A Study of Anomalous Pressure Build-Up Behavior

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1 T. P.8004 A Study of Anomalous Pressure Build-Up Behavior G. L. STEGEMEIER STUDENT MEMBER A/ME C. S. MA TTH EWS MEMBER A/ME UNIVERSITY OF TEXAS AUSTIN, TEX. SHELL OIL CO. HOUSTON, TEX. ABSTRACT In one field in South Texas, approximately 75 per cent of the pressure build-up results show a characteristic "hump" (i.e., the pressure builds up and then falls off) which makes interpretation by standard methods impossible. Correlation of size and time of hump with formation permeability, well productivity index, and method of completion led to the tentative conclusion that the humps were caused by segregation of gas and oil in the wellbore after closing-in *. This conclusion was confirmed by performance of simple laboratory bubble-rise experiments, by theoretical bubble-rise time calculations, and by a detailed calculation of PVT behavior in the wellbore of a particular well on which accurate surface and bottom-hole pressure measurements were made. The hump behavior has since been found to occur in many other fields. The cause, however, is not the same in all cases. In some of these the hump is traceable to leaks in the tubing which allow influx of gas from the annulus after closing-in. In other cases the hump is traceable to leaks in the device separating pay horizons in dually completed wells. It is concluded that the recording of both surface and bottom-hole pressures is desirable in wells which show an anomalous build-up behavior. A number of field examples is discussed where use of both sets of measurements enables the cause fer anomalous behavior to be found, and a reasonable interpretation of bottomhole pressure to be made. phenomenon-that of movement of fluids within the wellbore-has been neglected in most build-up studies to date. Fluid movements within the well bore after shut-in occur as a result of after-production, packer failures, leaks in the casing or tubing, or buoyancy of the gas phase when both gas and liquid are present in the well. Each of these movements can influence the pressure build-up, sometimes sufficiently to negate use of the data for computing permeability or stabilized build-up pressure. Examples of each of these phenomena are discussed below. FIELD OBSERVATIONS ON HUMP BUILD-UPS In approximately 75 per cent of the wells in a medium-sized field in South Texas the pressure build-up curves rise to a maximum and then decline to what appears to be a stabilized reservoir pressure as shown in Fig. 1. Similar behavior has also been observed in wells in other fields in Texas and Louisian~. Because of the possibility of such behavior being a mechanical failure of the pressure bomb, two bombs were run in tandem into one well which had been known to exhibit this behavior. When both bombs recorded identical curves with the characteristic hump, it was inferred that the unusual build-up is a result of well or forma- I II. INTRODUCTION Theoretically the pressure build-up in an infinite reservoir should be a linear function of In [(t + 1':,.t) /1':,.t] where t is the production time and 1':,.t is the closed-in time. Some of the variations from this behavior are well known, such as the curved portion immediately after shut-in which results from after-production and skin effect, and the flattened end portion which results from boundary effects in a limited reservoir. The effect of stratified producing zones and irregular geometrical drainage patterns may also contribute unusual characteristics to build-ups. However, the effect of still another Original manuscript received in Society of Petroleum Engineers office on July 15, Revised manuscript received Jan. 13, Paper presented at 32nd Annual Fall Meeting of Society of Petroleum Engineers in Dallas, Tex., Oct. 6-9, "This possibility had been suggested to one of the authors by A. B. Dyes of The Atlantic Refining Co. in SPE PETROLEUM TRANSACTIONS, AIME.L_---" ~ ~c / / ~ : // //--,:;-::-;:---- I /// // J // /// I /'/, "L ---'-_-'----LJ, FIG. I--PRESSURE BUILD-UP, SOUTH TEXAS WELL 1. i 44

2 tion behavior, rather than a recording instrument failure. In order to understand more fully the mechanism involved in these build-ups, a statistical study of 120 of these humping build-ups in one South Texas field was made. The results indicate that the humps may be as large as 180 psi, have an average size of about 45 psi, and always occur at the end of or shortly after the typical "swans-neck" part of build-up. The time of occurrence generally varies from 100 to J,000 minutes after shut-in, with the greatest number of curves humping at 300 to 400 minutes. In all cases in which the hump is later than 300 minutes, the steep part of the build-up is also late and there is a sizeable rate of build-up within 350 minutes of