Oilfield operators demand access to a great quantity of information regarding the conditions encountered downhole. Such information typically includes characteristics of the earth formations traversed by the borehole and data relating to the size and configuration of the borehole itself. The collection of information relating to conditions downhole, which commonly is referred to as “logging,” can be performed by several methods including wireline logging.
In wireline logging, a probe or “sonde” is lowered into the borehole after some or the entire well has been drilled. The sonde hangs at the end of a long cable (“wireline”) that provides mechanical support to the sonde and also provides an electrical connection between the sonde and electrical equipment located at the surface of the well. In accordance with existing logging techniques, various parameters of the earth's formations are measured and correlated with the position of the sonde in the borehole as the sonde is pulled uphole. The direct electrical connection between the surface and the sonde provides power and a relatively large bandwidth for conveying logging information.
One desirable formation parameter is water-filled porosity of the formation, as it is useful for determining the quantity and producibility of hydrocarbons within the formation. To obtain the water-filled porosity, knowledge regarding water salinity is usually required. The standard techniques for determining water salinity are: (1) take a water sample from the well after it has been drilled, or (2) extrapolate from other wells in the region. Experience has shown these approaches to be unreliable due to significant salinity variation within and between wells, particularly when fluid injection is employed for secondary recovery. In the latter case, the fluid injection causes substantial salinity variation laterally across the reservoir and vertically around the reservoir, making the standard techniques impractical or hopelessly inaccurate. In either case, a determination of water salinity in real time is not feasible, thus requiring additional time and money for analysis. Absent an accurate measure of water salinity, the consequent determinations of water-filled porosity and corresponding implications regarding hydrocarbons are unreliable.
Accordingly, there are disclosed herein method and associated systems for determining water salinity and water-filled porosity. In the drawings:
It should be understood, however, that the specific embodiments given in the drawings and detailed description thereto do not limit the disclosure. On the contrary, they provide the foundation for one of ordinary skill to discern the alternative forms, equivalents, and modifications that are encompassed together with one or more of the given embodiments in the scope of the appended claims.
Disclosed herein are methods and systems for determining water salinity and water-filled porosity. Certain illustrative method embodiments include acquiring a downhole temperature, along with a total porosity measurement and dielectric measurement of the formation, and determining water salinity from such measurements. Additionally, based at least in part on the water salinity, a dielectric constant of water and a refractive index of the water may be calculated, thereby enabling a calculation of a water-filled porosity. The temperature, porosity, and dielectric measurements may be acquired in log form, i.e., as a function of depth or position along a borehole. Temperature-dependent function coefficients may be used in calculating the water salinity. Moreover, the coefficients may be saved to memory for later recall and/or displayed to the user along with the water-filled porosity.
Alternatively, or in addition to being communicated to the surface, measurements collected by the tools 114, 116 may be stored in memory of the tool string 112 and/or processed by a downhole processor within the tool string 112. A computing or logging facility 118 which includes a computer system 120 having a processor may be arranged at the surface to receive the processed or unprocessed measurements. The computer system 120 may include a memory having software executed by the processor to configure the logging facility 118 to manage tool string 112 operations, acquire and store the measurements, and process the measurements for display to an operator.
For example, the computer system 120 and processor may be capable of receiving the downhole measurements from the tools 114, 116, and responsively calculating water salinity and/or water-filled porosity of the formation. Moreover, such calculations may be a function of the acquired temperature, dielectric, and porosity measurements from the tools 114, 116. In particular, the water-filled porosity calculations may be based at least in part on water salinity and down hole temperature. The memory of the computer system 120 may additionally store information for recall later, such as the water salinity and temperature dependent function coefficients used to determine the water salinity. Additionally, the logging facility 118 may present the raw or calculated information to a user via a user interface that includes a monitor or printer.
While the wireline environment 100 of
Notably, due to the empirical mixing law known as the Complex Refractive Index Method (CRIM), when the dielectric measurement tool operates at high frequencies (e.g., at approximately 1 Ghz or greater), the measured formation properties can be treated as being independent of the formation or rock texture. The complex dielectric value ε*rock is thus related to only the fluids and minerals that make up the formation.
At block 208, a processor determines the water salinity based on the acquired temperature, porosity, and dielectric measurements via the following equations. In general, the following nomenclature is used throughout the equations: variables having an “*” (e.g., (δ*) are a complex value having real and imaginary components. Variables having a single apostrophe (e.g., δ′) are the real component of the complex value and variables having a double apostrophe (e.g., δ″) are the imaginary component of the complex value.
