1. Field of the Invention
This invention relates broadly to the hydrocarbon industry. More particularly, this invention relates to apparatus and methods for measuring streaming potentials resulting from pressure transients in an earth formation traversed by a borehole. This invention also relates to manners of making determinations regarding earth formation characteristics as a result of streaming potential measurements. One such characteristic is the permeability of the formation at different depths thereof, although the invention is not limited thereto.
2. State of the Art
The history with respect to the possibility of making streaming potential measurements in a downhole formation is a long one. In U.S. Pat. No. 2,433,746, (1947) Doll suggested that vigorous vibration of a downhole apparatus in a borehole could generate pressure oscillations and fluid movement relative to the formation which in turn could give rise to measureable streaming potentials due to an electrokinetic potential phenomenon. In U.S. Pat. No. 2,814,017, (1957) Doll suggested methods for investigating the permeabilities of earth formations by observing the differences in phase between periodic pressure waves passed through the formations and potentials generated by the oscillatory motion of the formation fluid caused by these pressure waves. Conversely, a periodically varying electric current was suggested to be used to generate oscillatory motion of the formation fluid, which in turn generated periodic pressure waves in the formation. Measurements were to be made of the phase displacement between the generating and the generated quantities and a direct indication of the relative permeability of the formation thereby obtained.
In U.S. Pat. No. 3,599,085, to A. Semmelink, entitled, “Apparatus For Well Logging By Measuring And Comparing Potentials Caused By Sonic Excitation”, (1971) the application of low-frequency sonic energy to a formation surface was proposed so as to create large electrokinetic, or streaming, pulses in the immediate area of the sonic generator. In accordance with the disclosure of that patent, the electrokinetic pulses result from the squeezing (i.e. the competition of viscosity and inertia) of the formation, and the streaming potential pulses generate periodic movements of the formation fluid relative to the formation rock. The fluid movement produces detectable electrokinetic potentials of the same frequency as the applied sonic energy and having magnitudes at any given location directly proportional to the velocity of the fluid motion at that location and inversely proportional to the square of the distance from the locus of the streaming potential pulse. Since the fluid velocity was found to fall off from its initial value with increasing length of travel through the formation at a rate dependent in part upon the permeability of the formation rock, it was suggested that the magnitude of the electrokinetic potential at any given distance from the pulse provided a relative indication of formation permeability. By providing a ratio of the electrokinetic potential magnitudes (sinusoidal amplitudes) at spaced locations from the sonic generator, from which electrokinetic skin depth may be derived, actual permeability can in turn be determined.
In U.S. Pat. No. 4,427,944, (1984) Chandler suggested a stationary-type borehole tool and method for determining formation permeability. The borehole tool includes a pad device which is forced into engagement with the surface of the formation at a desired location, and which includes means for injecting fluid into the formation and electrodes for measuring electrokinetic streaming potential transients and response times resulting from the injection of the fluid. The fluid injection is effectively a pressure pulse excitation of the formation which causes a transient flow to occur in the formation. Chandler suggests a measurement of the characteristic response time of the transient streaming potentials generated in the formation by such flow in order to derive accurate information relating to formation permeability.
In U.S. Pat. No. 5,503,001 (1996), Wong proposed a process and apparatus for measuring at finite frequency the streaming potential and electro-osmotic induced voltage due to applied finite frequency pressure oscillations and alternating current. The suggested apparatus includes an electromechanical transducer which generates differential pressure oscillations between two points at a finite frequency and a plurality of electrodes which detect the pressure differential and streaming potential signal between the same two points near the source of the pressure application and at the same frequency using a lock-in amplifier or a digital frequency response analyzer. According to Wong, because the apparatus of the invention measures the differential pressure in the porous media between two points at finite frequencies close to the source of applied pressure (or current), it greatly reduces the effect of background caused by the hydrostatic pressure due to the depth of the formation being measured.
