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By R. C. Earlougher

Based on laboratory tests conducted with the use of fresh core samples as well as a considerable amount of field data obtained from numerous water floods in northeastern Oklahoma, it appears that for any given oil saturation there is a critical maximum velocity above which the oil-recovery efficiency falls off very rapidly. In effect, when a water flood is operated above this critical velocity, the injected water-oil ratio rises extremely fast, thus shortening the economic life of the flood and reducing the ultimate oil recovery. This critical velocity apparently varies considerably with the percentage of oil saturation of the sand, so that in effect the higher the oil saturation at the beginning of a flood the higher the velocity that can be used successfully. In reviewing several of the earlier floods in the Mid-Continent area, it is concluded that most of the failures were due to two things: (I) too low an oil saturation, such as 30 per cent, and (2) too high water-injection rates, Although considerably more field data are necessary to establish definite limits, it would seem that the proper field injection rate for a 330 by 330 or 440 by 440-ft. spacing varies from approximately I bbl. per foot of sand per day where the oil saturation is as low as 30 per cent up to 5 bbl per foot of sand per day when the oil saturation is as high as 45 to 50 per cent, Introduction With secondary recovery by water-flooding receiving more and more attention throughout the industry, a greater working knowledge of multiphase flow under field conditions becomes more and more necessary A great deal of research has been carried on in highly idealized laboratory conditions, from which certain trends have been indicated, but with few exceptions no direct application to field use has been reported. widely varying conclusions have been drawn from the mass of idealized laboratory experiments and often this divergence apparently was due to the neglect of connate or interstitial water. Since interstitial water is such an important factor in water-flooding operations, it then follows that any laboratory flooding experiment must necessarily take it into account; and since it is difficult to set up laboratory models to allow for interstitial water, the next best procedure is to use fresh core samples for such tests. Even this procedure has its difficulties, inasmuch as it is possible to run only one flooding test on each sample, as each sample differs somewhat in character from all other samples. However, this disadvantage can be overcome to a large degree by the use of an extremely large number of samples. The next question that arises is: "IS it possible to get uncontaminated core samples having a true oil and water saturation like that existing in the reservoir?" If the sand under consideration is still in the primary stage of production, with a normal or relatively high amount of gas still in solution in the oil, probably it is not possible to get a nonflushed core. On the other

Jan 1, 1943

By J. M. Bugbee

The engineer and the conservationist agree that effective water drive is the desirable reservoir production mechanism. Water drive may result either from the expansion of edge water, the reservoir water bordering an oil pool, or from the artesian flow of edge water from the outcrop. Thus, the extent of the reservoir has an important bearing upon both the rate and the ultimate quantity of water influx to an oil pool. Lens-type reservoirs are generally recognizable, but the complete structure of the more important domal types, having possible limitations from crestal and synclinal faulting, is not well understood. The delineation from cores, electrical logs and exploitation phenomena of the crestal portions of reservoirs is increasingly exact. This paper suggests that inference from these factual pictures, combined with the scattered well and geophysical data of the synclines and with consideration of the dynamics of structural formation, may be applied to solving the complete geologic structure. Since faulting on the domes and in the synclines may effectively seal and thus limit the size of a reservoir and bar additional water influx, consideration of geologic structure and its possible effects is essential to complete analysis and prediction of reservoir performance. Introduction Implicit in reservoir studies is the fact that the oil must be displaced from the reservoir rock by some other fluid, either gas or water, and this understanding yields the terms descriptive of the major reservoir production mechanisms, gas expansion and water drive' Three recent papers1-2-3 make clear the economic and conservation preeminence of Water drive as a production mechanism; in fact, the title of the latest of these is " Production under Effective Water Drive as a Standard for Conservation Practice." There appears to be an assumption at times among analysts that the effectiveness of a water drive is solely dependent on the rate of oil production; that is, if water drive appears to be insufficient or lacking, a lower oil-recovery rate would increase or reveal it. This assumption might result from the fact that the analysis has been wholly developed during the period of production curtailment; that is, since 1929. The writer takes it that the recurrent phrase in De Golyer's paper,3 "some degree of water drive," is related to this assumption. In California, an extraordinary phrase, "inactive water drive," is rather common and the connotation of uncertainty regarding our knowledge of reservoir performance is evident. Wyckoff2 speaks of the type of reservoir and performance as follows: "In general, reservoirs may be any one or a combination of domal, faulted, lenticular, or stratigraphic traps. Insofar as the dynamic performance of such reservoirs is concerned, the particular type merely determines whether regional flow is symmetrical as in a uniformly developed domal or lenticular type, or one-sided as in many stratigraphic or faulted traps." But whether the flow is

