Two complementary tools are taking the guesswork out of wellhead stress modeling and management, making intervention operations safer than ever before.

With increasingly complex well servicing operations being carried out, wellheads, normally designed to support little more than a Christmas tree, are being put to the test, especially on floating production platforms.

But along came massive snubbing units and coiled tubing (CT) injector heads. Engineers, contemplating all that weight balanced atop their wellheads, became concerned about the stresses being imposed. Simple axial stress, due to the weight of the equipment and the vertical component of guyline tension, became more complex when bending moments from sideward sway were factored in. And, with CT units, variations in reel back tension (RBT) caused additional cyclic sway toward and away from the tubing reel. When units were deployed from floating platforms, stresses became so complex that a formal project was undertaken to analyze and model them.

Enter Zeta

CTES of Conroe, Texas, developed two complementary tools to measure and model wellhead stress. The Zeta model is a software package containing a finite element analysis (FEA) that can be used for both pre-job analysis and design or for real-time stress monitoring during the job. The model calculates the stresses throughout the entire stack and warns the user when a stress limit is exceeded. For pre-job design applications, the Zeta model helps the user select the proper equipment and support system configuration (guy wires, crane, etc.) to ensure the job is designed with an adequate safety margin. On critical jobs where real-time stress monitoring is necessary, the model receives the force values from the Zeta gauge and then calculates the stress profile of the entire stack. Inputs to the model include all gauge values as well as crane and guyline loading, reel back tension, hanging weight of the CT string in the well and internal pressure/temperature. Thus, in addition to calculating the expected range of lubricator stresses prior to rig-up, the Zeta model acts as a dynamic safety monitor and alarm device during wellsite operations.

One particularly innovative and useful pre-job modeling feature of Zeta is its ability to model wellheads and offshore structures that are moving independently of each other. For example, the wellhead and topsides of a tension-leg platform or spar might both be moving in a figure eight pattern, but with differing amounts of total horizontal displacement and with differing periods. In spite of this independent movement, conventional rig-up procedures require each end of a well intervention lubricator to be attached to each of these moving structures. Furthermore, lubricator movement is routinely constrained as it passes through various deck levels of the floating structure, which makes the stress calculation even more challenging. However, the Zeta model can calculate the stress level along the entire length of the lubricator for this type of scenario with ease.

The second component of the Zeta Safety System is the Zeta gauge, which is used on critical jobs where real-time stress measurements are monitored. The gauge consists of a 2-ft (.61-m) long, 41/16-in. lubricator spool with studded API flanges on each end. It contains three axial fiber optic strain gauges spaced 90? apart around the center of the lubricator. In addition, it has a temperature gauge and an internal pressure monitor. All gauges are connected by a fiber optic cable to a control box that contains a microprocessor. In the microprocessor, real-time axial force is calculated as well as bi-directional bending moments. Data from the microprocessor is routed by serial cable to a PC, where it interfaces with the Zeta model to display calculated stress along the entire length of the stack.

Measurements are defined as follows:

• Axial force, measured in the X-direction with +X defined as vertically up the center of the lubricator stack. The axial force component of internal pressure is removed, so the reported axial force does not vary with changes in internal pressure.
• Bending moment in the Y-direction, defined as motion toward and away from the coiled tubing reel.
• Bending moment in the Z-direction, defined as side sway 90° to the left or right of the Y-direction.

The Zeta gauge is installed as close as possible to the area of maximum lubricator stress, as identified during pre-job design with the Zeta model.

Model accuracy

Some interesting facts emerged during Zeta model validation which illustrate the complexity of the problem solved by the tool. A simple textbook case was analyzed with the model, consisting of a vertical steel pipe rigidly supported at the bottom end, with half-inch wall thickness, 50-ft (15.25-m) long and 4 in. in diameter. The pipe's density was 0.283 lb/cu in. (38 g/cc), yield stress was 75,000 psi, the modulus of elasticity was 30 million psi and Poisson's ratio was 0.3.

The model divides the pipe into 50 sections or elements, each 1 ft (.3 m) long, and considers the center of each element to be a "node." This approach is important later for dynamic modeling. The true total weight of the pipe is 933.5 lb, thus each element weighs 18.7 lb. Since half of the weight of the bottom element is below the node, the model sees the total weight of the pipe as 924 lb.