Despite the long history and multiple teachings of the prior art, it is believed that in fact, prior to field measurements made in support of instant invention, no downhole measurements of streaming potential transients in actual oil fields have ever been made. The reasons for the lack of actual implementation of the proposed prior art embodiments are several. According to Wong, neither the streaming potential nor the electro-osmotic measurement alone is a reliable indication of formation permeability, especially in formations of low permeability. Wong states that attempts to measure the streaming potential signal with electrodes at distances greater than one wavelength from each other are flawed since pressure oscillation propagates as a sound wave and the pressure difference would depend on both the magnitude and the phase of the wave, and the streaming potential signal would be very much lower since considerable energy is lost to viscous dissipation over such a distance. In addition, Wong states that application of a DC flow to a formation and measurement of the response voltage in the time domain will not work in low permeability formations since the longer response time and very low streaming potential signal is dominated by drifts of the electrodes' interfacial voltage over time. Thus, despite the theoretical possibilities posed by the prior art, the conventional wisdom of those skilled in the art (of which Wong's comments are indicative) is that useful streaming potential measurements are not available due to low signal levels, high noise levels, poor spatial resolution, and poor long-term stability. Indeed, it is difficult to obtain pressure transient data with high spatial resolution as the borehole is essentially an isobaric region. The pressure sensor placed inside the borehole cannot give detailed information on the pressure transients inside the formation if the formation is heterogeneous. To do so, it is necessary to segment the borehole into hydraulically isolated zones, a difficult and expensive task to perform. Further, it will be appreciated that some of the proposed tools of the prior art, even if they were to function as proposed, are extremely limited in application. For example, the Chandler device will work only in drilled boreholes prior to casing and requires that the tool be stationed for a period of time at each location where measurements are to be made. Thus, the Chandler device cannot be used as an MWD/LWD (measurement or logging while drilling) device, is not applicable to finished wells for making measurements during production, and cannot even be used on a moving string of logging devices.
It is therefore an object of the invention to provide methods and apparatus for measuring streaming potential in an earth formation.
It is another object of the invention to provide methods and apparatus for measuring streaming potentials in a formation while drilling a borehole.
It is a further object of the invention to provide methods and apparatus for measuring streaming potentials in a formation around a device permanently installed in a wellbore.
It is also an object of the invention to provide methods and apparatus for measuring streaming potentials in a formation with a moving borehole tool.
It is an additional object of the invention to provide methods of determining formation characteristics using streaming potentials measurements.
Another object of the invention is to provide methods of characterizing fractures in a formation using streaming potential measurements.
A further object of the invention is to provide methods of determining one or more of formation permeability, skin permeability, effective fracture permeability, and horizontal and vertical permeabilities of a formation using streaming potential measurements.
In accord with these objects, which will be discussed in detail below, different methods and apparatus for measuring streaming potential in an earth formation are provided. A first embodiment of the invention relates to measuring streaming potential while drilling a borehole. For purposes herein, measurement-while-drilling (MWD) and logging-while-drilling (LWD) applications will be considered interchangeable. A second embodiment of the invention relates to measuring streaming potential with a borehole tool which is adapted to make measurements while moving through the borehole. A third embodiment of the invention relates to measuring streaming potential with apparatus which is permanently installed (e.g., cemented) about the wellbore. All embodiments of the invention can be utilized to find characteristics of the formation. In particular, since the streaming potential measurement relates directly to fluid flow, the streaming potential measurements can be used to track flow of fluids in the formation. In turn, this information may be used to find the permeability of the formation in different strata about the borehole and/or to find and characterize fractures in the formation.
Additional objects and advantages of the invention will become apparent to those skilled in the art upon reference to the detailed description taken in conjunction with the provided figures.
a is a schematic representing a forward model of a heterogeneous formation.
b is a plot of streaming potentials generated by the forward model of
c is a schematic representing a forward model of a fractured formation.
d is a plot of streaming potentials generated by the forward model of
a is a schematic representing a forward model of a vertical producing well having a fracture.
b is a plot of streaming potentials generated by the forward model of
a is a schematic representing a forward model of a wireline tool which is adapted to slit borehole mudcake.
b is a plot of streaming potentials generated by the forward model of
c is a plot of streaming potentials generated by the forward model of
d is a plot generated by the forward model of
e is a plot which shows an inversion for permeability of synthetic data and a best fit for a five parameter model.