Jan 1, 1943

By J. M. Bugbee

The engineer and the conservationist agree that effective water drive is the desirable reservoir production mechanism. Water drive may result either from the expansion of edge water, the reservoir water bordering an oil pool, or from the artesian flow of edge water from the outcrop. Thus, the extent of the reservoir has an important bearing upon both the rate and the ultimate quantity of water influx to an oil pool. Lens-type reservoirs are generally recognizable, but the complete structure of the more important domal types, having possible limitations from crestal and synclinal faulting, is not well understood. The delineation from cores, electrical logs and exploitation phenomena of the crestal portions of reservoirs is increasingly exact. This paper suggests that inference from these factual pictures, combined with the scattered well and geophysical data of the synclines and with consideration of the dynamics of structural formation, may be applied to solving the complete geologic structure. Since faulting on the domes and in the synclines may effectively seal and thus limit the size of a reservoir and bar additional water influx, consideration of geologic structure and its possible effects is essential to complete analysis and prediction of reservoir performance. Introduction Implicit in reservoir studies is the fact that the oil must be displaced from the reservoir rock by some other fluid, either gas or water, and this understanding yields the terms descriptive of the major reservoir production mechanisms, gas expansion and water drive' Three recent papers1-2-3 make clear the economic and conservation preeminence of Water drive as a production mechanism; in fact, the title of the latest of these is " Production under Effective Water Drive as a Standard for Conservation Practice." There appears to be an assumption at times among analysts that the effectiveness of a water drive is solely dependent on the rate of oil production; that is, if water drive appears to be insufficient or lacking, a lower oil-recovery rate would increase or reveal it. This assumption might result from the fact that the analysis has been wholly developed during the period of production curtailment; that is, since 1929. The writer takes it that the recurrent phrase in De Golyer's paper,3 "some degree of water drive," is related to this assumption. In California, an extraordinary phrase, "inactive water drive," is rather common and the connotation of uncertainty regarding our knowledge of reservoir performance is evident. Wyckoff2 speaks of the type of reservoir and performance as follows: "In general, reservoirs may be any one or a combination of domal, faulted, lenticular, or stratigraphic traps. Insofar as the dynamic performance of such reservoirs is concerned, the particular type merely determines whether regional flow is symmetrical as in a uniformly developed domal or lenticular type, or one-sided as in many stratigraphic or faulted traps." But whether the flow is

Jan 1, 1943

By George Fancher, R. L. Whitting

A typical drilling mud from the Hastings oil field, Brazoria County, Texas, containing only 8 per cent (dry basis) of material of colloidal dimensions, which is largely illite, was concentrated to a density of 10.2 lb. per gal. and used in this study. The effects of water dilution, treatment with complex polyphos-phates, temperature and the time of heating upon the rheological properties of the mud were investigated. It was found that water plays an important part in chemical treatment and that sodium acid pyrophosphate and sodium tripolyphosphate were more efficient than other complex polyphosphates for chemical treatment. Muds treated with either of these chemicals manifested maximum reduction in viscosity and minimum filtration rates at low concentrations. Furthermore, .mud treated to minimum viscosity with either of these two chemicals was virtually unaffected by heat-treatment. Introduction The drilling of deep wells is dependent upon the use of drilling mud, and problems frequently arise concerning the effects on mud of temperature, prolonged heating and aging. The use of chemicals to control the rheological properties of mud is a well-established practice. Salts of weak organic acids such as sodium tannate or gallate were used at first until the complex phosphates of sodium were found to be more efficient. Consequently, it seemed important to investigate the reaction of a mud to chemical treatment with phosphates, temperature, heat-treatment and aging, particularly since previous work in the laboratory at the University of Texas had provided the particle-size distribution and mineral composition of Hastings mud. Properties or Mud Used in Experiments A large sample of the mud from a drilling well in the Hastings field, Brazoria County, Texas, was obtained directly from the circulatory system. Some of the general physical characteristics of the mud and other data are presented in Table I. Table i.—General Properties of Hustings Drilling Mud Alex- Cur-ander keet Well Well Depth when sample was taken, It.. 5720 5700 Weight. lb. per gal............... 9.5 0.8 Viscosity, sec. A.P.I.............. 47 60 Viscosity, Stormer, grams......... 80 Viscosity, centipoises............. 13 Filtration rate, c.c. per 30 min.a. . . 19.6 22.8 Salt content (chlorides), per cent... 0.13 0.12 pH............................. 8.9 8.9 The Alexander mud was used for the experimental work. Comparison with Curkeet mud indicates a considerably greater dilution but otherwise suggests similarity. The mineral composition and particle-size distribution of Curkeet mud (Table 2) are available (Fancher and Oliphant6). It is suggested that Alexander mud would have a similar composition.

