Adam T. Bourgoyne Jr.Louisiana State University

Baton Rouge

L. William AbelWild Well Control Inc.

Spring, Tex.

The analysis of two-phase, high-velocity flow helps in the design of diverters and in planning dynamic kill operations for shallow gas blowouts.

An understanding of the mechanics of the shallow gas flow and the means available to control it are crucial to safe drilling operations. Such flows must be analyzed carefully, which is best done with computer assistance. Hand calculation methods and rules of thumb are not sufficient for diverter design or kill operations.

A dynamic kill uses both hydrostatic and frictional pressure to overcome the reservoir pressure in the producing zone. This type of kill usually requires massive pump rates and careful coordination of personnel and equipment. Dynamic kills are usually performed from a relief well or from a pipe string in the blowing well.

Some of the most prolific blowout flows have come from shallow gas reservoirs. Some shallow gas reservoirs can deliver flows in excess of 300 MMscfd of gas with associated formation fluids.

Shallow gas flows sometimes carry large quantities of abrasive formation, which can erode surface equipment and complicate the blowout. Some large flows have caused craters that have swallowed entire locations, drilling rigs, and platforms.

The abrasive solids and high velocities of the gas flow have also caused diverter systems and casings to fail in minutes. For these reasons, it is important to be aware of the potential hazards and to plan accordingly.

Dynamic kill operations become necessary when it is not possible to control a blowing well by conventional well control means (blowout preventers, drilling chokes, flow shut in, circulation). A dynamic kill is often the only available option after loss of safe access to surface wellhead equipment, especially for deepwater blowouts in a hostile marine environment. For some dynamic kill operations, a relief well is drilled to intersect the wild well at some depth beneath the surface, followed by the pumping of mud with sufficient density at a high enough rate to overcome the formation pressure. Care must be taken not to cause excessive leak off of fluid during such a kill operation to avoid fracturing to the surface.

In some cases, there may be access to the well through a string left in or snubbed into the well. A large number of variables must be optimized when designing such a dynamic kill. The design is best accomplished using a systems analysis approach.

Calculation of the pressure at various points in a flowing system is complicated by sonic flow at the exit, unusually rapid fluid acceleration in parts of the system (changes in geometry or direction), temperature changes, and the presence of two-phase flow.

The empirical correlations for predicting sonic exit pressures during multiphase flow can be adapted for practical use in dynamic kill analysis using a spreadsheet approach.1 A spreadsheet program is recommended for prediction of flowing pressure profiles, for the design of a diverter system, and for dynamic kill requirements.

### SOFTWARE ANALYSIS

A systems analysis procedure permits the simultaneous calculation of steady state pressures throughout the well and diverter system.2-4 A similar approach was presented in detail in API RP 645 (1991).5

One of the problems encountered with a systems analysis procedure is the need for an accurate prediction of the pressures occurring in the diverter system at potentially high gas flow rates in pipe diameters commonly used in oil field applications (8 in., 10 in., etc.). Most experimentation has been concentrated on smaller diameter pipe because of the cost to build laboratory simulators.

Calculation of the pressure at various points in a diverter system is complicated and does not lend itself to hand-calculation or approximate methods. Conventional equations and computer algorithms used by petroleum engineers to analyze producing wells cannot be applied with any confidence.

Experiments involving two-phase (gas and water) flow were conducted in 8-in. and 10-in. model diverter systems at rates sufficient to achieve sonic flow.1 The recommended algorithm for calculating pressures and fluid velocities at various points in a well system is based on this experimental study.

Portions of these procedures that can be applied to dynamic well control procedures have been programmed into a simulator which uses Microsoft Excel 4.0 operating in either a DOS 5.0 or Apple Macintosh environment.6

### ALGORITHM

The recommended diverter design calculations require the use of equations describing sonic exit pressure, flowing pressure gradients in the diverter and well, formation productivity, formation fracture gradient, and erosion.

- Sonic exit conditions

The limiting (sonic) velocity at the vent line exit can be computed for any fluid using Equation 1 (see box)(73154 bytes). For liquids, the density and compressibility can be assumed constant and are easily defined. For gases, the density at the exit can be determined from the real gas equation (Equation 2)(73154 bytes).

