CA1244880A - In-situ method for determining pore size distribution, capillary pressure and permeability - Google Patents
In-situ method for determining pore size distribution, capillary pressure and permeabilityInfo
- Publication number
- CA1244880A CA1244880A CA000475661A CA475661A CA1244880A CA 1244880 A CA1244880 A CA 1244880A CA 000475661 A CA000475661 A CA 000475661A CA 475661 A CA475661 A CA 475661A CA 1244880 A CA1244880 A CA 1244880A
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- CA
- Canada
- Prior art keywords
- permeability
- formation
- induced polarization
- pore
- pore size
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
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Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
- G01V3/00—Electric or magnetic prospecting or detecting; Measuring magnetic field characteristics of the earth, e.g. declination, deviation
- G01V3/18—Electric or magnetic prospecting or detecting; Measuring magnetic field characteristics of the earth, e.g. declination, deviation specially adapted for well-logging
- G01V3/26—Electric or magnetic prospecting or detecting; Measuring magnetic field characteristics of the earth, e.g. declination, deviation specially adapted for well-logging operating with magnetic or electric fields produced or modified either by the surrounding earth formation or by the detecting device
- G01V3/265—Operating with fields produced by spontaneous potentials, e.g. electrochemicals or produced by telluric currents
Abstract
A B S T R A C T
IN-SITU METHOD FOR DETERMINING PORE SIZE
DISTRIBUTION, CAPILLARY PRESSURE AND PERMEABILITY
An in-situ method of determining the pore size distribution, capillary pressure curve, and permeability of a formation using induced polarization logging measurements. The induced polarization (IP) voltage decay curve is measured opposite the formation of interest and the voltage decay curve is decomposed into a series of relaxation times related to the pore size distribution. The capillary pressure curve and the permeability are approximated from the pore size distribution. The measurements can also be made in the frequency domain using various frequencies to obtain the variation in phase shift with frequency. The variation in phase shift with frequency can be correlated with previous core measurements to obtain the pore size distribution, capillary pressure curve and formation permeability.
IN-SITU METHOD FOR DETERMINING PORE SIZE
DISTRIBUTION, CAPILLARY PRESSURE AND PERMEABILITY
An in-situ method of determining the pore size distribution, capillary pressure curve, and permeability of a formation using induced polarization logging measurements. The induced polarization (IP) voltage decay curve is measured opposite the formation of interest and the voltage decay curve is decomposed into a series of relaxation times related to the pore size distribution. The capillary pressure curve and the permeability are approximated from the pore size distribution. The measurements can also be made in the frequency domain using various frequencies to obtain the variation in phase shift with frequency. The variation in phase shift with frequency can be correlated with previous core measurements to obtain the pore size distribution, capillary pressure curve and formation permeability.
Description
~Le~Ba~
IN-SITU MET~OD FOR DETE~IWING PORE SIZE
DISTRIBUTION, CAP~ILARY PRESSURE AND PERME~BILITY
The invention relates to an in-situ method for determining the pore size distribu~ion, capillary pressure curve and penmeability of a formation surrounding a well. These are all important considexations in deciding whether hydrocarbon-bearing formations are commercial. A formation may contain a large amount of hydrocarbon but if the pores are too small and the permeabi-lity is too low it may not be possible to produce the hydro-carbons commercially. Thus, the determination of the pore size distribution, capillary pressure curve, and permeability of the formation is an important consideration in determining whether a well which has penetrated a hydrocarbon-bearing formation should be ccmpleted. The expense of cQmpleting a well is, of course, considerable since the well must first be cased and production tubing and well-head equip~ent installed.
At present there are only two reliable me~hods for determining the pore size distribution, capillary pressure curve and permeability of a formation. m e me~hod used most often is to take cores from the formation during the drilling o~ the well and then to analyse the cores in a laboratory. Coring enables high precision laboratory measurements of capillary pressure and permeability. Coring, hc~svsr, is very expensive and involves scme risk. While cor m g a well, one d oe s not have a~ much ccntr~1 over the ~ell as when drilling with conventional rcck bits and the possibility of sticking the drill string in the well is greatly increased during coring operations. Further, durm g coring operations, the penetration rates are greatly reduced, thus mcreas ~ g ~he tLme required to dxill the well to a ~ et depth. In~addition; measursments on core plugs may not be a good repres ~tion of the~f~rmstion as a whols, sincs core plugs ars :
~: . ' :
:
mall, discrete samples.
The only reliable logging method for determining pore size distribution, capillary pressure curves and permeability is the use of the nuclear magnetism logging (NML) tool. In this method the Tl decay curve of protons magnetically polarized in the formation is recorded and then mathematically inverted to obtain a pore size distribution and an approximate permeability (J.D.
Loren and J.D. Robinson, "Relations Between Pore Size, Fluid and Matrix Prcperties, and NML Measurements'l, Society o~ Petroleum Engineers Journal, September 1970, pages 268-278). The use of nuclear magnetism logging is ccmmercially practiced and readily available. While the technique is available, it does have several disadvantages. Among the disadvantages are the small depth of investigation of the nuclear magnetism log (about 6 inches) and the requirement that the borehole fluid be treated with magnetized particles to eliminate the borehole mud response frcm the log. Normally, magnetite particles in suspension æe added to the drilling mud to suppress the borehole respanse. This involves considerable expense and effort, because it is necessary to circulate the magnetite in the well to assure adequate mixing, and the circulated mud must be chec~ed to verify that the nuclear magnetic response has been eliminated.
A further disadvantage of the nuclear magnetism log is that the signal is extremely weak, often requiring several measurements at a fixed location for signal averaging. Thus, a good NMR decay curve of the quality required for capillary pressure and premeability determination is usually not obtained while continuously logging. ~not~er disadvantage of the NML is that the nuclear magnetism decay ti~es are so short in s e formations, for example in ti~ht gas sands, that the signals cannot be measured by existing NML tools (J.A. Brown, L.F~ Brown, J.A. Jackson, J.V. Milewski, B.J. Travis, "NMR Logging Tool Developments: Laboratory studies of Tight Gas Sands and Artificial Porous Material", SPE/DOE 10813, pages 203-208~. This is a severe disadvantage because it is precisely the marginal, low permeability formations where accurate neasurement of the premeability is req~lired most. Still another disadvantage of the NML is that the permeability determ med from nuclear magnetism is a ~hree-dimensional average, because the polarized protons on the water molecules diffuse randcmly until they relax at the pore walls. In many formations there is an order of magnitude difference between vertical and horizontal perm~ability. me MML
results will yield a three-dimensional averaged permeability rather than a separate vertical and horizontal permeability. Yet another difficulty with nuclear magnetism logging is that in oil-bearing formations, both the protons in water and in oil contribute to the Tl decay curve. Since the water phase and the oil phase have different decay rates, an unambiguous deter-mination of pore size often cannot be made. In addition, the Tldecay times depend on the character of the pore surface, such as hydrocarbon wetting, bound hydration ions and paramagnetic centres. As is well known in the art, these can all produce significant effects on the measured Tl relaxation times lJ.A.
Glasel, "NMR Relaxation in Heterogeneous Systems", Nature 227, 704-705 (1970); R.J.S. Brcwn and I. Fatt, "Measurements of Fractional Wettabilit~ of Oilfield Rocks by the Nuclear Magnetic Relaxation Method", Pet. Trans, AIME 207, 262-264 (1956)).
A final problem in relating the NMR relaxation times to formation permeability is that the pores probed by NMR need not be hydraulically connected. Therefore an Lmpermeable medium containing disconnected yugs,could yield the same Tl decay curve as a permeable rock containing connected pores.
