphase flow, slip operates differently than in vertical flow because gravity acts perpendicular to the flow direction rather than parallel: the phases tend to stratify by density, with gas occupying the upper portion of the pipe cross-section (stratified flow or stratified-wavy flow at low gas and liquid velocities) until the gas velocity is high enough to shatter the liquid layer into droplets and transition to slug or dispersed bubble flow; the slip velocity in horizontal flow is smaller than in vertical flow at comparable flow rates because the buoyant driving force for phase separation is weaker (gravity acts radially rather than axially), but phase separation still occurs and produces significant holdup effects in long horizontal sections of pipelines and flowlines, particularly at low flow rates or during shut-in and restart when static liquid accumulates in low points of horizontal or undulating pipes; slug catcher design at pipeline gathering facilities is dictated by the slug volume produced when flow restarts after a shut-in period and the accumulated liquid is swept out by the returning gas flow as a large liquid slug.
- Multiphase flow meters (Coriolis, gamma-ray densitometers, venturi-based meters) measure the slip velocity or holdup implicitly as part of their flow measurement algorithm, because the meter output requires a phase fraction measurement to separate the total volumetric flow into individual phase flow rates: gamma-ray or electrical capacitance/conductance sensors measure the average in-situ liquid holdup across the pipe cross-section at the meter location, and the individual phase velocities are then derived from the total mixture velocity (from differential pressure across a venturi) and the measured holdup using the slip velocity model appropriate for the flow regime and flow conditions; errors in the assumed slip velocity model propagate into errors in the individual phase flow rate measurements, making the slip velocity correlation a critical element of multiphase meter accuracy, particularly at high gas-oil ratios or high water cuts where the holdup sensitivity of the phase fraction measurement is critical for acceptable individual phase measurement uncertainty.
Fast Facts
The first comprehensive experimental study of slip velocity in gas-liquid vertical pipe flow was conducted by Griffith and Wallis at MIT in 1961, laying the experimental foundation for the vertical multiphase flow correlations that production engineers still use today. The landmark Turner, Hubbard, and Dukler paper of 1969 derived the critical gas velocity for liquid droplet entrainment from first principles using measured surface tension and density data from field gas wells, providing the theoretical basis for the liquid loading concept that explains why many gas wells decline rapidly when their rate falls below a critical threshold and which can be diagnosed by comparing actual wellhead tubing pressure and flow rate to the Turner velocity calculated from downhole conditions.
What Is Slip Velocity?
Slip velocity is the difference between the average in-situ velocities of two immiscible phases (typically gas and liquid) flowing simultaneously through the same pipe, arising because buoyancy accelerates the lighter phase relative to the heavier phase in vertical flow. Slip causes the slower liquid phase to occupy a greater fraction of the pipe cross-section (liquid holdup) than its input volume fraction, increasing the hydrostatic pressure head in the wellbore tubing. In gas wells, slip controls the minimum gas velocity (Turner critical velocity) required to continuously lift produced liquids to surface; falling below this threshold initiates liquid loading that progressively kills well production. Accurate slip velocity modeling is essential for wellbore pressure drop calculations, separator sizing, and multiphase flow meter accuracy.
Synonyms and Related Terminology
Slip velocity is also called phase velocity difference, relative velocity, or drift velocity in drift-flux multiphase flow models. Related terms include liquid holdup (the fraction of the pipe cross-sectional area occupied by liquid at a given location in a multiphase flow system, which exceeds the liquid input volume fraction in upward flow due to slip velocity, increasing the hydrostatic pressure head in the wellbore and the hydrostatic component of the total pressure drop that must be overcome by reservoir pressure to sustain production), liquid loading (the condition in a gas well where the actual gas velocity falls below the Turner critical velocity required to continuously lift produced liquids to surface, causing liquid accumulation in the tubing that increases hydrostatic backpressure on the formation, reduces gas influx, and can eventually kill the well without intervention by plunger lift, velocity string installation, compression, or surfactant injection), Turner critical velocity (the minimum gas velocity required to continuously entrain and lift the largest liquid droplets in a gas well's tubing string, derived from the drag-gravity force balance on a liquid droplet in the gas stream, approximately equal to 5.62 times the fourth root of (sigma times (rho_L minus rho_G) / rho_G squared), where sigma is liquid surface tension and rho denotes density at downhole conditions), flow regime (the spatial pattern of gas and liquid distribution in a multiphase pipe flow, including bubble flow (dispersed bubbles in continuous liquid), slug flow (alternating Taylor bubbles and liquid slugs), churn flow (chaotic transitional pattern), and annular flow (gas core with liquid film), each regime having different slip velocity characteristics and requiring different holdup correlations for accurate pressure drop prediction), and multiphase flow (the simultaneous flow of two or more immiscible fluid phases (gas, oil, water) through the same conduit, characterized by complex interactions including slip velocity, holdup, flow regime transitions, and pressure drop behavior that differ fundamentally from single-phase flow and require specialized correlations and models for accurate production system design and performance prediction).
Why Slip Velocity Is the Key Parameter in Gas Well Life Extension
A gas well that was profitable at 5 MMscfd becomes unprofitable at 1 MMscfd not because the reservoir is depleted but because the tubing velocity has fallen below the Turner critical velocity and liquid is accumulating in the wellbore. Installing a 1.5-inch velocity string inside the existing 2.875-inch tubing doubles the gas velocity at the same flow rate, pushing the well back above the critical velocity threshold and restoring production at a cost that pays out in weeks. That solution works because the engineer understood slip velocity: specifically, that the critical velocity scales with the fourth root of the density ratio and with the tubing cross-sectional area, and that reducing the tubing area achieves the required velocity at a lower absolute gas rate. The gas wells that fail prematurely are the ones where liquid loading was not recognized as a slip-velocity problem until the well was already dying. The ones that survive for twenty years are operated by engineers who check the Turner velocity every six months and act before the critical threshold is crossed.