Van Olphen Research Articles

A Practical Utilization of the Theory of Bingham Plastic Flow in Stationary Pipes and Annuli

Published in Petroleum Transactions, AIME, Volume 213, 1958, pages 316–324. Introduction The practical analysis of the hydrodynamics of the wellbore has long been a subject of interest to engineers. This paper presents a simplified solution to the problem of computing the pressure drop for the flow of drilling mud in the annulus of the wellbore. This solution is, however, an exact and rigorous solution under the assumptions which have been imposed. These assumptions are that the drilling fluid is a Bingham plastic fluid and that the annulus is formed by two concentric, stationary, cylindrical pipes. It is further assumed that the fluid is incompressible and that its motion is isothermal and in a steady state. This problem under the same assumptions has been attacked by previous authors. Beck, Nuss and Dunn proposed that the equation for the flow of a Bingham plastic fluid in a cylindrical pipe could be applied to an annulus if the pipe radius were replaced in the equation by the hydraulic radius. This equation, known as the Buckingham-Reiner equation (see Appendix 1), was also used in an approximate form. Van Olphen pointed out that even for a simple or Newtonian fluid the pipe equation (Poiseuille's law) could not be converted to the Lamb equation descriptive of flow in an annulus (see Appendix 1) by using the hydraulic radius. Van Olphen further attempted to give a solution for the annular flow of a Bingham plastic fluid by introducing approximations similar to those which have been used in the case of the Buckingham-Reiner equation. Other attempts to provide approximate or exact solutions have been made by Grodde and by Mori and Ototake. The present authors some years ago in unpublished work derived the correct expressions relating the pressure drop and flow rate for this problem. It was found that the solution consisted of two simultaneous equations, one of which contained a logarithmic term. Thus, obtaining numerical results for any particular case of interest involves very tedious trial-and-error computations. Very recently Laird presented the correct derivation of the two equations which are given in full detail in Appendix 1.

Forces Between Suspended Bentonite Particles Part II—Calcium Bentonite

AbstractIn a previous paper (van Olphen, 1956) data were presented for the rheological and sedimentation behavior of sodium bentonite suspensions in water. From these data particle interaction energies were derived. Analogous data have been collected for calcium bentonite suspensions. It was observed that more clay is required to obtain a gel or a certain sediment volume with calcium bentonite than with sodium bentonite. This result can be quantitatively interpreted on the basis of a larger average particle thickness in the calcium bentonite suspensions. It is furthermore concluded that the interparticle forces are of the same order in both calcium and sodium bentonite suspensions.

Flow Properties of Dilute Montmorillonite Dispersions

AbstractA viacomotrio study of dilute montnioritlonite dispersions, using lor tho most part dilution-typo capillary viscometers supplemented by a falling-head capillary viscometer, has involved a determination of the concentration dependence of viscosity of such dispersions in both distilled and electrolyte-containing water. The resulta of the study have been interpreted in terms of a theory of incremental viscosity, and of the Solmlz—Rlaschke (1941) equation. Use of this equation yields good extrapolations to zero concentration for the determination of limiting viscosity number, and permits calculation of “interaction indices” which are considered, for reasons discussed in detail, to be a measure of paitiele-particle interaction. These indices are related to the cationie heat of hydration of the electrolyte used, and relationship is demonstrated between the yield stress of a 3 percent montmorillonite—eleetrolyte—water system and such interaction indices. The recent work of Paekter (1956, 1957) is discussed, and the relation of the results of this investigation to the data of van Olphen (1956, p. 204) is noted.

Reply to E. A. Hauser's Criticism on H. van Olphen's Paper in “Report on the Fourth National Clay Conference”

Reply to E. A. Hauser's Criticism on H. van Olphen's Paper in “Report on the Fourth National Clay Conference”