the maximum. Apparently, there is no correlation in this field between this unusual behayior and rate of production previous to shut-in, cumulative production, GOR, bottom-hole pressure, magnitude of pressure build-up, or structural position. However, core data indicate that humping does not generally occur in wells having an average permeability greater than 200 md. Similarly, wells with moderate permeability (50 to 100 md) may have anomalies which appear and disappear throughout the life of the well. A plot of magnitude of hump vs productivity index (PI) is shown in Fig. 2. This plot shows that the humps are larger in wells with low PI's. In addition, for any given well, the humps get larger as the PI's get smaller. Thus, there is a possible relationship between presence of a skin zone (which would give a low PI) and size of hump. The presence or absence of a packer has a considerable effect on size and time of humping. The average size in wells having a packer is about 60 psi, whereas it is only 10 psi in wells without packers. The average time of humping is about 350 minutes in packed wells, and 500 minutes in non-packed wells. Summarizing all the facts obtained from this statistical study, it appears that for a hump to appear in the build-up it is necessary that the formation be only moderately permeable and have a low productivity index. The humps appear earlier and are of larger size when the annulus is packed-off. A physical explanation of many of the humps may be given in terms of a phase redistribution within the well bore involving rise of the gas phase through the oil and counter flow of oil downward"'; however, before ~ " < any application of this phenomenoll is made to a well, a discussion of the theoretical effect of phase redistribution win be made. THEORETICAL AND EXPERIMENTAL STUDIES ON PHASE REDISTRIBUTION STATIC THEORY AND EXPERIMENTS To illustrate the theory, suppose a frictionless piston separates a liquid phase above and a gas phase below in a cylinder. Assume the gas is weightless, the liquid incompressible, and the pressure at the top is A. The gas trapped below the piston then is at pressure A, plus the pressure due to the fluid head of the liouid, P. When the cylinder is inverted so that the gas phase is at the top, the following pressures result. (1) Since the liquid is incompressible, the piston will not move and the gas will occupy the same volume; consequently, the gas will remain at the same 9ressure as before, (A + P). (2) The pressure at the bottom is now the pressure exerted by the gas on the top of the piston (A + P) plus the fluid head, P, making the total pressure (A + 2P). Thus, by changing the relative position of the phases in the column the absolute pressure at both top and hottom is changed. The difference between the top and bottom pressure remains constant, however, and equal to the weight of the fluids between the two points divided by the cross-sectional area. The experiment described above was made in the laboratory, and the results were found to be in good agreement with the above theory. DYNAMIC EXPERIMENTS Following this static-phase-demonstration experiment, a second experiment, which more closely simulated wellbore performance, was carried out using equipment shown in Fig. 3. The column was almost filled with glycerine, and with Valve B open and Valve C closed, air was introduced through the core at the base of the column. When the air bubbles were sufficiently dispersed throughout the column, the air supply (Valve A), and Pressure Gaqe '::This possibility was suggested to one of the authors by A. B. Dyes of The Atlantic Refining Co. in H}50. IAI Inlet ValVe) Air 01 BHP+7" =-::::Glycerin :-= ~----- Choke Productivity IndU,bbl/daY-PSI FIG. 2-SIZE OF HUMP IN WELLS 1:'-1 A SOUTH Tf:XAS FIELD. FIG. 3-A DYNA:\UC PHASE-REDISTRIBUTIO:'-l EXPERIMENT. 15 VOL. 213, 1958

3 the outlet at the top of the column (Valve B) were closed simultaneously. A total pressure build-up at both top and bottom of about 13 in. of water was observed, due simply to bubble rise. An explanation of the pressure rise in this case may be seen by considering the bubbles at the bottom to be compressed by the fluid head just as the gas is compressed below the piston. The subsequent rise of gas through the liquid lessens the pressure on the bubble due to fluid head, but because the gas cannot expand in the closed system, it exerts a pressure on the liquid at the gas-liquid interface. This pressure is transmitted to the bottom, and when added to the hydrostatic pres sure, gives an additional pressure associated with bubble rise. Several runs of this type were made in which the amount of gas initially at the top of the column and then the volume of bubbles contained in the liquid were varied. It was found that (1) the pressure build-up due to bubble