Modeling Advances ER Openhole Horizontal Gravel Packing

Advances in drilling technology are producing record-breaking extended-reach (ER) wells. The record for -displacement from a floating installation has been pushed beyond 24,500 ft, and horizontal completions longer than 6,500 ft have become commonplace.

Well-completion technology is also evolving. To facilitate cost-effective well-construction programs, completions engineers are increasingly exploring materials science and incorporating computational/numerical-modeling techniques to anticipate induced material deformations from ER processes.

Sand-Screen Deployment

Many ER wells are openhole completions requiring sand management to guarantee trouble-free, interventionless production. Therefore, it is necessary to address the problem of sand-screen deployment and gravel placement.

In considering screen deployment, drag force on the screen must be analyzed. Greater well displacements imply higher total drag force. This force may become larger than the downward force available from the string weight, pre-venting the sand screen from reaching the required depth. Drag may also physically damage the sand screen. Reducing the drag force requires stronger, lighter screens and low-drag fluids.

Counteracting the drag forces exerted on openhole wells requires stronger, lighter screens and low-drag fluids. Meanwhile, circulating gravel packs are subject to the limitations of fluid frictional pressure loss during gravel placement vs. increased fluid leakoff and the fracture pressure of the exposed reservoir.

Placement fluids with low hydraulic frictional pressure loss are one avenue for study. Lightweight gravels requiring lower circulating rate for placement—and hence inducing lower friction pressures—are another.

Deepwater ER wells, in particular, are a significant challenge. These wells often have excessive fluid loss, variations in hole stability and hole geometry, and/or an extremely narrow window between bottomhole pressure and fracture gradient. The narrow pressure window, in particular, can be a significant concern because high pump rates required for long-distance proppant transport may fracture the formation, causing fluid loss and a sand bridge or early screenout during gravel placement.

The pumping boundaries for openhole gravel packing are Qmin, the rate at which a sand bridge is likely to form (typically considered to be a dune ratio of 85%), and Qmax, the rate that would result in formation fracturing pressure. Critical rates occur in washed-out hole sections and at extreme displacements, where Qmin can exceed Qmax.

Therefore, reducing Qmin is a critical element in planning a long, ER openhole gravel-packing operation. An ideal solution is to use the low settling velocities of reduced-density gravels. The issues affecting the suitability of these new materials are the main theme of this article.

Conventional gravels used for sand control have been sized natural sands and manufactured ceramics. The specific gravity (sg) of these materials varies between 2.65 and 2.71. For a typical wellbore configuration with an 8½-in. open hole, the ideal placement rate would be approximately 9.5 bbl/min, generating friction pressure greater than 5,000 psi in a borehole length of 5,000 ft. This additional pressure on the formation is generally well above the fracture pressure and would result in an aborted gravel-pack attempt.

Available lightweight gravels now have specific gravities of 1.75, 1.25, and as low as 1.08. A gravel of 1.25 sg could be emplaced in the typical wellbore example at a rate of only 3.4 bbl/min. These conditions would generate a pressure not much greater than 600 psi and create satisfactory operating conditions for a gravel pack. In fact, the technology has worked well in practice, as evidenced from results in six wells offshore Brazil and one in the Gulf of Mexico.

The lightweight materials still need to be fit for purpose from a sand-control viewpoint, and this requires under-standing the permeability changes in the gravels resulting from the internal stresses generated by increasing reservoir depletion and drawdown.

Stresses on Gravel Packs

Conventional gravel materials were engineered initially as proppants for hydraulic fracturing, and little attention has been paid to the stress analysis needed to assess these materials as potential gravel packs.

In an initial study by BJ Services, it was determined, as expected, that the stresses calculated in gravel-packing scenarios are far less than the stresses that would be induced on the proppant in hydraulic fracturing.

To evaluate the induced stresses on gravel in horizontal, openhole well configurations, a finite-element-analysis (FEA) model of the steady-state pore-fluid diffusion with stress was developed. The model has added a plasticity analysis of the gravel to determine if plastic straining will be induced with drawdown. The advantage of this model is that it can be used as a template to investigate sensitivity of well geometry, material parameters, and fluid flow for any constructed-well scenario. Also, the effects of compaction within the surrounding lithologies resulting from draw-down can be analyzed.

The basic input variables for the model are

Wellbore geometry (hole diameter, screen diameter, and screen eccentricity)
Material properties (reservoir rock, reservoir fluids, gravel, and screen)
Initial stress state (vertical stresses, horizontal stresses, and reservoir pressure)

Stress history or time dependence on temperature or other field parameters also can be included. Although a comprehensive laboratory data set of such parameters is desirable, sensitivity analyses on each variable can be performed.

