Dynamic model predicts well bore surge and swab pressures

Zhong Bing
Sichuan Union University
Chengdu, China

Zhou Kaiji
Southwest Petroleum Institute
Nanchong, China

• Equations [6899 bytes]

A dynamic well control model predicts surge and swab pressures more accurately than a steady-state model, thereby providing better estimates of pressure fluctuations when pipe is tripped.

Pressure fluctuations from tripping pipe into a well can contribute to lost circulation, kicks, and well control problems.

This dynamic method of predicting surge and swab pressures was verified in a full-scale test well in the Zhong Yuan oil field in China. Both the dynamic model and steady state model were verified through the test data.

Pressure fluctuations from running pipe (surge pressures) and pulling pipe (swab pressures) have long been known to contribute to lost circulation or gas kick problems. The prediction of surge and swab pressures has been studied by many in the industry.^1-3

The steady state surge and swab pressure model widely used in the oil field was developed by Burkhardt in 1961.³ This model, however, does not consider the effects of fluid inertia and compressibility, well bore elasticity, and the axial elasticity of the pipe; and the model does not compute steady state friction pressure loss in the annulus for surge pressures.

In 1977, Lubinski, et al., developed the first dynamic model.⁴ This work was improved upon by Lal, but both these models assumed that the moving pipe acted as a rigid body. Mitchell added axial pipe elasticity to dynamic surge analysis and compared the model with the field data presented by Burkhardt and by Clark and Fontenot.^3-7

The authors have studied dynamic surge and swab pressures since 1985, and detailed downhole pressure measurements were made in the full-scale test well in the Zhong Yuan oil field. The test data verified the dynamic model and gave a clear understanding of the regularity of surge and swab pressures and the effects on pressure from pipe velocity, tripping depth, mud properties, and pipe configuration.

The test data showed the dynamic model can correctly predict downhole pressures from running or pulling pipe in a well; steady state models may result in relatively large prediction errors, especially in deeper wells.

Dynamic model

In predicting surge and swab pressures with a dynamic model, the hydrodynamic system was analyzed with the following assumptions:

• The hydrodynamic system consists of different flow channels with different flow areas. Some are connected in series, and some in parallel.

• The pipe is run at a speed of Vp(t) at any position in the well.

• Formation elasticity and casing and drill pipe elasticity are all considered in determining the composite elastic response of the well bore.

• The drilling fluid is compressible.

• The hole bottom is rigid, and the top of the well is open to the atmosphere.

Because of the elasticity of the well bore and pipe and the compressibility of the drilling fluid, a series of pressure waves are caused continuously as the bottom of the pipe during tripping in. These pressure waves will propagate, be reflected, and fold over each other in the pipe conduit, annulus conduit, and pipe-to-bottom hole conduit.

Based on the balance of mass and momentum, the fluid pressures and velocities for one-dimensional unsteady flow are determined by two coupled partial differential equations (Equations 1 and 2).

To solve the two coupled partial differential equations, the boundary conditions and initial conditions at t=0 are given based on the assumptions in the hydrodynamic system in the well bore: The pressures are zero at any time at the top of the pipe and annulus conduits; the flow rate is zero at the bottom of the hole at any time; the boundary conditions at the other end points are determined from the pressure changes and the continuity of flow across the junctions; and the pressures and flow rates at t=0 are zero at any point along the Z axis.

Regarding frictional pressure loss, the power law model is used for the drilling fluid. The expression for the frictional pressure loss for the power law fluid, derived on the basis of steady flow in a stationary pipe and annulus, is modified to include the effect of pipe motion on the mean cross sectional fluid velocity.

Equation 2 becomes nonlinear for turbulent flow due to the nature of the frictional pressure loss, and the compositions of flow conduits are different for different hole structures and pipe tripping depths. The method of characteristics, which converts the two equations into ordinary differential equations and then algebraic equations with finite difference methods, is used for longer conduits. The implicit difference method, which converts the partial differential equations into algebraic equations directly, is used for the shorter conduits to save computing time.

Based on Equations 1 and 2 and boundary conditions, the algebraic equations for every composition of flow conduits can be obtained. Nonlinear algebraic equations can be solved by the Newton-Raphson method.

Testing

The test well in the Zhong Yuan oil field is 3,354 ft deep and is completed with 95/8-in. casing to 3,302 ft (Fig. 1 [17339 bytes]).

An 81/2-in. roller cone bit was used in the test. The bit was modified to ensure that the wire line-conveyed pressure tool could not become stuck when it was run or pulled or when the pipe was tripped with the tool in place. The equivalent diameter of the bit nozzles was 2.03 in.

The pipe velocity was measured by monitoring the variation of the traveling block position over time. This method has proven to be both a simple and very reliable means of gauging pipe speed.

A crystal harmonic pressure sensor, which can capture three to five values per second, was used to measure the surge and swab pressures. The pressure data were transmitted to surface by wire line and then processed by a computer and plotted over time. The measurement error was less than 5 psi.

Six types of water-based drilling fluids with different properties were used in the tests. Before testing began, the mud properties were measured every 15 min during circulation until the properties were relatively steady. The measured properties included density, plastic viscosity, yield point, flow behavior index, fluid consistency index, and temperature.