rise is inversely proportional to some power of the top gas volume, and (2) the pressure build-up is directly proportional to the total volume of bubbles in the column. Tn order to reproduce more closely the effect of a pressure build-up in a well, an inverted flask containing both glycerine and air was attached to the bottom of the column, this flask being analogous to the porous reservoir around the wellbore. Again air was flowed through the core and into the bottom of the column. This time the top valve was open, Valve C was slightly cracked, and the air pressure in the flask was adjusted to a value slightly above the flowing bottom-hole pressure. When a steady-state dispersion of bubbles throughout the column was reached, the air supply was shut-off and the top valve was closed. This time the pressure build-up resulted both from influx from the reservoir and from the bubble rise; however, the pressure build-up from bubble rise shortly after shut-in was so much greater than that from influx that the bottom-hole pressure rose above the reservoir pressure (see Fig. 4). This occurred because the liquid in the column was unable to flow back into the reservoir fast enough to prevent the anomalously high bottom-hole pressure caused by bubble rise. After rising above reservoir pressure the liquid in the column began to flow back into the reservoir until the bottom-hole pressure declined to the reservoir pressure. This model is an analog of a well having a high skin factor, simulated by the partly closed valve, and a considerable quantity of bubbles entrapped in the borehole liquid at shut-in. 0\;-' !;;;-o -- ""_" "L ~~ 8'1 :0.""". 5",G"~' FIG. 4-AN EXPERIME:'>TAL PRESSCRE HUMP CAl!SED BY BUBBLE RISE. PETROLEUM TRANSACTIONS. AIME ANOMALIES RESULTING FROM PHASE SEGREGATION ASSUMPTIONS USED IN CALCULATING WELL BEHAVIOR Temperature-Calculations take into account the effect of temperature gradient in a well on the volumetric properties of gases, but neglect the effect of changing temperature on liquid properties. Supersaturation-Unless otherwise specified, the gas and oil are assumed to be in equilibrium at all times. Friction loss in tubing-the pressure drop in the tubing due to friction was negligible in all cases considered in this report. BASIC CALCULATIONS An approximation of the limiting upward velocity of bubbles is needed to determine the length of time during which phase redistribution may be expected to occur. These limiting values were taken from the correlation of Peebles and Garber.' TIME OF BUBBLE RISE IN A SOUTH TEXAS WELL Assuming that no very small bubbles (i.e., radius < ft) occur, the minimum rate of rise obtained from this correlation is 0.35 ft/sec. Thus, the maximum time of rise in a 7,900-ft South Texas well is 377 minutes. The maximum rate of bubble rise is 0.55 ft/sec, which leads to a minimum rise time of 240 minutes. Earlier it was stated that the humps in the South Texas field never were more than 350 minutes removed from a sizable rate of pressure build-up. To cause a sizable rate of build-up a considerable quantity of gas bubbles must have been entering the bottom of the hole within 350 minutes of humping. The time required for such gas to rise to the top is 240 to 377 minutes, the right order of magnitude to account for the hump. ANAL YSIS OF BEHAVIOR OF SOUTH TEXAS WELL 1 PRESSURE BEHAVIOR Bottom-hole pressure (BHP) build-up data on Well 1 in a South Texas field were obtained by using the Shell Development Co.'s BHP telemetering device. This device allowed pressure to be measured to within less than 0.5 psia on an accurate time scale. Fig. 1 shows the change in BHP (BHP after shut-in minus flowing BHP) and the change in tubing pressure (tubing pressure after shut-in minus flowing tubing pressure). The difference between these two curves is also ploued in Fig. 1. This difference curve is seen to rise, reach a maximum, and then decline to a constant value. Since the friction loss at any time is negligible, the value of the difference curve is proportional to the amount of fluid which has entered after shut-in between the BHP bomb and the tubing head, regardless of the phase distribution. Any increase in the difference curve indicates an increase in mass of material in the tubing, and, conversely, a decrease indicates an outward flow of material from the tubing. Because this well has a packer, the fluid leaving the tubing can flow only into the formation. In view of these observations it is possible to analyze the pressure behavior shown in Fig. 1. The difference lreferences given at end of paper. 46