For the most accurate results, the gas compressibility at the exit should be computed assuming a polytropic process (Equation 3)(73154 bytes).

For an adiabatic expansion of an ideal gas, n becomes equal to the ratio, k, of specific heat at constant pressure, Cp, to specific heat at constant volume, Cv. For sonic gas flow through a restriction, k is often used as an approximate value for n.

When the fluid being produced from the well is a multiphase mixture rather than a single-phase gas, Equation 1(73154 bytes) can still be applied through use of appropriate values for effective density, effective compressibility, and effective polytropic expansion coefficient, n. The effective multiphase density should be calculated with Equation 4.(73154 bytes)

For sonic flow, the slip velocity between the phases can be neglected when the volume fractions are calculated. The effective compressibility can be calculated in a similar manner using Equation 5.7 (73154 bytes) This approach had been used previously, but for simplicity the second and third terms of this equation were negligible.8 Bourgoyne found that the effective value of n varied with gas weight percentage (quality), cg.1 For the range of conditions studied, n could be approximately defined by Equation 6.(73154 bytes)

Flowing pressure gradientUpstream of the vent line exit, the pressure gradient is given by Equation 7.(73154 bytes) The first term in Equation 7 (73154 bytes) accounts for hydrostatic pressure changes, the second term accounts for frictional pressure losses, and the third term describes pressure changes caused by fluid acceleration. The Moody friction factor, f, in the second term is given by Equation 8.9(73154 bytes) For the term e, a value of 16.5 mm (0.00065 in.) for roughness yields good agreement with experimental data obtained in pipe having a diameter of 0.1244 m (4.9 in.). Equation 9 (73154 bytes) defines the Reynolds number.

At a sudden decrease in the area of the flow path, such as at the vent line entrance, the pressure drop because of fluid acceleration can be estimated with Equation 10.(73154 bytes)

The downstream velocity, however, cannot exceed the sonic velocity (the physical limit because a pressure wave cannot travel faster than the speed of sound in the medium of interest) predicted by Equation 1.(73154 bytes) When sonic velocity occurs, the downstream pressure will be governed by Equation 1.(73154 bytes)

At a sudden increase in the area of the flow path, such as at the casing seat, at a large washout, or at the top of the drill collars, the increase in pressure because of fluid deceleration is generally small and can be neglected. In a typical drilling well geometry, there is no diffuser present that can provide a smooth transition to the larger flow area. Almost all of the theoretical pressure recovery predicted by Equation 10 (73154 bytes) is lost to turbulence.

For a multiphase fluid, Equations 8-10 (73154 bytes) can be applied with appropriate values for effective density, effective viscosity, and effective velocity. For high flow rates typical of shallow gas flows, the effective multiphase density, viscosity, and velocity can be calculated assuming no slippage between the phases. Thus, the effective multiphase density is given by Equation 4, (73154 bytes) and the effective multiphase viscosity is given by Equation 11.(73154 bytes)

The effective multiphase velocity is defined in terms of flow rate and cross sectional area by Equation 12.(73154 bytes)

Experiments conducted in model diverter systems have indicated that gas expansion significantly cools the flow stream.1 It is recommended that if a software package for calculating heat toss is not available, adiabatic flow rather than isothermal flow should be assumed in a surface diverter.

For adiabatic flow, temperature changes between points can be computed with Equation 13.(73154 bytes)

The temperature changes inside the well cannot be accurately represented using either isothermal or adiabatic conditions. A linear flowing temperature gradient is assumed to provide an approximation of the temperature behavior. The flowing bottom hole temperature will be close to the formation temperature. The flowing temperature near the surface

must be estimated based on experience or a heat flow model.

The spreadsheet model uses a finite difference (referred to as steps) approach for the description of the geometry of the well and system. Convenient distance step sizes can be assumed when using the pressure gradient to move upstream in a stepwise manner. It is often convenient to choose a step size that will end on a boundary when a diameter change or significant direction change occurs.

- Formation productivity

Resistance to flow is present in the gas reservoir as well as in the flow path to the surface. For shallow gas flows, little is generally known about the properties of the gas reservoir causing the unexpected flow, and detailed reservoir simulations are seldom justified.