Some of the surge pressures (positive), swab pressures (negative), and drillstring velocities recorded during the field tests are plotted in Figs. 2-8. These graphs compare the pressures predicted by the dynamic model with the pressures predicted by Burkhardt's steady state model, using the same mud properties, drillstring speed, and bottom hole assembly.

These graphs show that the dynamic model can predict surge and swab peak pressures and also simulate the variation of surge and swab pressures over time. The dynamic model also showed that surge pressures could occur when a pulled pipe is brought to rest and that swab pressure could occur when pipe run in the hole is brought to rest; the propagation of pressure waves continues after the pipe stops moving and then tends to fade away.

Fig. 2 [20687 bytes] shows the test and prediction results of surge pressures as a 5-in. drillstring is run at a depth of 2,954 ft with the well filled with 13.02-ppg mud with a plastic viscosity of 37 cp and a yield point of 20 lbf/100 sq ft. The prediction error of the maximum surge pressure of the steady state model is 64%, but the prediction error of the dynamic model is only 0.24%.

Fig. 3 [24557 bytes] presents the surge pressures while the 5-in. drillstring is run in the hole at 2,954 ft with the well filled with a 12.69-ppg mud with a plastic viscosity of 34 cp and a yield point of 15 lbf/100 sq ft. The measured pressure more closely matches the pressures predicted by the dynamic model.

Fig. 4 [21716 bytes] illustrates the effect of tripping depth on downhole pressures. The mud properties are the same as those used in the example shown in Fig. 2. Although the maximum trip speed in the two examples differed by less than 2%, the maximum test pressures differed by 77% because of the difference in depth (2,954 ft in Fig. 2, 1,930 ft in Fig. 6).

Fig. 5 [22981 bytes] and Fig. 6 [20536 bytes] show the swab pressures while the drillstring was pulled at nearly a constant speed (the maximum trip speed in the surge tests) in the well with 12.60-ppg mud with a plastic viscosity of 32 cp and a yield point of 13 lbf/100 sq ft. These figures illustrate the effect of tripping depth on downhole pressures. In both figures, the drillstring consisted of a bit and 174 ft of drill collars on 5-in. drill pipe; the bit was at 2,104 ft in Fig. 5 and 3,037 ft in Fig. 6.

Results

The steady state models do not predict surge and swab pressures accurately, particularly the negative pressure surges when the pipe is brought to rest. The maximum pressures predicted by the models may be higher or lower than field test values.

Dynamic surge and swab pressure models show an excellent agreement with the measurements of surge and swab pressures collected during the field tests. The models accurately predict maximum surge and swab pressures as well as the variation of pressure with time at any position in the well bore. Predicting surge and swab pressures using dynamic models can minimize potential problems in a well bore and allow more efficient trip speeds for running or pulling pipe.

Running pipe may generate negative pressures and pulling pipe may generate positive pressures when the pipe is brought to a stop.

The maximum value of trip speed has a very significant effect on surge and swab pressures. Initially, the driller should limit the maximum trip speed to control the maximum surge and swab pressures during operations. Additionally, the driller should not accelerate or decelerate the pipe too suddenly. Surge and swab pressures do not equal zero as soon as the pipe stops; pressure waves can propagate through the well bore.

Tripping depth and mud properties also affect surge and swab pressures. The tripping speed should be slower when the bit is closer to the bottom of the well. The mud properties to be used in a well should be included in the model to determine the optimum tripping speed.

References

1. Cannon, G.E., "Changes in Hydrostatic Pressure Due to Withdrawing Drill Pipe from the Hole," Drilling and Production Practices, American Petroleum Institute, 1934.

2. Goins, W.C., et al., "Down-the-Hole Pressure Surges and Their Effect on Loss of Circulation," Drilling and Production Practices, American Petroleum Institute, 1951.

3. Burkhardt, J.A., "Wellbore Pressure Surges Produced by Pipe Movement," Journal of Petroleum Technology, June 1961, pp. 595-605.

4. Lubinski, A., Hsu, F.H., and Nolte, K.G., "Transient Pressure Surges Due to Pipe Movement in an Oil Well," Revue de l'Institute Franais du Ptrole, May-June 1977, pp. 307-47.

5. Lal, M., "Surge and Swab Modeling for Dynamic Pressures and Safe Trip Velocities," paper No. 11412, presented at the Society of Petroleum Engineers/International Association of Drilling Contractors Annual Drilling Technology Conference, New Orleans, Feb. 20-23, 1983.

6. Mitchell, R.F., "Dynamic Surge/Swab Pressure Predictions," Society of Petroleum Engineers Drilling Engineering, September 1988, pp. 325-33.

7. Clark, R.K., and Fontenot, J.E., "Field Measurements of the Effects of Drillstring Velocity, Pump Speed, and Lost Circulation Material of Downhole Pressures," paper No. 4970, presented at the Society of Petroleum Engineers Annual Meeting, Houston, Oct. 6-9, 1974.

The Authors

Zhong Bing works in the hydraulics department at Sichuan Union University. Previously, he worked as an oil and gas exploitation lecturer in the oil engineering department of the Southwest Petroleum Institute. He has authored more than 30 technical papers and reports on drilling engineering.

Zhou Kaiji has professorial rank in oil and gas exploitation in the oil engineering department at the Southwest Petroleum Institute.

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