IL
APPLIED THERMODYNAMICS SYMPOSIUM
ROBERT H. JACOBY LYMAN YARBOROUGH
Reservoir Fluids and Their Uses The advancement of petroleum reservoir technology imposes a demand for more
fluid prop-
erties data than ever before, and for data of higher accuracy n engineer who desires to calculate qccurate thermoof petroleum reservoir fluids faces a formidable problem. At present, theory based on fundamental principles (intermolecular forces between molecules) will satisfactorily predict the properties of such simple gases as helium and argon (14). For more complex molecules and mixtures, especially for dense phases at higher pressures, the intermolecular potential functions are unknown and, in fact, they may have to be found from experimental data. Thus the reservoir engineer must use empirical equations and correlations to calculate physical properties for the multicomponent mixtures with which he works. These multicomponent mixtures contain so many components that the compounds heavier than pentanes are lumped together or broken into boiling range fractions. Usually the commercial value of the reservoir fluid is such that the engineer will require experimental data for the thermodynamic and transport properties instead of relying on empirical calculational methods. The equipment and methods for making precise PVT measurements on mixtures are largely available or are within the reach of present technology. In the past, the most work on multicomponent mixtures has been in the field of petroleum. Within this field, PVT data related to petroleum reservoir engineering are of great interest because of the large range of pressure and composition variables involved. The work described in this paper will be in that context. Some mention of viscosity and certain other phase behavior measurements will also
A dynamic and transport properties
be made; although these are not strictly PVT data, they are closely allied to reservoir engineering calculations. The subject matter is limited to the authors’ experience and is not intended to be a comprehensive review of all practice. Rather, it is an attempt to describe what we consider good practice and to suggest ideas for future progress in this field of work. PVT Measurements on Single-phase Systems
Gases. One of the easiest and most accurate PVT measurements possible is that of gas compressibility by use of the Burnett apparatus. For the details of a Burnett experiment, the reader may see the reference (7). Several research workers have used it for measurements on pure components and some binary mixtures (70, 37, 43, 45, 55, 58). Very few data on compressibility of multicomponent gas mixtures using the Burnett method have been published (50), although the method is used to some extent for measurements on pipeline sources of natural gas (44) up to about 2000 p.s i.a. In the natural gas production-transmission segment of the petroleum industry, the sale of large quantities of gas daily provides an incentive for accurate mass measurements. A logical extension of Burnett measurements on pipeline gas is to reservoir gases which will not condense liquid throughout their depletion from original reservoir pressure to abandonment pressure. Very few data of this kind are obtained, probably for two reasons: (1) ignorance of the dew point locus of the gas with the resultant fear that the measurements will be erroneous owing to some liquid condensation and (2) the immediate dollar value of the data is not obvious. There are many gas reservoir fluids containing small amounts of higher molecular weight hydrocarbons such that no dew point region will be encountered at reservoir temperatures. Good examples are the newly discovered gas reservoirs in the Netherlands and North Sea. Fluids
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which produce at surface separator gas-liquid ratios of 300,000 standard cubic feet (SCF) of gas/barrel of oil or greater are probably suitable for testing in a Burnett apparatus. If the equipment is designed with a particular geometry (8))it is possible to obtain data for two phase systems of constant composition However, the two-phase Burnett experiment has not been adequately tested, but it offers an opportunity for investigation. If doubt regarding any liquid condensation exists, the reservoir fluid can be tested in a windowed PVT cell to ascertain its dew point and liquid formation characteristics prior to a Burnett test. I t is also rather obvious from the Burnett data themselves when invalid data are being obtained. If liquid condenses selectively in the main chamber, the data points oscillate about a smooth curve when plotted for analysis (P,/P,+l us. P,). The immediate dollar value of highly accurate Burnett compressibility data on reservoir gases is difficult to assess numerically, but compelling reasons for having it are easily identified. When a gas reservoir is first discovered, and before many development wells have been drilled, it is advantageous to have a good estimate of the areal size of the field. The quality of such estimates depends on the precision of measurements of gas produced, bottom hole pressure, and reservoir gas cornpressibility. Good early estimates may save the drilling of dry holes, and further, they enable contracts for future production to be written on a reliable basis. Lack of a reliable basis for a contract results in costly dislocation of operations at a later date and a waste of engineering time then to deal with the attendant problems. A more recent demand for good reservoir gas compressibility data has come from the requirement of state regulatory commissions and pipeline companies for calculation of gas well flow capability at present and in the future. I n this work, an attempt is made to match calculated flow rates and pressure drops to actual test measurements on a well to determine the flow resistance parameters for the well and to extend the calculations to future conditions. The pressure and temperature conditions of the data required for this application cover the range between reservoir and surface conditions and thus are the most extensive of all the cases discussed. During the operation of a Burnett gas compressibility apparatus, the ability to hold constant temperature is a key to the accuracy obtainable. A difference in temperature of less than 0.05O F. on duplicate runs can be detected in the data. The pressure measuring system (dead weight gage and diaphragm separator unit) on the Burnett apparatus with which the authors are familiar can be balanced to the nearest 0.01 p.s.i. for pressures up to about 2000 p.s.i.a., and can be balanced to the nearest 0.05 p.s.i. for pressures from 2000 p.s.i.a. to 10,000 p.s.i.a. From calibrations using helium over a long period of 50
INDUSTRIAL A N D ENGINEERING CHEMISTRY