The dielectric value of the formation ε*rock can be measured in real-time by the high frequency dielectric tool (HFDT) ε*HFDT, and may be expressed in the form of Equation 1:
√{square root over (ε*HFDT)}=Vw*√{square root over (ε*w)}+Vma*√{square root over (ε*ma)}+VHC*√{square root over (ε*HC)} (1)
where ε*HFDT represents the dielectric measurement as taken by the HFDT as a function of three rock constituents: matrix (ma), water (w), and hydrocarbons (HC). V represents their relative volumes (which may be expressed as a percentage or dimensionless fraction of unity) and √{square root over (ε*)} is the root of their respective dielectric values (also defined as the refractive index ζ*). Equation 1 becomes equation 2:
ζ*HFDT=Vw*ζ*w+Vma*ζ*ma+VHC*ζ*HC (2)
Advantageously, eliminating the square root terms from equation 1 enables simplified calculations when solving equation 2. The refractive index is also a complex value, having real and imaginary parts, ζ*=ζ′+i*ζ″, thus equations representing the real and imaginary components may be represented as equation 3 (the real components) and 4 (the imaginary components):
ζ′HFDT=Vw*ζ′w+Vma*ζ′ma+VHC*′HC (3)
ζ″HFDT=Vw*ζ″w+Vma*ζ″ma+VHC*″HC (4)
Assuming the conductivity of both the hydrocarbons and the rock matrix is close to zero, the corresponding imaginary portion of the complex dielectric constants (ε″ma) and (ε″HC) are zero, thus their corresponding refractive index (ζ″ma) and (ζ″HC) are zero, and equation 4 becomes:
ζ″HFDT=Vw*ζ″w (5)
With φ representing the total porosity, the relative volumes may be represented as Vw=φw, VHC=(φ−φw), and Vma=(1−φ). Therefore, equations 3 and 5 become:
ζ′HFDT=φw*ζ′w+(φ−φw)*ζ′HC+(1−φ)*ζ′ma (6)
ζ″HFDT=φw*ζ″w (7)
Solving for water-filled porosity φw in equation 7, we obtain equation 8:
Expanding equation 6, isolating φw, and then substituting equation 8 for φw in equation 6 and solving for φw results in equation 9:
All the terms on the right hand side of equation are either measured or known. For example, the refractive index ζ′HFDt and ζ″HFDt are measurements from the HFDT tool. Similarly, the total porosity φ is known (i.e., from one of the downhole tools 114, 116, such as the density-neutron or NMR tool). The difference in porosity (1−φ) can be calculated, and the hydrocarbon refractive index ζ′HC and matrix refractive index ζ′ma are known or estimatable from previously obtained or calculated data. Specifically, the type of hydrocarbons may be determined by monitoring drilling fluids, acquiring formation fluid samples, or extrapolating from what is known from seismic data and/or nearby wells. The refractive index of the rock matrix can be determined in a similar fashion, and advantageously, such values are expected to be more readily determinable than water salinity.
On the left side of the equation, the hydrocarbon refractive index ζ′HC is also known from previously obtained or calculated data, such as √{square root over (ε′HC)}=ζ′HC≈√{square root over (2)}≈1.414. Thus, the real and imaginary refractive index components of water ζ′w and ζ″w are the only unknown variables in equation 9.
Both ζ′w and ζ″w are a function of pressure, temperature T, and water salinity Wsal. Assuming the pressure effects are negligible, ζ′w and ζ″w may be represented by corresponding functions, f1 and f2, dependent on only temperature (T) and water salinity (Wsal) as measured by the tools 114, 116 of the tool string 112 (
where c1 and c2 are calculated from the HFDT measurements, the porosity measurements, and the refractive indices of the formation matrix and hydrocarbons. When rearranged, equation 10 can be represented as:
f1−c1=c2*f2 (11)
It can be shown that the following polynomial equations are representative of f1 and f2:
f1=a0(T)+a1(T)*Wsal+a2(T)*Wsal2 (12)
f2=b0(T)+b1(T)*Wsal+b2(T)*Wsal2 (13)
The coefficients a0, a1, a2, b0, b1, b2 can be determined by fitting quadratic curves to laboratory measurements of saline water. Applying equations 12 and 13 to equation 11 results in equation 14:
a
0(T)+a1(T)*Wsal+a2(T)*Wsal2−c1=
c2*(b0(T)+b1(T)*Wsal+b2(T)*Wsal2) (14)
Equation 14 can also be represented as equation 15 by subtracting the right side of the equation and isolating Wsal and Wsal2.