The present invention provides a method using in-situ logging methods for measurement of the capillary pressure curve and formation per.,~ability. The method utilizes an induced polarization (IP) logging tool, preferably a focused induced polarization logging apparatus such as described in copending Canadian Patent application Serial No. 454,307. In this patent application there is described an induced polarization logging tool having means for focusing the electrodes to provide either horizontal or vertical measurements of the mduced polarization. ~easur~ments of the logging tool are recorded at the surface in the form of time domain IP decay curves or in the form of phase shift versus frequency of the applied electric field.
The present invention has several advantages cGmpared to the N~ tool described previously~ The electric field in this invention penetrates deep into the formation away from the borehole. In addition, the present method does not require any treatment of the borehole fluids. A major advantage is that the signal to noise in the present invention is sufficient that signal averaging is not required and a well can be logged continucusly. Another advantage of the present invention is that the IP voltage decay times are long enough even in low marginal reservoirs. Still another advantage is that the ions polarized by the present invention move along the direction of the applied electric field, so that both horizontal and vertical permeability can be separately determined. Yet another advantage is that, unlike the NML, the IP log observes only the water and not the oil in the formation. This is because oil is substantially nonconducting. A final advantage is that, unlike the nuclear magnatic response, the IP response is measured only along conducting pathways through the formation, therafore, disconnectad and dead-and pores, which do not contribute to permeability, are not measured by the IP logging tcol.
The method of the present invention requires that the above mentioned logging tool be operated cpposite the formation of interest to measure the tIme domain IP decay curve. The time domain IP decay curve is decomposed by a ccmpu~er algorithn into a set of exponential decays with different time constants. From the amplitude and time constant of each exponential, a pore size histogram is constructed. In particular, the relationship between diffusion constant D of sodium chl~ride electrolyte in aqueous solution (cm2/sec), the displac~ment length r (cm), and the time 12~r~8~0 constant t (sec) is used in the expression:
r2 (1) D = t The value of the diffusion coefficient at the formation tempera~ure is used in this expressio~. The diffusion constant of sodium chloride electrolyte is kncwn to be 1.5 x 10 5 cm2/sec at 25 C, and the effect of temperature on the diffusion constant is well known. We have discovered that the displacement length r is substantially the same as the pore size in clastic rocks. Thus, the IP decay curve yields the distribution of pore sizes in the formation.
Once the distribution of pore sizes is known, an a~proximate value for formation permeability can be ccmputed using various geometric models, which æ e well kncwn the the art. By proper calibration with core plugs from the formation of interest, the response of the i~duced polarization logging tool can be made ~;rectly in permeability units.
An alternative method of the present invention is to operate the IP logging tool of the aforementioned patent in the frequency domain. This requires that the logging tool be operated at several substantially different frequencies adjacent to the formation of interest. The phase shift for each frequency is measured and plotted to obtain a curve representing the phase shift versus frequency over a substantial range of frequencies.
This plot can also be obtained from the time domain IP decay curve described above using linear transform techm ques well known in the art. The phase shift ~ersus fre~uency curve can be decomposed into a set of amplitudes and time constants which are used with the above mentioned relation between diffusion constant D and displacement length r to obtain a pore size hi~togram.
A shortened form of the above procedure is to obtain the phase shift versus frequency plot as described above, and record the frequency (fmin) at which the phase shift starts to decrease rapidly toward zero with the frequsncy dependence substantially ~IL2~
as fl-. This frequency represents the largest pore size in the formation, again obtained frcm equation (1). Since the largest pores control the formation permeability, an approximate value of permEability can be obtained frcm the measure~ent of fm m alone.
The present invention will be more easily understood fr~m the following description when taken in conjunction with the drawings in which:
Figure 1 represents an idealized pore in a shaly sand and the charges carried by clay counterions and by sodium and cloride ions in the free electrolyte.
Figure 2 represents a plot of the induced polarization decay voltage present in the formation as the induced polarization logging tool is operated.
Figure 3 represents the deccmposition of the normalized in~uced polarization decay into a weighted series of four exponential decays.
Figure 4 represents the cumulative pore volume versus pore size curve calculated from the induced polarization voltage decay.
Figure 5 represents a ~g/~;r and oil/water capillary pressure curve determined from the induced pol æ ization voltage decay, cqmpared with ~he measured Hg/air capillary pressure curve.
Figure 6 represents the IP decay curves for a sandstone 100%
water-saturated and 50% oil-saturated.
Figure 7 represents a series of curves of phase shift versus frequency for various formations.
According to the teachings of this invention, there is shcwn in Figure 1 a schematic representation of a pore contained within a shaly sand. The pore is shown to be spherical in shape with radius A, and has a plurality of pore throats of radius R less than A which enter the pore. The pore contains a series of clay-rich zones 1 with a negatively charged surface and clay-free zones 2 filled with free electrolyte. The induced polarization logging tool of the aforementioned patent applies a substantially constant electric field E to the formation in the direction shcwn in Figure l~ m e negatively charged surfaces of the clay-rich zones act as cation s~lective membranes and restrict the flow of negatively charged cations under the influence of the electric field. m us, after sufficient time an electrochemical gradient is established across the clay-free æones 2 by the build-up of electrolyte concentration 3 at the edge of the clay-rich zone l.
When the electric field from the induced polarization logging tool is turned off, the concentration gradient disappears as the electrolyte ions diffuse back to their equilibrium positions.
This, in turn, decreases the induced potential gradient which constitutes the induce~ polarization decay curve.
A typical time dcmain I~ decay curve is illustrated in Figure 2. The voltage Vp is the equilibrium voltage after the electric field has been applied for a subs-tantial time, and the voltage Vs(t) is the time dcmain IP decay voltage as a ~unction of time. The voltage Vs (t=0) is the IP decay voltage at the instant the electric field is terminated.
If the porcus medium consisted of clay-free zanes all of the same size, the induced polarization deca~ curve would consist of a single exponential decay of time constant, t:
t = ~ (2) where D is the diffusion constant of electrolyte ions in the aqueous solution at formation temperature, and r is the length of the clay-free zone along the direction of the applied electric ield. For sodium chloride solution at 25 C, D = 1.5 x lO 5 cm2/ æc; r is in centimetres, and t is in seconds. Hcwever, naturally-occurring sandstones have a wide range of clay-free distances, so that the observed induced polarization decay curve is a complex éxponential decay consisting of a weighted series of exponentials with different time constants. The decomFosition of the IP decay curve of Figure 2 ~n~o four exponentials is shcwn in Figure 3.
~L~ 8~3 The longest time constant in the IP decay curve will be contributed by those ions with the longest relaxation distance~
For times longer than the longest time constant the ions have enough time to return to their equilibrium positions and the IP
decay voltage will have decreased to zero.
We have discovered that the clay-free relaxation distances are substantially the same as the pore size distribution. The explanation for this is that the clay occurs naturally as a pore lining material. In particular, referring to Figure l, the clay particles l in the pore throat are the m~st effective membranes for the electrolyte 2 contained in the pore. mus, the scale of relaxation distances is substantially the same as the pore scale. This discovery has not been previously recognized in the art and is the basis for determining a pore size histogram from an induced polarization logging tool.
The preferred method of this invention is to measure an IP
decay curve VS(t? opposite the formation using the focused IP
logging tool of copending patent application. Although a focused induced polarization logging tool is the preferred embodim nt, the method of this invention can also be applied to conventional induced polarization logging tools. m e IP logging tool applies a substantially constant current into the formation until e~uilibrium is substantially reached. This time is typically in the range O.Ol-lO0 seconds. The current is then term m ated and the IP decay curve is measured. m e IP decay curve Vs(t) shown in Fig. 2 is normalized in Fig. 3 by dividing by Vs (t=0) where t=0 is the instant ak which the applied electric field is term m ated.