time, the instrument constant [volume ratio of the two chambers, '%1 = (VI V,)/Vl] has been determined to be 1.487 X X , where X X has a mean value of 30 and has varied from 26 to 35. This variation undoubtedly includes some effect of temperature level, but calibration and use did not extend over a wide enough range to sort temperature and pressure effects from random variations. Under the conditions stated, the Z data appeared to be accurate within 0.057,. Most of the calibrations and data evaluations were made graphically, although more recently a nonlinear estimation program was used to fit the Redlich-Kwong equation of state to the experimental measurements of pressure and simultaneously to evaluate equation, instrument, and experiment parameters. By this procedure, widely varying instrument constants (S) were obtained, Therefore, it was considered more reliable to fix N by the helium calibration method and evaluate only the equation and experimental run parameters by the least square fit of the equation. Values of gas compressibility, 2, calculated in this way, appear to have the same accuracy as those determined by graphical treatment of the data when use of the equation is limited to the low pressure side of Z us. pressure isotherms. If an equation used in this manner will not fit the data points with the accuracy inherent in the instrument constant, then graphical treatment of the data should be used. Difficulty was experienced with the computer fitting program at higher pressures in that unique solutions were not always obtained. Thus, there is a need for better programs to fit nonlinear functions to data. Other workers (37, 55) have reported experience using the virial equation of state in a similar manner. Since the parameters of the Redlich-Kwong equation have only a small dependence on temperature (theoretically they are independent of temperature), it is particularly valuable for use in the manner described above for gas well flow rate calculations. Experimental runs on an actual gas can be limited to as few as two in number, and the resulting constants may be used to calculate gas behavior with accuracy over a much wider range of pressure and temperature conditions than were covered by the experiments. The more popular virial and Benedict-Webb-Rubin (BWR) equations of state are unable to do this as well as the Redlich-Kwong equation of state. Liquids. Liquid compressibility data are needed for the engineering evaluation of oil reservoirs whose initial
+
Robert H. Jacoby is a Senior Research Engineer at the Gulf Research and Development Co., Pittsburgh, Pa., and Lyman Yarborough is a Senior Research Engineer at the Pan American Petroleum Corp., Tulsa, Okla AUTHORS
Figure 7.
PvcMnUrcr sketch
condition is the compressed liquid state-i.e., original pressure is considerably above the bubble point preisure of the fluid. In most cases the data are obtained as part of the routine bottom hole oil sample analysis procedure (discussed later) using a variable volume cell; volumetric accuracy may be no better than 1%. Another important use of liquid compressibility of petroleum products is for the design of fuel injectors and hydraulic power equipment. The Bridgman-type apparatus (5) has been used repeatedly for research work (3, 75) on nonvolatile hydrocarbons and lubricating oils. Industrial work on hydraulic fluids was focused more on adiabatic compressibility measurements by acoustic methods, which are less accurate. Another means, the isoehoric (constant volume) method (42) is probably more appropriate for measurements on petroleum reservoir fluids, although none of these have actually been Used.
The Tait equation can be fitted to PV data on pure hydrocarbons (75, 23, 60),and the closeness of the fit approaches the precision of the experimental data themselves. A procedure for using the Tait equation for liquid mixturq analogous to the fitting of the RedlichKwong equation to a few experimental Bumett measurements, could be highly useful for industrial calculations involving compnepsed liquids. The density of a reservoir fluid at its original condition is required if performance predictions showing individual
component behavior are to be made. The density can be measured at a given temperature and pressure by using a pycnometer (“pyc”) and a gravimetric balance. Figure 1 shows a sketch of a 29.5-cc. instrument having a pressure rating of 15,000 p.s.i a at 250” F and a weight of 597 grams. In use either the pyc is charged to the system pressure while being held at the system temperature, or auxiliary volumetric measurements are used as an arbitrary volume of fluid at measured P,and f is displaced into the pyc. In the latter method the pyc can be held at any convenient temperature. The volumetric measurements can be made by a calibrated screw pump or using a variable volume cell. Injecting a known fluid volume (if the volume measurements of the auxiliary apparatus are accurate enough) is preferable to filling the pyt to the system pressure while keeping the pyc at the system temperature. This is true not because the pyc calibrations are less accnrate, but because of the flashing of gas out of solution oi of condensing liquid from a gas when the pyc is first filled and the necessity for re-establishing uniform single-phase conditions in the pyc before shutting it off from the supply of fluid being measured. Usually when the pyc is loaded to the system pressure, measurements for saturated liquid phases are made by isolating the phase and compressing it somewhat above its saturation pressure so that two phases do not separate in the transfer lines or exist in thi loaded pyc. In general, laboratory PV and density data for engineering use should be measured with an accuracy of 1.0 to 0.5%. With tke pycnometer shown in Figure 1, liquid densities can be obtained within this desired accuracy. Basic data for reference or research study should be measured with an accuracy of 0.1% or bett Mearunmenls on Two-Phase Systems
. .
PetrolGm reservoir situation. When the phase behavior of multicomponent mixtures is mentioned, a mental image often created is that of a p h a boundary ~ loop on P t coordinates, with its characteristic critical point. Actually such a P t phase boundary curve has relatively little use in petroleum reservoir engineering because it represents the behavior of only a single composite mixture. During depletion or gas injection operations of either an oil or gas ~ t ~ e ~ othe i rcomposite , fluid at any point. in the reservoir varies continuously with pressure and/or time. This is aLP0 true in the tubing string rising to the surface. Hence, even for one given original reservoir fluid composition, data are needed for an infinite number of compositions derivable from it. For this reason the approach to calculating the behavior of such systems should consider compositional changes, and this is where research on multicomponent systems is sorely needed today.
