5.2 Gas Migration Without Circulation & Surface Pressure Buildup

When a well is shut in following a gas kick, fluid circulation stops, but downhole dynamics remain active. Because formation gas has a significantly lower density ($0.05\text{ to }0.15\text{ psi/ft}$) than the surrounding drilling mud column ($0.50\text{ to }0.90\text{ psi/ft}$), net buoyant forces drive the gas upward through the stationary mud column.

If this migration occurs in a closed, shut-in well without controlled fluid release, the gas is prevented from expanding. In the idealized model below, assume a sealed, rigid well, incompressible mud, a discrete migrating free-gas slug, negligible temperature change and no losses, influx or fluid release. This explains the pressure-rise hazard; actual pressure data must be checked against these assumptions.

Buoyancy Dynamics & Gas Migration Velocity ($V_m$)

The upward migration of gas through stationary drilling mud is driven by the density differential between the two fluids: $F_b = V_{\text{bubble}} \times (\rho_{\text{mud}} - \rho_{\text{gas}}) \times g$

This buoyant force is counteracted by fluid viscous drag, yield stress, and the progressive gel strength of the drilling fluid.

Estimating Migration Speed

Gas migration is not a fixed design speed. Fluid rheology and gels, gas size/distribution, annular geometry and inclination affect movement. Gas can segregate along the high side in deviated wells, while a horizontal interval can limit vertical migration until circulation sweeps gas into an inclined/vertical section.

The worked example below assumes 750 ft/hr; it is supplied data, not a universal range. Under the closed-migration model, IWCF Formula 15 estimates vertical speed from measured surface-pressure rise: $V_m=\frac{d P/dt}{0.052\,\rho_{\text{mud}}}$ Usepsi/hr andppg to obtainft/hr. Assess whether the communicating-gauge and stable-fluid assumptions hold before applying it.

Constant Bubble Volume & Pressure Transmission in a Shut-In Well

When a well is shut in and all surface valves remain closed, the wellbore acts as a rigid, closed pressure vessel. Both the liquid drilling mud and the surrounding formation rock are essentially incompressible compared to gas.

Boyle's Law in a Closed System

According to Boyle's Law ($P_1 V_1 = P_2 V_2$), for gas to expand and decrease in pressure, it must displace an equivalent volume of liquid from the wellbore. If no mud is bled from the well: $V_{\text{gas}} = \text{constant} \implies P_{\text{gas}} \approx \text{constant}$

With negligible temperature change, approximately constant gas volume implies approximately constant gas pressure. As the finite slug rises, more mud lies beneath it, so bottomhole pressure rises. Its pressure does not fall by the gas gradient multiplied by the entire migration distance: gas hydrostatic head applies across the gas column itself.

In the negligible-gas-head approximation, gas reaching the top can bring a pressure close to its initial downhole pressure to the wellhead. Real well compliance, temperature and fluid movement modify the response; monitoring and pressure control remain essential.

Surface Pressure Buildup Rate Derivation ($dP/dt$)

As the gas bubble ascends a vertical distance $\Delta h$ during time interval $\Delta t$: $\Delta h = V_m \times \Delta t$

A column of drilling fluid of height $\Delta h$ that was previously located above the bubble is transferred beneath the bubble. The pressure at any point in the wellbore above the gas bubble increases by the hydrostatic pressure of the mud column transferred beneath it: $\Delta P = G_{\text{mud}} \times \Delta h = 0.052 \times \rho_{\text{mud}} \times V_m \times \Delta t$

Differentiating with respect to time yields the surface pressure buildup rate: $\frac{dP}{dt} = 0.052 \times \rho_{\text{mud}} \times V_m = G_{\text{mud}} \times V_m$

Where:

• $dP/dt$ is pressure buildup rate in $\text{psi/hr}$;
• $\rho_{\text{mud}}$ is mud density in $\text{lb/gal}$;
• $G_{\text{mud}}$ is mud gradient in $\text{psi/ft}$;
• $V_m$ is gas migration velocity in $\text{ft/hr}$.

