Alexandre Lavrov

Radial Flow of Non-Newtonian Power-Law Fluid in a Rough-Walled Fracture: Effect of Fluid Rheology

Fluid flow in a single rough-walled rock fracture has been extensively studied over the last three decades. All but few of these studies, however, have been done with Newtonian fluids and unidirectional flow in rectangular fractures. Notwithstanding the importance of such setups for theoretical understanding of fundamental issues in fracture flow, practical applications in drilling and petroleum engineering often involve radial flow of a non-Newtonian fluid. An example is a borehole intersecting a natural fracture during drilling in a fractured rock. In this study, steady-state incompressible radial flow from a circular well into a self-affine rough-walled fracture was simulated numerically using the lubrication theory approximation. The fluid rheology was power law. The flow behavior index was equal to 0.6, 0.8, 1.0 (Newtonian), 1.2, or 1.4. Asperities diverted the flow from an axisymmetric radial pattern that would be observed in a smooth-walled fracture. The extent of the deviation from radial flow was found to increase as the fluid became more shear-thickening. To reveal finer details of the flow, a tracer was introduced at the borehole wall and was transported by the flow. The front of the tracer propagating into the fracture was found to become slightly smoother with a more shear-thickening fluid. In the vicinity of contacts between fracture faces a more shear-thickening fluid could deliver the tracer closer to the contact spots.

Fracture permeability under normal stress: a fully computational approach

Fractures contribute significantly to the overall permeability of naturally or hydraulically fractured reservoirs. In the cap rock, fractures may provide unwanted pathways for reservoir or stimulation fluids. Predicting fluid flow in naturally fractured rocks under production or fluid injection requires that permeability of a single, rough-walled fracture be well understood and accurately described as a function of the effective stress. The lack of information about the properties of fractures at depth calls for a numerical approach that would enable predicting the fracture permeability as a function of the effective normal stress. Such fully computational approach is developed in this study. The fracture deformation is calculated by solving the contact problem using the finite-element method. At each deformation step, the steady-state fluid flow in the fracture is computed in two orthogonal directions using the lubrication theory approximation, in order to evaluate the permeability and the hydraulic aperture of the fracture. The computational approach is tested on two examples: a ‘brittle rock’ (linear elastic) and a ‘ductile rock’ (linear elastic perfectly plastic). Both mechanical and hydraulic behaviours of the fracture under cyclic normal loading are found to be in qualitative agreement with the results obtained in a number of published experimental studies. The computational approach provides an insight into the actual mechanics of the fracture deformation under stress, and the effect of the latter on the permeability. In particular, hysteresis in the fracture roughness is obtained with the ‘ductile rock’, suggesting that (at least some) fractured rocks may retain ‘memory’ about their loading history imprinted in the fracture landscapes.

Numerical modeling of non-Newtonian fluid flow in fractures and porous media

Non-Newtonian fluids having Bingham or power-law rheology are common in many applications within drilling and reservoir engineering. Examples of such fluids are drilling muds, foams, heavy oil, hydraulic-fracturing and other stimulation fluids, and cement slurries. Despite the importance of non-Newtonian rheology, it is rarely used in reservoir simulators and fracture flow simulations. We study two types of non-Newtonian rheology: the truncated power-law (Ostwald-de Waele) fluid and the Bingham fluid. For either of the two types of non-Newtonian rheology, we construct relationships between the superficial fluid velocity and the pressure gradient in fractures and porous media. The Bingham fluid is regularized by means of Papanastasiou-type regularization for porous media and by means of a simple hyperbolic function for fracture flow. Approximation by Taylor expansion is used to evaluate the fluid velocity for small pressure gradients to reduce rounding errors. We report simulations of flow in rough-walled fractures for different rheologies and study the effect of fluid parameters on the flow channelization in rough-walled fractures. This effect is known from previous studies. We demonstrate how rheologies on different domains can be included in a fully-unstructured reservoir simulation that incorporates discrete fracture modeling (DFM). The above formulation was implemented in the open-source MATLAB Reservoir Simulation Toolbox (MRST), which uses fully implicit discretization on general polyhedral grids, including industry standard grids with DFM. This robust implementation is an important step towards hydro-mechanically coupled simulation of hydraulic fracturing with realistic non-Newtonian fluid rheology since most hydraulic fracturing models implemented so far make use of oversimplified rheological models (e.g., Newtonian or pure power-law).

The Challenge of Lost Circulation

Drilling a well is the most common way to access oil and gas resources and geothermal reservoirs. During drilling, a fluid is circulated in the well in order to cool the bit, transport cuttings, and prevent the influx of formation fluids. Lost circulation is a situation where less fluid is returned from the wellbore than is pumped into it. Lost circulation may be caused by different mechanisms in different formations. The negative impact of lost circulation can be severe and result in nonproductive time, loss of drilling fluid, and possible well control issues. The concept of lost-circulation pressure is introduced in this chapter. Knowledge of lost-circulation pressure is crucial for setting up the casing program. Uncertainties involved in prediction of lost-circulation pressure are discussed. Published accounts of lost-circulation incidents are reviewed.

Thermal Stresses in Annular Cement

Heating of casing, e.g. by the drilling fluid returning to surface, expands the casing string. This results in the hoop stress in the cement sheath becoming less compressive (more tensile). Similarly, cooling of casing, e.g. by injecting cold water down the well, makes the casing contract. This results in the radial stress in cement sheath becoming less compressive (more tensile). These stress changes may induce radial cracks or debonding at cement-casing and cement-rock interfaces. Finite-element simulations are performed in order to estimate the magnitude of the stress variations in cement sheath caused by the temperature variation at the inner side of the casing. Simulations are performed for different combinations of thermal expansion coefficients of cement, steel, and rock. It is shown that, at least in some cases, it is beneficial to have cement formulations that result in lower Young’s modulus and higher tensile strength of cement upon hardening. The role of initial stresses in cement sheath for practical evaluation of cement sheath stability during wellbore heating/cooling is discussed.