Jan 1, 1943

By R. L. Whitting, George Fancher

A typical drilling mud from the Hastings oil field, Brazoria County, Texas, containing only 8 per cent (dry basis) of material of colloidal dimensions, which is largely illite, was concentrated to a density of 10.2 lb. per gal. and used in this study. The effects of water dilution, treatment with complex polyphos-phates, temperature and the time of heating upon the rheological properties of the mud were investigated. It was found that water plays an important part in chemical treatment and that sodium acid pyrophosphate and sodium tripolyphosphate were more efficient than other complex polyphosphates for chemical treatment. Muds treated with either of these chemicals manifested maximum reduction in viscosity and minimum filtration rates at low concentrations. Furthermore, .mud treated to minimum viscosity with either of these two chemicals was virtually unaffected by heat-treatment. Introduction The drilling of deep wells is dependent upon the use of drilling mud, and problems frequently arise concerning the effects on mud of temperature, prolonged heating and aging. The use of chemicals to control the rheological properties of mud is a well-established practice. Salts of weak organic acids such as sodium tannate or gallate were used at first until the complex phosphates of sodium were found to be more efficient. Consequently, it seemed important to investigate the reaction of a mud to chemical treatment with phosphates, temperature, heat-treatment and aging, particularly since previous work in the laboratory at the University of Texas had provided the particle-size distribution and mineral composition of Hastings mud. Properties or Mud Used in Experiments A large sample of the mud from a drilling well in the Hastings field, Brazoria County, Texas, was obtained directly from the circulatory system. Some of the general physical characteristics of the mud and other data are presented in Table I. Table i.—General Properties of Hustings Drilling Mud Alex- Cur-ander keet Well Well Depth when sample was taken, It.. 5720 5700 Weight. lb. per gal............... 9.5 0.8 Viscosity, sec. A.P.I.............. 47 60 Viscosity, Stormer, grams......... 80 Viscosity, centipoises............. 13 Filtration rate, c.c. per 30 min.a. . . 19.6 22.8 Salt content (chlorides), per cent... 0.13 0.12 pH............................. 8.9 8.9 The Alexander mud was used for the experimental work. Comparison with Curkeet mud indicates a considerably greater dilution but otherwise suggests similarity. The mineral composition and particle-size distribution of Curkeet mud (Table 2) are available (Fancher and Oliphant6). It is suggested that Alexander mud would have a similar composition.

Jan 1, 1943

By H. K. Livingston

A technique has been developed which makes it possible to determine the spreading pressure of liquids and solids, for simple systems. Data for surface tensions, interfacial tensions, spreading pressures, and contact angles for water, heptane, and silica are tabulated.' These results can be applied to the evaluation of capillary rise and displacement pressure in a petroleum reservoir. Appropriate equations are presented and the application of these equations is discussed. The presence of surface-active components affects both capillary rise and displacement pressure and also seems to influence the rate of fluid flow. The purpose of this paper is to supplement and bring up to date the last article on the subject of the surface chemistry of petroleum reservoirs, that of Garrison in the 1935 Oil and Gas Journa1.1 A discussion of the "adhesion tension" concept used by Garrison has been presented in another publication,2 together with the reasons for the recommendation that the term "adhesion tension" be abandoned. In view of the fact that some of the data used by Garrison have been superseded by more recent work, it seemed advisable to call attention to this fact and present the more important data currently believed to be correct. In the earlier paper, Garrison set up the equations that 'relate solid-oil and solid-water interfacial tensions to each other, and applied data from Bartell and Miller3 to these equations. However the adhesion tension measurements made by Bartell and Miller involved a confusion of symbols, so that they did not actually measure the spreading pressure, ?s — ?sf.2 The spreading pressure is a convenient method of indicating the amount by which the surface energy of a solid surface is lowered on immersion in a liquid or vapor. Since the initial value of the free surface energy is represented by the symbol ?s and the final value is ?sF, the spreading pressure is ?s — ?SF. A technique has now been developed4 that makes possible the determination of ?s — ?sF for simple systems. This method would be very difficult to carry out with a multicomponent system such as exists in the petroleum reservoir. However, already results have been obtained for ?s — ?sF for water and heptane in contact with silica and graphite. These values will be of the same order of magnitude as those in the petroleum reservoir. Accordingly, it is possible for the first time to discuss the surface-energy relations of the petroleum reservoir on a semi-quantitative basis. Preliminary Generalizations A petroleum reservoir may contain the following four phases: gas, hydrocarbon liquid, aqueous liquid, and solid. The three fluid phases are dispersed through the solid reservoir rock. If gravity were the only force acting, it is obvious that the