-
-
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The first problem concerning petroleum fluids in reservoir engineering is to obtain a representative sample of the original fluid in place and to define completely its composition and properties. Without this information, engineering calculations for predicting future performance of the reservoir are of poor quality, if not completely impossible. The problem begins with the collection of appropriate fluid samples from the field. Only one sampling situation will be considered here; for a more thorough discussion the reader is referred to the references (7, 48, 4 9 ) . Samples from a reservoir are most commonly obtained as companion oil and gas phases from a primary surface separator as shown in Figure 2. Samples of streams B and C are obtained and the flow rates of streams B and D are measured. From this information it is necessary to reconstruct a sample of stream A for physical measurements. This can be accomplished through the following steps: ( a ) Fractional analysis of samples of B and C and, depending on subsequent use of the data, a further fractionation of the heptanes and heavier portion of C into 50' F. boiling range cuts, and measurement of the molecular weight and specific gravity of each cut. It is adequate to stop fractionation at the equivalent atmospheric boiling point of 450' F. and then to measure molecular weight and specific gravity of the residue. ( b ) The composition of C is used with suitable Kvalues (27) (equilibrium vaporization ratios) to make flash calculations simulating the operation of the intermediate separator and stock tank. By use of these results and a liquid density correlation (57), the field measured volumetric rate of D is converted to the equivalent mass or moles of C. With a gas compressibility correlation (50), the field measured volumetric rate of B is converted to mass or moles, and the proportion of B to C is calculated as the recombination ratio required to reconstruct stream A . An appropriate quantity of gas B is charged to a (c) variable volume windowed cell. The P, V, and T measurements are taken at convenient conditions and are used to determine the mass charged to the cell. Usually a I-liter capacity cell is filled at a pressure below 1500 p.s.i.a. at a temperature from room to reservoir temperature (120' to 300' F.) where 2 can be calculated accurately (50). (d) Based on the mass of gas charged, the recombination ratio, and the liquid density, the correct amount of sample C is charged into the cell by a calibrated screw pump at a pressure which is above both its bubble point and cell gas pressure. ( e ) The mixture so charged is then heated to the test temperature (reservoir temperature in this case). The pressure is raised, and agitation of the mixture is commenced until the mixture is in single-phase condition. 52
INDUSTRIAL A N D ENGINEERING CHEMISTRY
Figure 2. Diagram of jield separator train
The steps given above can be shortened if a high pressure liquid meter is used in the field to measure the flow rate of stream C instead of relying on the indirect method of calculating it from the rate of stream D. After being recombined in the windowed cell, the mixture is ready for the measurements desired, but description of these is deferred until the PVT cells are described in a subsequent section. For research work with synthetic systems of a limited number of pure components, the components (or previously prepared mixtures of several components) are charged to the cell one at a time as gases or liquids, whichever is appropriate. A forthcoming paper (61) describes work of this sort. Often the accuracy with which mixtures can be prepared in this way is not limited by the accuracy with which pressures, volumes, and temperatures can be measured, but rather by the accuracy of the basic data available on the pure components involved. For example, the data for liquid ethane at room temperature (53) are notably poor. This is all the more surprising when it is considered that liquid ethane is now a large volume item of commerce. Also, for research purposes, each of the steps related above can be refined for higher accuracy. Instead of relying on calculated densities for the charging calculations, measured values of gas compressibility and liquid density can be determined by the methods outlined in the section on PVT measurements on single-phase systems. High pressure windowed cells. Two types of windowed cells which have been used for PVT studies and by the authors are sketched in Figures 3 and 4. Each cell has a maximum volume of about 1000 cc. The volume in each is varied by means of a piston driven by high pressure hydraulic oil which is, in turn, supplied by an air driven intensifier. The cells are enclosed in thermostated air baths, and agitation of the test fluids is accomplished by rocking the cells. I t is normally possible, using a Hallikainan controller, to maintain air temperature within * O . l ' F. Departures of 1'F. for an hour are readily noticed in the volumetric data.
The cell in Figure 3 is the more general purpose cell and it is particularly convenient to operate. The piston seals consist of Teflon V-rings facing opposite directions in an unsupported area-type design. No problems with hydraulic oil leaking into the test fluid are encountered; in fact, the seals can become too tight and make the piston difficult to move. A metal diaphragm gage protector is mounted in the top of the cell body and connected to Heise and dead-weight gages, and a small screw pump is provided for balancing the diaphragm. The dead weight gage measures pressure to the nearest 1 p.8.i. The window at the end of the bore is backed up with a closure having a vertical slit through it, coinciding with the diameter of the cylinder. By this means, the liquid height on the window can be observed with a cathetometer and liquid phase volume determined. Readings are usually taken with the cell in a perfect horizontal position, but to read very s m a l l phase volumes more accurately the cell was calibrated for liquid readings when tipped down 30°, and for small amounts of gas phase when tipped up 3 0 ' . The total cell volume is read by using a vernier on the piston rod and an adjacent scale. The AV between the smallest vernier divisions is 0.4 cc. Nonvariable or dead volume has been kept very small, to about 7.75 cc., largely by avoiding use of a circulating pump. The smallest readable volume of liquid is approximately 0.5 cc. with an accuracy of f 0.2 cc. Samples of the phases may be withdrawn from ports at the top of the cell and at the bottom, very clase to the
Figurc 4. Skfch of windowed cmtdansata call
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Table 1.
