Settling behavior of spherical particles in eccentric annulus filled with viscous inelastic fluid

Hole cleaning is a complex process as there are many variables affecting cuttings removal(e.g.drilling fluid type,density,flow rate and rheological properties,cuttings size,drill pipe rotation speed).With the increasing number of drilling small diameter wells(e.g.coiled tubing drilling applications,ultra-deep wells drilled for exploitations of unconventional oil and gas resources),the wall resistance of the micro annulus also emerges as one of the most critical factors affecting the cuttings accumulation in wellbore.The eccentricity of drill pipes commonly observed during the drilling process of ultra-deep well and coiled tubing well makes the wall resistance effect on the cuttings transport even more prominent.Understanding the wall resistance effect on the particle settling behavior in eccentric annuli is,therefore,crucial for hydraulic design of efficient cuttings transport operations in these wells.In this study,a total of 196 sets of particle settling experiments were carried out to investigate the particle settling behavior in eccentric annuli filled with power-law fluids.The test matrix included the eccentricity ranges of 0-0.80,the dimensionless diameter ranges of 0.13-0.75 and the particle Reynolds number ranges of 0.09-32.34.A high-speed camera was used to record the particle settling process and determine the influences of the eccentricity,the dimensionless diameter,the fluid rheological properties,and the solid particle characteristics on the wall factor and the particle settling velocity.The functional relationship among the dimensionless diameter,the particle Reynolds number,and the wall factor was determined by using the method of controlling variables.An eccentric annulus wall factor model with average relative error of 5.16%was established.Moreover,by introducing Archimedes number,an explicit model of particle settling velocity in the eccentric annulus with average relative error of 10.17%was established.A sample calculation of particle settling velocity was provided to show the application of the explicit model.Results of this study can be used as a guideline by field engineers to improve hydraulic design of cuttings transport operations in concentric and eccentric annuli.

PERTURBATION SOLUTION OF NON-NEWTONIAN FLUID AXIAL LAMINAR FLOW THROUGH ECCENTRIC ANNULI

Using the perturbation method, the axial laminar flow of Non-Newtonian fluid through an eccentric annulus is studied in the present paper. The relative eccentricity e is taken as a perturbation parameter, and the first order perturbation solutions of the problem, such as velocity field, limit velocity and pressure gradient, are all obtained.

PRESSURE DISTRIBUTION ON THE WALL OF THE INNER CYLINDER RECIPROCATING AXIALLY TO THE UNSTEADY FLOW OF VISCOELASTIC FLUID IN ECCENTRIC ANNULUS

In this article, the governing equations for the unsteady flow of viscoelastic fluid in the eccentric annulus with the inner cylinder reciprocating axially and the expression of the pressure distribution on the wall of the inner cylinder of the annulus are established and derived, respectively, under the bipolar coordinate system. The equations and the expression are solved and calculated numerically using the finite difference method, respectively. The curves of the pressure distribution on the wall of the inner cylinder of the aqueous solution of Hydrolyzed Polyacrylamide （HPAM） are plotted and the influences of annular eccentricity, stroke, and stroke frequency on the pressure distribution are analyzed.

NUMERICAL SI MULATION OF STEADY FLOWFOR VISCOELASTIC FLUID IN AN ECCENTRIC ANNULUS WITHINNER ROD MOVING AXIALLY

The governing equation about steady flow of viscoelastic fluids in an eccentric annulus with inner rod moving axially is established by using common conversion Maxwell constitutive model. The numerical solutions of the flow are obtained by control volume and ADI methods. The influence of the eccentricity, velocity of inner rod and elasticity of fluid to the velocity distribution, flow rate and radial force on the inner rod is obtained, and the reason for the severe eccentric wear of the sucker rod of polymer flood well is analyzed.

NUMERICAL SIMULATION OF UNSTEADY FLOW FOR VISCO- ELASTIC FLUID IN AN ECCENTRIC ANNULUS WITH INNER ROD RECIPROCATION

The equation governing the unsteady flow of viscoelastic fluids in an eccentric annulus was derived by using the common conversion Maxwell fluid constitutive equation and then discretized by the control volume method. The velocity distribution of flow field was computed by using the ADI method. The influences of the pressure gradient, eccentricity, stroke length, and stroke frequency on the velocity and flow capacity in the flow field was analyzed. The foundation for further research of the eccentric wear problem of the pumping rod in polymer-flood well was laid.

INVESTIGATION ON THE FLOW STABILITY OF NEWTONIAN FLUID IN ECCENTRIC ANNULUS VIA THE AXIAL RECIPROCATION OF THE INNER TUBE

The governing equation, together with the formulas of the averaged flux and the stability parameter for Newtonian fluid flowing in eccentric annulus via the axial reciprocation of the inner tube was established in the bipolar coordinate system. Numerical calculation was conducted for the measurement of water flow using the formulas above, of which the results agree well with the experimental data. It is shown that the flow instability can be induced by the increase of the stroke, the frequency, and the eccentricity of annulus, making the sucker rod more susceptible to partial abrasion. Some protecting methods, including adding centralizers, adjusting the stroke and frequency, are proposed to protect the sucker rod from the partial abrasion, and satisfactory results have been achieved in the oilfields.

Axial laminar velocity field calculation and optimization for power-law fluid in eccentric annulus with cutting bed

The formation of a cutting bed in an annulus involves safety problems in drilling especially in the horizontal well and the directional well. In this work, three axial laminar velocity field calculation models for the power-law fluid in an annulus are modified by considering the effect of the cutting bed. The proposed models are employed to numerically simulate the annulus flow with the cutting bed. Verified by the experimental data in literature, all of them can be applied to the situation of the annulus flow with the cutting bed. The modified concentric annulus model enjoys the best performance, while the flat channel flow model has the worst performance.