18.1 Influx Behavior and Hydrostatic Balance in Horizontal Lateral Sections

Influx Behavior and Hydrostatic Balance in Horizontal Lateral Sections

Horizontal and Extended Reach Drilling (ERD) operations represent some of the most hydraulically complex well geometries encountered in modern drilling. Laterals extending 5,000 to 15,000+ ft horizontally at constant True Vertical Depth (TVD) decouple the traditional relationships between borehole length, fluid volume, and hydrostatic pressure that govern vertical well control.

For an IWCF Level 4 Well Control Supervisor, managing kicks in horizontal sections requires an uncompromising grasp of downhole multiphase fluid dynamics. Gas in a flat lateral can have little effect on the vertical hydrostatic profile. Stable gauges therefore do not exclude an influx, and casing pressure alone does not determine its size or fluid type. Misunderstanding these mechanics leads to improper choke manipulation, premature bullheading, or induced formation fracture.

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The Fundamental Hydrostatic Law in Horizontal Geometries

Hydrostatic pressure ($P_{\text{hyd}}$) exerted by a static fluid column depends exclusively upon fluid density ($\rho$) and True Vertical Depth ($TVD$). In oilfield units:

$P_{\text{hyd}} = 0.052 \times \rho \times TVD$

In metric / SI units:

$P_{\text{hyd}} = \frac{\rho \times g \times TVD}{100,000}$

Where:

• $P_{\text{hyd}}$ = Hydrostatic pressure (psi or bar)
• $\rho$ = Fluid density (ppg or $\text{kg/m}^3$)
• $TVD$ = True Vertical Depth (ft or m)
• $g$ = Gravitational acceleration ($9.81\text{ m/s}^2$)

           IDEAL CONSTANT-TVD LATERAL
Surface
  | Vertical section
  | KOP: start of build
   \
    \ Build section
     +------------------------------> Toe / bit
     Heel                            20,000 ft MD
     10,000 ft MD                     8,500 ft TVD
     8,500 ft TVD

Lateral MD length = 10,000 ft; lateral TVD change = 0 ft
Additional hydrostatic head along the flat lateral = 0 psi

In a 10,000 ft horizontal lateral drilled at a constant 8,500 ft TVD, Measured Depth ($MD$) increases from 10,000 ft at the heel to 20,000 ft at the toe. However, the hydrostatic head exerted by an 11.5 ppg drilling fluid column remains precisely identical throughout the entire lateral:

$P_{\text{hyd}} = 0.052 \times 11.5 \times 8,500 = 5,083\text{ psi}$

Whether fluid moves 100 ft or 10,000 ft along this horizontal plane, $ΔTVD = 0$. Consequently, no hydrostatic pressure differential is created or lost by the lateral transit of fluids of differing densities.

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Limited Migration and Quiet Gauges

In a sealed vertical well, upward migration of a gas influx can increase well pressures. In the ideal constant-volume model, the pressure increase associated with upward travel is approximately the mud gradient multiplied by the vertical rise. Migration speed is not a fixed property of every kick; fluid properties, gas distribution and well geometry matter.

A perfectly horizontal interval supplies no vertical buoyancy component along its axis. Gas may segregate across the bore, spread or remain trapped; it must not be assumed to travel rapidly toward the heel. Small slopes and undulations change the favored direction of buoyant movement.

Multiphase Influx Mechanics: High-Side Segregation and Geometry

Free gas is less dense than drilling mud and tends to collect toward the high side of a horizontal bore. The fluid distribution can be stratified, dispersed or slugged according to flow conditions, geometry and fluid properties. A continuous frictionless ribbon is not a general model of every lateral kick.

         POSSIBLE SEGREGATED CROSS-SECTION
        High side: gas can accumulate here
       +--------------------------------+
       |       Gas-rich region          |
       |--------------------------------|
       |        Drilling mud            |
       |         (drillpipe)            |
       +--------------------------------+
        Low side: eccentric string possible

Distribution and Sweeping

• Segregation: Buoyancy favors gas on the high side, but the rate and completeness of separation depend on mud rheology, gas fraction and flow.
• Eccentric string: The drillstring often lies toward the low side. This changes the available flow channels; tool joints, cuttings beds and local geometry still affect transport.
• Influx length: With annular capacity 0.0459 bbl/ft, a 30 bbl influx has a full-annulus equivalent length of $30/0.0459=653.6$ ft. A gas layer occupying only part of the cross-section can extend farther. Volume divided by total annular capacity does not determine a segregated ribbon's actual length.
• Sweeping: Low-rate circulation can leave gas at crests or in an inclined lateral. Select a rate that removes gas while respecting formation and equipment limits; do not assume gas always travels faster than the average returning fluid.