Composition of Typical Reservoir Fluids snurhe. . w a r . m W l mu0
issaia
13,274
(NOOWdry rJ
R n n cendms&) Wdllk.om corn1
CooIpOI88l
0.30 94.41 2.78 1.44
Nitrogen Methane Carbon dioxide Wane Hydrogen witlde Propane ;-Butane n-Butane &Pentam n-Pentane Hexanes Heptanes
+
Mol. wt. C,+ Sp. gr. Cic Reservoir temperature Saturation preuum
1
Saturaticm density
0.34 0.07 0.10 0.04 0.04 0.04 0.44 160 0.8190 258' F. 750 p.s.i.a. (DP) 0.2002 g./cs.
1
1.79 78.87 1.94 6.61 0.11 3.22 0.71 1.32 0.57 0.60 0.92 3.34 18 0.7750 205' F. 5290 p.s.i.a. (DP) 0.2867 g./cc.
m
I
I
75
a9
I
05
R)
95
I
1W
wnh. Y
54
INDUSTRIAL A N D ENGINEERING CHEMISTRY
0.88 67.96 0.53 6.21 9.42 2.37 0.56 1.51 0.67 0.54 1.47 7.88 135 0.7925 217' F. 4415 p.s.i.a. (DP) 0.3666 g./cc.
1.55 51.97 0.29 11.72 9.23 1.06 3.07 0.81 1.01 1.59 17.70 185 0.8231 164' F. 4075 p.s.i.a. (BP) 0.5560 g./cc.
window. Visibility with thii window is reasonably good; difficulty is experienced principally with black oils. The window was not really designed to obtain excellent visibility per se-the prime p u ' p o ~ eis to enable satisfactory measurement of liquid volume. The cell shown in Figure 4 was originally designed to gain more visibility (but still minimize the number and sue of windows) and to increase the accuracy of measuring small amounts of liquid. The cell was designed specifically for measurements on gas condensate fluids which do not condense much liquid. The disadvantages of this cell are a large dead volume (60 cc.) plus the inability to measure one phase if it exceeds the visible volume of 50 cc. Other cells have been described in the recent literature (32,33) one of which (33) has good visibility and a small dead volume. These cells use mercury to vary the test volume-a feature that can be objectionable since large amounts of mercury increase the hazard of working in a PVT laboratory. Also mercury will form emulsions with some oils to make the oil-mercury interface measurement quite uncertain. The cell in Figure 3 was originally equipped with a magnetic pump to circulate the liquid phase and to achieve equilibrium behvecn the phases. Experience has also been obtained with a miniature motor driven vane pump for circulation purposes on another piece of equipment. Neither pump operated consistently with-
Table II. Composition of Reservoir Fluid Near Critical Point Componmt
Nitrogen Melhane Carbon dioxide Ethane Propane i-Butane n-Butane i-Pentane
n-Pentane Hexanes
Figwa 6. V o l m pcr cent liquid arvcs for vmiur types of resum>
pUi&
out a lot of maintenance and both introduce datively large uncertainty into the liquid phase volume measurement. Therefore, both cells were mounted on pivots and equipped with motor driven rocking mechanisms This has proved satisfactory. Mixing is obtained in the single phase (gas and light hydrocarbon phases) in a reasonable time (1 to 2 hours). The time necessary to reach equilibrium with a gas-heavy oil system (42’) (72, 27). Each particular type of test is not elaborated in detail here because all employ common equipment and basic operational methods which have already been described. In nearly all cases, complete determination of the fluid properties was not made VOL. 5 9
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pressure depletion in a reservoir. Since work of this nature is beliwed to hold major promise for future work, it will be discussed in some detail. The volumetric data used for the fitting process were the flash curve or volume per cent liquid us. pressure (for a given temperature) at constant composition (Figure 6). By use of the fluid composition and trial sets of K-values, flash calculations were made at pressure intervals from the saturation pressure down to 1000 p.s.i.a., with the objective of matching the observed per cent liquid at all pressures. The use of gas and liquid phase density correlations was involved, of necessity, and the assumption of suitable accuracy on their part was an integral part of the process. As a basis for starting, calculations were made at low pressures from 100 to 1000 p.s.i.a. with a correlation such as the Chao-Seader [in the form made available by the NGPA (27)l which is capable of assessing the nonideality of petroleum mixtures. The position and trend of the K us. pressure curves below 1000 p.s.i.a. were thus established-a material aid to extension of the K-curves to higher pressures by trial and error. For this work it was necessary to have a correlation of K-values based on convergence pressure as the correlating parameter.
