Drillstring Vibrations: Classic Ideas and Modern Approaches - Wave Propagation in Drilling, Well Logging and Reservoir Applications - page 235

different layers of earth strata. Thus, numerical simulators and real-time
measurements are best used in environments where their synergies can both be
exploited. The Fortran implementation given below is by no means final.
In numerical simulation and field implementation, care must be exercised
to ensure that any and all mesh widths used are smaller than the wavelengths of
the disturbances modeled. We ask: What do we mean by disturbance? In
general, a disturbance consists of axial, torsional and lateral bending modes, and
each will be characterized by different length scales, wavelengths and periods.
The disturbances must be resolvable on scales much smaller than a wavelength,
and on time scales smaller than a typical period; otherwise, the details of the
vibration process will be lost and truncation errors will dominate solutions. In
addition, it is important to satisfy all required CFL conditions to ensure that
causality and stability conditions are fulfilled. An understanding of stability that
goes beyond numerical analysis is paramount. The importance of numerical
stability in an integration algorithm cannot be deemphasized. However, it
should not be the end objective. After all, real instabilities , when they do arise,
for instance, from wave trapping at the neutral point or from conventional
resonance, are physical and not computational anomalies. A vibrations
algorithm should not be designed to suppress all high-amplitude phenomena,
since a major practical objective is the prediction of real high-amplitude events.
4.5.4.6 General Fortran implementation.
In this section, we give a “bird's eye view” of the Fortran source code
listing for coupled axial, torsional, and (dual) bending mode vibrations. Lower
order details are specifically deleted in order to convey “the big picture,” but
these details are re-introduced later in separate expanded discussion.
C .
C .
C Fortran dimension and common statements, parameter
C input queries, specific constants, etc., not shown.
C .
C .
C INITIALIZE AXIAL, ANGULAR AND BENDING DISPLACEMENTS
DO 130 I=1,IMAX
X = XS*(I-1)/(IMAX-1)
UNM1(I) = RHO*G*(X**2)/(2.*ELAST) +WZERO*X/AE
UNM2(I) = UNM1(I)
TNM1(I) = 0.
TNM2(I) = 0.
VNM1(I) = 0.
VNM2(I) = 0.
WNM1(I) = 0.
WNM2(I) = 0.
130 CONTINUE
Figure 4.5.3. Coupled vibrations, Fortran listing (to be continued).