METHODS OF CALCULATING A FLUID COMPOSITION N A WELLBORE

Abstract

The subject disclosure relates to methods for passively measuring a composition of a wellbore.

Description

CROSS-REFERENCE TO RELATED APPLICATION

This application claims benefit of U. S. Provisional Patent Application Ser. No. 61/480,642 filed on Apr. 29, 2011, which is incorporated herein by reference.

FIELD

The subject disclosure generally relates to wellbore fluid characterization. More particularly, the subject disclosure relates to passive methods for determining a wellbore fluid composition.

BACKGROUND

Gas injection may be used for enhanced oil, or enhanced natural gas recovery, and in sequestration of carbon dioxide. In certain circumstances it may be useful to know the injected gas composition introduced via an injection well into a reservoir. In the reservoir, the injected gas contacts and displaces the reservoir fluid. This changes the previously established thermodynamic equilibrium between the existing vapor, liquid and solid phases in the reservoir. The injected gas mixes first with the vapor phase and then diffuses into the liquid phase. Local drive to equilibrium may cause repartitioning of components into phases, e.g., injection of CO₂ into a methane saturated brine stream leads to preferential release of methane into the vapor phase and dissolution of CO₂ into the brine or the liquid phase. Subsequently, the change in liquid and/or vapor composition may lead to additional mass transfer with the solid phase, e.g., addition of CO₂ in the vapor and liquid phases leads to preferential release of methane adsorbed on solid mineral surfaces. Additionally, it may lead to dissolution/precipitation reactions with reservoir minerals. Consequently, the reservoir fluid and the injected fluid composition change due to mass transfer.

Observation wells are drilled away from injection wells to provide real-time measurements of the fluid composition at bottom-hole conditions. These measurements include sampling, well-well pressure interference, EM or seismic/acoustics, and well logs. The observation wells are usually perforated to allow fluid to enter the well if sampling is desired.

SUMMARY

This summary is provided to introduce a selection of concepts that are further described below in the detailed description. This summary is not intended to identify key or essential features of the claimed subject matter, or as an aid in limiting the scope of the claimed subject matter.

According to some embodiments, a method for obtaining a passive measurement of a composition is described. The method includes measuring a temperature and a pressure of a fluid in a wellbore; obtaining a density by differentiating the pressure with respect to vertical height and using an equation of state to infer the composition of the fluid.

According to some embodiments, a second method for obtaining a passive measurement of a composition is described. The method includes measuring a temperature, pressure and density of a fluid in a wellbore and using an equation of state to infer the composition of the fluid.

Further features and advantages of the subject disclosure will become more readily apparent from the following detailed description when taken in conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawings will be provided by the Office upon request and payment of the necessary fee. The subject disclosure is further described in the detailed description which follows, in reference to the noted plurality of drawings by way of non-limiting examples of embodiments of the subject disclosure, in which like reference numerals represent similar parts throughout the several views of the drawings, and wherein:

FIG. 1 depicts a cross-section of a reservoir between the injection well and the first and second observation wells;

FIG. 2 depicts brine displacement as a function of time in an observation well;

FIG. 3 is a graph of pressure versus depth for an injection well and a first and a second observation well;

FIG. 4 is a graph of temperature versus depth for an injection well and a first and a second observation well;

FIG. 5 is a graph of density versus depth for the injection well;

FIG. 6 is a graph of density versus depth for the injection well;

FIG. 7 is a graph of density versus depth for the injection well;

FIG. 8 is a graph of density versus depth for a first observation well;

FIG. 9 is a graph of density versus depth for a second observation well; and

FIG. 10 is a flow chart of the method steps of one embodiment of the subject disclosure;

FIG. 11 is a graph of density versus depth for a second observation well;

FIG. 12A is a graph of the concentration profile as a function of depth for a first observation well and FIG. 12B is a graph depicting the bottom-hole composition in a first observation well, as measured in samples;

FIG. 13 is a graph depicting the change in surface pressure at the injection well and a first and a second observation well;

FIG. 14 is a graph depicting the number of days for brine displacement;

FIG. 15 is a graph depicting the number of days a first observation well is being filled with the CO₂ rich fluid; and

FIG. 16A is a graph of the concentration profile as a function of depth for a first observation well and FIG. 16B is a graph depicting the bottom-hole composition in a first observation well, as measured in samples.