The normalized decay curve is then fit with a set of N
exponentials of the form:
Vs(t) N -t/Ti ~ ~ Sie (3) V ~t=0) i=l ~48~3 g where Si is the fraction of total pore volume in which the time constant equals Ti. The number of exponentials fit to the IP
decay curve depend on the signal-to~noi æ of the IP decay curve.
We have fcund that N between 3 and 5 gives satisfactory results for typical signal-to-noise conditions. Figure 3 shcws a typical example using four relaxation times for a sandstone core taken from the Berea oil reservoir. Each time constant is converted to a pore size using:
\~
Ai =V DTi (4) where Ai is the radius in cm of the ith pore size. This results in N data pairs of the ~orm ~Si, Ai) ~rom which a pore size histogram and cumulative pore volume versus pore size curve can be constructed. Figure 4 shows the cumulative pore volume (CPV) curve determined frQm the IP decay curve derived frcn the aforementioned tool. In Figure 4 the numbers along the horizontal axis represent the pore radius expressed in microns, so that - as the pore radius A. is expressed in the formula (4) in cm - the nu~kers along the horizontal axis correspond to Ai.10 4. In Fig.
4 the numbers along the vertical axis represent the cumulative pore volume (CPV) as a percentage of the cumulative volume (CV).
If the additional assumption is made that
IN-SITU MET~OD FOR DETE~IWING PORE SIZE
DISTRIBUTION, CAP~ILARY PRESSURE AND PERME~BILITY
The invention relates to an in-situ method for determining the pore size distribu~ion, capillary pressure curve and penmeability of a formation surrounding a well. These are all important considexations in deciding whether hydrocarbon-bearing formations are commercial. A formation may contain a large amount of hydrocarbon but if the pores are too small and the permeabi-lity is too low it may not be possible to produce the hydro-carbons commercially. Thus, the determination of the pore size distribution, capillary pressure curve, and permeability of the formation is an important consideration in determining whether a well which has penetrated a hydrocarbon-bearing formation should be ccmpleted. The expense of cQmpleting a well is, of course, considerable since the well must first be cased and production tubing and well-head equip~ent installed.
At present there are only two reliable me~hods for determining the pore size distribution, capillary pressure curve and permeability of a formation. m e me~hod used most often is to take cores from the formation during the drilling o~ the well and then to analyse the cores in a laboratory. Coring enables high precision laboratory measurements of capillary pressure and permeability. Coring, hc~svsr, is very expensive and involves scme risk. While cor m g a well, one d oe s not have a~ much ccntr~1 over the ~ell as when drilling with conventional rcck bits and the possibility of sticking the drill string in the well is greatly increased during coring operations. Further, durm g coring operations, the penetration rates are greatly reduced, thus mcreas ~ g ~he tLme required to dxill the well to a ~ et depth. In~addition; measursments on core plugs may not be a good repres ~tion of the~f~rmstion as a whols, sincs core plugs ars :
~: . ' :
:
mall, discrete samples.
The only reliable logging method for determining pore size distribution, capillary pressure curves and permeability is the use of the nuclear magnetism logging (NML) tool. In this method the Tl decay curve of protons magnetically polarized in the formation is recorded and then mathematically inverted to obtain a pore size distribution and an approximate permeability (J.D.
Loren and J.D. Robinson, "Relations Between Pore Size, Fluid and Matrix Prcperties, and NML Measurements'l, Society o~ Petroleum Engineers Journal, September 1970, pages 268-278). The use of nuclear magnetism logging is ccmmercially practiced and readily available. While the technique is available, it does have several disadvantages. Among the disadvantages are the small depth of investigation of the nuclear magnetism log (about 6 inches) and the requirement that the borehole fluid be treated with magnetized particles to eliminate the borehole mud response frcm the log. Normally, magnetite particles in suspension æe added to the drilling mud to suppress the borehole respanse. This involves considerable expense and effort, because it is necessary to circulate the magnetite in the well to assure adequate mixing, and the circulated mud must be chec~ed to verify that the nuclear magnetic response has been eliminated.
A further disadvantage of the nuclear magnetism log is that the signal is extremely weak, often requiring several measurements at a fixed location for signal averaging. Thus, a good NMR decay curve of the quality required for capillary pressure and premeability determination is usually not obtained while continuously logging. ~not~er disadvantage of the NML is that the nuclear magnetism decay ti~es are so short in s e formations, for example in ti~ht gas sands, that the signals cannot be measured by existing NML tools (J.A. Brown, L.F~ Brown, J.A. Jackson, J.V. Milewski, B.J. Travis, "NMR Logging Tool Developments: Laboratory studies of Tight Gas Sands and Artificial Porous Material", SPE/DOE 10813, pages 203-208~. This is a severe disadvantage because it is precisely the marginal, low permeability formations where accurate neasurement of the premeability is req~lired most. Still another disadvantage of the NML is that the permeability determ med from nuclear magnetism is a ~hree-dimensional average, because the polarized protons on the water molecules diffuse randcmly until they relax at the pore walls. In many formations there is an order of magnitude difference between vertical and horizontal perm~ability. me MML
results will yield a three-dimensional averaged permeability rather than a separate vertical and horizontal permeability. Yet another difficulty with nuclear magnetism logging is that in oil-bearing formations, both the protons in water and in oil contribute to the Tl decay curve. Since the water phase and the oil phase have different decay rates, an unambiguous deter-mination of pore size often cannot be made. In addition, the Tldecay times depend on the character of the pore surface, such as hydrocarbon wetting, bound hydration ions and paramagnetic centres. As is well known in the art, these can all produce significant effects on the measured Tl relaxation times lJ.A.
Glasel, "NMR Relaxation in Heterogeneous Systems", Nature 227, 704-705 (1970); R.J.S. Brcwn and I. Fatt, "Measurements of Fractional Wettabilit~ of Oilfield Rocks by the Nuclear Magnetic Relaxation Method", Pet. Trans, AIME 207, 262-264 (1956)).
A final problem in relating the NMR relaxation times to formation permeability is that the pores probed by NMR need not be hydraulically connected. Therefore an Lmpermeable medium containing disconnected yugs,could yield the same Tl decay curve as a permeable rock containing connected pores.
The present invention provides a method using in-situ logging methods for measurement of the capillary pressure curve and formation per.,~ability. The method utilizes an induced polarization (IP) logging tool, preferably a focused induced polarization logging apparatus such as described in copending Canadian Patent application Serial No. 454,307. In this patent application there is described an induced polarization logging tool having means for focusing the electrodes to provide either horizontal or vertical measurements of the mduced polarization. ~easur~ments of the logging tool are recorded at the surface in the form of time domain IP decay curves or in the form of phase shift versus frequency of the applied electric field.
The present invention has several advantages cGmpared to the N~ tool described previously~ The electric field in this invention penetrates deep into the formation away from the borehole. In addition, the present method does not require any treatment of the borehole fluids. A major advantage is that the signal to noise in the present invention is sufficient that signal averaging is not required and a well can be logged continucusly. Another advantage of the present invention is that the IP voltage decay times are long enough even in low marginal reservoirs. Still another advantage is that the ions polarized by the present invention move along the direction of the applied electric field, so that both horizontal and vertical permeability can be separately determined. Yet another advantage is that, unlike the NML, the IP log observes only the water and not the oil in the formation. This is because oil is substantially nonconducting. A final advantage is that, unlike the nuclear magnatic response, the IP response is measured only along conducting pathways through the formation, therafore, disconnectad and dead-and pores, which do not contribute to permeability, are not measured by the IP logging tcol.
