An idealized model has been developed for the purpose of studying the characteristic behavior of a permeable medium which contains regions which contribute significantly to the pore volume of the system but contribute negligibly to the flow capacity; e.g., a naturally fractured or vugular reservoir. Un:steady-state flow in this model reservoir has been investigated analytically. The pressure build-up performance has been examined in some detail; and, a technique for analyzing the build-up data to evaluate the desired parameters has been suggested. The use of this approach in the interpretation of field data has been discussed.As a result of this study, the following general conclusions can be drawn:1. Two parameters are sufficient to characterize the deviation of the behavior of a medium with "double porosity"from that of a homogeneously porous medium..2. These parameters can be evaluated by the proper analysis of pressure build-up data obtained from adequately designed tests.3. Since the build-up curve associated with this type of porous system is similar to that obtained from a stratified reservoir, an unambiguous interpretation is not possible without additional information.4. Differencing methods which utilize pressure data from the final stages of a build-up test should be used with extreme caution.

A mathematical model has been used to investigate cross flow effects in a stratified reservoir during an idealized displacement process. A process in which one incompressible fluid displaces completely another incompressible fluid of the same density and viscosity was considered. The reservoir was assumed to be composed of homogeneous layers which are discrete but interconnected. Approximate five-spot flow geometry was simulated by arranging two pie-shaped cylindrical (two-dimensional) wedges in series. Some of the common production methods rely, for their effectiveness, on the fact that the formation consists of isolated strata. This is particularly true of selective plugging and single-zone production- injection methods. The effectiveness of these techniques for several cases in which adjacent strata are in communication has been evaluated. The usual production-injection schemes for fluid injection processes involve using the same completion interval in both the production and the injection wells. The efficiency of this, as well as alternative production-injection procedures has been examined for some cases involving communicating strata. Introduction The performance of many fluid injection projects is marred by early breakthrough and by production of a high percentage of the displacing phase after breakthrough. This channeling effect, if it occurs in reservoirs which have large permeability variations, is often explained on the basis of a model composed of discrete, isolated strata. Corrective or preventive measures based on this same model are also common. The behavior of stratified models has been the subject of considerable study. An excellent review of the early literature was given by Seba. Studies of the depletion performance have since been made for continuous, unrestricted communication between strata and for production from one permeable bed in continuous but restricted communication with an adjacent permeable bed. Model studies of displacement processes in stratified systems with crossflow also have been reported. Finally, methods which account for crossflow have been developed for computing displacement behavior in stratified systems. Most methods for controlling or preventing channeling involve some change in the interval open to production and/or injection. Although many variations of the selective completion problem have been studied in regard to the depletion of a reservoir, little attention has been given to the behavior of a displacement process under similar conditions. Seba used a resistance network model to study the performance of a process in which one incompressible fluid displaces an identical fluid from a linear, stratified reservoir. He investigated the possibility of improving the vertical coverage by limiting the completion interval of the production well. This investigation deals with techniques in which selective completion of the production and/or the injection wells is used in an attempt to control channeling. At one extreme, selective plugging and single-zone isolation (assuming perfect execution) should be successful if the reservoir is actually made up of independent strata. At the other extreme, they can hardly be expected to be successful if the channeling is caused by a mechanism in which stratification effects are negligible even though there are extreme variations in the formation permeability and/or the injectivity profile of the wells is not uniform. By contrast, it is difficult to anticipate the effect that the amount of communication between the beds of a stratified system will have on the efficiency of selective completion techniques. The objective of this study is the quantitative determination of the effect of communication on the behavior of some particular stratified systems which will at least lead to qualitative conclusions. SPEJ P. 229ˆ

The relative costs of heating a reservoir LJYsteam itzjcc-. . tion and by kotnbustkwr hav; been examined, The comparison was based on a model similar to that proposed by Chu.' The cost of boiler feed water, the prtce of fueL pressure and plant capacity were parameters in detertnining the costs of air compression and steam generation. Tile anaIyses compare the cost of heating to the satne radius by the two methods. Results suggest tizat the two primary jactors for comparison are the price O! fuel and the atnount oj crude burned during underground cotnbustion. The cost of juel has a greater effect on the cost of heat from steam than it does on its cost by combustion. As a result, analyses indicate that when the price oj fuel is low, steam tnay be unequivocally cheaper than air. The in-j{uence of heat 10SS is such, however, that as the heated radius increases cotnbustion becomes relatively more cotnpetitive depending upon the atnount of crude burned. This implies titat. steatn tnay be cheaper for small stimulation jobs (huff and puf)) but cotnbustion may be more economically attractive for heating large areas (flooding).

American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc. This paper was prepared for the 46th Annual Fall Meeting of the Society of Petroleum Engineers of AIME, held in New Orleans, Oct. 3–6, 1971. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL OF presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor of the appropriate journal, provided agreement to give proper credit is made. provided agreement to give proper credit is made. Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers office. Such discussion may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines. Abstract Flow and displacement theories for non-Newtonian polymer solutions in porous media have not been advanced to porous media have not been advanced to nearly the extent as those for the Newtonian fluids. At present, the field and experimental data available pertaining to the flow mechanism of pertaining to the flow mechanism of polymer solutions through porous media, polymer solutions through porous media, albeit reliable, are not comprehensive nor complete. Both experimental and theoretical research in development of a more satisfactory theory to describe the flow behavior of polymer solutions in porous media are urgently needed. Laboratory experiments were performed to study the role of mobility performed to study the role of mobility ratio for a process in which oil is displaced from a porous medium by a polymer solution. A reduced friction polymer solution. A reduced friction factor-Reynolds number correlation is developed to predict the flow of various polymer solutions through consolidated porous media and a theory is advanced to explain more truly the flow behavior of a polymer solution as it passes through the cores. The cone and plate viscometer data obtained for a total of 88 solutions of twelve different polymers more frequently used by the petroleum industry appeared to fit the power law equation quite well. The effects on solution viscosity of temperature, sodium chloride concentration, polymer molecular weight and polymer concentration are also discussed. Introduction Among the methods of secondary recovery which have been developed is one which involves the injection of high-viscosity water into the reservoir to improve the mobility ratio and thereby increase the displacement efficiency. The mobility ratio, when two immisicible fluids displace each other, is defined as the ratio of the mobility of the displacing fluid to that of the displaced fluid: displacing M = (1)displaced The mobility ratio is a very important factor in secondary recovery predictions, governing the recovery efficiency of the oil by the displacing fluid. A mobility ratio of greater than one will result in an uneven and an inefficient displacement and a poor oil recovery.

d method of assessing and describing the degree of uncertainty involved in the dedication of capital for drilling an oil or gas well is presented. The problem involves associating probabilities with the range of profitabilities that might result from a particular drilling prospect.This method of risk analysis recognizes the probabilistic nature of the variables affecting profitability. The method systematically combines the distributions of each variable into a final distribution of ultimate profitability. The entire range and distribution of financial outcomes that might occur from the drilling of the prospect and their related probabilities of occurrenCe are provided. A numerical example is given t~illustrate the use of the method.