DETAILED DESCRIPTION

The particulars shown herein are by way of example and for purposes of illustrative discussion of the embodiments of the subject disclosure only and are presented in the cause of providing what is believed to be the most useful and readily understood description of the principles and conceptual aspects of the subject disclosure. In this regard, no attempt is made to show structural details in more detail than is necessary for the fundamental understanding of the subject disclosure, the description taken with the drawings making apparent to those skilled in the art how the several forms of the subject disclosure may be embodied in practice. Furthermore, like reference numbers and designations in the various drawings indicate like elements.

Methods of obtaining a composition of a wellbore fluid without the use of a sampling device are disclosed. Further, methods for determining the injected fluid composition in an injection well are disclosed. Finally, methods for obtaining a passive measurement of a gas composition in an observation well are disclosed. In a first embodiment the method comprises measuring a temperature and a pressure of a fluid in the observation well during or after the displacement of brine. The observation well is initially filled with brine and is subsequently displaced by the gas flowing past the perforations. The method further comprises obtaining a density by differentiating the pressure with respect to the vertical height, and using an appropriate equation of state, and the measured properties, to accurately calculate the composition of a binary mixture. This analysis could be expanded to multi-component mixtures if additional information is available. In a second embodiment, a second method for obtaining a passive measurement of a composition is described. The method includes measuring a temperature and a pressure of a fluid in a wellbore, and independently a density and using an equation of state to infer the composition of the fluid. A non-limiting example of an equation of state is GERG-2004 GERG-2008 (hereinafter “GERG”) (Groupe Européen de Recherches Gazières or European Gas Research Group) but other equations of state may be used without departing from the scope of the subject disclosure. See Kunz, O., Klimeck, R., Wagner, W., Jaeschke, M., “The GERG-2004 Wide-Range Equation of State for Natural Gases and Other Mixtures,” GERG Technical Monograph 15. Fortschr.-Ber. VDI, VDI-Verlag, Düsseldorf, 2007 and “The Properties of Gases and Liquids,” Robert C. Reid, John M. Prausnitz and Bruce E. Poling, the contents of which are herein incorporated by reference. Using an equation of state, the compositional profile is obtained as a function of well depth. The composition may be calculated at any depth and at any intervals of depth in the wellbore. The method may be used to confirm a wellbore fluid composition in injection wells or as a bottomhole fluid composition measurement tool in static observation wells.

Wellbore pressures and temperatures may be measured using Schlumberger's Platform Basic Measurement Sonde™ (PBMS). PBMS is merely one example and other examples may be used. The fluid density can be measured using known devices, such as Schlumberger's gradiomanometer sonde™ which measure the hydrostatic pressure of a column of fluid. A gradiomanometer sonde is merely one example and other examples may be used such as a vibrating tube, vibrating wire etc.

Referring generally to FIG. 1, one embodiment of a well system is illustrated. In the example illustrated, the injection well and a first and a second observation well are lined with a casing. The casing typically is perforated in a manner that places the perforations in the same reservoir or stratigraphic interval for all wells. The perforations enable flow of fluids into (or out of) a wellbore at each well zone. Referring generally to FIG. 1, one example of an injection well and a first and a second observation well is illustrated, according to embodiments of the subject disclosure. The CO₂ flows into the reservoir though the perforations in the injection well. The injected fluid migrates in the reservoir towards the first and the second observations wells. At the first observation well, some of the injected fluid enters the well through the perforations and bubbles up the brine column in the tubing thereby displacing the brine from the tubing because the density of the injected fluid is less than brine density at the same temperature and pressure. In time, all of the brine is displaced from the observation wells. The extent of the brine displacement is representative of the time that the injected fluid has been in the vicinity of the first or second observation wells. Once the brine is completely displaced from the well, there is no phase replacement in the observation well.

Fluid samples may be collected at the bottom of the observation wells using a U-tube sampling system or with a cased-hole formation tester. Initially the first and the second observation wells are filled with brine. As the CO₂-rich fluid phase arrives at the first and second observation wells, the CO₂ will bubble up through the perforations and displace the brine gradually from these wells. In the examples shown here, the brine is completely replaced by a CO₂-rich fluid phase in the first and second observation wells in approximately six days. The rate of uptake of fluid by the observation well can be controlled by total inlet area of perforations. Use of valves that may be remotely opened or closed (from the surface) may provide additional flexibility in sampling the temporal concentration profile of the fluid close to the wellbore.