The method of the present invention requires that the above mentioned logging tool be operated cpposite the formation of interest to measure the tIme domain IP decay curve. The time domain IP decay curve is decomposed by a ccmpu~er algorithn into a set of exponential decays with different time constants. From the amplitude and time constant of each exponential, a pore size histogram is constructed. In particular, the relationship between diffusion constant D of sodium chl~ride electrolyte in aqueous solution (cm2/sec), the displac~ment length r (cm), and the time 12~r~8~0 constant t (sec) is used in the expression:
r2 (1) D = t The value of the diffusion coefficient at the formation tempera~ure is used in this expressio~. The diffusion constant of sodium chloride electrolyte is kncwn to be 1.5 x 10 5 cm2/sec at 25 C, and the effect of temperature on the diffusion constant is well known. We have discovered that the displacement length r is substantially the same as the pore size in clastic rocks. Thus, the IP decay curve yields the distribution of pore sizes in the formation.
Once the distribution of pore sizes is known, an a~proximate value for formation permeability can be ccmputed using various geometric models, which æ e well kncwn the the art. By proper calibration with core plugs from the formation of interest, the response of the i~duced polarization logging tool can be made ~;rectly in permeability units.
An alternative method of the present invention is to operate the IP logging tool of the aforementioned patent in the frequency domain. This requires that the logging tool be operated at several substantially different frequencies adjacent to the formation of interest. The phase shift for each frequency is measured and plotted to obtain a curve representing the phase shift versus frequency over a substantial range of frequencies.
This plot can also be obtained from the time domain IP decay curve described above using linear transform techm ques well known in the art. The phase shift ~ersus fre~uency curve can be decomposed into a set of amplitudes and time constants which are used with the above mentioned relation between diffusion constant D and displacement length r to obtain a pore size hi~togram.
A shortened form of the above procedure is to obtain the phase shift versus frequency plot as described above, and record the frequency (fmin) at which the phase shift starts to decrease rapidly toward zero with the frequsncy dependence substantially ~IL2~
as fl-. This frequency represents the largest pore size in the formation, again obtained frcm equation (1). Since the largest pores control the formation permeability, an approximate value of permEability can be obtained frcm the measure~ent of fm m alone.
The present invention will be more easily understood fr~m the following description when taken in conjunction with the drawings in which:
Figure 1 represents an idealized pore in a shaly sand and the charges carried by clay counterions and by sodium and cloride ions in the free electrolyte.
Figure 2 represents a plot of the induced polarization decay voltage present in the formation as the induced polarization logging tool is operated.
Figure 3 represents the deccmposition of the normalized in~uced polarization decay into a weighted series of four exponential decays.
Figure 4 represents the cumulative pore volume versus pore size curve calculated from the induced polarization voltage decay.
Figure 5 represents a ~g/~;r and oil/water capillary pressure curve determined from the induced pol æ ization voltage decay, cqmpared with ~he measured Hg/air capillary pressure curve.
Figure 6 represents the IP decay curves for a sandstone 100%
water-saturated and 50% oil-saturated.
Figure 7 represents a series of curves of phase shift versus frequency for various formations.
According to the teachings of this invention, there is shcwn in Figure 1 a schematic representation of a pore contained within a shaly sand. The pore is shown to be spherical in shape with radius A, and has a plurality of pore throats of radius R less than A which enter the pore. The pore contains a series of clay-rich zones 1 with a negatively charged surface and clay-free zones 2 filled with free electrolyte. The induced polarization logging tool of the aforementioned patent applies a substantially constant electric field E to the formation in the direction shcwn in Figure l~ m e negatively charged surfaces of the clay-rich zones act as cation s~lective membranes and restrict the flow of negatively charged cations under the influence of the electric field. m us, after sufficient time an electrochemical gradient is established across the clay-free æones 2 by the build-up of electrolyte concentration 3 at the edge of the clay-rich zone l.
When the electric field from the induced polarization logging tool is turned off, the concentration gradient disappears as the electrolyte ions diffuse back to their equilibrium positions.
This, in turn, decreases the induced potential gradient which constitutes the induce~ polarization decay curve.
A typical time dcmain I~ decay curve is illustrated in Figure 2. The voltage Vp is the equilibrium voltage after the electric field has been applied for a subs-tantial time, and the voltage Vs(t) is the time dcmain IP decay voltage as a ~unction of time. The voltage Vs (t=0) is the IP decay voltage at the instant the electric field is terminated.
If the porcus medium consisted of clay-free zanes all of the same size, the induced polarization deca~ curve would consist of a single exponential decay of time constant, t:
t = ~ (2) where D is the diffusion constant of electrolyte ions in the aqueous solution at formation temperature, and r is the length of the clay-free zone along the direction of the applied electric ield. For sodium chloride solution at 25 C, D = 1.5 x lO 5 cm2/ æc; r is in centimetres, and t is in seconds. Hcwever, naturally-occurring sandstones have a wide range of clay-free distances, so that the observed induced polarization decay curve is a complex éxponential decay consisting of a weighted series of exponentials with different time constants. The decomFosition of the IP decay curve of Figure 2 ~n~o four exponentials is shcwn in Figure 3.
~L~ 8~3 The longest time constant in the IP decay curve will be contributed by those ions with the longest relaxation distance~
For times longer than the longest time constant the ions have enough time to return to their equilibrium positions and the IP
decay voltage will have decreased to zero.
We have discovered that the clay-free relaxation distances are substantially the same as the pore size distribution. The explanation for this is that the clay occurs naturally as a pore lining material. In particular, referring to Figure l, the clay particles l in the pore throat are the m~st effective membranes for the electrolyte 2 contained in the pore. mus, the scale of relaxation distances is substantially the same as the pore scale. This discovery has not been previously recognized in the art and is the basis for determining a pore size histogram from an induced polarization logging tool.
The preferred method of this invention is to measure an IP
decay curve VS(t? opposite the formation using the focused IP
logging tool of copending patent application. Although a focused induced polarization logging tool is the preferred embodim nt, the method of this invention can also be applied to conventional induced polarization logging tools. m e IP logging tool applies a substantially constant current into the formation until e~uilibrium is substantially reached. This time is typically in the range O.Ol-lO0 seconds. The current is then term m ated and the IP decay curve is measured. m e IP decay curve Vs(t) shown in Fig. 2 is normalized in Fig. 3 by dividing by Vs (t=0) where t=0 is the instant ak which the applied electric field is term m ated.
The normalized decay curve is then fit with a set of N
exponentials of the form:
Vs(t) N -t/Ti ~ ~ Sie (3) V ~t=0) i=l ~48~3 g where Si is the fraction of total pore volume in which the time constant equals Ti. The number of exponentials fit to the IP
decay curve depend on the signal-to~noi æ of the IP decay curve.
We have fcund that N between 3 and 5 gives satisfactory results for typical signal-to-noise conditions. Figure 3 shcws a typical example using four relaxation times for a sandstone core taken from the Berea oil reservoir. Each time constant is converted to a pore size using:
\~
Ai =V DTi (4) where Ai is the radius in cm of the ith pore size. This results in N data pairs of the ~orm ~Si, Ai) ~rom which a pore size histogram and cumulative pore volume versus pore size curve can be constructed. Figure 4 shows the cumulative pore volume (CPV) curve determined frQm the IP decay curve derived frcn the aforementioned tool. In Figure 4 the numbers along the horizontal axis represent the pore radius expressed in microns, so that - as the pore radius A. is expressed in the formula (4) in cm - the nu~kers along the horizontal axis correspond to Ai.10 4. In Fig.