Prior to turning to the Figures, some theoretical considerations governing the physics of the invention are useful. In reservoir rocks there exists a thin charged double layer at the interface between the rock matrix and the water in the pore. The matrix surface is negatively charged, and the water is positively charged. When water moves under a pressure gradient ∇p, an electrical current ie is created with the water current. The electrical current is proportional to the water current, which is proportional to the pressure gradient:
ie=L∇p. (1)
where L is a coupling constant which is a property of the rock.
Pressure transients are created in the formation by many different operations that occur over the lifetime of a well such as drilling, mud invasion, cementing, water and acid injection, fracturing, and oil and gas production. Pressure transient testing is an established technique to determine reservoir properties such as permeability, reservoir size, and communication between different zones and between different wells. As is set forth below, streaming potential transients associated with the pressure transients can also be used to determine these properties.
The modeling of the reservoir pressure p can be carried out with multiphase flow models. For the modeling of the streaming potential, it is useful to start with the diffusion equation of a single-phase flow:
where k is the permeability, μ is the viscosity, Φ is the porosity, and c is the fluid compressibility. From the modeled pressure field p, the streaming potential V can be calculated by solving the Poisson Equation:
−∇·σ∇V=∇·L∇p, (3)
where σ is the electrical conductivity.
From Eq. (2) it follows that the time Δt for a pressure transient and the associated streaming potential transient created at the borehole surface to diffuse through a distance Δx into the formation is given by
The early time pressure and streaming potential transients are sensitive mainly to reservoir properties near the borehole, and the late time transients are sensitive to reservoir properties both near the borehole and farther away from the borehole. By interpreting the measured transients in a time ordered fashion, reservoir properties at different distances to the borehole can be determined. The interpretation of pressure transients in this time ordered fashion is an established art. For example, early time pressure transients are used to determine damage to permeabilities or “skin”, and late time pressure transients are used to determine reservoir boundaries.
The applications are much more limited if the steady state values of the streaming potentials are the only measurements available. At a steady state, equation (2) becomes
The pressure drop Δp across a depth interval Δx is then proportional to
The drop in the streaming potential ΔV is related to Δp by
which is proportional to
The steady state streaming potential can only give information on the average value of a reservoir property and as a result is dominated by intervals with high values of (Lμ)/(σk). It is believed that in the presence of a mudcake, the steady state streaming potential is dominated by the mudcake and is insensitive to reservoir properties. The permeability of the mudcake is extremely low, and the steady state pressure drop mainly exists across the mudcake.
While in principle it is possible to determine reservoir properties at all distances to the borehole (i.e., radially from the borehole) by interpreting the transients in a time ordered fashion, the critical question in practice is whether the measurements can be made with sufficient quality: accuracy, spatial resolution, and stability over long time. It is difficult to get pressure transient data with high spatial resolution as the borehole is essentially an isobaric region. A pressure sensor placed inside the borehole cannot give detailed information on the pressure transients inside the formation if the formation is heterogeneous. To do so, it would be necessary to segment the borehole into hydraulically isolated zones, a difficult and expensive task to perform. On the other hand, the borehole is not an equipotential surface for electric current flow. Thus, streaming potential transients may be measured by an array of electrodes placed inside the borehole and electrically isolated (i.e., insulated) one from the other and can provide equivalent information to that of hydraulically isolated zone pressure transient testing because the streaming potential is determined by the pressure gradient. In fact, by utilizing an array of isolated streaming potential electrodes, the streaming potential can be measured with a higher spatial resolution than hydraulically isolated zone pressure transient testing.
Given the theoretical understandings above, according to one aspect of the invention, insulated electrodes are deployed in or about a borehole or a well in order to measure streaming potential transients. According to different embodiments of the invention, and as will be discussed in more detail below, the electrodes may be deployed on insulated sections of a drill pipe in while-drilling (MWD or LWD) applications, or on the body of a tool which is moved through the borehole in wireline logging applications. In post-completion applications, the electrodes may be deployed on an insulating sonde placed in an open hole for an open-hole completion, or on (or as part of) centralizers in sand-screen completions, or in insulation surrounding a casing in a cemented completion. In a cased-hole completion with electrically isolated casing sections, the metal casings can serve as electrodes. Regardless of how the electrodes are deployed, DC voltage differences indicative of streaming potentials are measured between a reference electrode and other electrodes of an array. Initial voltage difference values between the reference electrode and other electrodes typically due to surface chemistry differences of the electrodes are subtracted from all data subsequent to the creation of pressure transients.