Parallel Gauge Behavior as a Diagnostic Rule

In this model, with the bit below the gas and an unobstructed drillstring pressure path, the standpipe and casing gauges rise at approximately the same rate: $\frac{d(\text{SIDPP})}{dt} = \frac{d(\text{SICP})}{dt} = G_{\text{mud}} \times V_m$

Wellbore Integrity Threats: Shoe Breakdown & Casing Burst

Allowing gas to migrate upward in a closed well without controlled expansion creates catastrophic wellbore integrity hazards:

1. Casing Shoe Fracture and MAASP Breach

Use the identified weak formation for the actual well; it is often, but not always, at the casing shoe. The Maximum Allowable Annular Surface Pressure (MAASP) is the permitted surface annular pressure based on the specified weak-point integrity and current fluid profile. For the simple uniform-mud shoe model: $\text{MAASP} = 0.052 \times (\text{EMW}_{\text{LOT}} - \rho_{\text{mud}}) \times \text{TVD}_{\text{shoe}}$

When gas is migrating below the casing shoe, the pressure at the shoe ($P_{\text{shoe}}$) increases in direct lockstep with surface casing pressure: $P_{\text{shoe}}(t) = P_{\text{shoe,init}} + \Delta \text{SICP}(t) = P_{\text{shoe,init}} + (G_{\text{mud}} \times V_m \times t)$

If the supervisor takes no action, $P_{\text{shoe}}$ rapidly exceeds the formation breakdown pressure. The shoe fractures, resulting in fluid loss, loss of primary containment, and an underground blowout—where high-pressure gas from the bottom zone flows uncontrollably across open hole into the fractured upper formation.

2. Casing Burst and Wellhead Overpressure

If gas is permitted to migrate all the way to surface without expansion, the pressure at the wellhead will reach: $\text{SICP}_{\text{surface}} \approx P_{\text{gas,initial}}\approx P_{\text{pore}}\quad\text{(gas head neglected)}$

In a $12,000\text{ ft}$ well with a $9,000\text{ psi}$ pore pressure, surface pressure could approach $9,000\text{ psi}$ in this simplified no-expansion model. In many well designs, this easily exceeds the internal yield (burst) rating of intermediate casing strings, casing hanger seals, or surface BOP equipment.

Worked Numerical Example: Pressure Buildup and Time to MAASP Breach

Well Parameters:

• Total Depth (TVD): $12,500\text{ ft}$
• Mud Density ($\rho_{\text{mud}}$): $13.5\text{ lb/gal}$ ($G_{\text{mud}} = 0.052 \times 13.5 = 0.702\text{ psi/ft}$)
• Casing Shoe Depth (TVD): $8,500\text{ ft}$
• Leak-Off Test EMW at Shoe ($\text{EMW}_{\text{LOT}}$): $16.0\text{ lb/gal}$
• Initial Stabilized $\text{SIDPP}$: $550\text{ psi}$
• Initial Stabilized $\text{SICP}$: $850\text{ psi}$
• Estimated Gas Migration Velocity ($V_m$): $750\text{ ft/hr}$

Step 1: Calculate Surface Pressure Buildup Rate ($dP/dt$)

$\frac{dP}{dt} = G_{\text{mud}} \times V_m = 0.702\text{ psi/ft} \times 750\text{ ft/hr} = 526.5\text{ psi/hr}$ $\text{Rate per minute} = \frac{526.5\text{ psi/hr}}{60\text{ min/hr}} \approx 8.78\text{ psi/min}$

Step 2: Calculate Current MAASP at the Casing Shoe

$\text{MAASP} = 0.052 \times (\text{EMW}_{\text{LOT}} - \rho_{\text{mud}}) \times \text{TVD}_{\text{shoe}}$ $\text{MAASP} = 0.052 \times (16.0 - 13.5) \times 8,500 = 0.052 \times 2.5 \times 8,500 = 1,105\text{ psi}$

Step 3: Determine Allowable Pressure Margin and Time to Shoe Breach

The remaining pressure margin before the shoe fractures is: $\text{Margin} = \text{MAASP} - \text{SICP}_{\text{init}} = 1,105\text{ psi} - 850\text{ psi} = 255\text{ psi}$

The time elapsed before the casing shoe fractures is: $t_{\text{breach}} = \frac{\text{Margin}}{dP/dt} = \frac{255\text{ psi}}{526.5\text{ psi/hr}} = 0.484\text{ hours} \approx 29.1\text{ minutes}$

Operational Conclusion: The assumed closed-migration model reaches the stated MAASP in about 29.1 minutes; this is a projected pressure-limit crossing, not permission to wait. Control migration promptly through circulation when feasible or the approved volumetric plan when circulation is unavailable. Maintain the planned pressure band and current weak-point/equipment limits.