It is important to take into account turbulence and other factors that become important at high gas velocities. The Forchheimer equation as adapted for horizontal, radial, and semisteady state flow in a homogeneous gas reservoir is recommended for use in design calculations for diverter systems.10 This equation can be arranged to give flowing bottom bole pressure within a well bore (Equation 14).(73154 bytes)

The terms in brackets reduce to a constant for a given reservoir. The second term is needed to model high-velocity gas flow properly where the velocity coefficient is determined empirically. Note that once the bracketed terms are reduced to a constant, a relatively simple relationship between gas flow rate and flowing bottom hole pressure results.

Laboratory core data show that the velocity coefficient tends to decrease with increasing permeability. Because shallow sands tend to be unconsolidated, a correlation based on data taken in unconsolidated samples is recommended for diverter system design calculations (Equation 15).11(73154 bytes)

Choosing a representative value for the reservoir thickness is complicated by the fact that the well bore often penetrates through only part of the gas reservoir before the shallow gas flow is detected and drilling is stopped. When this occurs, the gas flow is not radial as assumed by Equation 14,(73154 bytes) and an effective thickness value must be used. This effective thickness depends on the ratio of the horizontal to the vertical permeability, the well bore radius, the total formation thickness, and the formation thickness penetrated by the bit. When the vertical permeability is much less than the horizontal permeability, the effective thickness is approximately equal to the thickness penetrated by the bit. As the vertical permeability increases and approaches the horizontal permeability, Equation 16 (73154 bytes) can be used to estimate the effective thickness for the first term of Equation 14.11(73154 bytes)

The thickness penetrated by the bit is always used for the second term in Equation 14 (73154 bytes) because non-Darcy flow is generally limited to a region very close to the borehole.

- Formation fracture pressure

The recommended fracture pressure equation for offshore drilling operations based on Eaton's correlation gives the absolute overburden stress in terms of the sea water depth and the sediment depth below the seafloor (Equation 17).13(73154 bytes)

The minimum expected absolute formation fracture pressure is then determined from the absolute formation pore pressure and the overburden pressure (Equation 18).(73154 bytes)

This minimum fracture pressure would correspond to extending an existing fracture in a sandy formation. Higher formation fracture pressures would be expected for fracture initiation and in plastic gumbo shale formations. The maximum expected pressure for fracture extension is the overburden pressure given by Equation 17.(73154 bytes)

- Erosion

Erosion in diverted flows is a large concern. Erosion can be controlled, not prevented. Hardness and thickness of the material will extend the life of the component. The following diverter sections will rapidly erode: turns (900, field-fabricated 450, etc.), transitions from one diameter to another, and the exit where the gas expands to atmospheric pressure.

### SPREADSHEET APPROACH

These systems of equations can be conveniently programmed using any modern spreadsheet program. This approach minimizes the programming time required yet retains considerable flexibility with respect to modifying the program to handle unusual well or diverter configurations. It also provides easy access to the powerful graphics packages available on modern spreadsheets and allows the results to be easily transported to a word processor program for presentations.

The goal of the diverter design is to size the line and choose the casing setting depth so that erosion will be controlled and the well will not crater while on diversion, will not breach while unloading (peak pressure), and can be killed by pumping down the drillstring.

To prevent cratering, the flowing pressure profile must not exert pressure greater than the formation fracture pressure (injection pressure in shallow horizons). For a given set of conditions, the flowing pressure profile decreases as the diameter of the diverter line increases.

This relationship is shown by using the DYN-X spreadsheet as an analytical tool to predict flow rates and pressure profiles for a given set of parameters. This spreadsheet also predicts the rate required to kill the flow.

### DIVERTER DESIGN

Fig. 1 (48467 bytes) is the well bore diagram for the example diverter design.

The program requires a model to be built representing the case to be studied, with the following information required:

- Formation fluid composition and the gas/liquid equilibria of the model
- Well conditions and formation characteristics
- The minimum rate for sonic conditions at exit, the actual conditions at exit, and the formation inflow performance
- Well bore and diverter geometry and the pressure drop calculations for a specified kill rate.

For the example, the reservoir parameters were assumed to allow an open hole flow potential of 250 MMscfd gas flow from a shallow zone below the conductor in a 17.5-in. hole. The first design was to set conductor at about 200 ft with an 8-in. diverter line. A 17.5-in. hole would then be drilled below the conductor.