-gas and oil phase densities and compositions were seldom measured-so the results lack research value. New methods for handling reservoir fluid systems. The fundamental way of calculating the phase behavior for a multicomponent system is through the use of equilibrium vaporization ratios (R-values) in flash calculations. The differentiation of an equation of state to obtain component fugacities is a means for obtaining the needed K-values. It has also been traditional to develop empirical correlations of K-values directly. However, the pap between the available correlations and the quality of data required to accurately predict the behavior of high pressure reservoir fluid systems is large. Furthermore, there is little promise that this gap will be filled in the reasonable future. This is true for fluid systems in other important areas of industrial interest; for example, low temperature processing of natural gas (26),high temperature refinery operations (4, and the separation of chemical mixtures. An effort (28) to bridge this gap was made by “fitting” a set of K-values to volumetric data on a particular reservoir fluid, and it was assumed that the K-values thus obtained have validity over the range of compositional variations encountered as this same fluid undergoes
Table 111.
Senritivih of Volumetric Data to K-Valuer
-
.-.: ,,,.t ,
., .. :.
I
’r .~, . , . . , . p : : . ~ ~
K-vdur d
Mefhane Carbon dioxide
i-Butane n-Butane i-Pentane n-Pentane Hexanes
250’ F., av. b.p. 300’ F., av. b.p. 350” ,.F av. b.p.
pda.
K-vmlur m~ 7500 p.s.1 -
K-va~ues 7000 p.s.~.m.
1.14 1.10,1.1011, 1.1016 1.02 1 .oo 0.98 0.95 0.938 0.907 0.900 0.848 0.820 0.786 0.740 0.700 0.630 0.560 0.325
1.30 1.165, 1.166, 1.1664 1.07 1 .oo 0.95 0.902 0.883 0.838 0.820 0.755 0.715 0.675 0.625 0.575 0.512 0.440 0.230
1.245, 1.2485, 1.255 1.10 1 .oo 0.921 0.86 0.83 0.76 0.74 0.66 0.615 0.573 0.525 0.475 0.405 0.340 0.155
0.5 2.23,O. 96,O. 40
3.3 3.72,3.41, 3.29
7.0 7.44,7.00, 6.21
I .46
Dew paint pres. Expt. vol.
% liquid
Calcd. vol.
58
% liauid
I N D U S T R I A L A N D ENGINEERING C H E M I S T R Y
Such a correlation should include data for hydrocarbons or petroleum fractions boiling up to 600' F., and it is also important that the correlation have a high degree of internal consistency; its absolute accuracy need not be high. Probably the best existing example of such a correlation is the unpublished thesis of Hinshaw (24, although the NGPA K-charts (79)and the Rzasa, Glass, Opfel charts (52) are acceptable substitutes. Using these, one would begin the trial and error fitting by selecting-for a given pressur-era1 sets of Kvalues for different convergence pressures and by testing each for prediction of per cent liquid. After a match is made for a full series of pressures, the K-values which prcduced the match are plotted on the K us. P grid. At this point one usually finds that the Kvalues are irregular and do not produce smooth curves. The process becomes one of arbitrary trial and error adjustment to produce a match to volume per cent liquid and still maintain completely smooth K us. P and K us. nBP plots. This seems rather arbitrary, as stated, but if it is done within all the appropriate restraints, the freedom for arbitrary adjustment is quite limited. Certainly such a process needs all the help it can derive from good correlations and valid theoretical restraints to govern the fitting, but it is believed to be capable of generating a set of K-values for a fluid which are more accurate than those from use of the convergence pressure cornlation directly. Thus, it is not necessary to predict the convergence pressure, nor does the correlation itself have to meet stringent requirements of accuracy. To illustrate this, some results are given in Table I11 which show the sensitivity of the volumetric data to the K-values. Note
that at 8000 p.s.i.a., the methane K-value must be adjusted to the nearest 0.01% to match the per cent liquid the accuracy of the experimental data while at 7500 p.s.i.a. the methane K-value must be adjusted to the nearest 0.06% and, at 7000 p.s.i.a., the methane R-value must be adjusted to the nearest 0.16%. I t is immediately obvious that no misting K-correlation or anything even contemplated could p d i c t Rs with such accuracy. This is the easence of the situation. The volumetric data are easily and accurately measured, and they are a sensitive measure of the phase behavior. If the Kfitting techniques can be developed to a high order of validity, it will be possible to predict the behavior of systems which cannot be described accurately by any other foreseeable means. K-values fitted to a flash Curve in this manner are then used to calculate the depletion performance of a gas condensatttype reservoir fluid. The applicability of IC's fitted to the one original mixture composition and used for predicting the behavior of other mixtures derived from the first one has been questioned. The first rationale for so doing was based on the idea that in the region immediately M o w the saturation pressure (down to about 3600 p.s.i.a. in Figure 7), total mixture composition changes slowly during the reservoir depletion process. It was postulated that such small composition changes had a negligible effect on the R-values. This conclusion is also encouraged by the volumetric data from the depletion process (also shown in Figure 7)they follow the flash curve c l d y down to the maximun) per cent liquid point. From about 2000 p.8.i. down, the volumetric data become quite insensitive to the K-values and depend largely on the mixture compajition itself. Thus, the fitted K-values are very appropriate as shown by the comparison between calculated and experimental depletions for the two gas condensates shown in Figure 7. Moreover, the literature (78) and recent reseamh (67) have produced data to substantiate the assumption that in a series of mixtures prepared from varying proportions of given gas and oil components, the total mixture composition (or mixture GOR) does not affect the Kvalues noticeably until the fraction of oil components in the mixture reaches very small values. At this point changes in saturation pressure (or convergence pressure) can become important. The data given in Table IV illustrate both points. The R-values do remain relatively constant over a wide GOR range, but at 1040 p.s.i.a. some changes in the IC-values can be seen for the leaner (high GOR) mixtures. At 1538 and 2037 p.s.i.a., the GOR effect is less because the convergence pressure (and saturated pressure) for the leanest mixture is lower than for the other mixtures. Large composition changes can take place in the resuvoir during a gas injection operation. Important compajition gradients are established as a result of injecting a fluid which is substantially different from the mixtures in situ. Therefore, it may be necessary to m o d i the K-fitting concept by fitting volumetric data VOL 59
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Figure 8. Viscosity redu " and
.'Afhabarca Im by propons at 90' F.