FIG. 2 depicts brine displacement as a function of time in a first and a second observation well. FIG. 2 is only for illustration and is not intended to restrict the scope of the subject disclosure. The number of observation wells may increase or decrease depending on the field location. As can be seen in FIG. 2 the brine within the tubing of the observation well is gradually replaced by the fluid from the reservoir. In one non-limiting example, the injection well and the first and second observation wells are collinear. The first observation well is approximately 227 feet from the injection well and the second observation well is 140 feet farther. The distances are only for illustration and are not intended to restrict the scope of the subject disclosure. The first and second observation wells are initially filled with brine but have perforations that allow for fluid communication with the reservoir. As the CO₂ plume migrates to the first and second observation wells, bubbles of the CO₂-rich phase rise within the wellbore and displace brine until nearly the entire wellbore is filled with the CO₂-rich phase. The wellbore in this instance is approximately 10,000 feet deep so the process of filling the entire wellbore with the CO₂-rich phase takes several days. During this time, the plume continues to migrate past the first and second observation wells and the fluid composition in the CO₂-rich plume may change with time due to (i) changes in injected fluid composition and (ii) mass transfer with the reservoir brine including desorption of gases from solids. The compositional variation of the CO₂-rich fluid as a function of depth in the wellbore reflects this change in the plume concentration at different points in time as the fluid flows past the wells. The fluid displacement in the wellbore is stable only when progressively heavier fluid intrudes into the wellbore. If not, convective motion is induced, which asymptotically establishes a thermodynamically consistent profile, in which gravity adjusted chemical potential is the same throughout the wellbore. For stable displacement, the effect of evolving composition will be captured in the compositional profile of the gas in the wellbore.

FIG. 3 is a graph of pressure versus depth for an injection well and a first and a second observation well. In the injection well the bottom-hole pressure is higher than in the first and second observation wells, which are at reservoir pressure, as fluid is being injected into the reservoir at a set flow rate. The vertical pressure gradient in the first and the second observation wells is however different because the fluid composition in the two wellbores is different.

FIG. 4 is a graph of temperature versus depth for an injection well and a first and a second observation well. As can be seen in FIG. 4 the temperature in the injector well increases as a function of depth. This increase is expected due to heat transfer from the formation and due to increase in pressure, and the concomitant temperature increase due to near adiabatic compression. The static temperature profiles in the first and second observation well are identical and thus are reflective of the local geothermal gradient.

FIG. 5 is a graph of density versus depth for the injection well. The dotted line is the density calculated at wellbore pressure and temperature conditions, assuming pure CO₂. The solid lines connecting the data points are the measured density profile in the wellbore using the PGMS sonde. The discrepancy between the measured density profile and the calculated density profile for pure CO₂ is evident.

FIG. 6 is a graph of density versus depth for the injection well. Data consistency for the measured densities was confirmed by cross-checking against the calculated density form the differential of pressure with depth, shown as the yellow dashed lines connecting the derived density points. Although there the inferred density calculated from the differential of pressure with depth is noisy, the mean density overlays well with the density measured using the PGMS sonde. The least square error between the measured and calculated densities was minimized by adjusting methane mole fraction, a likely contaminant, using the GERG equation of state for the mixture. The resulting amount of methane, calculated as above, was calculated to be about 8% (mol) (see FIG. 7). Subsequently, it was confirmed that the injected gas included a fraction of recycled CO₂ from an enhanced oil recovery (EOR) site that contained significant quantities of methane.