This design was built into the DYN-X program, and the case was run to determine that the shoe would crater under these conditions. The program was run again with larger diverter lines until the shoe did not crater, but the kill rates were too high to be able to kill the well with rig pumping equipment. Slight reductions in kill rates were achieved by increasing the mud weight.

An 8.5-in. pilot hole was added to the model. The result was that the shoe did not crater with the pressure from the flow, and a kill rate that could be accomplished with some effort using equipment on the rig.

The DYN-X program was also run for a deeper conductor depth of 600 ft with a 17.5-in. hole below the conductor. This design resulted in shoe integrity, but again the kill rates were excessively high. The kill rate could be reduced by decreasing the size of the diverter line.

The change in geometry, using an 8.5-in. pilot hole, reduced the flow potential from 250 to 200 MMscfd, keeping the same reservoir parameters. Table 1 (16454 bytes) shows the results of various DYN-X runs for this example.18-19

### SHALLOW GAS BLOWOUT

A Far East onshore well had reached 723 ft without incident as a 17.5-in. hole was drilled below 30-in. drive pipe at 232 ft. This drive pipe had a 21.25-in. diverter with a single 152-ft run of 7-in. casing as a diverter line.

At a drilling depth around 700 ft, there were indications that a shallow gas carbonate reservoir had been penetrated. Because of abnormal gas readings and concern for the 30-in. casing seat, the decision was made to stop drilling and to run casing. The well was circulated in preparation for pulling out of the hole. The well began to flow just after the kelly was set back. The kelly was installed and the well was put on diversion.

A kill attempt was made by pumping mud down the drill pipe at the maximum rate available from the rig pumps, but this effort failed to stop the flow. The hole unloaded and flowed a steady rate of gas and water (75 psig flowing wellhead pressure or FWHP). The concern was that the pressure at the shoe would exceed its pressure integrity and the well would crater.

Gas bubbling was observed in the cellar, outside the rat and mouse hole shucks, in an area near the V-door (approximately 15 x 30 ft) and around the edge of the location membrane (Fig. 2)(80148 bytes). The shoe had been breached, and gas was traveling to the surface outside the pipe. The activity in the rat hole was more than minor bubbling and could be described as a small flow which could raise water 2-3 ft.

Additionally, there were several pinhole leaks in the field-fabricated 30 in. x 20 in. transition on the wellhead. These pinholes resulted from flaws in the welding and leaked a very minor amount of gas.

One key problem was how to maintain well bore stability while rigging up for the kill, during the actual pumping operation, and after the kill operation. The design needed to use local equipment and personnel to avoid excessive air freight expense and delays.

The following were the main concerns:

- Personnel and equipment safety
- Maintaining minimal pressure at the shoe to avoid a crater
- Not exceeding the integrity of the surface equipment and drill pipe
- Pressure transients and surges during the kill operation
- Logistical support and pumping availability
- Erosion of surface equipment.

The major consideration was preventing the well from cratering during the kill operation.

### DESIGN PHASE

The design of the kill operation was conducted in the operator's office in the U.S., with support and assistance from the field operational staff. The off site design team consisted of a small group of operator employees and one consultant, and an on site project team implemented the design as well as checked on feasibility (local logistics, etc.).

The design used the operator's in-house diverter kill program and the DYN-X program. Both programs are two-phase flow models and account for the reservoir's inflow performance relationship (IPR), well geometry, and multiphase gas flow behavior.

The two-phase flow modeling showed that if the flow were subsonic at the diverter exit, the kill requirements would be about 35 bbl/min and that if the exit conditions were sonic, the kill requirements would be about 44 bbl/min. Based on experience and the guidelines of these calculations, the minimum kill rate requirements would be 45 bbl/min. Table 2 (13850 bytes) is a guideline for the pumping frictional losses and horsepower.

The design consisted of determining what density mud and kill rate would be required to kill the flow if it were pumped down the drillstring (Fig. 3)(70099 bytes). This modeling technique required assumptions to be made for actual well bore geometry, reservoir fluids produced (gas flow and water cut), reservoir parameters (IPR, gas lift parameters, etc.), and the dynamic aspects of the reservoir pressure buildup.