4 the numbers along the vertical axis represent the cumulative pore volume (CPV) as a percentage of the cumulative volume (CV).
If the additional assumption is made that
2 ycos ~ 2 ycos ~
Pc . = -- (S) l Ri (Ai / h) where Pc is the capillary pressure in dynes/cm2, y is the interfacial tension between the wetting and non-wetting fluid (dynes/cm), ~ is the contact angle, Ri is the pore throat radius m cm, Ai is the pore radius in cm, and h is a constant relating pore throat radius to p~re radius, then a capillary pressure curve can be constructed fr~m the N data pairs (Si, Pc ) This ~.2~
assumption is based on the relation between Pc and R for capillaries of circular cross section and by the assumption that pore throat radius and pore radius may be directly proportional to one another. m e constant y is typically 35 dynes/cm for oil/water, and cos 9 = l Por water-wet rocks; y = 480 dynes/cm for mercury/air and cos 3 = -0.7666, as is well known in the art.
The constant h is typically in the range 2.5 - 4 and may be determined more accurately from correlating capillary pressure measurements and IP decay curves on cores. Figure 5 shows a Hg/air capillary pressure curve 5 and an oil/water capillary pressure curve 6 determined from the induced polarization voltage decay of Figure 3 (using h = 2.5), as well as the actual Hg/air capillary pressure curve 7 measured for this sample.
In Fig. 5 the numbers indicated along the horizontal axis represent the percentage of the pore volume occupied by Hg or oil. The numbers indicat~d along the vertical axis at the right side of the diagram represent the capillary oil pressure in PSI
(lPSI = 0.07 BAR), whereas the numbers indicated along the vertical axis at the left side of the diagram represent the capillary Hg pressure m PSI (l PSI-0.07 BAR).
Several empirical relations have been shown to reflect ho~
permeability, K, depends on pore size and pore distribution. The simplest appro~imation is that:
K - ~ l6~
where K lS the penmeabilit~ in millidarcies and ~ is the mean square pore radius in square microns~ A more accurate empirlcal relation is:
* ~`
~ i, where c is a constant, p is the porosity which may be determined from a porosity log, m is the cementation factor which is typically in the range 1.5-2.5, and Ai is the mean square pore radius detexmined from the pore size distr~bution. In this relation, if X is in millidarcies, Ai in microns, and ~ is in decimal, then ~he constant c = 20. From the Waxman-Smits relation S (M.H. Waxman, L.J. Smits, "Electrical Conducti~ity in Oil-Bearing Shaly Sands", Soc. Petroleum Engineers Jouxnal, June 1968, pp.
107-122):
1 +m* (8) * =
F
*
~here F is the formation resistivity factor. The ~ormation resistivity factor can be determined from the in-phase 10 resistivity measured by the induced polarization logging tool if the formation salinity is know. Thus, if Cw i~ the conductivity of the formation brine (mho-metres 1), CI is the in-phase conductivity (mho-metres 1) mPasured by the IP logging tool, then: C
- 1 = I (9) F Cw As an example of the application of these equations, the penmeability computed for the sandstone of Figure 3 is 477 millidarcies using equation 7 and 604 millidarcies u~sing equation 8 (~ = 0~21, m = 1.78, F 15.8). ~he measured brine permeability is 425 millidarcies at 1.0 Molar NaCl.
Other permeability relations based on the shape of the capillary pressure curve are also well known in ~he art (W.R.
Purcell, "Capillary Pressures-Their Measurement and the Calculation of Permeability Therefrom", Pet. Trans. AIME, February 1949, PP. 39-48i J.H. m omeer, "Introduction of a Pore 25 Gecmetrical Factor Defined by the Capillary Pressure Curve", Pet.
Irans. AIME 219, 1960, pp. 354-358). If core plugs are available, permeability measured on the core plugs can be used to calibrate the pore scale determined from the IP log measurements of relaxation time. Once the correlation between core measurements and in-situ ~asurements is made, nc~Dgra~s or tables can be provided for obtaining perme~bility directly from the borehole measurements. m is correlation may be programmed into a cGmputer algorithm so tha~. the response of the induced pol æization logging tcol is displayed directly in permeability units.
When both water and oil are present in a water-wet formation at capillary equilibrium, the oil phase occupies the larger pores and the water phase occupies the smaller pores. m is results m a reduc~ion in the IP decay curves at the longer tImes, corresponding to the larger pores entered by the oil phase.
Figure 6 shows in a diagram similar to the diagram of Fig. 3 the more rapid decay at long times for a ~erea sandstone with 50% oil saturation (decay curve 9) relati~e to the same core at 100%
water saturation (decay curve lO)o If equations 6 or 7 are utilized for an oil-bearing formation, the reduced pexmeability calculated will be indicative of the relative permeability to water at the p~rticular oil saturation present in thP formation.
Frcm Figure 6 it is evide~t that comparison of the IP decay curve 10 for the 100% water-saturated core and the IP decay curve 9 for the oil-bearing core can be used to determine the pore size entered by the oil phase. Thus, in Figure 6 the oil phase has - entered all pores larger t~n the pores corresponding to a relaxation ~ime of 0.08 second. The 100% water-saturated core IP
measurements can be ob~ained from core material from t~e formatian of interest which has been extracted of brine and hydrocarbons and resaturated with formation brine. In addition, if capillary pressure curves æ e measured on the cleaned core material, the in-situ oil saturation can be determined ~y comparing the 100%
water-saturated core IP measured with the loggin~ IP
measurements. The capillary pressure can be ccmputed from the relaxation time using equations (4) and (5). Entering the capillary pressure curve of Figure 5 at this capillary pressure gives the in-sltu oil saturation and ~he height of the oil column by well known techniques (E.J. Lynch, "Formation Evaluation", Harper and Row, New York, 1962, pp. 43).
The method of the present mvention also applies if a repetitive bipolar time-dcmain waveform or a bipolar time-dcmain waveform with dead time is utilized. As is well known in the art, a decay curve from these and similar waveforms can always be S constructed b~v linear suparposition of the basic step function response described above (J.R. Wait, "Overvoltage Research and Geophysical Applications", Pergamon Press, New York, 1959).
The use of a focused induced polarization logging tool has several advantages in accordance with the teachings of this invention. The IP decay curve can be obtained with the electric current frcm the aforementioned IP logging tool focused either horizontally or vertically. According to the teachings of this invention, since electrolyte diffusion occurs substantially in the direction of the applied electric field, separate horizontal and vertical pore size distributions and permeabilities will be obtained. If a conventional induced pol æ ization logging tool without focusing is utilized, separate vertical and horizontal values cannot be determ m ed. In addition, the depth of investigation, thin bed resolution, and borehole corrections are all poorer with a non-focused IP logging tool. Nevertheless the other teachings of this invention can still be applied to logging with a non-focused IP logging apparatus.
An alternative methcd of thè present invention is to cperate the IP logging tool in the frequency domain. This requires that the tool be operated at several substantially different frequencies in the low frequency range, preferably between 10 3 and 102 Hz, and adjacent the fonmation of interest. The IP
measurements at the different frequencies can be made either sequentially or sim~ltaneously by us~ng a superposition of the different discrete ~requencies. The phase shift for each frequency is measured and plotted to obta m a curve represent m g the phase shift versus frequency over a substantial range of frequencles.
.
Referring to Figure 7, there is shown a log-log plot of phase shift versus frequency for three different formations A, B
and C. In Figure 7 the numbers along the vertical axis represent the log (phase) expressed in milliradians and the nu~bers along the horizontal axis represent the log (frequency) in Hz. The formation A has the largest pore dimensions, while the formation C has the smallest pore dimensions. Point a in Figure 7 shows the frequency at which the phase shift in formation A starts to decrease at least as fast as ~ . This frequency corresponds to the longest time constant in the IP decay curve and also to the largest pore size in the formation.