Theoretically, if you push 100 lb in the Y-direction at the top of the 50-ft (15.25-m) pipe, you should create a bending moment of 5,000 ft-lb. However, this calculation ignores the weight of the pipe. The model, gives a much more accurate answer - 5,979 ft-lb. Similarly, the theoretical solution for deflection of a cantilever beam under these conditions shows lateral displacement of the top of the pipe to be 27.94 in. The model calculates 33.4 in. To validate these findings, one only needs to multiply the average of the Y-displacements calculated by the model at each node (1.056 ft or .32 m) by the pipe weight (933 lb) to get the bending moment due to pipe weight - 985 ft-lb. Adding this to the theoretical moment (5,000 ft-lb) yields 5,985 ft-lb - within 0.1% of the moment calculated by the Zeta model. Ignoring the weight of the equipment (as in the theoretical case) caused the bending moment to be underestimated by almost 20%.
When dynamics are factored-in, the effect of equipment weight becomes even more significant. Finite difference equations are used to calculate the acceleration components that are used by the stiffness matrix of the finite element analysis (FEA). The FEA is then used to calculate the displacements for the next time step. Using the Zeta model, the effects of vibration can be accurately simulated by using its dynamic capabilities to determine the structure's natural vibration frequency under all the applied loads as set by the user. The node with the largest apparent displacement is identified. Then the model drops all loads to zero, causing the (modeled) structure to vibrate. The motion of any selected node can be tracked and its frequency of vibration calculated. The user can examine several different modes of vibration simply by changing the applied loads set at the beginning of the simulation.

The purpose of the dynamic calculation is to ensure that the momentum effects of large stack components like injector heads and BOPs are correctly factored into the force calculations. Additionally, it allows the user to anticipate incipient destructive conditions - for example, if the natural vibration frequency should correspond to the surging of the CT reel, a dangerous unstable condition could result.

The Zeta model looks for the practical solution to the dynamic environment. It determines the lesser of the weights that lead to yielding or buckling and warns the user that a dangerous condition exists.

Field test results

The Zeta Safety System was field tested recently by BP using CT equipment supplied by Halliburton on a land well in West Texas. The smallest element in the stack, the Zeta gauge is capable of withstanding almost 1 million ft-lbs of axial force and a bending moment of about 87,500 ft-lb. At all times during the test, stresses were less than 30% of the calculated yield stress of the equipment. Dynamic forces were attributed to increasing axial force as more CT was spooled off into the hole, and an oscillating Z-moment from fleet angle variations during spooling. As expected, the Y-moment varied due to periodic surges in reel back tension. Expected step changes in Y were recorded when the CT spooling changed directions.

Throughout CT operations, the Zeta gauge provided realistic measurements of bending moments, axial force and internal pressure.

On its initial test, the actual rig-up did not match all the components stored in the database, as was expected. The user made simple additions to the model hardware toolkit while onsite and took about 1 hour to bring the model into congruence with actual field conditions. Once all components were created, guyline tensions, crane supports and weights of hydraulic hoses were factored in, along with the forces of reel back tension.

Zeta system accuracy was illustrated upon initiation of field operations on the third day. The measured stress levels were significantly different than what was observed during the prior two days. By analyzing the stress curves, the change in the lubricator stress levels was traced to the fact that crane hydraulic pressure had bled off during the night. The condition was easily compensated by increasing crane tension, and the model readings returned to normal.

The model was run in real-time during the operation and despite the unknowns (specifically guyline tension) it was possible to match Zeta gauge results with actual string weight from the crane and CT unit weight indicators. The only differences observed resulted from stuffing box friction, seen by the weight indicator, but not affecting axial force measured by the Zeta gauge, and variations in crane tension, which affect Zeta, but not the CT weight indicator.

Promising conclusions

There are several areas that BP views will be of value for well servicing operations. Wellhead movement on floating platforms can be measured for a variety of operating conditions to help understand the possible extent of loads when intervention risers are used. Those loads are estimated values that can help in job design and planning, but as with all calculated estimates, it is important to determine how they represent actual conditions. This tool should also provide insight to the way operational parameters can affect the system. Riser configuration and support from crane or motion compensator devices can be evaluated for a variety of conditions including wellhead movement, system pressure and tension/compression from the crane or compensator. The ability to incorporate real-time data for comparison to pre-job planning and design is a vital part of operational success to understand the nature of a problem. Once a true understanding of a problem has been achieved, there is always a way to manage its impact on value to operations.

For its part, CTES observed that the Zeta gauge performed well, providing interesting measurements for monitoring stack stresses at the point of the gauge. Rig up and operation of the gauge were straightforward and simple. By detecting the bleed-off of the crane hydraulics, the gauge proved itself as a useful safety monitor.

Unlike the model, the Zeta gauge does require a trained operator to set up and monitor the stress values in real-time. Transducers measuring guyline and crane tension should be utilized. Once the Zeta Safety System was properly set up, it performed as designed. It calculated Von Mises yield stresses in the stack, and even though these were well below safety limits, the system proved its ability to provide adequate warning should stresses approach dangerous conditions.

Comments