The most important factors were the flow rate and amount of water produced. To get an estimate of the flow rate, a second gauge was installed near the end of the diverter line. The diverter line was thus used as a meter run and the two-phase dynamic model was used to estimate the flow rate. The IPR was altered until the model results reasonably fit the observed FWHP and exit pressure.

The well was making an undetermined amount of water, and it was concluded that it was not feasible to separate the gas and water for an accurate water measurement. Separation equipment would have added additional back pressure, and the intense bubbling near the wellhead also made this not a viable option. Water flow was visually estimated at 100-500 gpm.

The computer model was constructed using finite element segments to describe well bore geometry. Various sensitivity runs were made to determine the effects of various water cuts and varying IPRs. This work was assisted by having some knowledge of the flowing bottom hole pressure (FBHP), which was estimated from standpipe pressure during an aborted kill attempt. The flowing reservoir pressure was estimated to be 100-125 psig. With this information, the IPR could be matched to the actual FWHP and exit pressure.

In diverter system design, one often assumes that the reservoir has infinite deliverability, and there is no drawdown of the FBHP from the static reservoir pressure. Fig. 4 (39015 bytes) shows the best estimate of IPR and the absolute maximum IPR thought possible in the reservoir. In this situation, FBHP is set to reservoir shut in pressure and a flow rate determined. If this were done, a flow rate of 170 MMscfd would result, and the FWHP and exit pressures would not match observed values. So one must expect the reservoir deliverability to be much less than the 500 MMscfd assumed.

To obtain a reasonable estimate of the actual IPR, the observed FWHP, exit pressure, and estimated FBHP can be used. The model's IPR is adjusted until the observed rates result (Fig. 5)(38261 bytes).

Because data indicated that the well had drawn down (FBHP

In addition to the kill rates required to perform a dynamic kill, the reservoir build-up characteristics were studied. Neither of the two-phase flow models accounted for time required for the bottom hole pressure to build up. Therefore, the build up was analyzed separately.

Fig. 6 (59606 bytes) shows that if the kill begins at a high rate, the reservoir flow is stopped, and the build up begins. At 30 bbl/min, it only takes 0.6 sec for the hydrostatic mud column to produce more hydrostatic pressure than the rate of buildup at the sand face. Two independent analyses showed that a 30 bbl/min rate would kill the well, and the well would remain dead (no additional kicks). Thus, the 45 bbl/min rate would provide adequate safety factors for errors in the analysis and provide assurance that kill operation could be accomplished in one try.

The two-phase model indicated that at low kill rates (15-25 bbl/min) there would be high pressure losses in the diverter lines which would cause a pressure transient to be applied to the casing shoe that was already showing signs of breaching (gas bubbling).

The mud weight chosen was the minimum to kill the well statically and had thin Theological properties. Thin rheology was desirable to minimize the pressure losses and thus reduce the required hydraulic horsepower (Table 3)(6500 bytes).

### OPERATIONAL PHASE

The operational phase began almost immediately with a local search for pumping capacity. The operational phase followed the design as prescribed with minor exceptions. Sufficient horsepower was brought to the island location and rigged up and tested. Approximately 4,500 bbl of kill mud (9.5 ppg) was placed on site and manifolded to the blenders (charging pumps).

The testing consisted of body tests (10,000 psi on all pump lines) and a dynamic test against a choke at anticipated pump rates and pressures. The dynamic test was labeled "running the loop" because a loop back to the mud storage tanks was constructed for the testing.

In line with the objective of taking the minimal risk of breaching, it was decided the kill plan would bring the pump rate to the design rate as quickly as possible. The choice was either to run the loop and divert to the drill pipe or "ramp-up" the pumps once on line to the drill pipe.

The loop test showed the slow-ahead rate to be 20 bbl/min (with all pumps on line and idling in the desired gear). The design rate of 45 bbl/min at 6,000 psi discharge pressure could be obtained in about 15 sec (given the pumps were all on line and idling ahead, and the operators only had to increase engine rpm and not change gears).

After approximately 3 days of testing and final changes in the piping runs and control procedures, the kill system, personnel, and procedures were ready. Final musters, operational meeting, line testing, and running of the loop as a test and priming exercise were done.

