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By D. E. Menzie, D. L. Dauben

This paper discusses the physical parameters involved in the slow flow of high molecular weight polymer solutions in porous media. The interacting effects of polymer properties and porous media properties on flow performance are considered. Experiments were conducted with the polyethylene oxides, with molecular weights ranging from 200,000 to over 5,000,000. Frontal advance velocities ranged from I to 30 ft/day. The porous matrix consisted of a flow cell packed with glass beads. Polymer solutions were characterized by viscosity and normal stress measurements. Under certain conditions, unexpectedly high flow resistance was observed. This behavior was observed to be a function of flow rate, pore size, polymer molecular weight and concentration. The polymer solutions exhibit "dilatant" flow behavior in porour media in contrast with the pseudo-plastic behavior in simple flow systems. A theoretical ex-planation of such behavior is presented. INTRODUCTION The use of polymers in the injected water of a waterflood increases oil displacement efficiency by reducing the mobility (k,/pu) of the driving phase. A reduced driving phase mobility results in improvements in the areal sweep efficiency and in the vertical coverage in stratified reservoirs. This mobility reduction may be achieved by a permeability reduction, a viscosity increase or by a combination of the two. Early attempts at increasing the injected water viscosity were not successful because of the poor economics involved. The use of such materials as glycerin, sugar or glycols to increase water viscosity was not economically feasible. Attempts in using certain naturally occurring polymers were not too successful because of the high polymer losses to the rock. A high molecular weight, partially hydrolyzed polyacry-lamide was introduced 3 years ago as a waterflood additive.',' Initial work by Pye' indicated that the presence of these polymers in dilute concentrations decreases the water mobility 5 to 20 times more than would be expected from measurements of the solution viscosity. Such an effect would be of obvious economic value since only a small polymer concentration would be required to accomplish a large reduction in water mobility. This research was designed to study the basic flow mech anisms of polymer solutions in porous media. The interacting effects of polymer properties and porous media properties on flow performance are considered. This study indicates some of the conditions under which these interactions can lead to significant mobility effects. is valid only for Newtonian fluids. For polymer solutions and other non-Newtonian fluids the equation must be modified to consider that viscosity is a variable quantity. Modification of the Darcy equation to include non-Newtonian effects has been the subject of several recent investigations."" The modifications generally adopt a rheological model. such as an Ellis or Dower law model. to Dorous media by defining some characteristic channel radius. Most of these studies showed the porous media flow behavior to be predictable from viscometric data. Investigations involving the flow of high molecular weight polyacrylamide solutions through cores have generally encountered the high flow resistances reported previously by Pye. This high flow resistance has generally been attributed to an in-depth permeability reduction, as evidenced by a reduced permeability to water which has displaced polymer solution from the porous media. Marshall and Metzner" report high flow resistances, which they attribute to viscoelastic effects. In this paper, the effects of polymer molecular weight, pore size, flow rate and concentration are considered. The polymers used are the polyethylene oxides known as Poly-ox. This class of polymers was used because of its availability in a wide range of molecular weights and because of its known ability to propagate well through porous media. THEORY PHYSICAL PROPERTIES OF POLYMER SOLUTIONS The polymer molecule dissolves in water by means of hydrogen bonding, but retains some of its own structural identity while in solution. Nonionic polymers, such as polyethylene oxide, are generally considered to have a random coiling configration. This type of molecule has the ability to "sequester" or hold a large volume of solvent within its coils in a manner similar to that of a sponge. The random coil is easily deformed and under an applied stress

By G. L. Chierici

Starting from Muskat's theory of water and gas coning, maximum permissible oil production rates without water and/or free-gas production have been determined, in a broad range of reservoir and well parameters, using the potentiometric model technique. The main assumptions made are as follows: (1) the reservoir rock is homogeneeous (either isotropic or anisotropic); (2) the volume of the aquifer underlying the oil zone is very small, so that it does not contribute to reservoir energy; and (3) the gas cap expands at a very low rate, so that it can be assumed to be in quasi-static conditions. The results obtained are presented in the form of diagrams which can be used for solving two types of problems: (1) given the reservoir and fluids characteristics, as well as the position and length of the perforated interval, determine the maximum oil production rate without water and/or free-gas production; and (2) given the reservoir and fluids characteristics only, determine the position and length of the perforated interval which optimize the maximum permissible oil production rate, without water and/or free-gas production. INTRODUCTION In oil reservoirs where the oil-bearing formation is underlain by an aquifer which does not participate in the production mechanism, water-coning is a limiting factor to the flow rates of producing wells. Production rates are usually kept to a value that will prevent the water from entering the wells. The entry of water into a well lowers its productivity by increasing the weigbt of the fluid column; moreover, the separation of water from the effluent, at the surface, may constitute a very difficult problem in cases of heavy viscous oils. A similar situation is encountered in oil reservoirs with a gas cap overlying the oil-saturated zone; here a downward gas cone is induced by the flow of oil towards the producing wells. Production rates must be low enough to prevent the gas from being produced; producing gas from the gas cap would be a waste of energy. Of course, water-coning and gas-coning phenomena can occur at the same time in the same reservoir if the oil-producing formation is both overlain by a gas zone and underlain by a water zone. Due to its relevant practical importance, the mechanism of coning was studied by many people.2,3,5-8 Defining the conditions for getting the maximum water-free and/or gas-free oil production rate is a difficult problem, often encountered under one of the following aspects: 1. Predict the maximum flow rate that can be assigned to a completed well without the simultaneous production of water and/or free-gas. 2. Define the optimum length and position of the interval to be perforated in a well, in order to obtain the maximum water and gas-free production rate. A systematic study of these problems was made by means of the electrical analog technique. The results of this study are presented here, under the form of a set of curves providing solutions for the above stated problems. These curves are valid only for homogeneous forrnations, either isotropic or anisotropic. Should the formation be non-homogeneous (by horizontal or vertical variation of permeability, shale diaphragms, fractures, etc.), a specific potentiometric study would be required for each specific case. Especially when shale diaphragms of some radial extension are present, the critical rates observed are much larger than would be expected from the diagrams. STATEMENT OF THE PROBLEM In the present study the aquifer is supposed to be of such limited volume that it does not contribute to the energy of the reservoir. Moreover, the gas cap is supposed to expand at such a low rate that the potential gradient in the gas cap is negligible. Under static conditions water-oil and gas-oil interfaces (T1 and T2) are both horizontal. When the reservoir production starts, below each well these interfaces take a cone-like shape (Fig. 1) having as an axis the axis of the well. This shape results from the equilibrium between potential gradients in the oil zone and gravitational forces due to density differences between oil and water and between oil and gas. Assuming the oil-bearing formation to be homogeneous and the oil to be incompressible, the analysis of the problem (see Appendix) shows that the oil-water and gas-oil interfaces are stable only if the oil production rate of the well is not higher than the following values.