According to another aspect of the invention, the streaming potential transients are generated in any of various manners. According to one embodiment of the invention associated with drilling a borehole, the pressure difference between the formation and the borehole creates mud invasion, pressure transients and streaming potential transients. In another embodiment of the invention associated with wireline logging of the borehole, streaming potential transients are generated by providing the wireline tool with one or more cutting edges mounted on one or more retractable arms which cut slits across the mudcake while logging. Because of a large overbalancing pressure difference between the formation and the borehole, when the mudcake is slit, fluid will flow through the slit and the resulting pressure transient can be measured. According to another embodiment of the invention associated with completion and post-completion applications, streaming potential transients are generated by injection of completion fluid, cement, gravel, acids, fracturing propellant, water injection testing, production testing, etc. In fact, any change in the rate of production will also create streaming potential transients. As long as there is a flow of conducting fluids associated with pressure transients, a streaming potential transient will be created and will be measurable with high precision using the deployed electrodes.
According to another aspect of the invention, data related to streaming potential transients obtained by the electrodes is interpreted to provide useful information. Those skilled in the art will appreciate that the interpretation of pressure transient data (as opposed to streaming potential transient data) to obtain reservoir properties such as permeability is a well-established art. In formations with high permeability, the pressure transients change with time rapidly, while in formations with low permeability, the pressure transients change slowly. The streaming potential transients produced by the pressure transients depend on the formation permeability in the same way as the pressure transients.
As will be appreciated by those skilled in the art, there exist analytical and numerical tools to model the pressure transients. The reservoir parameters of interest can be determined by varying the parameters in the model until the calculated pressure matches with the measured data. Formally, let R denote the set of reservoir parameters to be determined, and let fp(R) denote the modeled pressure transient. A mismatch between the modeled and the measured pressure transient is defined:
E
p(R)=∥fp(R)−p∥. (9)
The mismatch is minimized at R=R0 to get the inverted values of the reservoir parameters.
The quantitative interpretation of streaming potential data to determine reservoir parameters such as formation permeability can be carried out in the same way as the interpretation of the pressure transient data. Let s denote a set of measured transients. The set may contain only the streaming potential transients V, or it may contain both the streaming potential transients and the pressure transients. Let fs(R, L) denote the modeled transients, which depend on an additional set of parameters: the coupling constants L in equation (3). (The conductivity σ in equation (3) is usually known from resistivity logging data.) A mismatch between the modeled and the measured pressure transients is defined according to:
E
s(R,L)=∥fs(R,L)−s∥. (10)
The mismatch is minimized at R=R0 and L=L0 to get the inverted values of the reservoir parameters.
It will be appreciated by those skilled in the art that the Poisson equation (3) is linear in the coupling constants L, since the coupling of the streaming potential back into the governing equations for the pressure by electro-osmosis is completely negligible. Therefore, the inversion for the coupling constants is a straightforward linear inversion. Indeed, the minimization of equation (10) is carried out in two steps. The first step is to fix R and vary L, and find the sub-optimal minimum of the mismatch by solving a linear problem for L. The solution gives L as a function of R. The sub-optimal minimum is then a function of R only:
E
s1(R)≡Es(R,L(R)). (11)
The second step is a nonlinear search for the minimum of equation (11), containing the same number of unknowns as equation (9). Therefore, the additional task of estimating the coupling constants does not add to the computational complexity or mathematical uncertainly to the inversion problem.
