Chemical agents capable of sealing pores and micro-fractures can be used to solve wellbore instability in shales. Nanomaterials, as sealing agents, have been applied to test fluids, and their wellbore strengthening effects were evaluated by triaxial tests. A recommended workflow is given to first conduct pore pressure transmission tests, and then perform triaxial tests to evaluate the influence of drilling fluids (sealing agents) on the strength of shales. Due to the low permeability of shales, the small sample (0.25 in. height and one in. diameter) is used in pore pressure transmission tests. This research gives special loading to handle small samples in triaxial testing and innovative calculation procedure to produce stress-strain curves for the shales. After Pore Pressure Transmission (PPT) tests with nanoparticles of various sizes (10, 40 nm), concentrations (3%, 10%), and types (aluminum oxide, magnesium oxide), triaxial tests were performed on Mancos Shale and Eagle Ford Shale. The best combinations for increasing UCS values (Uniaxial Compressive Strengths) are 10% 40-nm Al2O3 for Eagle Ford Shale and 3% 40-nm MgO for Mancos Shale, according to our test matrix. As shown by the experiments, the application of the appropriate nanoparticles on shales will improve their strength and reduce the risk of wellbore collapse. The methodology developed in this research can be extended to triaxial testing on cuttings-size samples, which provides useful rock characterization information for samples that do not meet standard testing conditions.

Summary In this paper, an extensive series of experiments was performed to investigate the evolution of poromechanical (dry, drained, undrained, and unjacketed moduli), transport (permeability), and strength properties during reservoir depletion and injection in a high-porosity sandstone (Castlegate). An overdetermined set of eight poroelastic moduli was measured as a function of confining pressure (Pc) and pore pressure (Pp). The results showed larger effect on pore pressure at low Terzaghi’s effective stress (nonlinear trend) during depletion and injection. Moreover, the rock sample is stiffer during injection than depletion. At the same Pc and Pp, Biot’s coefficient and Skempton’s coefficient are larger in depletion than injection. Under deviatoric loading, absolute permeability decreased by 35% with increasing effective confining stress up to 20.68 MPa. Given these variations in rock properties, modeling of in-situ-stress changes using constant properties could attain erroneous predictions. Moreover, constant deviatoric stress-depletion/injection failure tests showed no changes or infinitesimal variations of strength properties with depletion and injection. It was found that failure of Castlegate sandstone is controlled by simple effective stress, as postulated by Terzaghi. Effective-stress coefficients at failure (effective-stress coefficient for strength) were found to be close to unity (actual numbers, however, were 1.03 for Samples CS-5 and CS-9 and 1.04 for Sample CS-10). Microstructural analysis of Castlegate sandstone using both scanning electron microscope (SEM) and optical microscope revealed that the changes in poroelastic and transport properties as well as the significant hysteresis between depletion and injection are attributed to the existence and distribution of compliant components such as pores, microcracks, and clay minerals.

One way to reduce wellbore instability in shales is to use agents capable of sealing pores and micro-fractures. The main objectives are 1) to perform pore pressure transmission experiments with test fluids containing nanomaterials, and 2) to develop a model to characterize pore pressure transmission with pore plugging. Pore pressure transmission experiments were performed on two types of shales, Mancos Shale and Eagle Ford Shale, using test fluids containing nanoparticles. An orthogonal test matrix has been developed, which includes different nanoparticle sizes (10 nm, 20 nm, 40 nm), particle types (aluminum oxide, magnesium oxide) and particle concentrations (3 %, 10 %). A mathematical model that incorporates chemical potential, pore plugging, and time-dependent permeability is developed to characterize pore pressure response. The best combinations to decrease pore pressure at the equilibrium state, according to the test matrix, are 10 % 10 nm Al2O3 for Eagle Ford Shale and 10 % 30 nm Al2O3 for Mancos Shale. This nanoparticle-based plugging technique will minimize pore pressure transmission and delay the time to equilibrium, reducing hydration and swelling problems in shale formation. As a result, this research will help to better define drilling fluid properties to enhance wellbore stability in actual wells containing shales.

