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By C. O. Bundranl, Peter Dehlinger, W. H. Browne

Brief laboratory investigations are described which attempt to determine optimum .sand concentrations in gel-sand and oil-sand1 well-treatments. The investigations apply to the case where sand acts as a propping agent in formation fractures. Both analytically and experimentally it is demonstrated that optimum sand concentrations can be defined. It is difficult to translate laboratory results to field treatments, however, since the relative distribution of sand and fluid in fractures may not be the same as injected. This is because fluid may penetrate the furtherest narrow portions of fractures, which would not pass sand. Optimum concentration of a monolayer of Ottawa sand in fractures of 0.025-in. width at the usual range of pressures encountered in treatments appears to be about 95 to 2 lb/gal. of gel. An investigation of abrasion of rock-walls by sand in treatments, described in the Appendix, shows that such abrasion is not probable in significant amounts. INTRODUCTION Experience in the Spraberry formation of West Texas, as well as in other formations, has shown that. sand is a necessary and vital part of gel-sand and oil-sand treatments. Many observers of treatments have also concluded that there seems to be an optimum range of sand concentration for these injections. Brief laboratory investigations were made at Battelle Memorial Institute to study flow in fractures with different sand concen- trations. To investigate the existence and range of optimum concentrations in the laboratory, however, necessitates knowledge of the mechanism by which the sand aids in increasing subsequent production. The action of sand in fractures is usually thought to be either that of a propping agent, thus providing a greater effective formation permeability; that of an abrasive in eroding fill material in fractures; or that of an abrasive eroding rock-wall irregularities along fracture surfaces. Investigations described in the Appendix show that sand does not appear to erode rock-wall materials appreciably. In a subsequent paper it is reasoned, at least for the Spraberry formation of West Texas, that the primary action of sand is not in removing fill materials in fractures. In this formation, and probably others, too, the main effect of sand appears to be that of a propping agent. Both analytical and experimental investigations were made for the case of a monolayer of sand acting as a propper, in which sand concentrations were determined that would, after treatment, permit flow of the maximum quantities of oil from the formation into a well. If too few sand grains are injected into fractures in which the bottom hole pressure has decreased appreciably below the original formation pressure, the confining pressure in the formation may become relatively large, thus compress the rock-walls around the sand grains, essentially close fractures, and so decrease the subsequent flow of oil. Similarly, if too much sand is used, the flow of oil will he impeded by the volume of sand present. THEORY Although an analytical approach to determining optimum sand concentrations involves gross assumptions.

Jan 1, 1955

By S. S. Shen, M. J. Pool, P. J. Spencer, J. R. Guadagno

VERY few thermodynamic data are available for rare-earth alloys, partly because of the difficulties of obtaining the metals in sufficiently pure form and also because of their comparative scarcity up to the present time. The rare earths form a very interesting series in the periodic table in view of the progressive filling of their 4f subvalence electron shell and would be expected to provide useful information with regard to alloying characteristics of transition elements. It has been found in recent calorimetric investigations that the heats of solution of a number of the rare-earth metals in liquid tin are highly exothermic.1-4 Exceptionally strong bonding between rare-earth and tin atoms is clearly indicated in the liquid solutions. Continued thermodynamic studies of the behavior of rare earths in solution could thus contribute a great deal to present theoretical knowledge of alloying behavior and would yield an insight into bonding of a strength hitherto unencountered in liquid alloys. The determination of the heats of solution of the pure components in liquid tin is an essential preliminary to calorimetric work of this nature. Heats of solution of praseodymium, neodymium, and samarium in liquid tin at 750" ' and the heats of mixing of Pr-Nd solid solutions' have already been determined in this laboratory. The present investigations with lanthanum continue the study of rare-earth elements. Details of the construction and operation of the liquid metal solution calorimeter used in this work have been published previously by Pool and Peluso and no further description will be given here. The lanthanum used in heat of solution determinations was supplied by Lunex who quoted the purity as 99.9 pct. Their detailed analysis of the material is given in Table I. Samples of 0.0003 to 0.0005 g-atom were used for each run and great care was taken to remove all surface oxide prior to weighing. The samples were stored at all other times in a beaker of oil to prevent their otherwise rapid oxidation. The compounds LaSn (Cudu, L1P type structure) and La&, (structure not classified) were prepared from the appropriate quantities of the two pure components by arc melting under a purified argon atmosphere and once again great precautions were taken to avoid any subsequent oxidation of the specimens. Although no structural examination of the compounds was made, the consistency of thermodynarnic measurements carried out on twenty or so individual samples of each indicates that the compounds were in fact homogeneous, single phase alloys. Samples of the compounds consisting of 0.0003 to 0.002 moles were used in the calorimetric measurements. A solvent bath consisting of approximately 80 g of 99.9 pct pure Sn was used for each series of runs and its heat capacity was determined at regular intervals throughout the experiments using pure tin or tungsten calibration samples. Measurements were made of the heat of solution of lanthanum in liquid tin at 725", 750C, and 775°K and at compositions up to 2.21, 4.76, and 5.25 at. pct La at the three temperatures respectively. In every case, the heat of solution of lanthanum remained constant at its limiting value, within experimental limits, up to the highest lanthanum concentration investigated. Since no change in was observed, it was concluded that the liquid/liquid + LaSn, phase boundary had not been

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