According to another aspect of the invention, the measured streaming potential transients associated with the fluid movement in the formation can be used inter alia to: track movement of cement slurries during cementing thereby detecting possible cementing problems; track slurries carrying gravel thereby monitoring gravel packing; track acid movement during injection of acid into the formation as acid injection will create streaming potential transients; monitor fracturing of formations in real time; evaluate fracture jobs quantitatively; track water movement resulting from water injection; improve the effectiveness of pressure transient testing; and monitor reservoir parameter changes over long periods of time, including water saturation, relative permeability and water cut.
Using the various aspects of the invention previously described, field tests were run on a horizontal production well, part of which is shown schematically in
Turning now to
It will be appreciated by those skilled in the art that the completion string, being made of metal, forms a short circuit for electrical currents. The screen sections 114 used to complete well 100 were fifteen feet long, and the joint sections 116 were five feet long. Since the insulated joint sections 116 of the completion string covered only a small area near the electrodes 118, much of the electrical currents were able to leak through the exposed screen sections 114, resulting in the reduction of signal level. However, as shown hereinafter, there still existed significant levels of signal to be measured. It should be noted that for quantitative interpretation, it is sufficient to include the current leakage in the forward modeling.
As shown in
Pressure testing data gathered by the pressure gauges on both sides of the completion string showed that Zone 1 is hydraulically isolated from Zone 2 and Zone 3. This is seen in
In order to create a streaming potential transient, the three electrical valves 113a, 113b, 113c, and a rod pump (not shown) at the formation surface were utilized to control the fluid flow. The fluid in the annulus of each zone flowed into the tubing through the valve opening. The pressure gauge 115-1 on the tubing side of the opening measured the tubing pressure, and the pressure gauge 115-2 on the annulus side measured the pressure in the annulus region between the formation and the screen. By turning the pump on and off and by opening and closing the valves 113, pressure transients were created in the formation 105 and measured by the pressure gauges 115-2 on the annulus side.
For each of the three zones, the annulus pressure was equal to the formation pressure. As seen in
It will be appreciated by those skilled in the art, that immediately after the opening of valves, the pressure gradient existed mainly in the damaged zone near the well. The permeability of the damaged zone, or skin, is known to be lower than that of the undamaged formation. If the coupling constant between the pressure gradient and the electric current is also lower in the skin than in the formation, then the streaming potential should increase with time initially when the pressure gradient diffuses from the skin to the undamaged formation. At later times, the pressure builds back to the formation pressure, the pressure gradient diminishes and diffuses deep into the formation farther away from the electrodes, and the streaming potential decreases. The rates of the initial increase and the subsequent decrease of the streaming potential are determined by the permeability of the skin, the thickness of the skin, and the permeability of the undamaged formation. The streaming potential transient recorded by electrode 118-8 in Zone 2, shown alongside with the pressure transient in
The Zone 2 streaming potential data recorded by all seven electrodes 118-8 through 118-14 in Zone 2 are shown alongside the pressure data in
Careful review of the curve from electrode 118-12 in
According to the invention, the magnitude of the streaming potential is an indicator of the water fraction of flow, and it varies from electrode to electrode. As seen in
The voltages of the Zone 1 electrodes are shown in
In a later production test, Zone 2 and Zone 3 valves were shut and Zone 1 valve was opened and remained open. The pressure transient and the streaming potentials resulting from that test are shown in
Turning now to
The qualitative interpretations summarized in
In light of the above, with the streaming potential information, it is clear that an appropriate forward modeling and inversion can be carried out with a Laplace equation solver and a two-phase flow model (i.e., oil/water) as discussed above with reference to equations (9)-(11) or with a multi-phase flow model. As a result, the streaming potential transient data obtained can be used to quantify formation permeability, skin permeability, effective fracture permeability, horizontal and vertical permeabilities, communication between zones and wells, and reservoir boundaries in much greater detail than pressure transient testing alone can. As a result, a better understanding of the well and the reservoir may be obtained, leading to better management of the well and reservoir.