The phase shift versus frequency curve can be decGmposed into a set of amplitudes and time constants, using linear transform methods well kncwn in the art. The amplitudes and time constants are the same as those from the IP decay curve, and the method of this invention proceeds as above to determLne pore size histogram, capillary pressure curve, and permeability.
A shortened form of the above procedure is to obtain the phase shift versus frequency plot as described above, and measure the frequency, fmu~ at which the phase shift starts to decrease substantially as f . This frequency fmin can be used in the following simple apprc~imation for formation permeability:
K ~ 10~ D (10) 2 ~ f .
mln where K is the premeability in millidarcies, D is the diffusion coefficient in cm2/sec, and fmin is in Hz. Other empirical relations relating premeability to fm m are also possible as derived from correlations between measured permeabiIity on core plugs nd fmIn determined frcm the IP log. This approach is illustrated m Figure 7 wherein the phase versus frequency curves for three formations A, B and C are shown. The fmln for the three formations are indicated at a, b and c, respectively.
Pc . = -- (S) l Ri (Ai / h) where Pc is the capillary pressure in dynes/cm2, y is the interfacial tension between the wetting and non-wetting fluid (dynes/cm), ~ is the contact angle, Ri is the pore throat radius m cm, Ai is the pore radius in cm, and h is a constant relating pore throat radius to p~re radius, then a capillary pressure curve can be constructed fr~m the N data pairs (Si, Pc ) This ~.2~
assumption is based on the relation between Pc and R for capillaries of circular cross section and by the assumption that pore throat radius and pore radius may be directly proportional to one another. m e constant y is typically 35 dynes/cm for oil/water, and cos 9 = l Por water-wet rocks; y = 480 dynes/cm for mercury/air and cos 3 = -0.7666, as is well known in the art.
The constant h is typically in the range 2.5 - 4 and may be determined more accurately from correlating capillary pressure measurements and IP decay curves on cores. Figure 5 shows a Hg/air capillary pressure curve 5 and an oil/water capillary pressure curve 6 determined from the induced polarization voltage decay of Figure 3 (using h = 2.5), as well as the actual Hg/air capillary pressure curve 7 measured for this sample.
In Fig. 5 the numbers indicated along the horizontal axis represent the percentage of the pore volume occupied by Hg or oil. The numbers indicat~d along the vertical axis at the right side of the diagram represent the capillary oil pressure in PSI
(lPSI = 0.07 BAR), whereas the numbers indicated along the vertical axis at the left side of the diagram represent the capillary Hg pressure m PSI (l PSI-0.07 BAR).
Several empirical relations have been shown to reflect ho~
permeability, K, depends on pore size and pore distribution. The simplest appro~imation is that:
K - ~ l6~
where K lS the penmeabilit~ in millidarcies and ~ is the mean square pore radius in square microns~ A more accurate empirlcal relation is:
* ~`
~ i, where c is a constant, p is the porosity which may be determined from a porosity log, m is the cementation factor which is typically in the range 1.5-2.5, and Ai is the mean square pore radius detexmined from the pore size distr~bution. In this relation, if X is in millidarcies, Ai in microns, and ~ is in decimal, then ~he constant c = 20. From the Waxman-Smits relation S (M.H. Waxman, L.J. Smits, "Electrical Conducti~ity in Oil-Bearing Shaly Sands", Soc. Petroleum Engineers Jouxnal, June 1968, pp.
107-122):
1 +m* (8) * =
F
*
~here F is the formation resistivity factor. The ~ormation resistivity factor can be determined from the in-phase 10 resistivity measured by the induced polarization logging tool if the formation salinity is know. Thus, if Cw i~ the conductivity of the formation brine (mho-metres 1), CI is the in-phase conductivity (mho-metres 1) mPasured by the IP logging tool, then: C
- 1 = I (9) F Cw As an example of the application of these equations, the penmeability computed for the sandstone of Figure 3 is 477 millidarcies using equation 7 and 604 millidarcies u~sing equation 8 (~ = 0~21, m = 1.78, F 15.8). ~he measured brine permeability is 425 millidarcies at 1.0 Molar NaCl.
Other permeability relations based on the shape of the capillary pressure curve are also well known in ~he art (W.R.
Purcell, "Capillary Pressures-Their Measurement and the Calculation of Permeability Therefrom", Pet. Trans. AIME, February 1949, PP. 39-48i J.H. m omeer, "Introduction of a Pore 25 Gecmetrical Factor Defined by the Capillary Pressure Curve", Pet.
Irans. AIME 219, 1960, pp. 354-358). If core plugs are available, permeability measured on the core plugs can be used to calibrate the pore scale determined from the IP log measurements of relaxation time. Once the correlation between core measurements and in-situ ~asurements is made, nc~Dgra~s or tables can be provided for obtaining perme~bility directly from the borehole measurements. m is correlation may be programmed into a cGmputer algorithm so tha~. the response of the induced pol æization logging tcol is displayed directly in permeability units.
When both water and oil are present in a water-wet formation at capillary equilibrium, the oil phase occupies the larger pores and the water phase occupies the smaller pores. m is results m a reduc~ion in the IP decay curves at the longer tImes, corresponding to the larger pores entered by the oil phase.
Figure 6 shows in a diagram similar to the diagram of Fig. 3 the more rapid decay at long times for a ~erea sandstone with 50% oil saturation (decay curve 9) relati~e to the same core at 100%
water saturation (decay curve lO)o If equations 6 or 7 are utilized for an oil-bearing formation, the reduced pexmeability calculated will be indicative of the relative permeability to water at the p~rticular oil saturation present in thP formation.
Frcm Figure 6 it is evide~t that comparison of the IP decay curve 10 for the 100% water-saturated core and the IP decay curve 9 for the oil-bearing core can be used to determine the pore size entered by the oil phase. Thus, in Figure 6 the oil phase has - entered all pores larger t~n the pores corresponding to a relaxation ~ime of 0.08 second. The 100% water-saturated core IP
measurements can be ob~ained from core material from t~e formatian of interest which has been extracted of brine and hydrocarbons and resaturated with formation brine. In addition, if capillary pressure curves æ e measured on the cleaned core material, the in-situ oil saturation can be determined ~y comparing the 100%
water-saturated core IP measured with the loggin~ IP
measurements. The capillary pressure can be ccmputed from the relaxation time using equations (4) and (5). Entering the capillary pressure curve of Figure 5 at this capillary pressure gives the in-sltu oil saturation and ~he height of the oil column by well known techniques (E.J. Lynch, "Formation Evaluation", Harper and Row, New York, 1962, pp. 43).
The method of the present mvention also applies if a repetitive bipolar time-dcmain waveform or a bipolar time-dcmain waveform with dead time is utilized. As is well known in the art, a decay curve from these and similar waveforms can always be S constructed b~v linear suparposition of the basic step function response described above (J.R. Wait, "Overvoltage Research and Geophysical Applications", Pergamon Press, New York, 1959).
The use of a focused induced polarization logging tool has several advantages in accordance with the teachings of this invention. The IP decay curve can be obtained with the electric current frcm the aforementioned IP logging tool focused either horizontally or vertically. According to the teachings of this invention, since electrolyte diffusion occurs substantially in the direction of the applied electric field, separate horizontal and vertical pore size distributions and permeabilities will be obtained. If a conventional induced pol æ ization logging tool without focusing is utilized, separate vertical and horizontal values cannot be determ m ed. In addition, the depth of investigation, thin bed resolution, and borehole corrections are all poorer with a non-focused IP logging tool. Nevertheless the other teachings of this invention can still be applied to logging with a non-focused IP logging apparatus.