Abstract Frequently, shales are treated as isotropic formations. However, organic rich shales are anisotropic due to their laminated structure and chemical properties. In this study, shale mechanical properties with respect to different bedding plane orientations was studied. The goal of this study is to evaluate anisotropic mechanical properties of shale by triaxial tests and to predict these properties by well logging data along with a 3-D transversely-isotropic wellbore stability analysis (WBS) in Bakken formation. Shale samples were prepared with bedding plane angles equal to 0, 45, and 90 degrees. Young's modulus, shear modulus, and Poisson's ratio in different directions were measured. Parameters of stiffness tensor were calculated by mechanical properties. The compressive strength of shale samples was measured under different confining pressures: 0, 500, 1000, and 1500 psi. Simple Plane of Weakness was applied to describe shear failure mechanism. Well logging data was used to connect experimental and field data. Next, a three-dimensional numerical wellbore stability model based on finite difference method was used to evaluate stress and deformation alterations due to drilling of vertical to extended reach wellbores in Bakken formation, Williston Basin, North Dakota. Both anisotropic and isotropic conditions were considered and the Mohr- constitutive relations were implemented in the numerical model. Vertical Young's modulus (perpendicular to the bedding plane) found to be smaller than horizontal Young's modulus (parallel to the bedding plane). Shale is a transversely isotropic rock; which isotropy plane is generally the bedding plane. The result of tests for stiffness tensor showed that the shale can be characterized by only five independent stiffness constants. The Simple Plane of Weakness model is suitable to estimate shale anisotropic compressive strength. The P-wave velocity calculated from the stiffness tensor is a used to connect the experimental data and field data. P-wave velocity is increasing as the bedding inclination angle increases. The predicted compressional wave velocity for a 45-degree inclination angle showed a perfect fit with the field logging data. Steps of inverse sonic log data to stiffness parameters were shown by a flow chart. From the WBS model, the effects of anisptropy on stress distribution and wellbore convergence was investigated for two different constitutive models: isotropic model (IM) and transversely isotropic model (TIM). It was found that neglecting shale anisotropy will lead to erroneous prediction of wellbore deformation.

A cuttings bed formed on the lower side of the wellbore is the most common drilling problem confronted when horizontal or highly deviated wells are drilled. The phenomenon is undesirable and has a detrimental effect on wellbore hydraulics and drilling performance. To achieve an efficient drilling operation, hydraulics optimization should be implemented by precisely predicting annular pressure loss and other hydraulic parameters. The accumulation of cuttings at the lower side of horizontal or highly inclined wellbores, combined with wellbore eccentricity and fluid rheological properties, create a complex behavior of pressure loss. In this study, a numerical approach is used to investigate the influence of the aforementioned factors. A numerical solution is performed for laminar flow of non-Newtonian fluids. A non -orthogonal, boundary-fitted curvilinear coordinate is developed, which is based on elliptic partial differential equations (PDE) to accommodate annular flow geometry with arbitrary cross-sections. Finite difference numerical schemes adapted to the coordinates is then used to analyze the problem. The numerical model determines the effect of hydraulic parameters of fluid flow thorough an irregularly shaped annulus and considers the following factors: flow rate, fluid rheological parameters, annular geometry and bed appearance. Numerical predictions from the model are verified against existing models and experimental data in literature; and good agreements are obtained. The developed numerical model can be combined with a 1-D solids transport model for designing oil and gas well drilling operations.

This work presents an analytical solution for an inclined wellbore drilled in a fractured formation displaying a high contrast between the diffusion rates in the fractures and in the porous matrix, with the latter treated as a storage phase and thus not participating in the fluid transport. This scenario may result from different mud cake building rates, and/or adverse wettability of the rock matrix with respect to the drilling fluid being used. Different from the models available in the literature, the fractures are characterized by a more realistic finite radial fluid discharge (namely, the fractures network hydraulically connected to the wellbore is of limited extent). The models output in terms of pore pressures, total stresses and effective stresses response has been compared with the results of a widely accepted dual-porosity/dual-permeability model. Major differences and asymptotic behaviors have been analyzed. Subsequently, the results of the model have been used to perform a comprehensive wellbore stability analysis. The effect of time dependency, fractures network length and rock properties on the instability of the borehole have been investigated, and upper and lower mud weight bounds have been determined using several failure criteria. This investigation shows that under the specified conditions where dual-porosity/single-permeability conditions arise, the proposed model provides with theoretically more conservative mud weights predictions.