Coupling in hydraulic fracturing simulation

Abstract Fluid-driven fracture propagation is a multiscale, multiphysics phenomenon. In order to model hydraulic fracturing numerically, different processes should be coupled in the simulator. Fluid injected into the fracture works to advance the fracture tip. Part of the fluid leaks through the fracture face (wall) into the surrounding porous rocks. Filter cake may build up on the fracture faces and behind the fracture tip. The fluid pressure opens up the fracture. This changes the fracture aperture and, thus, the fracture permeability. The permeability is affected not only by the average fracture aperture, but also by the tortuosity of the flow paths inside the fracture. The tortuosity is different in different rock types. It is also affected by asperities crushing caused, for example, by shear displacement of the fracture faces. If the fracturing fluid contains solid particles (proppant), the solids concentration affects the rheological properties of the slurry and, thus, influences the flow and the pressure distribution in the fracture, affecting the fracture opening. The fracture opening, in turn, affects the proppant transport as proppant particles can be detained in the narrow parts of the fracture (proppant screenout). At the beginning of the Chapter, a classification of coupling types/strengths in computational geomechanics is provided using hydro-mechanical (HM) coupling as an example. We then proceed to introduce couplings between different physical processes used in modern hydraulic fracturing simulators.

Properties of Well Cement

Well cementing involves pumping a sequence of fluids into the well. Often these fluids, such as spacers and cement slurries, have non-Newtonian yield-stress rheology. After the cement slurry has been placed in the annulus, it hardens into a low-permeability annular seal. The complexity of these processes and the multitude of materials involved (drilling fluid, spacer, chemical wash, cement, casing, rocks) call for a sufficiently detailed material characterization in order to design and optimize cement jobs. A review of properties describing cements and other materials used in primary cementing is presented in this chapter. Rheological properties of washes, spacers, and cement slurries that control their flow down the well and up the annulus are discussed. Basics of non-Newtonian fluid rheology required to understand the subsequent chapters are laid out. Transition properties of cement slurry related to its solidification are reviewed. Mechanical, interfacial, hydraulic, and thermal properties of hardened cement that control e.g. response of cement to thermal stresses, vibrations, etc. are introduced, along with laboratory techniques used for their measurement (Brazilian test, uniaxial test, triaxial test, push-out test).

Heterogeneities in Cement

It is not possible to create a perfectly homogeneous annular cement sheath in a well. Defects will always be present at different scales, ranging from intergranular microcracks to bubbles and gas channels. Defects can be produced at all stages of primary cementing, i.e. during cement slurry mixing, placement, hardening, and subsequent loading. Defects have a strong impact on well integrity since they may provide leakage paths for formation fluids along the cemented annulus. In this chapter we discuss some important heterogeneities in cement (channels, pockets, cement porosity, slurry segregation issues, and interface defects). It is outlined how they can be studied by state-of-the-art imaging techniques, such as X-ray computed tomography. Special emphasis is given to the unavoidable interface transition zone (ITZ) forming along cement interfaces, and the debonding of cement from steel/rock. The chapter forms the basis for the further discussion of operation-induced defects in Chaps. 5 and 6.

Fluid Flow and Displacement in the Annulus

During a primary cementing job, a sequence of fluids is pumped into the annulus in order to displace the mud and prepare the annulus for cement placement. The factors affecting the mud displacement efficiency are discussed in this chapter. The effects of pipe eccentricity, breakouts, and irregular wellbore cross-section on the displacement efficiency are demonstrated using a simple kinematic model of annular cementing. In particular, it is shown that breakouts may have a substantial detrimental effect on the displacement efficiency since the displacing fluids might be flowing only in the breakouts. Channelization is also shown to occur when the wellbore has neither breakouts nor washouts, but rather a slightly irregular cross-section, like real wells normally do in sedimentary formations. In this case, viscous instabilities occur for unfavorable mobility ratios. Channelization may in this case be prevented most effectively by increasing the yield stress of the displacing fluid. The effects of well inclination, pipe movement and flow regime are discussed. A brief overview of numerical models of well cementing is provided. Unresolved issues in modelling are summarized.

Knowledge Gaps and Outstanding Issues

Despite substantial progress made in research and development of cement formulations, preflush engineering, cementing technologies, and numerical modelling over the past decades, several knowledge gaps and unresolved problems still exist. These problems are likely to persist in the future as more complicated cementing conditions are encountered, e.g. in deepwater wells, HPHT wells, geothermal wells, and during underground CO2 storage. New challenges are due either to harsh downhole conditions (e.g. HPHT) or more stringent environmental and safety regulations (e.g. geothermal and CO2 wells). Challenges are found in the design, where perfect mud displacement and cement placement are still rare. Numerical models used to design cementing jobs are still often either too complicated (i.e. too slow) or inaccurate. Uncertainties about the formation properties (permeability, temperature, etc) and about the behavior of cement at downhole conditions reduce the practical value of even the most promising models. Despite these knowledge gaps, continuous progress over the past decades suggests that, in the years to come, the technology of primary cementing will continue to improve, based on our steadily improving knowledge of its physics and mechanics.