Jan 1, 1943

By H. K. Livingston

A technique has been developed which makes it possible to determine the spreading pressure of liquids and solids, for simple systems. Data for surface tensions, interfacial tensions, spreading pressures, and contact angles for water, heptane, and silica are tabulated.' These results can be applied to the evaluation of capillary rise and displacement pressure in a petroleum reservoir. Appropriate equations are presented and the application of these equations is discussed. The presence of surface-active components affects both capillary rise and displacement pressure and also seems to influence the rate of fluid flow. The purpose of this paper is to supplement and bring up to date the last article on the subject of the surface chemistry of petroleum reservoirs, that of Garrison in the 1935 Oil and Gas Journa1.1 A discussion of the "adhesion tension" concept used by Garrison has been presented in another publication,2 together with the reasons for the recommendation that the term "adhesion tension" be abandoned. In view of the fact that some of the data used by Garrison have been superseded by more recent work, it seemed advisable to call attention to this fact and present the more important data currently believed to be correct. In the earlier paper, Garrison set up the equations that 'relate solid-oil and solid-water interfacial tensions to each other, and applied data from Bartell and Miller3 to these equations. However the adhesion tension measurements made by Bartell and Miller involved a confusion of symbols, so that they did not actually measure the spreading pressure, ?s — ?sf.2 The spreading pressure is a convenient method of indicating the amount by which the surface energy of a solid surface is lowered on immersion in a liquid or vapor. Since the initial value of the free surface energy is represented by the symbol ?s and the final value is ?sF, the spreading pressure is ?s — ?SF. A technique has now been developed4 that makes possible the determination of ?s — ?sF for simple systems. This method would be very difficult to carry out with a multicomponent system such as exists in the petroleum reservoir. However, already results have been obtained for ?s — ?sF for water and heptane in contact with silica and graphite. These values will be of the same order of magnitude as those in the petroleum reservoir. Accordingly, it is possible for the first time to discuss the surface-energy relations of the petroleum reservoir on a semi-quantitative basis. Preliminary Generalizations A petroleum reservoir may contain the following four phases: gas, hydrocarbon liquid, aqueous liquid, and solid. The three fluid phases are dispersed through the solid reservoir rock. If gravity were the only force acting, it is obvious that the

Jan 1, 1943

By Richard Zinszer

Application of electric logs has been used in correlation of subsurface structure to determine the size and shape of the oil reservoir. Such a knowledge is hardly complete until saturation and productivity are determined for the various horizons. It is difficult to use electric logs successfully for this purpose because of the many factors that influence the curves. In this work an effort was made to establish an empirical correlation between formation resistivity for a series of electric-log curves and water saturation and oil productivity of sand. Electric logs were obtained by recording with 10 different electrode spacings through the same interval of a well. In the analysis of these curves all factors except two, a dependent and independent variable, were held constant. The interval studied had been cored and a large number of samples were analyzed in the core laboratory in order to compare the values of permeability and saturation with the measured values of formation resistivity. Results of this analysis indicate: (1) the depth to which mud filtrate enters a sand body, (2) a correlation between permeability and sand resistivity for shallow penetration depths, and (3) that the water saturation for an oil sand can be determined from the measured sand resistivity after making suitable correc- tions for sand thickness. The proceduer in the last method depends on a correction for thickness factor and a theoretical curve. The accuracy of the theoretical curve is now being tested in the laboratory. In an effort to place the analysis of electric logs on a quantitative basis, there is need for a better understanding of the many factors that influence an electric-log curve. These factors may be large differences in sand thickness, permeability of the sand, salinity of the interstitial water, mud resistivity, formation temperature, and other sources. A number of examples were presented by Archie,' which treat the effect of sand thickness on measured resistivity. He compared the true resistivity of a sand with the observed resistivity for sands 8 ft., 16 ft., and 24 ft. thick, and found the observed resistivity Of the 8-ft. sand to be approximately

Jan 1, 1943

By Richard Zinszer

Application of electric logs has been used in correlation of subsurface structure to determine the size and shape of the oil reservoir. Such a knowledge is hardly complete until saturation and productivity are determined for the various horizons. It is difficult to use electric logs successfully for this purpose because of the many factors that influence the curves. In this work an effort was made to establish an empirical correlation between formation resistivity for a series of electric-log curves and water saturation and oil productivity of sand. Electric logs were obtained by recording with 10 different electrode spacings through the same interval of a well. In the analysis of these curves all factors except two, a dependent and independent variable, were held constant. The interval studied had been cored and a large number of samples were analyzed in the core laboratory in order to compare the values of permeability and saturation with the measured values of formation resistivity. Results of this analysis indicate: (1) the depth to which mud filtrate enters a sand body, (2) a correlation between permeability and sand resistivity for shallow penetration depths, and (3) that the water saturation for an oil sand can be determined from the measured sand resistivity after making suitable correc- tions for sand thickness. The proceduer in the last method depends on a correction for thickness factor and a theoretical curve. The accuracy of the theoretical curve is now being tested in the laboratory. In an effort to place the analysis of electric logs on a quantitative basis, there is need for a better understanding of the many factors that influence an electric-log curve. These factors may be large differences in sand thickness, permeability of the sand, salinity of the interstitial water, mud resistivity, formation temperature, and other sources. A number of examples were presented by Archie,' which treat the effect of sand thickness on measured resistivity. He compared the true resistivity of a sand with the observed resistivity for sands 8 ft., 16 ft., and 24 ft. thick, and found the observed resistivity Of the 8-ft. sand to be approximately