from a simplified experiment of some kind in which the in situ reservoir fluid is successively contacted with the gas to be injected. In other words, the general concept is still applicable; K-values are fitted to appropriate and sufficient experimental data as required by the circumstances. Thereby, a set of quite accurate K-values are derived from l i i t e d experimental data (volumetric) which are far easier to measure than compositional data, and the resulting Rs may be used for calculations involving a much larger series of mixtures than the few tested. Since these notions were first presented (28)they have been used increasingly (2,6). Standing (57)described a simpler procedure earlier, but regardless of historical origin, methods of this nature deserve more research attention. They need development to the point where they can be uniformly and conveniently applied in regular engineering use. Within the past two years a number of computer programs have appeared (9, 77, 35,40,46,59)which attempt to calculate phase behavior in a reservoir in more detail than ever before. The reservoir area is subdivided into a large number of unit volumes, each of which is treated as a theoretical plate or transfer unit. Significantly, many of the investigators (9,77,35) chose not to base their computations on fundamentals, but attempted to simulate phase behavior in an empirical way. This illustrates the difficulties one faces in attempting to calculate multicomponent mixture behavior rigorously, but the strong interest in developing programs to calculate such behavior also illustrates the desire to have the results. It will be a major advance when such programs become valid and practical for engineering use. 60
Figwe 9. Darnmind
I
the wax point o j a CI
1
15oOp.s.i.
INDUSTRIAL AND E N G l N E e R l N G CHEMISTRY
Miscellaneaus Phase Behavior Mearunments
The PVT behavior of reservoir fluids is of major importance in making material and volume balances. The requirements for fluid viscosity data rank equally high for use in flow rate calculations. The phase behavior of systems in which a solid phase forms has not attracted as much interest, although such behavior may cause critical operating problems when it occurs. A residual area of interest in reservoir technology is the PVT and phase behavior of water solutions in contact with hydrocarbon phases. Much of the recent viscosity data on hydrocarbons at high pressure have been obtained a t the Institute of Gas Technology, Chicago, and they are summarized in a new monograph (37). Correlations of these data applicable to light hydrocarbon solutions were presented (37),and Thodos' correlation (30)has been made useful for crude oils (39). However, few research data on crude oil systems have been presented recently. Engineering needs exist for use in calculating the behavior of new secondary recovery processes in which flue gas, air, or carbon dioxide may be injected. Their use is postulated for the reduction of oil viscosity due to solution of the injected gas in the oil, but the most appropriate use of solutcl to lower viscosity is for very heavy oils or tars. Figure 8 shows some rough measurements on mixtures of Athabasca tar and propane. Such behavior is typical of oils below 20' API in gravity. Carbon dioxide is not a suitable solute for heavy oils because it causes precipitation of asphaltic components when the oil is saturated with pure CO, at pressures approaching the CO* critical pressure. On the other hand, substantial quantities
of propane may be dissolved in tars and heavy oils without the precipitation of solids. Qualitatively the limit is approximately 40 weight per cent propane in solution at the onset of precipitation. I n more general terms, it is known that the addition of methane and the light hydrocarbons into solution with heavy oils tends t? solubilize the hydrocarbon waxes and prevent their precipitation, but they likewise tend to cause the precipitation of the asphaltic constituents in crude oils. Thus, when natural gas is dissolved in heavy crude oils under pressure, the net effect will depend on the quantity of gas dissolved (pressure) and the composition of the crude. The accumulation of paraffin wax deposits in the well tubing near the surface was always thought of as a temperature-solubility effect, but recognition of the composition-solubility relationship has raised questions as to the possibility of wax precipitation within the reservoir as gas evolves from solution during pressure depletion. An interesting series of measurements appropriate to this problem can be made using a rolling ball viscometer. A series of oil phases, such as those obtained in the
DVA analysis of a bottom hole sample, was tested in the viscometer at a series of decreasing temperatures. Typical data are shown in Figure 9, where roll time is plotted as a function of temperature for an oil phase having a given saturation pressure at reservoir temperature. The data define a discontinuity analogous to the saturation pressure on a PV curve. For a series of such curves at decreasing pressures, the discontinuity is seen to advance to higher temperatures. Since there is a very small clearance (0.001 to 0.005 inch) between ball and tube in this instrument, the discontinuity is believed to occur when paraffin wax starts to precipitate and causes increased resistance to ball movement. The ball will roll in a normal way for some distance below the break point temperature before enough wax accumulates to stop it entirely. The stopping point may be more analogous to the ordinary pour point measurement at atmospheric pressure, whereas the break point described above is the onset of precipitation. I t is not known whether similar observations could be made with a capillary viscometer, or whether the rolling ball is peculiarly suited for this task.
F.