This paper studies the integrated effect of double cutters on cutting rock. The rock being cut is subjected to hydrostatic pressure. Double cutters paralleled to each other and separated with a distance are advancing in the same direction and removing rock materials over constant depths of cut. The integrated effect indicates the situation where stresses in rock induced by double cutters can be large enough to even fragment the rock between double cutters. Once this happens, double cutters will have a large cutting area, thus increasing cutting efficiency. A cutting model is built in this paper to study the integrated effect of double cutters. The model calculates coupled stresses and pore pressure in the rock induced by double cutters and predicts cutting forces and MSE. The influences of depths of cut and cutter interval on the integrated effect are discussed. The MSE of double cutters is compared to that of a single cutter under the same cutting condition. Case studies on Indiana limestone show that when the depths of cut are large and the cutter interval is small enough, the integrated effect of double cutters can help reduce the MSE by 5-25 percent. Results in this paper can provide new insights on bit-rock interaction and PDC bit design.

Fracture-based wellbore strengthening is a widely used preventive technique for lost circulation control. However, there were limited experimental studies on wellbore strengthening with an anisotropic stress state. In this paper, we describe an experimental investigation of fracture-based wellbore strengthening on cubic Berea sandstone samples (size of 12 in(3)) using a large-scale true triaxial cell. The true triaxial cell allows fracture containment to simulate wellbore strengthening, which was not available using a traditional small-scale traixial cell. We used drill cuttings and Chevron loss prevention material (LPM) as wellbore strengthening materials (WSM). Three independent stresses were applied on the rock samples and bi-wing fractures were generated. The final fracture reopening pressure (FROP) exceeded the formation breakdown pressure (FBP) after plugging the WSM. Further comparison between the experimental results and modeling results from a numerical model shows a good match for the injection pressure profile.

When cutting a saturated rock under pressure, the PDC cutter is not only fragmenting the rock matrix, but also driving the pore fluid ahead of it. Because of the solid-fluid coupling in rock, different pore pressures induced by cutter will affect rock failure and lead to different MSE. The fact that cutting process is influenced by the pore pressure response in the rock is referred to as poroelastic effects in this paper. This paper continues the research in our previous work (Chen et al., 2018) and gives more insights into the poroelastic effects during rock cutting process. The influences of rock diffusivity coefficient and cutter speed are studied. The results show that the two parameters will affect pore pressure response in rock and further affect rock failure and MSE during cutting process. Based on the results, the cutting process can be identified as three conditions: undrained, drained and a transition zone between undrained and drained condition. In undrained and drained condition, MSE will be independent of cutter speed; while in transition condition, MSE decreases with increasing cutter speed. The transition boundaries for the three conditions are given. Cavitation in intact rock during cutting process is also studied. The results show that cavitation is easy to occur when cutting a hard rock with low original pore pressure. Cutting tests were conducted on Torrey Buff sandstone and Carthage marble to verify the poroelastic effects in cutting process. A good agreement between the model results and experiments is found. In general, the results in this paper can give a good understanding on the combined influence of formation permeability, depth of cut and RPM on cutting rock during drilling.