Jan 1, 1965

By A. E. Hall

The paper gives a general solution of ventilation net- works where densities play an important role and fans operating at different densities from branch densities are considered. Both the physics and computing techniques needed to deal with these networks are discussed.

Jan 1, 1977

By D. E. Norquist, J. E. Moeller

The results of wear on marked balls, 4, 31/2, 3, and 2 in. diam are given. All balls were forged steel of practically the same chemical analysis and hardness. The results indicate that balls in a given mill for a given length of time will have equal diameter losses, regardless of size.

Jan 6, 1950

Jan 1, 1935

1-Iron and Steel JOHN A MATHEWS, Chairman Ralph H SWEETSER Vice-chairman WILLIAM CAMPBELL, Vice-chairman MAX ROESLER, Secretary Iron Ore CHARLES B MURRAY, Chairman R C ALLEN W O HOTCHKISS MAX ROESLER ERNEST F BURCHARD THOMAS T READ DWIGHT E WOODBRIDGE M M DUNCAN WILLIAM KELLY CARL ZAPFFE C T FAIRBAIRN CHARLES F RAND

Jan 1, 1923

Jan 1, 1945

By T. Chen

One of the limitations of the 3-dimensional Lerchs-Grossmann pit optimisation algorithm has been the difficulty in calculating an optimum pit with variable wall slopes. The difficulties have been related to establishing various wall slopes without changing the sizes of the blocks used in the normal computation, but still retaining an optimum solution.

Jan 1, 1977

Jan 1, 1903

Jan 1, 1940

Jan 1, 1940

By A. L. Holley

IN order to put sufficient work on steel ingots for rails, they must be reduced from about 12 inches square. As this cannot be done at one heat, they are first drawn down to about 7 inches square, and then reheated and rolled into rails. This first reduction or " blooming," is usually done in this country in a 30-inch 3-high rolling-mill, with movable rolls, so as to get several reductions in each set of grooves. The first of these mills has been running at the Troy Steel-works above a year, with great success. Another at the Cambria Iron-

Jan 1, 1873

By Oswald J. Heinrich

In conclusion of a series of deep exploration-borings with the diamond drill, I beg to submit the following statements, supplementary to those in my former papers on this subject: Since my communications read at the St. Louis Meeting, in May last, I have finished two more borings, one terminating at the depth of 922 feet 7 inches, the other at the depth of 715 feet 6 inches. The results in regard to time and expenditure have been highly favorable and fully confirmatory of my opinion stated in previous

By Kirby D. Mellegard, Ralph A. Wagner, Paul E. Senseny

Six creep laws for salt, each fitted to the same laboratory data base, are used in a numerical model of the deformation of an opening in salt to determine the influence of creep law form on the predicted closures. Results show that predicted closures can be very sensitive to the functional form of the creep law chosen to model the laboratory data.

Jan 1, 1982

H. A. SCHWARTZ, ? Indianapolis, Inc. (written discussion§).-Re-ferring to the very interesting paper on the graphitization of white cast iron, the writer desires to present certain facts and conclusions, entirely, in harmony with those of the authors but which may he not without interest as furnishing additional evidence upon the same subject. The graphitization of white cast iron, being the basis of malleable

Jan 10, 1919

By Walter Weeks

THE process of cooling air by allowing it to expand and do work in an engine is well known, but the theory of obtaining cold air by free expansion without the aid of an engine operating with cutoff has been little discussed. CASE I If compressed air is allowed to expand to the atmospheric pressure through an orifice in an air line that is supplied by a running compressor, no cooling results except the negligible one due to the Joule-Thompson effect, which will not be considered in this discussion. The effect of moisture will also be neglected.

Jan 1, 1937

Jan 1, 1940

By Simon D. Handelsman, Reg M. M. Rowe

The mechanism of using gold as the basis for a loan was suggested to the treasurer of a mining company operating two gold heap leach mines at a time of high interest rates. Due to the seasonal nature of cash flows from operations, and the relatively low cost of funds this scheme was attractive. The paper describes the agreement with the bank, gives an example of the transactions, and describes other types of gold loans.

Jan 1, 1985

Jan 1, 1957

By R. E. Lund, D. E. Warnes

SELECTIVE sulfation of individual constituents in ores or metalliferous products has received increased attention in recent years. The fluid-bed reactor with its advantages of close control of both temperature and atmosphere promises to have ap-

Jan 1, 1958