Jan 1, 1943

By William Hurst

This is a presentation of the diffusivity theory for the calculation of the water drive on an oil reservoir in which the history of reservoir pressure with time are the essential parameters for the determination of the rate and cumulative water encroachment into a field. The main body of the paper is essentially the application of the principles underlined here to actual field data. It consists of the work plots of the radial-flow case, and includes a discussion of an illustrated problem for which the water-drive calculations are treated in conjunction with the volumetric-balance equation. The appendix is a mathematical treatment of the linear, radial, and spherical cases of water influx into a reservoir. Introduction The evaluation of oil reserves and the prediction of pressure behavior with different rates of production are related to the volumetric balance of the fluids entering and leaving the space occupied by the oil and gas originally present in the formation; that is to say, important information can be gleaned from a volumetric study of the oil, gas, and water produced from a formation as it affects the extent of change in volume of oil zone, the gas cap, and the amount of water influx from the adjoining water sands. It is not the purpose of this paper to enter into a discussion of the equation of volumetric balance, in which such pertinent information as subsurface sampling and the measurement of reservoir pressures play a predominant part, as this has been discussed in detail by others.1,2 However, there is an inherent difficulty that has limited the general application of this equation to a study of oil reservoirs; that is, the insufficient knowledge of the analytics for expressing the water drive on a field as a function of reservoir pressure. This to a large degree has been overcome and it is the purpose of this paper to present this theory in such form as to be applicable for reservoir calculations. Water Drive If the amount of oil originally in place and the gas space are known, it is a relatively simple matter to determine, by the volumetric equation, the cumulative water influx into a reservoir from the adjoining water sands. Often, however, the oil reserve as well as water influx must be 'determined, and in order to be able to make this calculation it is essential to assign a mathematical relationship for the varying water term that is compatible with conditions known to exist in the formation and gives an accuracy acceptable for engineering calculations. Various equations have been employed empirically by different investigators in making reservoir studies of water drive. One form used by Schilthuis2 expresses the rate of water influx into a reservoir at any time as proportional to the pressure

Jan 1, 1943

By William Hurst

This is a presentation of the diffusivity theory for the calculation of the water drive on an oil reservoir in which the history of reservoir pressure with time are the essential parameters for the determination of the rate and cumulative water encroachment into a field. The main body of the paper is essentially the application of the principles underlined here to actual field data. It consists of the work plots of the radial-flow case, and includes a discussion of an illustrated problem for which the water-drive calculations are treated in conjunction with the volumetric-balance equation. The appendix is a mathematical treatment of the linear, radial, and spherical cases of water influx into a reservoir. Introduction The evaluation of oil reserves and the prediction of pressure behavior with different rates of production are related to the volumetric balance of the fluids entering and leaving the space occupied by the oil and gas originally present in the formation; that is to say, important information can be gleaned from a volumetric study of the oil, gas, and water produced from a formation as it affects the extent of change in volume of oil zone, the gas cap, and the amount of water influx from the adjoining water sands. It is not the purpose of this paper to enter into a discussion of the equation of volumetric balance, in which such pertinent information as subsurface sampling and the measurement of reservoir pressures play a predominant part, as this has been discussed in detail by others.1,2 However, there is an inherent difficulty that has limited the general application of this equation to a study of oil reservoirs; that is, the insufficient knowledge of the analytics for expressing the water drive on a field as a function of reservoir pressure. This to a large degree has been overcome and it is the purpose of this paper to present this theory in such form as to be applicable for reservoir calculations. Water Drive If the amount of oil originally in place and the gas space are known, it is a relatively simple matter to determine, by the volumetric equation, the cumulative water influx into a reservoir from the adjoining water sands. Often, however, the oil reserve as well as water influx must be 'determined, and in order to be able to make this calculation it is essential to assign a mathematical relationship for the varying water term that is compatible with conditions known to exist in the formation and gives an accuracy acceptable for engineering calculations. Various equations have been employed empirically by different investigators in making reservoir studies of water drive. One form used by Schilthuis2 expresses the rate of water influx into a reservoir at any time as proportional to the pressure

Jan 1, 1943

The movement for Federal endowment of engineering and industrial research was revived early in the present Congress by the introduction of two bills into the Senate. The first bill, introduced by Senator Smith of Georgia, provides for the establishment of an engineering experiment station in each state under the direction of and in connection with some university, engineering school, or land-grant college. The state legislature of each state is authorized to designate the institution best equipped to conduct the work but wherever the land-grant college has facilities approximately equal to those of the other institutions of the state, it shall be designated. All designations of institutions are made subject to the approval of the Secretary of Commerce. The Secretary of Commerce is authorized to secure practical uniformity of methods, and efficiency and economical expenditure of funds by indicating such lines of work as shall seem to him important from a military; naval, industrial or national standpoint, but the responsibility for the initiation and conduct of research shall rest with the individual engineering experiment stations. Uniform standards of research are further provided for by making each experiment station a depository of the Department of Commerce and the Bureau of Standards, and the work of each station shall conform to the standards established by the U. S. Government through said bureau, which may whenever practicable utilize the facilities of the station for the prosecution of research.