Abstract Lost circulation is one of the most costly drilling issues and a major contributor of non-productive time. Wellbore strengthening has been successfully applied to reduce the associated cost and increased the wellbore stability in the industry over the past two decades. It is of critical importance to accurately predict the extra drilling mud weight after wellbore strengthening. However, previous research assumed fixed boundary conditions and only considered the stress intensity factor in the calculation of fracture reopening pressure (FROP). The change of pressure boundary on the fracture surfaces was ignored, which may overestimate the FROP. This paper employed a dislocation-based fracture model to determine the FROP in wellbore strengthening. The proposed model is compared with finite element simulation. An excellent match is obtained for the fracture profile and a clear inflection point can be observed between the plugged zone and unplugged zone. We present how wellbore pressure can change the pressure boundary in the model. Thus, the FROP calculation should be modified with the consideration of fracture plug width. Results show that the fracture plugged zone pressure can affect the fracture profile. Specifically, lower fracture plugged zone pressure results in higher FROP. Thus, better wellbore strengthening can be achieved in the depleted sections during drilling. On the other hand, the fracture plug width plays an important role in determining FROP. With a fixed fracture plug location, larger fracture plug width can lead to higher FROP. However, there exists a critical fracture plug width for the maximum FROP, which is the value predicted by the previous research. The study reveals the importance of fracture plugged zone pressure and fracture plug width for FROP in wellbore strengthening. The model is useful for the design of wellbore strengthening materials (WSM), which are critical to achieve the best wellbore strengthening effects.

The low density enables lightweight cement to be an ideal candidate for petroleum drilling in depleted formations. Lightweight cement is able to tolerate more deformation due to its high strain capacity. The major challenge, however, is its relatively low strength properties. Carbon nanotubes (CNTs) have been used in multiple industries to improve the strength, strain capacity, and durability of materials. In this study, the effect of CNTs on the mechanical properties of lightweight cement under triaxial loading conditions was analyzed. Two different lightweight cement systems, foam and microsphere cements, mixed with multi-walled carbon nanotubes at the concentration of 0.5%wt. were investigated and compared to conventional cement. Young's modulus, compressive strength, brittleness and strain capacity were measured under elevated confining pressures. Permeability and splitting tensile strength were calculated based on test data. Results suggest that the addition of CNTs to the lightweight cements enhances the compressive and splitting tensile strength, Young's modulus, strain capacity and ductility, while it decreases the permeability. Moreover, Scanning Electron Microscopy (SEM) was employed to analyze the dispersion of foam, microspheres and CNTs in cement composites.

Cutting rock in pressurized conditions is essentially different as compared to the ambient conditions. Under pressurized condition, cutter is not only fragmenting the rock matrix, but also driving pore fluid to flow forward. Due to the coupling of stresses and pore pressure, the pore pressure change caused by cutter will affect effective stresses in the rock and eventually affect mechanical specific energy (MSE). The change in stresses and pore pressure caused by cutter movement are the poroelastic effects in cutting process. To study pressurized cutting process, we developed a cutting model based on the theory of linear poroelasticity. The model can predict coupled stresses and pore pressure in the rock and give a better understanding of the poroelastic effect in the cutting process. To obtain the desired solution, a Fourier Transform is employed. After the analytic solution in Fourier space is obtained, a Discrete Fourier Transform is employed to numerically invert the solution back to the real space. The Mohr-Coulomb failure criterion is also introduced to determine failure of the rock ahead of the cutter. Eventually, the model can predict cutting forces and MSE in pressurized cutting process. The model is also compared to the published experimental data and a good consistency between model and experiment results was found. The influence of hydrostatic pressure and the existence of cuttings on MSE are studied and poroelastic effect during cutting process is also discussed. The results in this paper can be applied to bit-rock interaction in well drilling.

Wellbore stability remains as one of the major challenges to drilling engineers. Results of recent survey showed about one third of non-productive time of drilling operation is classified as borehole problem, where a significant part is attributed to borehole instability. The thermal regime of a formation in the vicinity of a wellbore affects the stability of the well significantly during drilling operations, especially in High pressure High Temperature (HPHT) wells. This paper describes how the thermal behavior of a tubular-wellbore-reservoir system is altered during mud loss, as well as its consequent impact on near-wellbore state of stresses and critical mud weights. A fully coupled three dimensional thermal-poro-elastic model, integrated with a transient tubular-wellbore-reservoir heat flow model, is developed to evaluate near-wellbore stresses and pore pressure redistribution during mud loss. The forced convective heat transfer coefficients in both conduits-drillpipe and annulus-are rigorously determined as a function of local flow and fluid properties. The results reveal that continuous mud loss destabilizes the wellbore as the pressure window shifts considerably over time. Critical mud weights for both tensile and compressive failures decrease during mud loss over the entire length of the wellbore, in addition to the point of loss. During severe losses, the fracture gradient at the bottom of the well can decrease by over 1 ppg within the first hour. This can intensify the existing fracturing condition and allow the development of new fractures at other locations, which leads to further losses as time progresses. This model enables prediction of a more realistic operating window during lost circulation by taking additional thermally-induced effects into account. In addition, failure indexes during mud loss considering P-rho-T coupling effect on a compressible mud column in the annulus are investigated with the proposed model. During drilling operations, especially Managed Pressure Drilling (MPD) and offshore applications with moderate to severe mud loss, the operation window should be modified by taking mud loss-induced thermal stresses into account. The mud type, wellbore geometry, circulation rate, and other parameters affect the magnitude of shift in critical mud weight during mud loss, hence evaluations should be based on specific cases.

