Computer Processing Improves Hydraulics Optimization with New Methods
- A.A. Gavignet (Sedco Forex) | C.J. Wick (Anadrill Schlumberger)
- Document ID
- Society of Petroleum Engineers
- SPE Drilling Engineering
- Publication Date
- December 1987
- Document Type
- Journal Paper
- 309 - 315
- 1987. Society of Petroleum Engineers
- 1.11.2 Drilling Fluid Selection and Formulation (Chemistry, Properties), 1.6 Drilling Operations, 1.7.7 Cuttings Transport, 1.5.4 Bit hydraulics, 1.11.5 Drilling Hydraulics, 4.3.4 Scale, 1.11 Drilling Fluids and Materials, 4.1.5 Processing Equipment, 4.2 Pipelines, Flowlines and Risers, 4.1.2 Separation and Treating, 4.2.4 Risers, 1.10 Drilling Equipment
- 1 in the last 30 days
- 277 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 5.00|
|SPE Non-Member Price:||USD 35.00|
Summary. In current practice, pressure drops in the mud circulating system and the settling velocity of cuttings are calculated with simple rheological models and simple equations. Wellsite computers now allow more sophistication in drilling computations. In this paper, experimental results on the settling velocity of spheres in drilling fluids are reported, along with rheograms done over a wide range of shear rates. The flow curves are fitted to polynomials and general methods are developed to predict friction losses and settling velocities as functions of the polynomial coefficients. These methods were incorporated in a software package that can handle any rig configuration system, including riser booster. Graphic displays show the effect of each parameter on the performance of the circulating system.
The optimization of drilling hydraulics requires the calculation of frictional pressure drops in the system and of the settling velocity of the cuttings in the annulus. Both require a good description of the fluid rheology to yield accurate results. In addition, friction losses are strongly dependent on the geometry of the system, while settling velocities are influenced by the shape of the cuttings.
In current practice, drilling fluids are assumed to fit two-parameter rheological models (power-law or Bingham), and the equations used for calculating pressure drops are simplified versions of more accurate, but more complex algorithms. Optimization methods look for the maximum value of a chosen parameter (jet impact or hydraulic power at the bit), but there is no analysis of the sensitivity of the parameter to variations in the nozzle area.
These simplifications were justified because complete hydraulic calculations are cumbersome when done by hand. The situation improved with the introduction of software packages designed for pocket calculators and desk-top computers. The first generation of computer programs, however, only do faster and better what drilling engineers were doing manually. Computers can do more. They can handle complicated hydraulic geometries, and they can process complex algorithms on the basis of more sophisticated hydraulic models.
The purpose of this paper is to show how computers can improve hydraulic optimization mostly in the areas of pressure-drop calculations and prediction of settling velocities. The objective is to calculate both quantities directly from multispeed rheological measurements (i.e., the six-speed Fann rheometer).
Settling velocities will be emphasized more than pressure drops because they are very sensitive to mud rheology and are important for the transport of cuttings up the annulus, as shown by several authors. When a particle falls through a stagnant fluid, gravity and drag forces equilibrate. The drag forces in most situations cannot be calculated, and the drag coefficient, Kd, must be determined empirically.
Sample and Bourgoyne compared four settling velocity correlations to their experimental results, as well as those of other authors. They found differences between the predictions of the various correlations and also with the measured values. Such disparities may be a result of the rheological models and of the various cutting geometries that were used in the experiments. Therefore, it was decided for this study to focus first on the settling velocity of spheres and to consider the effect of cuttings shape separately.
In the first part of this paper, measurements of the settling velocity of spheres in drilling fluids are reported. The rheology of the muds used was controlled with multispeed viscometers, and the data were fitted to polynomial expressions. The drag coefficients were calculated, and a method was found to relate their values to a dimensionless parameter, referred to as the dynamic parameter, that can be calculated from the polynomial coefficients.
The second part of the paper shows how this polynomial fit of rheology can be used to predict laminar pressure drops and the onset of turbulence in pipes.
These methods were incorporated in a new hydraulics optimization program that can handle any rig hydraulic system configuration, including riser boosting systems. For bottomhole cleaning and for annular cuttings transport, the effect of each parameter can be visualized on a graphic display showing the sensitivity of the system to variations in parameter values. The structure of the program is outlined in the paper, and the results of calculations are compared with field data.
Settling Velocity of Cuttings
Background. The settling velocity, vs, of a sphere of diameter ds and density p in a fluid of density pf is given by
Vs = -----------------,............................(1)
where g is the acceleration of gravity.
For Newtonian fluids, the drag coefficient has been shown to be related to the sphere Reynolds number, NRep, defined as
Pf Vs D NRep = -----------,....................................(2)
where mu is the viscosity of the fluid.
Fig. 1 is a plot of Kd vs. NRep for a sphere. Several empirical formulas can be fitted to the plot in Fig. 1. One convenient form of equation, which was suggested by Concha and Almendra, is
24 3.73 0.00483 N 1/2 Re Kd=O.49 + ----+------- - ------------------.............(3) NRe N 1/2 Re 1+3.10 -(6) N 3/2 Re
This formula is valid for Reynolds numbers from 0.1 to 10,000.
The situation is more complex in the case of non-Newtonian fluids, because the fluid rheology cannot be characterized with one number.
|File Size||515 KB||Number of Pages||7|