4 curve rises after shut-in, indicating a normal afterproduction into the well bore; however, at 300 minutes the difference curve reaches a maximum. This time coincides with the time at which the BHP curve first reaches the eventual stabilized pressure. As one might expect, the direction of flow after the BHP exceeds the stabilized BHP is from the tubing into the formation. This is seen in the fact that the difference curve decreases after the 300-minute point. The BHP continues to rise even after the pressure at this point exceeds the stabilized formation pressure because the pressure rise caused by rise of the gas occurs at a greater rate than the pressure decrease due to outflow. However, since no more gas is entering the tubing, the rate of pressure increase due to bubble rise finally decreases, and at 390 minutes equals the rate of pressure decrease due to outflow. This is the point at which the BHP reaches a maximum and begins its decline. After this time the tubing pressure will continue to increase, this rise being attributable to rise of the gas bubbles which last entered the tubing. When most of the gas has risen to the surface (500 minutes) the tubing pressure will finally begin to decline because of continued negative afterproduction. The final state of build-up is a stabilization of all three curves to constant values. TOTAL PRESSURE RISE CAUSED BY PHASE SEGREGATION The effect of phase redistribution on the South Texas Well 1 build-up discussed previously will now be computed by: (a) finding the amount of gas and oil in the tubing at the time of closing-in, (b) finding the rate and amount of after-production, (c) calculating the pressure increase caused by this after-production, and (d) attributing the difference between the observed and calculated pressure increase to phase redistribution. The amount of gas and oil in the tubing at time of closing-in is calculated by the method discussed in Appendix 1. The results indicate that at time of closingin there were 2,910 ft of gas (at tubing conditions) and 4,990 ft of liquid in the tubing. The rate and amount of after-production are calculated in Appendix 2. Rate results are shown in Fig. 5. The initial rate is about 20 ft/min, but this drops rapidly to about 1 ft/min at the end of 200 minutes. Note that the results do not follow the often-used assumption that the rate of influx is proportional to the rate of change of BHP. However, the mass rate of influx is proportional to the rate of change of the difference between tubing and bottom-hole pressure. To a good approximation the total volumetric rate of influx is also proportional to the rate of change of this same difference. This suggests that tubing, casing, and BHP's should be measured during build-up when it is desired to make calculations of after-production for pressure build-up interpretation. Then by using the difference between top-hole and bottom-hole pressures one can calculate the rate of after-production accurately. Knowing the amount of after-production in any period, one may calculate the pressure increase caused by the addition of this volume of fluid to the volume of fluid in the tubing. This is the pressure increase due to compression. This influx also increases the BHP by virtue of its weight, which is reflected directly in the difference between tubing-head and bottom-hole pressure. If there were no disturbing factors, the pressure increase due to compression plus the pressure increase due to weight of this after-production should equal the total increase in BHP. However, Curves A or B in Fig. 6 show that the sum of difference curve (which gives the pressure increase due to weight) and the pressure increase due to compression (obtained from Appendix 2) is always less than the BHP increase. This is true regardless of whether the gas in the tubing is assumed to go into solution or not. This indicates that another factor is causing a change in BHP. A plot of this factor (the difference between observed and calculated BHP) is also shown in Fig. 6 by Curves C and D. The curve for the case of solution equilibrium in the tubing (Curve C) closely resembles the experimental curve of pressure rise due to rise of bubbles. This analysis indicates that there may be a maximum total pressure increase due to bubble rise alone of about 300 psi. However, a large part of this increase is masked by the pressure build-up,.and only a smali part (20 psi) appears as a hump in this case. DISCUSSION OF HUMPING BUILD-UP It is believed that the preceding detailed analysis of behavior of South Texas Well 1 demonstrates the validity of the concept that phase segregation within the wellbore can cause an anomalous hump in the pressure build-up curve. The time required for bubble rise is of the right order of magnitude to account for the phenomenon. The difference curve indicates that liquid is pushed back into the formation. ~ j 800,oot 600 I 500~ 'TTTTITrr-- CUflVE e ASSUMES EQUiliBR'UM SOLUTION OF GAS -----~ OBSERV ;D [ltp OBSERVE:) -MP, lelj: Sri'IIM ",Cu"1t"IO[O,,"',",".," fro~ ~8""-ATp FIG. 5-RArE OF AFTER'PRODUCTION, SOUTH TEXAS WELL 1. ASSUMES NO SOLUTION OFGAS.-+c-t;-'-~,*,-=~;---'-~ Icfoo-----dao FIG. 6-PRESSURE BEHAVIOR IN SOUTH TEXAS WELL VOL. 213, 1958