Heel-to-Toe Hydrostatic Mechanics: Trajectory Undulations

In real-world directional drilling, horizontal laterals are rarely mathematically flat (90.0° inclination). Geosteering adjustments through undulating reservoir targets introduce significant deviations in inclination that profoundly affect hydrostatic balance between the heel and the toe.

                 LATERAL TRAJECTORY PROFILES & GAS MIGRATION

 1. TOE-DOWN TRAJECTORY (Inclination < 90°):
    Heel (Shallower TVD: 8,450 ft) ◄───────────────────┐
                                                     │   BUOYANT MIGRATION
                                                     │   TOWARD HEEL (UPHILL)
                                                     ▼
                                              Toe (Deeper TVD: 8,600 ft)

 2. TOE-UP TRAJECTORY (Inclination > 90°):
    Heel (Deeper TVD: 8,600 ft)                       Toe (Shallower TVD: 8,450 ft)
              ▲                                       ▲
              │    BUOYANT MIGRATION                  │
              │    TOWARD TOE (UPHILL) ───────────────┘
              ▼

 3. UNDULATING TRAJECTORY (Structural Dips and Crests):
    Heel ──┐         ┌─── Crest (Gas Trapped) ───┐         ┌── Toe
           │         │                           │         │
           └─────────┘ Sump (Mud Accumulates)    └─────────┘ Sump

1. Toe-Down Trajectory (Inclination < 90°)

• Geometry: The wellbore drills downward relative to true vertical depth; the toe is deeper in TVD than the heel (e.g., heel at 8,450 ft TVD, toe at 8,600 ft TVD).
• Hydrostatic Effect: The hydrostatic pressure at the toe is higher than at the heel.
• Gas Migration Direction: Buoyancy drives gas uphill toward the heel. Because the gas ascends in TVD as it moves toward the heel ($ΔTVD = 150\text{ ft}$), the ideal sealed, constant-volume migration model predicts a pressure rise of $ΔP = 0.052 \times \rho_m \times 150\text{ ft}$ if the gas makes that full vertical rise. Actual movement and readings require verification.

2. Toe-Up Trajectory (Inclination > 90°)

• Geometry: The lateral climbs stratigraphically; the toe is shallower in TVD than the heel (e.g., heel at 8,600 ft TVD, toe at 8,450 ft TVD).
• Hydrostatic Effect: Hydrostatic head is lower at the toe than at the heel.
• Gas Migration Direction: Buoyancy drives gas uphill toward the toe (away from the heel and toward the bit). Gas may collect toward the toe or a local crest, complicating removal. The actual distribution depends on the profile and fluid conditions.

3. Trajectory Undulations and Gas Trapping

In undulating laterals containing local structural crests (anticlines) and sumps (troughs):

• Gas naturally migrates to the crests (high points) of the undulations and becomes trapped.
• During low-rate circulating kills, the drag force of the drilling mud may be insufficient to displace the buoyant gas downward through the structural troughs, leaving pockets of unswept gas behind.

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Worked Scenario: Quiet Gauges in an ERD Well

ILLUSTRATIVE NORTH SEA GEOMETRY
 • Toe / bit: 22,500 ft MD, 9,220 ft TVD
 • Heel / shoe: 12,000 ft MD, 9,180 ft TVD
 • Lateral: 10,500 ft MD, 40 ft TVD drop toward toe
 • Average inclination: about 89.78 degrees, toe-down
 • Original mud: 12.2 ppg OBM
 • After positive flow and shut-in: SIDPP 380 psi, SICP 385 psi, gain 28 bbl

Stable 380/385 psi readings over 90 minutes do not justify delaying control or declaring the gas dormant. The survey favors buoyant movement toward the shallower heel, but neither it nor the gauges establish a migration speed.

For a sensitivity calculation only, assume gas travels 400 ft MD/hr along a uniform version of this slope. In 90 minutes it travels 600 ft MD and rises: $\Delta TVD=600\times 40/10,500=2.286\text{ ft}$ The ideal sealed, constant-volume pressure rise would be: $\Delta P=0.052\times 12.2\times 2.286=1.45\text{ psi}$ This small predicted change illustrates why pressure trends can be inconclusive. It is not evidence of actual gas movement, instrument resolution or imminent arrival at the heel. Plan the approved circulation using the known volumes, fluid properties, pressure limits and safe return handling; anticipate greater expansion as gas rises into the build and vertical section.