Turning now to
As seen in
With well 200, streaming potential transients were created by injecting water into the well. The injection of water was controlled by a surface pump 221 and a surface valve 223 (both shown schematically in
The uphole injection pressure is shown in
The streaming potential transients sensed by the electrodes of primary interest inside the reservoir interval of interest are shown in
The streaming potential transients sensed by the electrodes above the reservoir interval of interest are shown in
Turning now to
Given the measurements made by the electrodes as shown in
The qualitative interpretation of
The streaming potential data of electrodes 218-13 through 218-15 shown in
As seen in
According to another aspect of the invention, the electrodes of the electrode array utilized to sense and measure streaming potential transients are preferably covered or coated with a semi-porous covering material (such as cement), whether utilized as centralizers as shown with reference to a sand-screen completion or in other permanent installations, or when used in MWD or wireline applications as discussed hereinafter. The semi-porous covering material should have a significant electrical conductivity but a very low permeability so that ions can reach the electrode to enable voltage measurements, but no new fluid reaches the electrode surface during the time period of measurement. The surfaces of the electrodes are in a stable chemical environment, which gives rise to measurement stability. A presently preferred semi-porous material is cement, although a semi-porous ceramic, clay, or other material could be utilized. As an alternative, liquid junction electrodes can be utilized, as the semi-porous plug of a liquid junction electrode stops fluid movement but allows ionic diffusion. A stable electrode allows the measurement of a transient over a longer period of time, thereby permitting an analysis deeper into the formation, and also permitting measurements at weaker signal levels.
With the streaming potential measurements described with reference to
Turning now to
A cased hole completion is shown in
According to another embodiment of the invention, a tool and method for measuring streaming potentials while drilling a borehole is provided. In particular, during drilling, a pressure difference between the formation and the borehole creates mud invasion and pressure transients, and thus, streaming potential transients. In wells drilled with an oil-based mud, a streaming potential will exist if the mud contains a water fraction.
Turning now to
With the while-drilling tool 510, the streaming potential measurements made are passive voltage measurements, which can be made in a highly resistive borehole by using high impedance electronics. In wells drilled with oil-based mud, the electrodes need to be as large as possible and placed as close as possible to the formation to reduce electrode impedance.
It will be appreciated by those skilled in the art that in order to properly analyze the data obtained by the LWD tool 510, a model of mudcake built up during drilling should be included in the forward model. Accurate models such as disclosed in E. J. Fordham and H. K. J. Ladva, “Crossflow Filtration of Bentonite Suspensions”, Physico-Chemical Hydrodynamics, 11(4), 411-439 (1989) can be utilized.
Given the while-drilling tool 510 and an appropriate model, the streaming potential information obtained by the tool and processed can yield various answer products. Since the streaming potential transients created by drilling will change rapidly with time for a formation with high permeability and slowly for formation with low permeability, with an inversion model that contains the mudcake built-up model, formation permeability of the invaded zone and the uninvaded zone can be obtained.
With the LWD tool 510 and an appropriate model, a system for early detection of drilling fluid loss may be implemented. In particular, there may be sudden fluid loss from natural or induced fractures during drilling. In that case, streaming potential will rise instantaneously as fluids rush into the formation. The changes in borehole pressure will be somewhat slower, since the borehole has a storage capacity. Noticeable fluid loss at the surface will happen much later. For drilling induced fractures, large changes in the streaming potential will be detectable long before the fractures becomes serious. Therefore, monitoring of the streaming potential measurements can be used for early detection of fluid loss.
Likewise, the streaming potential information can be utilized for the early detection of abnormal formation pressures. For example, if the formation pressure becomes higher than the borehole pressure, the signs of the streaming potential will reverse. This reversal of sign will be observable before sufficient amount of fluid has flowed into the borehole for the pressure kick to be observable. The build-up of the flow reversal may happen over a short but finite period of time as the abnormal pressure zone is being drilled. Any reversal of flow will be immediately observable in the streaming potential measurements. Therefore, streaming potential measurements have value in the early detection of abnormal formation pressure.