5 The fact that wells without packers have smaller humps than wells with packers seems reasonable in view of our experiments with bubble-columns. There it was found that the amount of the pressure build-up caused by bubble rise diminished as the initial gas volume in the wellbore increased. Since the wells without packers have much more gas initially in the wellbore than wells with packers, they should have smaller humps. It was also observed that wells without packers had the hump later than wells with packers. This is reasonable because more influx will be required to bring the pressure in the wellbore up to that required to balance the reservoir pressure. Having concluded that bubble rise is probably the cause for most of the hump anomalies at this South Texas field, an examination of an anomaly slightly different than found in South Texas Well 1 was made. SOUTH TEXAS WELL 2 An example of a well in which phase redistribution influences the build-up, but is not large enough to cause the BHP to exceed the reservoir pressure, is shown in Fig. 7 for South Texas Well 2. The difference curve for this well shows a maximum at about the same time as that for South Texas Well 1, indicating that well bore conditions were similar at time of closing-in. However, the continued slow rise in pressure in Well 2, which tends to mask the hump, indicates that the formation permeability around this well is somewhat lower than that around Well l. On comparing the behavior of Well 2 with Well 1, it appears that there is probably an optimum permeability for humping; formations of low permeability will still be building up at the time of separation of most of the gas so that the hump may be partially masked, as in Well 2. In formations of high permeability and no skin effect, equilibrium can always exist between well bore and formation with the result that no hump will occur. The optimum conditions appear to be found in formations of moderate permeability where there is a considerable skin effect. the two previous examples, as shown in Fig. 8. The phase redistribution build-up occurs early, the tubing pressure reaching a maximum at about 120 minutes. This time the BHP exceeds the adjacent reservoir pressure so much that it reaches a maximum and humps even though the well has not built up to average reservoir pressure. Following the temporary decrease, the build-up continues toward the stabilized reservoir pressure with the complication that a slow leak in the tubing head causes this pressure to decrease. To balance this decrease in tubing pressures, the difference curve increases, i.e., the well loads with liquid. Because the rate of this loading (after-production) will influence the BHP, it appears that a straight-line portion is not reached during this build-up. WILLISTON BASIN WELL 1 * Three build-up curves on two wells in a Williston Basin field showed an anomaly caused by leakage between zones of different pressure. These wells were completed in two zones which were separated by a ';'This anomaly and its explanation were brought to OUt' attention by A. Hois of the Shell Oil Co f- I! i _~ool j """'1 200 ANOMALIES RESULTING FROM TUBING OR PACKER LEAKS NORTH TEXAS WELL A This well exhibits a behavior slightly different from 1 '00 ~'t., CPo"n9,n, M,n"' ,~- _ !o FIG. 8-PRESSURE BUILD-UP, NORTH TEXAS WELL A ; r , FAIL J~l "-- L a~[r lo~e BuiLDuP L '0'.)' FIG. 7-PRESSURE BUILD-UP, SOUTH TEXAS WELL 2. FIG. 9-EFFECT OF PACKER FAILURE ON PRESSURE BUILD-UP, WILLISTON BASIN WELL 1 (UPPER ZONE PACKED-OFF). PETROLEUM TRANSACTIONS, AIME 48

6 casing packer. The tubing contained a nipple which allowed selective production of either zone through the tubing. In Well'! initial production was obtained from the lower zone, a choke being used to seal off the upper zone. After some months it was decided to switch the productive interval to the upper zone to conform to a recommended drainage pattern. Prior to this switch a build-up survey was conducted on the lower zone. Results are shown in Fig. 9. When the pressure differential between zones became small, the packing in the choke failed. Since the upper zone had already built up the annulus pressure, there was a rapid rise in pressure, as shown. After the choke was pulled, a separation tool was run for an upper zone recompletion. A build-up survey conducted some months later gave results very similar to those shown in Fig. 9. When the pressure differential between zones became small the packing in the separation tool failed, which again caused an anomalous rise in pressure. WEST TEXAS WELL A The West Texas Well A build-up had an unusually high tubing pressure build-up in addition