Jan 8, 1919

By K. C. Ten Brink, Allen D. Garrison

A rrevious paper1 reviewed some of the properties of clays and shales and presented some data on the nature of the gelling phenomenon. It included a brief discussion of origin of clays and shales, their composition, structure, retention of water, ionization, base exchange, and the nature of the gelling of water suspensions. Other publications of the Institute2-8 have discussed the properties of clays and their relations to drilling-fluid behavior and control. It is the purpose of this article to present some new data obtained and arranged in a different manner and making possible a better understanding of the chemical reactions involved in the control of drilling-fluid characteristics during the normal drilling operations. Experimental Procedure The difficulties involved in the measurements of the flow characteristics of plastic fluids are too familiar to recite. The possible applications of some of the well-known instruments to this problem have been adequately discussed by Hobson9 and he has given an excellent bibliography. Although there are many viscosimeters of varied design, none of them appear to fulfill the most obvious demands of accuracy in the measurement of clay or shale suspensions. Since the fluid characteristics are dependent on the rate of flow of the fluid, and the viscosity usually falls off very rapidly as the rate is increased, it is clear that the first requirement is that the instrument shall be capable of a wide variety of speeds. The viscosity of the fluid at any fixed and constant rate of flow is also a function of time, so that the second demand is that the instrument shall be capable of a constant and continuous motion for a prolonged period of time.

Jan 1, 1940

By K. C. Ten Brink, Allen D. Garrison

A rrevious paper1 reviewed some of the properties of clays and shales and presented some data on the nature of the gelling phenomenon. It included a brief discussion of origin of clays and shales, their composition, structure, retention of water, ionization, base exchange, and the nature of the gelling of water suspensions. Other publications of the Institute2-8 have discussed the properties of clays and their relations to drilling-fluid behavior and control. It is the purpose of this article to present some new data obtained and arranged in a different manner and making possible a better understanding of the chemical reactions involved in the control of drilling-fluid characteristics during the normal drilling operations. Experimental Procedure The difficulties involved in the measurements of the flow characteristics of plastic fluids are too familiar to recite. The possible applications of some of the well-known instruments to this problem have been adequately discussed by Hobson9 and he has given an excellent bibliography. Although there are many viscosimeters of varied design, none of them appear to fulfill the most obvious demands of accuracy in the measurement of clay or shale suspensions. Since the fluid characteristics are dependent on the rate of flow of the fluid, and the viscosity usually falls off very rapidly as the rate is increased, it is clear that the first requirement is that the instrument shall be capable of a wide variety of speeds. The viscosity of the fluid at any fixed and constant rate of flow is also a function of time, so that the second demand is that the instrument shall be capable of a constant and continuous motion for a prolonged period of time.

Jan 1, 1940

By B. H. Sage, W. N. Lacey

An apparatus is described for the measurement of the pressure-volume-temperature relations of pure substances, simple mixtures and complex mixtures with an over-all absolute uncertainty, which is usually not more than 0.2 per cent. The equipment is suitable for studies in the gaseous, two-phase, and liquid regions. The behavior of such systems may be investigated at pressures as high as 10,000 lb. per sq. in. for temperatures between 70 and 600 F. The methods of measurement and the construction of the apparatus are described in some detail. The measurement of the volumetric behavior of multicomponent systems requires the simultaneous measurement of the pressure, volume, temperature and weight of each component of the system. In the present apparatus a sample having constant weight is investigated at a number of independently controlled pressures and temperatures, therefore it is necessary only to establish the weight of each component added before a given set of measurements. This method is in distinction to that in which the total volume remains constant and the pressure is varied by addition or removal of material, the system having variable weight. An objective in the design of the apparatus to be described was to develop equipment that would yield results involving no uncertainties larger than 0.25 per cent throughout the range of pressures from 150 to 10,000 Ib. per sq. in. at temperatures between 70" and 600" F. Although this over-all absolute uncertainty of measurement may not appear to be small, it necessitated care in the plans for control and measurement of each of the fundamental variables. In general, any uncertainty greater than 0.05 per cent in the pressure, volume, absolute temperature or weight of each component was considered undesirable; therefore the attempt was made to obtain a precision of measurement in each case such that the absolute uncertainty would be only half this amount except in certain regions near the ends of the experimental range of the variable under consideration.

