Research Papers: Offshore Technology

Modeling of Wave Propagation in Drilling Fluid

[+] Author and Article Information
Mona Golbabaei-Asl

Mechanical Engineering Department,
University of Akron,
Akron, OH 44325-3903
e-mail: M.Golbabaie@gmail.com

Alex Povitsky

Mechanical Engineering Department,
University of Akron,
Akron, OH 44325-3903
e-mail: Alex14@uarkon.edu

Lev Ring

Weatherford International, Inc.,
Technology Development,
Houston, TX 77041-3000
e-mail: lev.ring@sbcglobal.net

1Corresponding author.

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received October 11, 2016; final manuscript received February 25, 2018; published online April 24, 2018. Assoc. Editor: Theodoro Antoun Netto.

J. Offshore Mech. Arct. Eng 140(4), 041304 (Apr 24, 2018) (9 pages) Paper No: OMAE-16-1124; doi: 10.1115/1.4039565 History: Received October 11, 2016; Revised February 25, 2018

The study presents a one-dimensional (1D) numerical model of wave propagation as well as transmission/reflection phenomena in Newtonian and non-Newtonian drilling mud flow associated with oil/gas drilling activities. Propagation of wave formed due to back pressure changes by means of a choke is investigated. In general, the reflection and transmission of pressure waves at intersection of conduits with different cross sections or in case of partial blockage typical of drilling practices is multidimensional and caused by nonuniform boundary conditions over the cross section. The 1D approach is investigated to approximate the multidimensional reflection and transmission of pressure pulse at areal discontinuity in conduit. The approach is facilitated by introduction of a local force exerted by solid wall on the fluid at the intersection of the conduits into conservative form of the equation for momentum conservation. In addition, nonconservative formulation of momentum equation was explored. To solve the differential equations, MacCormack numerical scheme with second-order accuracy is applied to the nonlinear Euler and 1D viscous conservation equations. A grid refinement study is performed. It is shown that nonconservative form of the conservation laws results in more accurate prediction of transmission and reflection in case of areal discontinuity. The results of the numerical modeling are presented in terms of pressure wave propagation and attenuation upon reflection and transmission at consequent interfaces.

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Grahic Jump Location
Fig. 1

Problem schematics: (a) drilling channel with controlled back pressure at the choke, (b) uniform channel with upward mud motion (shaded area on top view), and (c) nonuniform channel with upward mud motion (shaded area on top view)

Grahic Jump Location
Fig. 2

Transient pressure profile at the outlet boundary: (a) step pressure pulse, (b) saw pressure pulse, and (c) triangular pressure pulse

Grahic Jump Location
Fig. 3

Static pressure at tc/L=0 and the pressure wave (p/pinitial) at tc/L=0.5 generated by step increase of the back pressure in flow with: (a) normal viscosity and (b) enhanced viscosity

Grahic Jump Location
Fig. 4

Static pressure at tc/L=0 and the pressure wave (p/pinitial) at tc/L=5 generated by saw pulse at the back pressure: (a) normal viscosity and (b) enhanced viscosity

Grahic Jump Location
Fig. 5

Capability of wave capturing by compact versus MacCormack scheme

Grahic Jump Location
Fig. 6

Grid refinement study for step pulse initiated as back pressure: (a) normal viscosity (pressure profile depicted in Fig. 3(a)) and (b) enhanced viscosity (pressure profile depicted in Fig. 3(b))

Grahic Jump Location
Fig. 7

Triangular pressure pulse propagation: (a) Newtonian flow, μ=μwater, (b) non-Newtonian flow, power law: n=0.73 and K=0.1347lbf/100ft2·sn, and (c) non-Newtonian flow, yield power law: n=0.705,K=0.2318lbf/100ft2·sn, and τy=1.44lbf/100ft2

Grahic Jump Location
Fig. 8

Computational results for dimensionless triangular pulse pressure pwave/pinitial traveling across the areal discontinuity (tc/L denotes dimensionless time): (a) pressure contour plots subsequent to passage from narrow to the wide section of the conduit (top) and pressure profiles at different time intervals before, at, and after passage across areal discontinuity (bottom) and (b) pressure contour plots subsequent to passage from wide to the narrow section of the conduit (top) and pressure profiles at different time intervals before, at, and after passage across areal discontinuity (bottom)

Grahic Jump Location
Fig. 9

Pressure pulse interacting with partial blockage of drilling channel: (a) pressure wave pwave/pinitial contour plot when the pulse has traveled across the second areal discontinuity, (b) dimensionless wave pressure obtained from solution of conservative governing equations with forcing term (Eq. (4b)), and (c) dimensionless wave pressure obtained from solution ofnonconservative governing equation (Eq. (5)) (tc/L denotes dimensionless time)



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