to other difficulties which will be subsequently discussed. Since this was very much greater than the bottom-hole build-up, it appears that high pressure gas leaked from the casing into the tubing, thereby causing the tubing to unload. Such a redistribution can theoretically change the BHP if outflow from the well to the formation is restricted. A theoretical example (see Fig. 10) is calculated to show how a phase redistribution due to a tubing leak can affect the BHP. In this example the densities of gas and oil are assumed constant, and the casing volume is taken as five times the tubing volume. As shown in Fig. 10 the liquid level will rise 500 ft in the casing as the liquid levels in tubing and casing equalize (x = 500 ft). Since the number of moles of gas does not change, the new average gas pressure can be calculated to be 1,842.6 psi. The final BHP can be calculated from this and from the gradients. It is found in this manner that if there is no outflow, the final BHP will increase by psi because of the leak. Thus, such a leak could seriously affect the slope of a pressure build-up curve. CONCLUSIONS Phase redistribution within the wellbore can influence BHP behavior considerably, often leading to humps and irregularities. Optimum conditions for the forma- C,P.= BEFORE T.P: AFTER tion of humps are encountered in formations of moderate permeability with some skin effect. Tubing and packer leaks can also cause humps. Measurement of surface tubing and casing pressure during build-up can be of aid in helping to unravel the cause of apparently anomalous behavior. Development of a bottom-hole tool which would allow the well to be shut-in near the bottom just above the pressure bomb would eliminate many anomalies. As was noted in Fig. 5, because of disturbing effects of bubble rise and of compression of the fluid in the wellbore, the rate of influx after closing-in may not be proportional to the rate of change of BHP. In this light our method of making inflow calculations should be re-examined. NOMENCLATURE':' BHP = bottom-hole pressure GOR = gas-oil ratio, scf of gas produced per barrel tank oil GLR = gas-liquid ratio, the ratio in a small interval of tubing of total volume of gas (free and dissolved) when measured at standard conditions to volume of stock-tank oil, scf/bbl TP = tubing pressure G = gas after-production into bottom of tubing fe/ft' cross section H = height of a point in well bore above bottom of pay, ft f::,h = incremental height in wellbore, ft H" = height of oil column in wellbore, ft L = liquid after-production into bottom of tubing, ft"/f1' cross section f::,p = pressure drop, or difference, psia f::,p,. = pressure rise due to compression of fluid in the well bore by after-production, psia Vii = total volume of gas in tubing at time of closingin, ft"/ft' cross section V,,, = the volume occupied by oil when saturated with gas at some temperature and pressure relative to its volume at bubble point conditions. REFERENCES 1. Peebles and Garber: "Studies on the Motion of Gas Bubbles in Liquids." Chem. Eng. Prog. (1953), 49, Gilbert: "Flowing and Gas-Lift Well Performance," Drill. and Prod. Prac.. API (954), Perrine: '-Analysis of Pressur.e Build-Up Curves," Drill. and Prod. Prac.. API (1956), West, W. 1., Garvin. W. W., and Sheldon, J. W.: "Solution of the Equations of Unsteady State Two-Phase Flow in Oil Reservoirs." Trans. AIME (954), 201, Mueller, T. D., Warren, J. E., and West, W. J.: "Analysis of Reservoir Performance K,/K" Curves and a Laboratory K,/K" Curve Measured on a Core Sample," Trans. AIME (1955 ). 204, 240. APPENDIX 1 GAS AND OIL IN TUBING AT TIME OF CLOSING-IN It is possible to approximate the volume of gas and oil in the tubing at flowing conditions assuming PVT FIG. 10-EFFECT OF TUBING LEAK 0:\ PRESSURE BUlLD-l:P. ':'See AIME symbols List in Trans. AIME (lh57) 207, 363, for other symbol definitions. 49 VOL. 21:i. 1958

7 equilibrium at all points, neglecting friction drop, and assuming that the GLR * (the ratio of standard cubic feet of free and dissolved gas to barrels tank oil) is the same in any interval in the column. With the above assumptions one may solve, by trial and error, for a curve of pressure vs depth which fits the known surface and bottom-hole flowing pressure. For South Texas Well 1 it was found that the calculated curve of pressure vs depth fits the observed end points when a gas-liquid ratio equal to 455 scf/stb is used (the flowing GOR was 700). In the final calculation the effect of a temperature gradient from 246 to F at tubing head was included. These results were only slightly different from those assuming constant temperature of F in the flowing tubing system. From this same set of calculations the gas saturation at any level, and, therefore, the total amount of gas, can also be found. For South Texas