FIGS. 8 and 9 are graphs of density versus depth for the first and second observation wells, respectively. The solid red line is the measured density profile in the wellbore. The yellow lines are the calculated density from the differentiated pressure, and are therefore noisy. The dotted red line is the density for pure CO₂ calculated at wellbore pressure and temperature conditions. The dotted blue curve is the curve best-fitted to the measured density profile for an optimized CO₂-CH₄ mixture fraction. The density profiles measured in the first observation well and the second observation wells indicate non-uniformity in composition. Moreover, the estimated pure CO₂ density using the measured pressure-temperature profiles and the GERG equation of state was not close to the measured density profiles in the first and second observation wells. Therefore, a least-square analysis was carried out on both the first and the second observation wells for the mixture composition based on the measured density profile. The best fit curve in FIG. 8 indicates that the first observation well contains greater than 18 mol % CH₄ near the surface decreasing to significantly less than 18 mol % at the well bottom. The solid red curve with a lower density than the best fit indicates that the methane concentration is higher nearer the top of the wellbore and that the CO₂ concentration is higher deeper in the wellbore. FIG. 9 points to the second observation well containing approximately 8 mol % CH₄ in the top two-thirds of the well with almost pure CO₂ near the bottom. The remarkable change in density at about 60% of the depth of the wellbore is difficult to explain based on the temperature or pressure profile and our analysis indicates that this density jump is a result of a steep change in the relative concentration of the CO₂ methane mixture. In this well, apparently some of the wellbore fluid was vented for an indeterminate period of time although that time must be less than the time necessary to have completely purged the well of CO₂-rich gas. The surface venting caused additional fluid, notably of a different composition than that which existed in the wellbore prior to venting, to be drawn into the wellbore. The composition of this fluid, drawn into the bottom of the wellbore, is different due to the fact that the CO₂ plume is continuously migrating past the wellbore with the composition changing in the near wellbore region. Thus, an additional use for the method proposed in this disclosure is a diagnostic method for identifying intended and unintended interventions.

FIG. 10 is a flow chart of the calculation sequence for one embodiment of the subject disclosure. To calculate the composition that best fits the wellbore density profile, a contaminant is judiciously selected based on whether the measured density profile is greater or less than the calculated density profile for pure carbon dioxide. The choice of contaminant is also constrained by likelihood of occurrence within the wells. Iteration begins with a starting guess for the contaminant mole fraction. The second step comprises using the measured wellbore pressure, temperature profile and the guessed composition to calculate the density using the GERG equation of state, as a function of depth. The third step comprises calculating a sum of the least square errors between the calculated and measured density. The fourth step involves reviewing the sum of the errors. If the sum of the errors is less than the tolerance, then the converged density profile is accepted. If the sum of the errors is not less than tolerance, then the mole fraction of the contaminate is calculated using an appropriate convergence scheme, for example, Newton-Raphson algorithm or the Van Wijngaarden-Dekker-Brent method, which is documented in W. Press et al., Numerical Recipes: The Art of Scientific Computing, Cambridge University Press, New York (1992), and is herein incorporated by reference. The steps are then repeated until the sum of the errors between the calculated and measured densities is less than a previously specified tolerance. Note that any other error specification, for example, sum of absolute differences, may be used for minimization.

FIG. 11 is a graph of density versus depth for a first observation well. This figure shows an additional black curve fitted to the measured density profile in the wellbore. This curve was generated by subdividing the wellbore and then repeating the analysis for each section using a different composition. Each fitted section represents a different composition, with the higher methane content present at lower depths (see FIGS. 12A and 12B).

FIG. 12A is a graph of the concentration profile as a function of depth for a first observation well, as calculated using GERG. FIG. 12B is a graph depicting the bottomhole composition in a first observation well, as measured in samples collected using U-tube sampling technology. The correlation in CH₄ concentration between the two curves is obvious with the shallow depths corresponding to earlier times.

FIG. 13 is a graph of surface pressure at the injection well and the first and the second observation wells. As expected, pressure at the injection well is relatively stable. The onset of bubble entry into a first observation well is measured by an increase in the surface pressure for both the first and second observation wells. It appears that it takes approximately six days for both the first and second observation wells to be filled with the fluid moving past the perforations. This is shown in greater detail in FIG. 14.

It is also interesting to note that the final pressure in the first observation well is higher than the final pressure achieved in the second observation well and that they are both higher than the surface pressure for the injection well. Between the static first and second observation wells, the comparison is straightforward. A higher pressure for the first observation well indicates that the overall average density of the fluid that has filled the wellbore is of a lower density than the fluid in the second observation well. An easy way to look at this is—initially, the wellbore was filled with brine with a density higher than the fluid that displaced it. At this time, the surface gauge pressure was zero as the column of dense brine compensated for the bottomhole pressure. In comparison to the injection well, even though the bottomhole pressure in the injection well is significantly higher than the first or second observation well, the injection well is filled with a denser fluid than either the first or second observation well fluids. The pressure head of the denser fluid column offsets the higher bottomhole pressure so that surface pressure is lower.

