Roland May

Detailed Modeling of Drilling Fluid Flow in a Wellbore Annulus While Drilling

To produce a well safely, the wellbore pressure during drilling must be in a range that prevents collapse yet avoids fracturing. This range is often called “the operating window”. Exceeding the limits of this range can trigger wellbore instability or initiate well control incidents. Pressure prediction requires an understanding of the hydrodynamics processes that occur in a borehole while drilling.Describing these processes is complicated by many factors: the mud rheology is usually non-Newtonian, the flow mode can be laminar or turbulent, and the drillstring can rotate and be positioned eccentrically. Known semi-analytical approaches cannot account for the full range of fluid flows that can arise during drilling. These techniques don’t take into account all factors. Accurate numerical simulation of the flow of drilling fluids is a means to describe the fluid behavior in detail.For numerical solutions of hydrodynamics equations a unique algorithm based on a finite-volume method and a new model of turbulence for non-Newtonian fluids was developed. The model considers string rotation and eccentricity of the drillstring. Newtonian and non-Newtonian fluids as described by the Herschel–Bulkley rheological model have been implemented. Data obtained via systematic parameter studies of the flow in a borehole are available for fast determination of parameters like pressure drop, velocity field, and stresses corresponding to any drilling condition.Applying the new model for the annulus flow and comparing the results to the parallel plate flow approximation enabled us to quantify the error made due to the approximated solution for non-Newtonian fluid rheology.The difference between the solutions grows as the annular gap increases. This situation is a function of the rheological parameters. Secondary flow effects can only be seen when applying the new solution method.Copyright

On a criterion of incipient motion and entrainment into suspension of a particle from cuttings bed in shear flow of non-Newtonian fluid

Solids transport is a major issue in high angle wells. Bed-load forms by sediment while transport and accompanied by intermittent contact with stream-bed by rolling, sliding and bouncing. The study presents the results of a numerical simulation of a laminar steady-state flow around a particle at rest and in free motion in a shear flow of Herschel–Bulkley fluid. The simulation was performed using the OpenFOAM open-source CFD package. A criterion for particle incipient motion and entrainment into suspension from cuttings bed (Shields criteria) based on forces and torques balance is discussed. Deflection of the fluid parameters from the ones of Newtonian fluid leads to decreasing of the drag and lift forces and the hydrodynamic moment. Thus, the critical shear stress (Shields parameter) for the considered non-Newtonian fluid must be greater than the one for a Newtonian fluid.

Movement of a Sphere on a Flat Wall in Non-Newtonian Shear Flow

For a particle on a wall or cuttings bed in a multiphase flow in confined geometries a condition for onset and lift-off is very important. In this case, a fundamental problem of hydrodynamic forces and torque acting on a particle moving near and on the wall in a viscous fluid needs to be solved.In this paper, systematical simulation of a flow was performed around a perfect rolling or sliding spherical particle near the wall. A shear flow of Newtonian and Herschel-Bulkley fluids was investigated. The simulation was conducted for Reynolds numbers up to 200 and the dimensionless positive particle velocity Vp < 1.4. The relative particle velocity was made dimensionless by dividing it by the incoming flow velocity in front of the particle. The simulation was performed using the open-source CFD package OpenFOAM. The simulation results for Newtonian fluid agree with data presented in the literature.For the particle’s low translational velocity the drag force coefficient in the non-Newtonian fluid is lower than in Newtonian fluid, but for increasing translational velocity the drag force coefficient increases.The lift force coefficient behavior is non-monotonic versus rheology parameters. Lift and drag force show a sudden drop for very small translational velocities.Our simulation shows that in the case of large Bingham numbers the particle’s lift force can be negative for steady perfect particle rolling. Thus, friction between particle and surface prevents particle’s take-off in some cases.Knowing the dependence of the lift force on Reynolds number and rheological parameters allows one to determine incipient motion and take-off conditions for a spherical particle.Copyright