An alternative methcd of thè present invention is to cperate the IP logging tool in the frequency domain. This requires that the tool be operated at several substantially different frequencies in the low frequency range, preferably between 10 3 and 102 Hz, and adjacent the fonmation of interest. The IP
measurements at the different frequencies can be made either sequentially or sim~ltaneously by us~ng a superposition of the different discrete ~requencies. The phase shift for each frequency is measured and plotted to obta m a curve represent m g the phase shift versus frequency over a substantial range of frequencles.
.
Referring to Figure 7, there is shown a log-log plot of phase shift versus frequency for three different formations A, B
and C. In Figure 7 the numbers along the vertical axis represent the log (phase) expressed in milliradians and the nu~bers along the horizontal axis represent the log (frequency) in Hz. The formation A has the largest pore dimensions, while the formation C has the smallest pore dimensions. Point a in Figure 7 shows the frequency at which the phase shift in formation A starts to decrease at least as fast as ~ . This frequency corresponds to the longest time constant in the IP decay curve and also to the largest pore size in the formation.
The phase shift versus frequency curve can be decGmposed into a set of amplitudes and time constants, using linear transform methods well kncwn in the art. The amplitudes and time constants are the same as those from the IP decay curve, and the method of this invention proceeds as above to determLne pore size histogram, capillary pressure curve, and permeability.
A shortened form of the above procedure is to obtain the phase shift versus frequency plot as described above, and measure the frequency, fmu~ at which the phase shift starts to decrease substantially as f . This frequency fmin can be used in the following simple apprc~imation for formation permeability:
K ~ 10~ D (10) 2 ~ f .
mln where K is the premeability in millidarcies, D is the diffusion coefficient in cm2/sec, and fmin is in Hz. Other empirical relations relating premeability to fm m are also possible as derived from correlations between measured permeabiIity on core plugs nd fmIn determined frcm the IP log. This approach is illustrated m Figure 7 wherein the phase versus frequency curves for three formations A, B and C are shown. The fmln for the three formations are indicated at a, b and c, respectively.
Claims (28)
PROPERTY OR PRIVILEGE IS CLAIMED ARE DEFINED AS FOLLOWS:
1. A method for the in-situ determination of permeability of a formation, comprising the steps of:
logging the formation of interest with an induced polar-ization logging tool;
converting the measurements to an induced polarization decay curve; and determining the permeability from the induced pol-arization decay curve.
logging the formation of interest with an induced polar-ization logging tool;
converting the measurements to an induced polarization decay curve; and determining the permeability from the induced pol-arization decay curve.
2. The method of claim 1 and in addition determining the pore size distribution and using the pore size distribution to determine the permeability of the formation.
3. The method of claim 2 and in addition determining the cap-illary pressure histogram from the pore size distribution.
4. The method of claim 1, wherein said logging step consists of induced polarization measurements made in the time domain, and said decay curve is a time domain voltage decay curve.
5. The method of claim 1, wherein said logging step consists of induced polarization measurements made in the frequency domain, at a plurality of frequencies, and said decay curve is a plot of induced polarization phase shift versus frequency.
6. The method of claim 1, or 5, wherein said logging step consists of measurements made using a focused electrode induced polarization logging tool, containing at least one focused source electrode.
- 15a -
- 15a -
7. The method of claims 1, 4 or 5 wherein said logging step consists of measurements made using a focused electrode induced polarization logging tool containing at least one focused source electrode, and which is focused alternately in a horizontal and vertical direction, and the permeability is determined separately in the horizontal and vertical directions.
8. The method of claim 4, wherein said logging step consists of induced polarization measurements made using a current-on time and current-off time in the range from on 1/100 to 100 seconds duration.
9. The method of claim 5, wherein said logging step consists of induced polarization frequency domain measurements made in the frequency range 0.001 Hz to 100 Hz.
10. The method of claim 8, wherein said induced polarization (IP) time domain voltage decay curve is normalized by dividing by the IP decay voltage at the time the current flow is terminated, and the normalized curve is then fit with N exponentials in the expression:
where Vs(t) is the IP decay voltage at time t, Vs(t=0) is the IP
decay voltage at the time after the primary charging voltage is terminated, Si is the fraction of pore volume whose time constant equals Ti.
where Vs(t) is the IP decay voltage at time t, Vs(t=0) is the IP
decay voltage at the time after the primary charging voltage is terminated, Si is the fraction of pore volume whose time constant equals Ti.
11. The method of claim 10, wherein a pore size distribution is determined from the equation:
where Ai is the radius of the ith pore size of pore volume fraction Si for which the time constant equals Ti, and D is the diffusion constant of electrolyte ions in the formation brine in cm2/sec at formation temperature.
where Ai is the radius of the ith pore size of pore volume fraction Si for which the time constant equals Ti, and D is the diffusion constant of electrolyte ions in the formation brine in cm2/sec at formation temperature.
12. The method of claim 11, wherein a capillary pressure histogram consisting of data pairs is derived from the equations:
where is the capillary pressure in dynes/cm2 for the ith pore throat size, Si is the pore volume fraction corresponding to .gamma. is the interfacial tension between the wetting and non-wetting fluids in dynes/cm at formation conditions, .theta. is the contact angle, Ri is the pore throat radius in cm, and h is a constant relating pore throat radius to pore radius.
where is the capillary pressure in dynes/cm2 for the ith pore throat size, Si is the pore volume fraction corresponding to .gamma. is the interfacial tension between the wetting and non-wetting fluids in dynes/cm at formation conditions, .theta. is the contact angle, Ri is the pore throat radius in cm, and h is a constant relating pore throat radius to pore radius.
13. The method of claim 11, wherein the permeability K is derived from the equation:
where K is the permeability, an, the mean square pore radius.
where K is the permeability, an, the mean square pore radius.
14. The method of claim 11, wherein the permeability of K is derived from the equation:
where K is the permeability, c is a constant, ? is the fractional porosity, m* is the cementation exponent having a value between 1.5 and 2.5, and is the mean square pore radius.
where K is the permeability, c is a constant, ? is the fractional porosity, m* is the cementation exponent having a value between 1.5 and 2.5, and is the mean square pore radius.
15. The method of claim 14, wherein logging measurements made with resistivity and density logging tools opposite the aforesaid formation are used to obtain the factor ?m*.
16. The method of claim 5, wherein the permeability is determined from the following equation:
where K is the permeability in millidarcies, D is the diffusion constant for electrolyte ions in the formation brine in cm2/sec at formation temperature, and fmin is the frequency in Hz at which the frequency decay curve decreases substantially as f1Ø
where K is the permeability in millidarcies, D is the diffusion constant for electrolyte ions in the formation brine in cm2/sec at formation temperature, and fmin is the frequency in Hz at which the frequency decay curve decreases substantially as f1Ø
17. The method of claim 5, wherein the frequency decay curve is decomposed into a set of amplitudes and time constants using linear transforms and the resulting amplitudes and time constants are used in the method of claim 10.