Coupled Pore-Fluid Diffusion and Stress Analysis. The commercial software package ABAQUS was used to model a coupled pore-fluid-diffusion and stress analysis. This analysis has two components: a framework of the solid grains and the void space in between these, where liquid or gas may be present. This porous medium is modeled by attaching the finite-element mesh to the solid phase and allowing fluid flow through the mesh.

Permeability in ABAQUS is defined by Forchheimer’s law, which accounts for changes in permeability as a function of fluid-flow velocity. It can be isotropic, orthotropic, or fully anisotropic and is a function of void ratio, saturation, temperature, and other field variables. Assuming nonturbulent, low-velocity fluid flow, Forchheimer’s law reduces to an approximation of Darcy’s law.

Plasticity Modeling. To model the integrity and possible changes in permeability in the gravel resulting from drawdown pressures, an elastic/plastic material property was used. Laboratory analysis of the gravel under triaxial stress conditions at different confining pressures was conducted. The data are entered directly into ABAQUS to calculate the yield surface for the gravel. The yield surface determines the stress conditions under which the gravel will deform permanently and that ultimately will affect its permeability.

Model Capabilities. To illustrate the model capabilities, we used the following input variables:

Wellbore diameter=8.5 in.; screen outer diameter=6.4 in.; screen offset=0.75 in.
Initial effective overburden stress sigma1=3,200 psi; effective horizontal stress sigma2=2,200 psi.

Typical soft-rock and screen-material properties were used in addition to mechanical properties of various conventional and lightweight gravels determined in laboratory studies. Finally, drawdowns of 500, 1,000, 1,500, and 2,000 psi were induced in the system.

Model Output. As an illustration of model capabilities, output parameters for drawdowns of 500 and 2,000 psi are illustrated in Fig. 1. As shown in both models, the stress distribution is nonuniform. The greatest stresses on the gravel are in the lower portion of the pack (Figs. 1a, 1b ,1e, and 1f). The principal-stress directions are plotted at selected element locations for clarity. They are scaled to the greatest stress magnitude.

Fig. 1—Principal-stress magnitudes and directions for 500- (a–d) and 2000-psi (e–h) drawdown pressures.

For the 500-psi-drawdown model, the maximum-principal-stress direction is radial within the gravel pack and then undergoes a directional change to vertical within the formation (Figs. 1a and 1b). This is because of the decreasing influence of the drawdown pressure from the borehole toward the far field.

At 2,000 psi, the maximum principal stress is now in the tangential direction within the gravel pack (Figs. 1e and 1f). Also note the greater influence of the 2,000-psi drawdown within the formation proximate to the gravel pack (compare Figs. 1c and 1d with Figs. 1g and 1h).

Fig. 2 illustrates the changes on the stress state, pressure, and porosity of a lightweight-gravel material with a drawdown of 2,000 psi.

Fig. 2—Maximum (a) and minimum (b) principal stresses, von Mises stress (c), void ratio (d), and pore pressure (e) within the gravel pack for a drawdown pressure of 2,000 psi.

A significant result of this study is that plastic deformation is not initiated in the gravel pack. None of the model runs predict plastic straining in the gravel pack at the emplacement stage, or at substantial drawdown pressures. However, a measure of deviatoric strain may be helpful in identifying locations of potential failure and permeability changes within a gravel pack of different material properties.

Von Mises (deviatoric) stress and void ratios are calculated for each drawdown pressure. The highest values of von Mises stress would indicate where failure would likely occur first within the gravel pack. This area is at the bottom of the gravel pack. As the void ratio is dependent on the von Mises stress, the same area within the gravel pack shows the high-est deviation from the original void ratio. In the lower area of the gravel pack, the void ratio decreases with increasing drawdown pressure—indicating a decrease in porosity and permeability within the gravel pack. However, even at the upper limit of 2,000-psi drawdown, the change in porosity within the gravel pack calculated from the model amounts to less than 4%.

Additions to the Existing Model. The results from this study assume constant fluid-flow properties within the screen, gravel pack, and formation. Only the material properties of the gravel pack under drawdown pressure were investigated to date. With the existing model, sensitivity studies for changes in reservoir stress state, as well as fluid viscosities and permeability differences between materials, can be readily analyzed. It is possible to develop a suite of model studies, wherein a single model parameter is varied with constant conditions in other parameters, to define the role of each component in the model with changes in reservoir depletion and drawdown.

Further Work. In addition to FEA-model enhancements, experimental work is ongoing to determine the changes in permeability of gravels with changes in triaxial stress. With these powerful computational models, coupled with permeability and stress data, it will be possible to screen newer lightweight-gravel materials to ensure that they help to maintain optimum well productivity for the next generation of extreme-ER wells.

Information provided by Andy Jordan, John Panian, and Russ Maharidge, BJ Services.