The kill operation followed the design with only minor exceptions. A dramatic change was seen in the flow at the moment the drillstring saw 20 bbl/min, and this was accompanied by a sudden drop in the FWHP. These two indicators were positive support that the flow from the reservoir was being restricted (killed). The kill rate was brought up to maximum rate in 10 sec, and the well was killed before the buildup could continue.

The flow never recovered, and the FWHP continued to drop. Eventually the gas phase from the diverter line disappeared, and clear water returns were observed. Approximately 1,000 bbl were lost to the formation during the kill. The kill schedule (holding rate until FWHP was reduced by 50% and then staging down) was followed until clean mud returns were observed. The returns were routed through the gas buster until it was safe to circulate over the shakers. Full returns were maintained and the well was returned to normal drilling operations.

### REFERENCES

- Bourgoyne, A.T., "Improved Method of Predicting Wellhead Pressure During Diverter Operations," International Association of Drilling Contractors Third Annual European Well Control Conference, Noordwijkerhout, The Netherlands, June 2-4, 1992,
- Brown, K.E., and Beggs, H.D., The Technology of Artificial Lift Vol. 1: Methods, PennWell Books, Tulsa, 1977.
- Crouch, E C., and Pack, K.J., "Systems Analysis Use for the Design and Evaluation of High Rate Gas Wells," Society of Petroleum Engineers paper 9422, SPE Arm,at Meeting, Dallas, Sept. 21-24, 1980.
- Clark, A.R., and Perkins, T.K., "Wellbore and Near Surface Hydraulics of a Blown-Out Oil Well," paper 9257, SPE Annual Meeting, Dallas, Sept. 21-24, 1980.
- API RP 64, Recommended Practices for Diverter Systems Equipment and Operations, first edition, API, Washington, D.C., July 1, 1991.
- DYN-X two phase flow and dynamic kill simulator, developed by A.T. Bourgoyne for Wild Well Control Inc., Spring, Tex., 1993.
- Wallis, G.B., One Dimensional Two-Phase Flow, McGraw-Hill Book Co., New York, 1969.
- Ross, N.C., "An Analysis of Critical Simultaneous Gas-Liquid Flow Through a Restriction and Its Application to How Metering," Applied Science Research, Vol. 9, 1960.
- Moody, L.F., "Friction Factors for Pipe Flow," Transactions of the American Society of Mechanical Engineers, Vol. 66, 1944.
- Forchheimer, P., Wasserbewegung Dutch Boden, Zeitz, Ver Dutch, Ing., Vol. 45, 1901.
- Johnson, T.W., and Taliaferro, D.B., "Flow of Air and Natural Gas through Porous Media," 1938.
- Craft, B.C, and Hawkins, M.R., Applied Petroleum Reservoir Engineering, Prentice Hall Inc., New Jersey, 1959.
- Constant, W.D., and Bourgoyne, A.T., "Fracture Gradient Prediction for Offshore Wells," SPE Drilling Engineering, June 1988, pp. 136-40.
- Bourgoyne, A.T., "Experimental Study of Erosion in Diverter Systems Due to Sand Production, paper 18716, SPE/IADC Drilling Conference, New Orleans, 1989.
- Beck, F.E., Langlinais, J.P., and Bourgoyne, A.T., "Experimental and Theoretical Considerations for Diverter Evaluation and Design," paper 15111, SPE California Regional Meeting, Oakland, Calif., Apr. 3-6, 1986.
- Beck, I.E., Langlinais, J.P., and Bourgoyne, A.T., "An Analysis of the Design Loads Placed on a Well by a Diverter System," paper 16129, SPE/IADC Drilling Conference, New Orleans, 1987.
- Gilbert, W.E., "Flowing and Gaslift Well Performance," Drilling and Production Practices, API, Washington, D.C., 1954.
- Santos, O., and Bourgoyne, A.T., "Estimation of Peak Pressures Occurring When Diverting Shallow Gas," paper 19559, SPE Annual Meeting, San Antonio, Oct. 7-8, 1989.
- PEAK, software program developed by Santos and Bourgoyne, licensed to Wild Well Control Inc., 1992.

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