Well 1 it was found that there are 2,910 ft of free gas and 4,990 ft of liquid in the tubing under flowing conditions. It is realized that the assumption of a constant gasliquid ratio throughout the tubing is not necessarily true. However, the method seems to give reliable results in South Texas wells, as will be discussed more fully in Appendix 2. At this point it should be mentioned, however, that the curve of pressure vs depth obtained above has a shape similar to the curves obtained by Gilbert' from field measurements. APPENDIX 2 RATE AND AMOUNT OF AFTER-PRODUCTION RATE OF AFTER-PRODUCTION The difference between the change in bottom-hole pressure and the change in tubing pressure may be related directly to the amount of material flowing into the well. If the flowing gas-oil ratio is assumed to persist after shut-in* *, the incremental difference relationship is: where 6(6p) 6(6BHP - 6 TP) 6t 6t = PII- 6G [ + p,,- 6L], 6t 6t "Note that the gas-liquid ratio (GLR) is not the same as the flowing gas-oil ratio (GOR) at steady state. The GOR at standard conditions of the total fluid entering the tubing at the bottom must be the same as the GOR at standard conditions of the total fluid leaving the tubing at the top. Because of liquid hold-up the G LR at standard conditions in the tubing is not the same as the flowing GOR. It is possible, for example, to have many feet of water in the tubing, and yet never produce any liquid water. ':::;'Using calculations of pressure and saturation distribution in a depletion-type reservoir, mooe on the IBM 701 computer by Perrine3. West, Garvin. and Sheldon4, and Mueller, Warren, and West:.>, it was found that the flowing GOR (when measured at surface conditions) is very nearly constant throughout a flowing reservoir. ~rherefore, when the reservoir is clo-sed-in, the outlying gas and oil should continue to flow in at the same GOR. rate of oil after produc 6L/6t Bo 5.61 tion at tubing conditions = B (GOR R) = rate of free gas oftert:::" G/ t:::,,1 (I - S production, at tubing conditio.~ By solving these two equations simultaneously we may obtain 6L/6t and 6G/6t. By summing the 6L's and the 6 G's we obtain the total liquid and gas afterproduction, Land G. Using this method of calculation, the net liquid after-production is found to be 1,218 ft (l,317-ft positive after-production and 99-ft negative). Fig. 5 gives a plot of rate of total influx vs time in minutes. If a gradient survey had been made while the bomb was being removed from South Texas Well 1, it would have been possible to check on some of these calculations by comparing the calculated and measured gasoil interface in the tubing. Although no gradient survey was available on South Texas Well 1, one was available on South Texas Well 2, which may be closely compared since the two wells have similar GOR, rate of production, and depth. In this well the amount of gas was ascertained to be 1,700 ft at the end of the buildup. In the previous calculation for South Texas Well 1 the amount of gas at the beginning of shut-in was found to be 2,910 ft. Subtraction of the net after-production of 1,218 ft of liquid gives the height of gas remaining at the end of the South Texas Well 1 build-up-1,692 ft. The fact that this calculated height checks closely with that found by gradient survey in Well 2 indicates that these calculations are approximately correct. COMPRESSION CAUSED BY AFTER-PRODUCTION Knowing the cumulative volume of oil and gas flowing into the well at any time, the compression of the gas phase and the consequent increase in tubing head pressure can be calculated from p,v" (1) P, - P, = 6p, = V" _ (L + G) - P,, where V" is the volume of gas in tubing when flowing, ft"/ft' area; P, is the flowing gas pressure at tubing head; and p, is the final gas pressure at tubing head. If it is decided to take solution of gas into account, G is replaced by G' in the above equation, where G' = G - (decrease in gas volume due to solution - increase in oil volume) = G - (6 V, - 6 V,). The volume of gas going into solution per unit cross sectional area is: 6 V, = [1K] i\ph"b". dp 5.61 B" The increase in oil volume per unit cross sectional area is: 6V, = dv",:] 6pH" [ dp V",' where R, is the dissolved gas, H" is the feet of oil in tubing, and 6p is the average pressure change. Results of these calculations are used in plotting Fig. 6, where 6pl, is obtained from Eq. 1 by substituting G' for G. *** PETROLEUM TRANSACTIONS, AIME 50

SPE Copyright 2001, Society of Petroleum Engineers Inc.

SPE Copyright 2001, Society of Petroleum Engineers Inc. SPE 67232 Sampling Volatile Oil Wells Ahmed H. El-Banbi, SPE, Cairo University/Schlumberger Holditch-Reservoir Technologies, and William D. McCain, Jr., SPE, Texas A&M University Copyright 2001, Society

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