Jan 1, 1940

By W. N. Lacey, B. H. Sage

An apparatus is described for the measurement of the pressure-volume-temperature relations of pure substances, simple mixtures and complex mixtures with an over-all absolute uncertainty, which is usually not more than 0.2 per cent. The equipment is suitable for studies in the gaseous, two-phase, and liquid regions. The behavior of such systems may be investigated at pressures as high as 10,000 lb. per sq. in. for temperatures between 70 and 600 F. The methods of measurement and the construction of the apparatus are described in some detail. The measurement of the volumetric behavior of multicomponent systems requires the simultaneous measurement of the pressure, volume, temperature and weight of each component of the system. In the present apparatus a sample having constant weight is investigated at a number of independently controlled pressures and temperatures, therefore it is necessary only to establish the weight of each component added before a given set of measurements. This method is in distinction to that in which the total volume remains constant and the pressure is varied by addition or removal of material, the system having variable weight. An objective in the design of the apparatus to be described was to develop equipment that would yield results involving no uncertainties larger than 0.25 per cent throughout the range of pressures from 150 to 10,000 Ib. per sq. in. at temperatures between 70" and 600" F. Although this over-all absolute uncertainty of measurement may not appear to be small, it necessitated care in the plans for control and measurement of each of the fundamental variables. In general, any uncertainty greater than 0.05 per cent in the pressure, volume, absolute temperature or weight of each component was considered undesirable; therefore the attempt was made to obtain a precision of measurement in each case such that the absolute uncertainty would be only half this amount except in certain regions near the ends of the experimental range of the variable under consideration.

Jan 1, 1940

By H. H. Evinger, M. Muskat

A methoD of calculating productivity factors for oil, gas, and water systems in the steady state is presented as an illustration of the quantitative application of the fundamental data on the flow properties of heterogeneous fluid systems. While the numerical results of the calculations cannot be applied directly to field conditions, because they are based on permea-bility data for unconsolidated sands and involve specific assumptions regarding the nature of the reservoir fluids, the methods of analysis and interpretation should havc significance in considering certain specific field situations when the necessary field and laboratory data become available. Moreover, it is felt that even under the idealized conditions to which the numerical calculations refer they should serve to give at least the orders of magnitude of the effects of gas-oil ratio and connate water on observed productivity factors. Within the indicated limitations, the computations imply that the foregoing factors can explain only a part of the apparent discrepancy between the homogeneous fluid productivity factors and those obtained recently in field measurements on the West Coast. IntroductioN Sufficient laboratory research has been carried out in the last several years on the fundamental features of the flow of heterogeneous fluids through porous media to call for consideration of what can be done with this type of information. It has, of course, already led to a, much clearer general understanding of the mechanics of oil production. However, examples of the quantitative application of the results of such laboratory studies are few in the literature. part of the explanation for this fact lies undoubtedly in the lack of sufficient laboratory data relating to practical fluids and sand systems such as would occur ill actual oil reservoirs. However, unless it can be shown that if such data were obtained quantitative applications could be made, serious doubt may be cast upon the desirability of carrying on further extensive experimental research work on fluid flow. The purpose of this paper is to present one approach to the problem of quantitative application of laboratory data to practical field problems. Because the published results on the basic experiments with three-phase fluid systems in porous media are limited entirely to uncon-solidated sands, the numerical applications made here will not pertain directly to any actual field situation. However, they should serve to illustrate what could be done with fundamental laboratory data if they were extended to cover the field of consolidated sands. From this point of view, it is hoped it will serve to encourage further laboratory research on this problem. The particular application to be treated here relates to the calculation of the productivity factors for oil-gas-water systems in the steady state. This specific problem seems especially appropriate for discussion in view of the recent publication by Johnston1 of the results of produc-

Jan 1, 1942

By M. Muskat, H. H. Evinger

A methoD of calculating productivity factors for oil, gas, and water systems in the steady state is presented as an illustration of the quantitative application of the fundamental data on the flow properties of heterogeneous fluid systems. While the numerical results of the calculations cannot be applied directly to field conditions, because they are based on permea-bility data for unconsolidated sands and involve specific assumptions regarding the nature of the reservoir fluids, the methods of analysis and interpretation should havc significance in considering certain specific field situations when the necessary field and laboratory data become available. Moreover, it is felt that even under the idealized conditions to which the numerical calculations refer they should serve to give at least the orders of magnitude of the effects of gas-oil ratio and connate water on observed productivity factors. Within the indicated limitations, the computations imply that the foregoing factors can explain only a part of the apparent discrepancy between the homogeneous fluid productivity factors and those obtained recently in field measurements on the West Coast. IntroductioN Sufficient laboratory research has been carried out in the last several years on the fundamental features of the flow of heterogeneous fluids through porous media to call for consideration of what can be done with this type of information. It has, of course, already led to a, much clearer general understanding of the mechanics of oil production. However, examples of the quantitative application of the results of such laboratory studies are few in the literature. part of the explanation for this fact lies undoubtedly in the lack of sufficient laboratory data relating to practical fluids and sand systems such as would occur ill actual oil reservoirs. However, unless it can be shown that if such data were obtained quantitative applications could be made, serious doubt may be cast upon the desirability of carrying on further extensive experimental research work on fluid flow. The purpose of this paper is to present one approach to the problem of quantitative application of laboratory data to practical field problems. Because the published results on the basic experiments with three-phase fluid systems in porous media are limited entirely to uncon-solidated sands, the numerical applications made here will not pertain directly to any actual field situation. However, they should serve to illustrate what could be done with fundamental laboratory data if they were extended to cover the field of consolidated sands. From this point of view, it is hoped it will serve to encourage further laboratory research on this problem. The particular application to be treated here relates to the calculation of the productivity factors for oil-gas-water systems in the steady state. This specific problem seems especially appropriate for discussion in view of the recent publication by Johnston1 of the results of produc-