Solids suspension has broad applications in the oil and gas industry (i.e., sand production, cuttings transportation during drilling, and barite sag in drilling fluids). The conventional modeling approaches for solids suspension and transportation include mechanics models (i.e., layer models) and computational fluid dynamics (CFD) based Eulerian-Lagrangian models. One of the most important assumptions for these approaches is that the solid particles have uniform size, which is not true in the actual applications. The computational fluid dynamics/discrete element method (CFD-DEM) approach can track each single particle in the system; however, the computational time is not practical for industrial applications. This paper presents a relatively simple Eulerian approach for characterizing solids suspension in multiphase flow systems. The multiphase flow equations are derived by using a proper averaging procedure without considering interphase mass transfer. A proposed new solids suspension model, which is based on the fluid-solid interaction and kinetic theory, account for multiple solids sizes in the flow. The suspension characterizations for particles with different sizes are considered by introducing a particle size distribution function, which also captures detailed particle distribution and fluid/particle and particle/particle interactions. Therefore, a more realistic solids transportation prediction can be achieved. A simulation package is developed by solving the model using the finite difference method. The boundary-fitted coordinate system is applied to integrate the irregular geometry caused by drillpipe eccentricity and a packed solids bed. The influence of the solid phase on the carrier fluid is considered, and solid-liquid two-way coupling is implemented. The simulation package has been used for transient hole cleaning simulations during drilling. Simulation results show that cuttings’ backsliding makes the hole cleaning process in intermediate inclined wells different from that in horizontal and highly inclined wells. The cuttings movement in this part of the well follows the two-steps-forward, one-step-back routine. Well packoff is also captured by the program for improper hole cleaning operations in an intermediated inclined position. Transient hole cleaning tests were conducted on a 90 ft long, 8 × 4.5 in. flow loop. Experimental data are compared with the simulation results, and good matching is obtained. This method can also be used as a general tool for solids suspension and transportation simulation in multiphase systems.

This study concentrates on the use of materials known as hollow glass spheres, also known as glass bubbles, to reduce the drilling fluid density below the base fluid density without introducing a compressible phase to the wellbore. Four types of lightweight glass spheres with different physical properties were tested for their impact on rheological behavior, density reduction effect, survival ratio at elevated pressures, and hydraulic drag reduction effect when mixed with water-based fluids. A Fann75 high pressure high temperature (HPHT) viscometer and a flow loop were used for the experiments. Results show that glass spheres successfully reduce the density of the base drilling fluid while maintaining an average of 0.93 survival ratio, the rheological behavior of the tested fluids at elevated concentrations of glass bubbles is similar to the rheological behavior of conventional drilling fluids and hydraulic drag reduction is present up to certain concentrations. All results were integrated into hydraulics calculations for a wellbore scenario that accounts for the effect of temperature and pressure on rheological properties, as well as the effect of glass bubble concentration on mud temperature distribution along the wellbore. The effect of drag reduction was also considered in the calculations.