Modelling of Pressure Fluctuations in a Wellbore While Tripping

Assembling or dismantling drillstring sections during tripping operations results in a periodically accelerated or decelerated motion of the drillstring in the borehole. While running in or pulling out of hole the drillstring induces a flow of displaced fluid and a pressure change in the borehole. These pressure changes can be divided into two components: First, the “steady” pressure change associated with the mud viscous friction; and second, the pressure fluctuations caused by induced acceleration of the drilling fluid. Pressure surges are especially dangerous for the uncased well sections and at the bottom of the well, because they can damage and destroy the wellbore. The accurate prediction of pressure fluctuations is significant for wells where the pressure must be maintained within a narrow range to enable safe drilling and completion of the well. Sudden pressure changes in such wells may lead to the so-called water-hammer effect that can be observed in wells when pump operation modes change or when the string is accelerated. A large-scale water-hammer effect may damage the uncased section of a well, leading to fractures or formation fluid inflow.The objective of this paper is to estimate the magnitude of the pressure surges caused by accelerated movement of the drillstring. A mathematical model was formulated to describe the unsteady behavior of flow rate and pressure change along the well. The model involves a one-dimensional system of equations, which are a modification of the equations for hydraulic shocks in the annulus, and the cylindrical part of a well.When frictional losses are neglected, it is possible to derive an exact analytical solution of the problem. This analytical solution was used to estimate the maximum and minimum pressure in the borehole.When combined with the methods for frictional pressure losses, the suggested method can predict the pressure change in a wellbore while tripping. Newtonian and power law fluids were considered for the parameter study.Copyright

Evaluation of Pressure Change While Steady-State Tripping

Excessive tripping speed in an uncased borehole increases the risk of having formation damage or influx of formation fluid (kick). However, if the tripping is performed at lower speeds, the operation requires more rig time. Hence, increased trip speed cuts expensive rig time. These opposing goals require thorough planning and optimization of the tripping operation to avoid operational problems and reduce financial expenditures. To maximize the tripping speed, accurate prediction of the pressure change occurring due to the axial pipe movement (surge or swab pressure) is necessary. The pressure change is influenced by the hole and string diameters, eccentricity, fluid properties and trip speed. The tripping speed is one of the operational parameters, which are regularly adjusted at the rig site.Analytical solutions exist only for special scenarios. The semi-analytical models for calculation of the steady-state pressure change cannot provide accurate predictions. They are mostly based on disputable assumptions which make the model to underestimate the pressure change. Most of the existing models are based on the parallel-plate approximation of the annular geometry. In another approach, the parameter, which reflects the amount of fluid which is dragged the direction of the string, assumed to be constant or calculated independent of the fluid viscosity.In this paper, accurate solutions were obtained from direct numerical simulation of flow in a cylindrical annulus with axial movement of the inner cylinder. The numerical algorithm is based on finite volume method and incorporates laminar flows of Newtonian, Power Law, Bingham Plastic and Herschel-Bulkley fluids. The method predicts the pressure change occurring in concentric and eccentric annuli with and without rotation of the inner cylinder. The goals of this work are to: i) study the influence of the eccentricity, fluid properties and tripping speed on the pressure change; and ii) evaluate the accuracy of the simplified approaches by comparing experimental data and numerical solutions, and determine their validity ranges.This paper presents a new method for finding trip-caused pressure change in the wellbore through systematic analysis of the numerical solutions. Parametric study was performed to examine the effects of different influential parameters on the pressure change. In addition, the results obtained from the numerical method are compared with the simplified solutions and the discrepancies are analyzed to show the improved accuracy of the new method.Copyright

Transition Criteria for Laminar to Turbulent Flow for Yield Power Law (YPL) Fluids Based on Stability Analysis

It is well known that a Newtonian fluid with the presence of solid particles in suspension behaves non-Newtonian. Higher the solid content, more significant the yield stress of the fluid. Determination of the hydraulic behavior of fluids having a significant yield stress is a challenging task. For engineering purposes, pressure drop within the system, during pipeline transportation, has to be estimated carefully and accurately. Flow regime plays a vital role during hydraulic calculations. The inaccurate determination of flow regime can lead us to large errors in frictional pressure drop calculations and ultimately leads to error in designing and flow assurance point of view, since hydraulic calculations are including a friction factor term, which is a direct function of flow regime. In general, Reynolds number is the main parameter used by the industry for determining the flow regime, and the friction factor. This approach works reasonably accurate for Newtonian fluids. However, as the yield stress of the fluid increases, this conventional technique for determining the flow regime is not as accurate. Although many approaches have been introduced for estimating the flow regime for non-Newtonian fluids, there exists a lack of information and confidence of such predictions for fluids having high yield stress, such as Yield Power Law (YPL) fluids (i.e., Herchel-Bulkley). Display Formula(1)τ=τy+KγmThis study presents an analytical solution for predicting the transition from laminar to non-laminar flow regime based on Ryan & Johnson’s approach using the stability analysis and equation of motion for YPL fluids. Comparing with the experimental results for YPL fluids under different flow conditions, including laminar and non-laminar flow regimes, show that presented approach gives a better estimation of the transition from laminar to non-laminar flow regime than conventional Reynolds number approach. In some cases, it is observed that although the Reynolds number is high, flow is still laminar, which is predicted accurately using the presented model. This study provides a higher accuracy in estimating the flow regime, which leads to a higher confidence in hydraulic designs and determining limitations of the system in concern.Copyright