18. A method for determining in-situ the permeability of a formation surrounding a borehole, comprising:
logging the borehole with an induced polarization logging tool having at least one focused source electrode;
applying current to the electrodes at a plurality of frequencies in the range 0.001 Hz to 100 Hz while the logging tool is opposite the formation of interest;
measuring the phase shift at the various frequencies;
transforming the phase shift versus frequency measurements into amplitude versus time constants;
determining the pore size distribution from the expression:
where Ai is the radius of the ith pore size, Ti is the time constant for the ith pore size, and D is the electrolyte diffusion constant at formation temperature in cm2/sec;
determining a capillary pressure histogram consisting of data pairs (, Si) from the pore size distribution using the expression:
where is the capillary pressure in dynes/cm2, .gamma. is the interracial tension between the wetting and non-wetting fluids in dynes/cm, .theta. is the contact angle, Ri is the pore throat radius in cm, and h is a constant relating pore throat radius to pore radius; and determining the permeability from the pore size distribution using the expression:
where c is a constant, ? is the fractional porosity, m* is the cementation factor, and is the mean square pore size.
logging the borehole with an induced polarization logging tool having at least one focused source electrode;
applying current to the electrodes at a plurality of frequencies in the range 0.001 Hz to 100 Hz while the logging tool is opposite the formation of interest;
measuring the phase shift at the various frequencies;
transforming the phase shift versus frequency measurements into amplitude versus time constants;
determining the pore size distribution from the expression:
where Ai is the radius of the ith pore size, Ti is the time constant for the ith pore size, and D is the electrolyte diffusion constant at formation temperature in cm2/sec;
determining a capillary pressure histogram consisting of data pairs (, Si) from the pore size distribution using the expression:
where is the capillary pressure in dynes/cm2, .gamma. is the interracial tension between the wetting and non-wetting fluids in dynes/cm, .theta. is the contact angle, Ri is the pore throat radius in cm, and h is a constant relating pore throat radius to pore radius; and determining the permeability from the pore size distribution using the expression:
where c is a constant, ? is the fractional porosity, m* is the cementation factor, and is the mean square pore size.
19. A method of for determining in-situ the permeability of a formation surrounding a borehole, comprising:
logging the borehole with an induced polarization logging tool having at least one focused source electrode;
measuring the phase shift at a plurality of frequencies in the range 0.001 Hz to 100 Hz;
determining the frequency fmin at which the phase shift decreases substantially as f1.0; and determining the permeability from frequency fmin
logging the borehole with an induced polarization logging tool having at least one focused source electrode;
measuring the phase shift at a plurality of frequencies in the range 0.001 Hz to 100 Hz;
determining the frequency fmin at which the phase shift decreases substantially as f1.0; and determining the permeability from frequency fmin
20. The method of claim 19 wherein the permeability is determined from the expression:
where K is the premeability in millidarcies, D is the diffusion constant for electrolyte ions in the formation brine in cm2/sec at formation temperature, and fmin is the frequency in Hz at which the frequency decay curve decreases substantially as f1Ø
where K is the premeability in millidarcies, D is the diffusion constant for electrolyte ions in the formation brine in cm2/sec at formation temperature, and fmin is the frequency in Hz at which the frequency decay curve decreases substantially as f1Ø
21. The method of claim 19, wherein the focused electrode array is adjusted to obtain separate vertical and horizontal permeabilities.
22. The method of claim 19, wherein the permeability is determined using a nomogram relating permeability and fmin.
23. The method of claim 1 , wherein the induced polarization decay curve is correlated with values of permeability obtained from core measurements to produce a direct output permeability log.
24. The method of claim 1 , wherein the induced polarization decay curve is correlated with capillary pressure curves obtained from core measurements to produce a direct output capillary pressure curve.
25. The method of claim 5, wherein the induced polarization frequency domain measurements are made simultaneously at a plurality of frequencies using a waveform which is a superposition of the desired frequencies.
26. A method for determining the pore sizes entered by the oil phase in an oil-bearing formation, comprising:
logging the formation of interest with an induced polarization logging tool having at least one focused source electrode;
computing from the induced polarization measurements a normalized induced polarization decay curve;
obtaining core material from the formation of interest;
extracting the water and hydrocarbons from the core material;
resaturating the core material with formation brine;
measuring the normalized induced polarization decay curve for the core material; and comparing the normalized induced polarization decay curve from the formation with the normalized induced polarization decay curve of the core to determine the pore sizes containing oil in the formation.
logging the formation of interest with an induced polarization logging tool having at least one focused source electrode;
computing from the induced polarization measurements a normalized induced polarization decay curve;
obtaining core material from the formation of interest;
extracting the water and hydrocarbons from the core material;
resaturating the core material with formation brine;
measuring the normalized induced polarization decay curve for the core material; and comparing the normalized induced polarization decay curve from the formation with the normalized induced polarization decay curve of the core to determine the pore sizes containing oil in the formation.
27. The method of claim 26 and in addition determining the oil saturation of the formation by measuring a capillary pressure curve for the core material.
28. The method of claim 27 and in addition determining the height of the oil column from the oil/water capillary pressure at the in-situ oil saturation.
Applications Claiming Priority (2)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| US06/591,140 US4644283A (en) | 1984-03-19 | 1984-03-19 | In-situ method for determining pore size distribution, capillary pressure and permeability |
| US591,140 | 1984-03-19 |
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| Publication Number | Publication Date |
|---|---|
| CA1244880A true CA1244880A (en) | 1988-11-15 |
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| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CA000475661A Expired CA1244880A (en) | 1984-03-19 | 1985-03-04 | In-situ method for determining pore size distribution, capillary pressure and permeability |
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|---|---|
| US (2) | US4644283A (en) |
| AU (1) | AU572052B2 (en) |
| CA (1) | CA1244880A (en) |
| GB (1) | GB2158244B (en) |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US4903207A (en) * | 1986-05-15 | 1990-02-20 | Restech, Inc. | Method for determining reservoir bulk volume of hydrocarbons from reservoir porosity and distance to oil-water contact level |
| US4751646A (en) * | 1986-05-15 | 1988-06-14 | Restech, Inc. | Method for determining original saturations in a produced field |
| US4786873A (en) * | 1986-06-06 | 1988-11-22 | Amoco Corporation | Method for evaluating water saturation in petroleum reservoirs from dielectric permittivity |
| US4769602A (en) * | 1986-07-02 | 1988-09-06 | Shell Oil Company | Determining multiphase saturations by NMR imaging of multiple nuclides |
| US4769606A (en) * | 1986-09-30 | 1988-09-06 | Shell Oil Company | Induced polarization method and apparatus for distinguishing dispersed and laminated clay in earth formations |
| US4864845A (en) * | 1987-09-29 | 1989-09-12 | Board Of Regents University Of Texas System | Electronic field permeameter |
| US4876512A (en) * | 1988-03-30 | 1989-10-24 | Exxon Production Research Company | Method for rapidly determining the swelling-clay content in shales and shaly sandstone formations by high-frequency dielectric constant measurements |
| US4926128A (en) * | 1989-02-13 | 1990-05-15 | Mobil Oil Corporation | Method for utilizing measured resistivities of porous rock under differing fluid saturations to identify fluid distribution equilibrium |
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1984
- 1984-03-19 US US06/591,140 patent/US4644283A/en not_active Expired - Lifetime
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1985
- 1985-03-04 CA CA000475661A patent/CA1244880A/en not_active Expired
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- 1985-03-18 NO NO851074A patent/NO168004C/en unknown
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1986
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| NL8500754A (en) | 1985-10-16 |
| NO168004C (en) | 1992-01-02 |
| GB2158244A (en) | 1985-11-06 |
| AU4007385A (en) | 1985-10-10 |
| GB8506937D0 (en) | 1985-04-24 |
| US4644283A (en) | 1987-02-17 |
| US4743854A (en) | 1988-05-10 |
| NO168004B (en) | 1991-09-23 |
| NO851074L (en) | 1985-09-20 |
| GB2158244B (en) | 1987-10-07 |
| AU572052B2 (en) | 1988-04-28 |
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