Inaccurate calculation of settling and slip velocities of cuttings leads to inaccurate determination of cuttings concentration and, hence, borehole pressure, as well as inaccurate lag times. To minimize these problems, an understanding of the relation between drilling fluid characteristics and the cuttings transport process is essential. It is desirable for drilling fluids to form a gel structure to help cuttings transportation and suspension of solids. The gel structure development is proportional to increase in aging time. The increase in aging time yields higher shear stress responses at a constant rate of deformation to the drilling fluid sample. The gel structure development helps keep cuttings in suspension and shows a viscoelastic response to small deformations. Understanding these viscoelastic responses is important in rheological characterization and settling velocity prediction. Thus, viscoelastic drilling fluid characteristics should be investigated in depth to better estimate settling and slip velocities of cuttings and to increase cutting transport efficiency. The main focus of this project is to work on viscoelastic and time-dependent fluid characterization to identify the relation between rheological properties and settling velocities of cuttings. Rheological experiments were conducted using an Anton Paar Physica MCR 301 Rheometer. Three different drilling fluids, Water Based Mud (WBM), Oil Based Mud (OBM) and Synthetic Based Mud (SBM), are used for rheological and settling velocity experiments. Stress Overshoot Tests (SOTs) and Steady-Shear experiments were performed to investigate viscoelastic properties and gel structure of the fluids, and to examine time and temperature dependence of WBM, OBM and SBM. Information obtained from the viscoelastic and time-dependent fluid characterization tests was coupled with settling velocity data using both arbitrary shape of cuttings and spherical particles. A mathematical model that considers viscoelastic properties and time dependency of drilling fluids was developed to estimate settling and slip velocities of the cuttings. Comparisons between the proposed models and existing models based on standard rheological measurements were also done. The results show that the proposed model has good agreement with the experimental data.

Fracture-based wellbore strengthening techniques are preventive methods that can reduce the cost of lost circulation and non-productive time. The mud weight window can be extended by plugging fractures with wellbore strengthening materials (WSM) in the near-wellbore region. To maximize the strengthening effect, accurate fracture geometry prediction is of critical importance to the design of WSM. This paper presents a novel, coupled fluid flow and fracture mechanics model for wellbore strengthening applications that accounts for near-wellboreinduced fracture behavior. For fluid flow, mass conservation is considered and momentum conservation is examined; the latter shows that pressure loss with near-wellbore fracturing is low. Thus, we can neglect the pressure drop in the fractures and assume the fluid pressure inside the fractures is equal to the wellbore pressure. The pressure-width relationship (rock elastic deformation) and stress intensity factor are obtained by a dislocation- based approach. For the fracture propagation criterion, the calculated stress intensity factor is compared with fracture toughness at each time step. The stress intensity factor and fracture reopening pressure (FROP) are verified with Tada's model and Feng's model, respectively. Then, simulation results are compared with the large leak-off solutions of the Perkins-KernNordgren (PKN) fracture model. The simulation results reveal that the PKN model overestimates the fracture mouth width, fracture length, and wellbore pressure. Furthermore, the simulation results of wellbore pressure show a different trend. Therefore, we cannot directly use the PKN model to design wellbore strengthening applications. The main reason is the presence of wellbore can generate near-wellbore effects that cannot be disregarded. Finally, we conduct a comprehensive parametric study (i.e., fracture toughness, Young's modulus, Poisson's ratio, horizontal stress ratio, and permeability) on wellbore strengthening fracturing. The proposed model is useful for wellbore strengthening applications using the intentionally induced fractures (i.e., near-wellbore fracturing). Particle size distribution (PSD) of WSM can be designed based on the simulated fracture geometry. No complex model mesh generation or assignment of boundary conditions are needed, which are commonly used in finite element simulation or other numerical methods. The proposed model can also be used to optimize wellbore strengthening operations by performing sensitivity analysis.

SummaryIn this paper, a set of charts is developed to allow drilling engineers to quickly estimate the cuttings volumetric concentration in the wellbore. The most-important parameters for hole cleaning are divided into several ranges on the basis of their sensitivity to cuttings concentration in the wellbore. A series of charts is obtained by running a hole-cleaning simulator, which is based on a large number of experimental and modeling studies of cuttings transport. The difference between the charts’ prediction results and experimental data is within 20%. Drilling engineers can quickly estimate the cuttings volumetric concentration by looking up the charts and conducting very-simple calculations.