Jan 1, 1942

By H. H. Evinger, M. Muskat

A method has been developed whereby one may calculate the productivity factors of producing formations from a knowledge of the reservoir conditions. Account is taken not only of the heterogeneous character of the gas-oil flow system but also of the detailed variations with pressure of the shrinkage and viscosity of the oil, the solubility of the gas in the oil, and even the variability of the gas viscosity and the deviation of the gas from ideal behavior. Curves are shown giving the results of numerical calculations on the production rate as a function of the pressure differential for a high-prcssure and a low-pressure system, three values of gas-oil ratio being treated in each case. Curves are also given showing the variation with distance from the well of the pressure, oil saturation, and permeability. The effect of connate water is briefly discussed in relation to the apparently large discrepancies between the calculated and observed productivity-factor values. Introduction The significance of the productivity factor as a measure of the capacity of an oil-bearing formation to produce is well recognized; for it is the composite and integrated resultant of the physical prop-crties of both the porous medium and the fluid stream passing through it with respect to the ease with which the particular petroleum fluids present in the formation can flow through it and into producing wells. The most direct method of determining the productivity factor of a well consists, as is well known, in the simultaneous measurement of reservoir-pressure differentials and rates of production and the expression of the data in terms of rate of flow per unit pressure drop.' Actual measurements carried out in this manner on producing wells have given factors that generally lie in the range of o to Ioo bbl. per day per pound pressure drop. This wide range arises not only from variations in permeability but also from the varying sand thickness of producing formations. One of the aims of developing a theory of the mechanics of oil production obviously is that of predicting what the productivity factor should be from a knowledge of the individual characteristics of the producing formation and the fluids produced. For homogeneous fluid systems passing through a porous medium into a producing well, it has been known for some time that the steady-state rate of liquid flow Q is given by the formula:* Q ? u log r?/r? where k is the sand permeability, h its thickness, µ the liquid viscosity, ?p the pressure drop between the well and the distant parts of the reservoir, in particular that at a radius re, and r? is the well radius. This gives the productivity factor: f= Q/kh?p ? 2p/µ log re/r? f=Q/ kh?p ? 2p/µ log re/r? which will have a numerical value for a

Jan 1, 1942

By M. Muskat, H. H. Evinger

A method has been developed whereby one may calculate the productivity factors of producing formations from a knowledge of the reservoir conditions. Account is taken not only of the heterogeneous character of the gas-oil flow system but also of the detailed variations with pressure of the shrinkage and viscosity of the oil, the solubility of the gas in the oil, and even the variability of the gas viscosity and the deviation of the gas from ideal behavior. Curves are shown giving the results of numerical calculations on the production rate as a function of the pressure differential for a high-prcssure and a low-pressure system, three values of gas-oil ratio being treated in each case. Curves are also given showing the variation with distance from the well of the pressure, oil saturation, and permeability. The effect of connate water is briefly discussed in relation to the apparently large discrepancies between the calculated and observed productivity-factor values. Introduction The significance of the productivity factor as a measure of the capacity of an oil-bearing formation to produce is well recognized; for it is the composite and integrated resultant of the physical prop-crties of both the porous medium and the fluid stream passing through it with respect to the ease with which the particular petroleum fluids present in the formation can flow through it and into producing wells. The most direct method of determining the productivity factor of a well consists, as is well known, in the simultaneous measurement of reservoir-pressure differentials and rates of production and the expression of the data in terms of rate of flow per unit pressure drop.' Actual measurements carried out in this manner on producing wells have given factors that generally lie in the range of o to Ioo bbl. per day per pound pressure drop. This wide range arises not only from variations in permeability but also from the varying sand thickness of producing formations. One of the aims of developing a theory of the mechanics of oil production obviously is that of predicting what the productivity factor should be from a knowledge of the individual characteristics of the producing formation and the fluids produced. For homogeneous fluid systems passing through a porous medium into a producing well, it has been known for some time that the steady-state rate of liquid flow Q is given by the formula:* Q ? u log r?/r? where k is the sand permeability, h its thickness, µ the liquid viscosity, ?p the pressure drop between the well and the distant parts of the reservoir, in particular that at a radius re, and r? is the well radius. This gives the productivity factor: f= Q/kh?p ? 2p/µ log re/r? f=Q/ kh?p ? 2p/µ log re/r? which will have a numerical value for a

Jan 1, 1942