Turning now to
As will be appreciated by those skilled in the art, the electrodes 618 move with the tool 610 in a continuous logging mode. Different electrodes in the array sense the streaming potential transient at a fixed spatial point. The spacing between the electrodes in the array and the logging speed determines the temporal sampling rate of the streaming potential transient. The top electrode 618-R is used as the voltage reference electrode, as it is farthest from the cutting edges and no streaming potential transient has yet been created there. Wires connecting the electrodes, measuring electronics, and telemetry are provided but not shown in
As previously mentioned, the arms 631 are preferably retractable. As a result, the cutting edges 635 can be retracted where streaming potential information is not desired, and the tool used for repeated runs to acquire streaming potential data over long period of time, if desired. A gamma ray detector 640 is provided in order to help align data from repeat runs.
As was discussed above with reference to the LWD tool 510, streaming potential measurements are passive voltage measurements which can be made in a highly resistive borehole by using high impedance electronics. In wells drilled with oil-based mud (without a water fraction), the electrodes are preferably relatively large (by way of example and not limitation, twelve inches by two inches) and are preferably placed on articulated pads (not shown) or on a skid sonde to insure close contact with the formation.
Using the wireline tool 610, the spurt loss from the cutting of mudcake is likely to happen over a short time period compared with the time needed for the pressure transient to diffuse beyond the invaded zone. If that is the case, then the source of the streaming potential transient created by the cutting of mudcake can be treated as a delta function of time. The inversion of the data for a short period of time can be carried out without any input from the mudcake build-up model. After the spurt loss, the mudcake will build back up by a static process. The thickness of the mudcake will increase with the square root of time. The inversion of streaming potential data over a longer period of time with a mudcake that increases with the square root of time is still quite robust.
The mud invasion is a continual process even with a good mud system. The streaming potential transients created by the mud invasion are likely to be measurable when the logging time is not too far away from the time when the well is drilled or reamed. Thus, the tool shown in
The ability of the wireline tool of
b shows that the early time transients are insensitive to the uninvaded zone. It takes a time interval given by equation (4) for the pressure transient to diffuse to the uninvaded zone.
d shows the dependence of the streaming potential on the thickness of the invaded zone. Equation (4) shows that the time it takes for the pressure transient to diffuse through the invaded zone depends on the invaded zone thickness Δ and invaded zone permeability k through the combination Δ2/k . Equation (8) shows that in approaching the steady state, the streaming potential from the invaded zone depends on A and k through the combination Δ/k . The difference between these two combinations suggests that the thickness and the permeability of the invaded zone can be individually determined by inversion.
The results of inversion with synthetic data calculated from the forward model and 5% added noise are shown in
There have been described and illustrated herein several embodiments of apparatus and methods for measuring streaming potentials and characterizing earth formation characteristics therefrom. While particular embodiments of the invention have been described, it is not intended that the invention be limited thereto, as it is intended that the invention be as broad in scope as the art will allow and that the specification be read likewise. Thus, while particular tools and electrode arrangements have been disclosed, it will be appreciated that modifications can be made, provided the tool or arrangement includes an electrode array capable of measuring streaming potentials. Thus, for example, the invention could be modified so that a two-dimensional array of electrodes can be utilized in certain circumstances in order to provide azimuthal streaming potential information. It will therefore be appreciated by those skilled in the art that yet other modifications could be made to the provided invention without deviating from its spirit and scope as claimed.
This patent application is a divisional of U.S. patent application Ser. No. 10/871,446, entitled “COMPLETION APPARATUS FOR MEASURING STREAMING POTENTIALS AND DETERMINING EARTH FORMATION CHARACTERISTICS” which is related to commonly-assigned U.S. Pat. No. 7,233,150, entitled “WHILE-DRILLING APPARATUS FOR MEASURING STREAMING POTENTIALS AND DETERMINING EARTH FORMATION CHARACTERISTICS”; commonly-assigned U.S. Pat. No. 6,978,672, entitled “WIRELINE APPARATUS FOR MEASURING STREAMING POTENTIALS AND DETERMINING EARTH FORMATION CHARACTERISTICS”; and commonly-assigned U.S. Pat. No. 7,243,718, entitled “METHODS FOR LOCATING FORMATION FRACTURES AND MONITORING WELL COMPLETION USING STREAMING POTENTIAL TRANSIENTS INFORMATION”.
Number | Date | Country | |
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Parent | 10871446 | Jun 2004 | US |
Child | 12400241 | US |