Vapor-liquid equilibrium K-valuer at 200' Component
Methane Ethane Propane n-Pentane n-Heptane Toluene n-Decane
Methane Ethane Propane n-Pentane n-Heptane Toluene +Decane
Methane Ethane Propa ne n-Pentane n-Heptane Toluene n-Decane
GOR = 2052a
GOR = 5502b
2.788 1.160 0.651 0.204 0.0657 0.0524 0.0156
2037 P.s.i.a. 2.152 1.030 0.626 0.236 0.0992 0.0762 0.0250 1538 P.s.i.a. 2.803 1.150 0.633 0.193 0.0640 0.0509 0.01 1 1
4.015 1.493 0.708 0.177 0.0497 0.0416 0.0061
4.020 1.475 0.710 0.176 0.0490 0.0403 0.0063
2.173 1.009 0.619 0.237 0.0958 0.0807 0.0243
OOR = 10,087c
GOR = 24,01iSd
2.266 1.082 0.631 0.233 0 0945 0,0772 0.0265
2.265 1.060 0.624 0.232 0.0916 0.0736 0.0251
2.936 1.203 0.637 0.190 0.0648 0.0512 0.0134
2.927 1.201 0.637 0.186 0.0603 0.0475 0.0109
4.318 1.549 0.722 0.177 0.0474 0.0351 0.0054
4.666 1.565 0.712 0.160 0.0450 0.0350 0.0058
VOL. 5 9
NO. 1 0 O C T O B E R 1 9 6 7
61
The significance for reservoir operations is whether the break point temperature ever exceeds reservoir temperature before abandonment pressure is reached. If so, a pressure maintenance program would be necessary in the reservoir to avoid plugging and cessation of oil flow.
are poor (38, 47, 54). I n practice, it is nowhere near meeting requirements for data. Hence, the suggestions here are made in the context of requirements for substantially better accuracy than is obtainable from the bulk of material now available and for methods of practical use for petroleum-type mixtures.
Summary
Some present laboratory methods for measuring the PVT and phase behavior of multicomponent systems have been described, and the engineering uses of these data have been pointed out. An attempt to assess the real need for various data in terms of operational value was made in order to develop more appreciation and incentive for research in this field. I n essence, two major approaches for practical progress are outlined : (1) The fitting of equations of state to PVT data on pure components, binary mixtures, and multicomponent mixtures. Suitable equations must have no more constants than are absolutely necessary; the Redlich-Kwong equation for gas or liquid phases and the Tait equation for liquids are good examples, but the field is wide open for generation of new forms based on analysis of actual data. It would be particularly desirable to have an equation form to describe well both gas phase and liquid phase behavior. A system for making the experimental measurements and suitable computer programs for fitting an equation to the data would be highly useful for calculating the behavior of operations through which constant fluid composition is maintained. For operations in which two phases are present, it will be necessary to develop the composition dependence (mixing rules) of the constants in the equation of state. The composition dependence expressions must be applicable to narrow boiling fractions, as are commonly defined in the petroleum industry. A significant advance can probably be made by considering binary interaction coefficients only, hence the need for fitting the equations to pure component and binary data, and then testing the mixing rules on multicomponent data. If good enough these equations should then be differentiable to obtain thermodynamic properties and phase behavior. (2) A means for systematizing or organizing to a higher degree the procedure for fitting K-values to volumetric data on multicomponent systems. Ideally, this would comprise an analytical function which has the typical shape of a multicomponent set of K-values from low pressure to single-phase pressure of the system and one which relates the curves of individual components to one another. Again, it must have relatively few parameters so that it is practical to fit it to data for each fluid of interest. In this case, an equation of state suitable for calculating phase densities is also needed. One could say with some justification that many of the things suggested above have already been done. This is true only in a very limited context; for example, one might say that the BWR equation exemplifies approach 1 above. I n concept it does, except that its form does not inherently fit data well and its extrapolation possibilities 62
INDUSTRIAL A N D ENGINEERING CHEMISTRY