FIG. 14 shows that in both the first and second observation wells it takes about six days for the brine to get completely displaced by the CO₂-rich fluid flowing past the perforations, as shown by the blue and green rectangles that overlay the pressure profiles. Note that this time to displace the brine can be controlled by modifying the total perforation area.

In FIG. 15, where U-tube sampled fluid composition versus time is shown, the blue shaded rectangle represents the temporal interval within which the first observation well brine is replaced by the CO₂-rich fluid flowing past the perforations. This interval is relevant for comparison with the concentration profile that we calculate using the equation of state.

FIG. 16A is a graph of the concentration profile as a function of depth for a first observation well, as calculated using GERG. FIG. 16B is a graph of the bottomhole composition in a first observation well obtained from the U-tube sampling over six days, the exact time interval over which the wellbore was being filled with the CO₂-rich fluid. Both curves show that the methane concentration in the fluid flowing past the perforations declines with time. Some embodiments may benefit from an equation of state that is any cubic or virial equation of state that allows mixing rules.

There are many applications for the subject disclosure. Non-limiting examples include determining the injected CO₂ composition in a carbon sequestration project. Methods of the subject disclosure will determine what compositions are injected at the wellhead and also will determine the purity of the CO₂ injected. Furthermore, methods of the subject disclosure determine if chemical or physical processes are occurring within the reservoir and thus changing the compositions in the observation wellbores. The compositional profile may be indicative of interactions with the injected CO₂.

While the subject disclosure is described through the above embodiments, it will be understood by those of ordinary skill in the art that modification to and variation of the illustrated embodiments may be made without departing from the inventive concepts herein disclosed. Moreover, while the preferred embodiments are described in connection with various illustrative structures, one skilled in the art will recognize that the system may be embodied using a variety of specific structures. Accordingly, the subject disclosure should not be viewed as limited except by the scope and spirit of the appended claims.

Claims

1. A method for obtaining a composition estimate of a fluid in a wellbore traversing a subterranean formation, comprising:

measuring a temperature and a pressure of a fluid in the wellbore;

obtaining a density by differentiating the pressure with respect to vertical height; and

calculating the composition of the fluid using an equation of state.

2. The method of claim 1, further comprising introducing carbon dioxide to the formation.

3. The method of claim 1, further comprising measuring brine displacement.

4. The method of claim 1, further comprising using an observation wellbore and an injection wellbore.

5. The method of claim 1, further comprising identifying interventions.

6. The method of claim 1, further comprising determining the injected carbon dioxide composition.

7. The method of claim 1, wherein the equation of state is European Gas Research Group—2004.

8. The method of claim 1, wherein the equation of state is European Gas Research Group—2008.

9. The method of claim 1, wherein the equation of state is virial.

10. The method of claim 1, wherein the equation of state is cubic.

11. The method of claim 1, wherein the measuring comprises using a device selected from the group consisting of a gradiomanometer, vibrating tube, and vibrating wire.

12. The method of claim 1, further comprising comparing the obtained and observed density measurements.

13. The method of claim 12, further comprising repeating the obtaining the density measurement.

14. A method for obtaining a composition estimate of a fluid in a wellbore traversing a subterranean formation, comprising:

measuring density, temperature, and a pressure of a fluid in the wellbore; and

calculating the composition of the fluid using an equation of state.

15. The method of claim 14, further comprising introducing carbon dioxide to the formation.

16. The method of claim 14, further comprising measuring brine displacement.

17. The method of claim 14, further comprising using an observation wellbore and an injection wellbore.

18. The method of claim 14, further comprising identifying interventions.

19. The method of claim 14, further comprising determining the injected carbon dioxide composition.

20. The method of claim 14, wherein the equation of state is European Gas Research Group—2004.

21. The method of claim 14, wherein the equation of state is European Gas Research Group—2008.

22. The method of claim 14, wherein the equation of state is virial.

23. The method of claim 14, wherein the equation of state is cubic.

24. The method of claim 14, further comprising comparing the obtained and observed density measurements and repeating the obtaining the density measurement.