Scaling Formulae for the Wellbore Hydraulics Similitude with Drill Pipe Rotation and Eccentricity

Equivalent circulation density of the fluid circulation system in drilling rigs is determined by the frictional pressure losses in the wellbore annulus. Flow loop experiments are commonly used to simulate the annular wellbore hydraulics in the laboratory. However, proper scaling of the experiment design parameters including the drill pipe rotation and eccentricity has been a weak link in the literature. Our study uses the similarity laws and dimensional analysis to obtain a complete set of scaling formulae that would relate the pressure loss gradients of annular flows at the laboratory and wellbore scales while considering the effects of inner pipe rotation and eccentricity. Dimensional analysis is conducted for commonly encountered types of drilling fluid rheology, namely, Newtonian, power-law, and yield power-law. Appropriate dimensionless groups of the involved variables are developed to characterize fluid flow in an eccentric annulus with a rotating inner pipe. Characteristic shear strain rate at the pipe walls is obtained from the characteristic velocity and length scale of the considered annular flow. The relation between lab-scale and wellbore scale variables are obtained by imposing the geometric, kinematic, and dynamic similarities between the laboratory flow loop and wellbore annular flows. The outcomes of the considered scaling scheme is expressed in terms of closed-form formulae that would determine the flow rate and inner pipe rotation speed of the laboratory experiments in terms of the wellbore flow rate and drill pipe rotation speed, as well as other parameters of the problem, in such a way that the resulting Fanning friction factors of the laboratory and wellbore-scale annular flows become identical. Findings suggest that the appropriate value for lab flow rate and pipe rotation speed are linearly related to those of the field condition for all fluid types. The length ratio, density ratio, consistency index ratio, and power index determine the proportionality constant. Attaining complete similarity between the similitude and wellbore-scale annular flow may require the fluid rheology of the lab experiments to be different from the drilling fluid. The expressions of lab flow rate and rotational speed for the yield power-law fluid are identical to those of the power-law fluid case, provided that the yield stress of the lab fluid is constrained to a proper value.

Study of interface gas-liquid flow characteristics in a rectangular microchannel for wavy-annular flow

The aim of this work is an experimental study of a gas-liquid flow in a rectangular slit microchannel with a cross-section of 200 × 2045 μm. Ethanol/water (95/5) mixture and nitrogen are used as working liquid and gas, accordingly. The external T-mixer is used for obtaining of wavy-annular flow pattern. The experimental data on interfacial waves and their characteristics in the meniscus area on the short side of the microchannel are obtained using high-speed visualization for a wide range of gas and liquid superficial velocities. Images are processed using the Python libraries to define the average liquid layer thickness and maximum amplitude of waves. An increase of gas superficial velocity causes decreasing in the average liquid layer thickness and maximal amplitude of the liquid layer thickness. The waves on the liquid layer surface (maximal amplitude) can be three times larger than the average liquid layer thickness for presented liquid and gas velocities. With increasing gas superficial velocities more liquid displace from the meniscus area to the liquid film on the wide side of the microchannel.

Experimental study of wavy-annular flow in a rectangular microchannel using LIF method

This article aims at studying gas-liquid flow in a rectangular microchannel with a high aspect ratio (200 × 2045 μm). Liquid and gas phases were 95% ethanol and nitrogen mixture. Experimental flow characteristics are obtained using high-speed visualization and laser-induced fluorescence (LIF) methods. Using the LIF method for wavy-annular flow, the average film thickness, liquid film distribution, and liquid film width were measured. The dependences of the liquid film width and the average film thickness on gas superficial velocity are presented in graphical form and analyzed. An increase in gas superficial velocity causes growth of the liquid film width and thickness of the liquid film, which indicates the process of liquid transfer from the menisci area to the liquid film. For different liquid velocities and the same gas superficial velocities, close values of averaged liquid film thickness were observed for flow with 2D waves and 3D waves on liquid film.

Experimental investigation of water-nitrogen flow in microchannel with high aspect ratio (with the 20 µm gap)

This study is devoted to the experimental investigation of two-phase water-nitrogen flow in the slit microchannel with a gap of 20 µm and a width of 10 mm. The technology of microchannel fabrication has been developed and described in detail. Experiments were conducted in adiabatic conditions. Using a modified schlieren system, four flow patterns have been observed and described: jet, bubble, churn, and annular. Flow pattern map was plotted according to obtained patterns. Moreover, a two-phase pressure drop was measured. Dependencies between two-phase pressure drop and superficial liquid and gas velocities have been investigated.