REFER ENCES (1) “API Recommended Practice for Sampling Petroleum Reservoir Fluids,” API R P 44 Bull., 1st Ed., API Division of Production, Dallas, Tex., January 1966. (2) Berryman, J. E., Trans. A I M E 210, 102 (1957). (3) Bradbury, D., Mark, M., Kleinschmidt, R. V., Trans. A S M E 73, 667 (1951). (4) Braun, W.G.,Thompson, W. H., Fenske, M. R., Proc. A P I 4 6 , 111 (1966). (5) Bridgman, P. W., Proc. Am. Acad. ArtsSci. 6 6 , 185 (1931). (6) Brinkman, F. H., Sieking, J.N., Trans. A I M E 2 1 9 , 313 (1960). (7) Burnett,E. S., J . Appl. Mech. 58, A136 (1936). (8) Burnett, E. S., USBM R.I. 6267 (1963). (9) Butterfield, 0. R., Clark, J. D., Brauer, E . B., SPE Paper No. 1219 (1965). (10) Canfield, F. B., Leland, T. W., Kobayashi, Riki, J . Chem. Eng. Data 10, 92 (1965). (11) Clark, N. J., “Elements of Petroleum Reservoirs,” SOC.Petrol. Engrs., p. 49 Dallas, Tex., 1960. (12) Cook, A. B., Johnson, F. S., Spencer, G. B., Bayazeed, A. F., J . Petrol. Technol. p. 245 (February 1967). (13) Cook, A. B., Spencer, G . B., Bobrowski, F. P., Trans. A I M E 192,37 (1951). (14) Coulson, C. A., DiscussionsFaraday Sot. 40,285 (1965). (15) Cutler TV. G., McMickle, R . H., Webb, W., Schiessler, R. W.,J. Chsm. Phys. 29, 727 (i758). (16) Dodson, C. R., Goodwill, D., biayer, E. H., Trans. A I M E 198, 287 (1953). (17) Eilerts, C. K., Sumner, E. F., SOC.Petrol. Engrs., Paper S o . 1499 (1966). (18) Eilerts, Kenneth, Smith, R. V., L’SBSBM R.I. 3642 (April 1942). (19) “Engineering Data Book,” Natl. Gas Proc. Assoc., Tulsa, Okla., 1957 and 1966. (20) Ibid., p. 47. (21) Erbar, I.,Persyn, C. L., Edmister, W. C., Proc., Natl. Gas Proc. Assoc., p. 26 (1964). (22) Evans, R. B., 111, Harris, D., Ind. Eng. Chem. Data Series 1 (l), 45 (1956). (23) Ginell, R . , “Advances in Thermophysical Properties at Extreme Temperatures and Pressures,” Third Symposium, p. 41, ASME, New York, 1965. (24) Hinshaw, D. F., “Correlation of the Vapor Li uid Equilibrium Constants of Hydrocarbons,” Ph.D. Thesis, Univ. of Michigan, 4955. (25) Hutchinson, C. A., Jr.,Braun, P. H., A.I.Ch.E.J. 7,64 (1961). (26) Jacoby, R . H., Proc. A P I 44, 111, 288 (1964). (27) Jacoby, R. H., Trans. A I M E 213, 57 (1958). (28) Jacoby, R . K., Berry, V. J., Ibid., 210,27 (1957). (29) Jacoby, R . H., Rzasa, M. J., Ibid., 195, 99 (1952). (30) Jossi, J.A., Stiel, L. I., Thodos, G., A.I.Ch.E. J . 8, 59 (1962). (31) Kalfogiov, N. K., Miller, J. G., J . Phys. Chem. 71, 1256 (1967). (32) Kehn, D. H., J . Petrol. Technol. 16, 435 (1964). (33) Kilgren, K . H., Ibid., 18, 1001 (1966). (34) Kilgren, K. H., Proc., Natl. Gas Proc. Assoc., p . 39 (1963). (35) Kniazeff, V. J., Naville, S. A., Soc. Petrol. Engrs. J. 5 , 3 7 (1965). (36) Koch, H. A , , Jr., Hutchinson, C. A., Jr., Tranr. A I M E 213,7 (1958). (37) Lee, A . L., “Viscosity of Light Hydrocarbons,” Am. Petrol. Inst., New York, 1965. (38) Lin, M.,Naphtali, L. M., A.I.Ch.E. J . 9, 580 (1963). (39) Lohrentz, J., Bray, B. G., Clark, C. R., Trans. AIME231, 1171 (1964). (40) McFarlane, R. C., Mueller, T. D., Miller, F. G., S P E Tech. Paper No. 1500 (1966). (41) .Meldau, R . S., Simon, R., SPE Tech. Paper No. 226 (November 1961). (42) Michels, A., Wassenaar, T., Zwietering, T h . N., Physicn 19, 371 (1953). (43) Mueller, W . H., Leland, T. W., Kobayashi, Riki, A.I.Ch.E. J . 7,267 (1961). (44) Nelson P. 1V Proc 38th Southwestern Gas Measurements Short Course, Norman, bkla., 178 ’(1963). (45) Nicholson, G. A., Schneider, W.G., Can. J . Chem. 33,589 (1955). (46) Price, H. S., Donohue, D . A . T., S P E , Paper KO.1533 (1966). (47) Redlich, O., Can. J . Chem. Eng., p. 131 (June 1965). (48) Reudelhuber, F. O., Oil 0” G a s J . 53 (71, 138 (June21, 1954). (49) Ibid., No. 27, 181 (Nov. 8, 1954). (50) Robinson, R. L., Jr., Jacoby, R . H., Hjdrocarb. Process. Petrol. Refner 44, (4), 141 (1965). (51) Rutherford, W. M., Trans. A I M E 225, 11, 340 (1962). (52) Rzasa, M. J., Glass, E. D., Opfel, J. B., Chem. Eng. Pros. Sjmp. Sere 4 8 (Z), 28 (1952). (53) Sage, B. H., Webster, D. C., Lacey, W. N., I N n . ENO.CHEM.29,658 (1937). (54) Shah, K. K., Thodos, G., Ibid., 57,30 (1965). (55) Silberberg, I. H., McKetta, J. J., Kobe, K . A,, J . Chem. Eng. Dnta 4, 314, 323 (1959). (56) Simon, R., Grave, D. J., Trans. A I M E 234, 102 (1965). (57) Standing, M. B., “Volumetric and Phase Behavior of Oil Field Hydrocarbon Systems,” pp. 33, 47 Reinhold, New York, 1952. (58) Stroud, L., Miller, J. E., Brandt, L. W., J. Chem. Eng. Data 5 , 51 (1960). (59) Taylor, J. G., Ph.D. Dissertation, Stanford University (1 966). (60) Winnick, J., Powers, J. E., A.I.Ch.E. J . 12 (3), 460, 466 (1966).
