Drillstring Vibrations: Classic Ideas and Modern Approaches - Wave Propagation in Drilling, Well Logging and Reservoir Applications - page 163

... W 0

WZERO

... X position

X

... u(0,t)/ x at bit

XDERIV

... Drillstring length L

XS

... Spatial x index

I

... Spatial index at drillbit centroid

IBIT

... Spatial index at surface end of drillstring

IMAX

... x

DX

.
T ... Time

... Time step index

N

... t

DT

... " A " matrix coefficient in Equation 4.2.76 A(I)

... " B " matrix coefficient in Equation 4.2.76

B(I)

... " C " matrix coefficient in Equation 4.2.76

C(I)

... " W" matrix coefficient in Equation 4.2.76

W(I)

... " V " matrix coefficient in Equation 4.2.76

VECTOR(I)

.
UN(I)

... U i,n axial displacement

... U i-1,n axial displacement

UNM1(I)

... U i-2,n axial displacement UNM2(I)

.
TN(I)

...

i,n angular displacement

...

i-1,n angular displacement

TNM1(I)

...

i-2,n angular displacement

TNM2(I)

.
VN(I) ... V i,n lateral displacement

... V i-1,n lateral displacement

VNM1(I)

... V i-2,n lateral displacement

VNM2(I)

.
WN(I)

... W i,n lateral displacement

... W i-1,n lateral displacement WNM1(I)

... W i-2,n lateral displacement

WNM2(I)

Not shown in Figure 4.2.8 are the Fortran “dimension statements” for the
arrays used and the interactive input queries for specific simulation parameters.
The first block initializes the drillstring to simple compression, without torsional
twist or lateral deflection. Then, time iterations commence. At each step in the
time loop, the matrix coefficients corresponding to Equation 4.2.89 are given in
the 200 sub-loop. This is followed, respectively, by program logic for the