[a0(T)−c2*b0(T)−c1]+[a1(T)−c2*b1(T)]*Wsal+[a2(T)−c2*b2(T)]*Wsal2=0 (15)
As discussed above, c1 and c2, along with the temperature T are known. In some embodiments, the temperature-dependent coefficients (a0, a1, a2, b0, b1, and b2) may also be known from prior calculations, thus allowing a determination of water salinity Wsal.
In other embodiments, the coefficients (a0, a1, a2, b0, b1, and b2) may be unknown and need to be solved for at block 208. To determine the coefficients, Stroud, Milton & De (Physical Review B Vol. 34, No. 8, Oct. 15, 1986) shows that at 1 GHz, the water's dielectric ε′w and ε″w can be approximated by the empirical relationship shown in equations 16 and 17.
Stroud et. al. do not include the water diffusion loss term ED(T, 1 Ghz) as depicted in equation 17, however addition of this term helps to better describe the asymptotic behavior of ε″w at low salinities and temperatures.
Illustrative results of equations 16 and 17 are depicted in
A second order polynomial can be fit to each of the temperature curves 302, 304, 306, 308. Alternatively, for increased accuracy, a piecewise polynomial fit may be performed on each curve. For example, generating a first polynomial fit for a salinity Wsal of 0 to 10, a second polynomial fit from 10 to 100, and a third polynomial fit from 100 upwards, resulting in the following equations:
a
0(T)=k*a00+k*a01*(T)+k*a02*(T2)+k*a03*(T3) (18)
a
1(T)=k*a10+k*a11*(T)+k*a12*(T2)+k*a13*(T3) (19)
a
2(T)=k*a20+k*a21*(T)+k*a22*(T2)+k*a23*(T3) (20)
b
0(T)=k*b00+k*b01*(T)+k*b02*(T2)+k*b03*(T3) (21)
b
1(T)=k*b10+k*b11*(T)+k*b12*(T2)+k*b13*(T3) (22)
b
2(T)=k*b20+k*b21*(T)+k*b22*(T2)+k*b23*(T3) (23)
Upon determining the coefficients (a0, a1, a2, b0, b1, and b2), they may be graphed as depicted in
a
2(T)=k*a20+k*a21*(T)+k*a22*(T2)+k*a23*(T3) (24)
b
2(T)=k*b20+k*b21*(T)+k*b22*(T2)+k*b23*(T3) (25)
In one example, the following numbers may be derived: ka20=5.20*10−4, ka21=1.40*10−5, ka22=2.27*10−7, ka23=7.21*10−10, kb20=8.09*10−5, kb21=2.71*10−6, kb22=2.27*10−7, and kb23=0.
Upon determining the coefficients (a0, a1, a2, b0, b1, and b2), they may be employed in equation 15, thereby enabling the determination of water salinity Wsal. It is likely that the coefficients can be extrapolated for use in additional or future calculations for unmeasured temperatures.
With the determination of water salinity in hand, and referring back to
Having calculated the water's dielectric constants ε′w and ε″w, equations 28 and 29 may now be solved to find the water's refractive index components. Resulting therefrom, equation 7 (ζ″HFDT=φw*ζ″w) may be used to find the water-filled porosity φw as the refractive index of the formation ζ″HFDT is known from measurements of the HFDT and the water's refractive index ζ″ is also known.
Advantageously, by no longer relying on ex-situ measurements or an iterative process, these calculations can now be performed in near real-time, for example, by the processor of the computer system 120 (
Numerous other modifications, equivalents, and alternatives, will become apparent to those skilled in the art once the above disclosure is fully appreciated. It is intended that the following claims be interpreted to embrace all such modifications, equivalents, and alternatives where applicable.
Embodiments disclosed herein include:
A: A method of determining water-filled porosity of a formation that includes acquiring a downhole temperature, acquiring a total porosity of the formation, acquiring a dielectric measurement of the formation, determining a water salinity based on the temperature, total porosity, and dielectric measurement, and determining a water-filled porosity of the formation based at least in part on the water salinity.
B: A system for determining and logging water-filled porosity having a downhole tool assembly that acquires downhole temperature measurements, the tool assembly including a dielectric measurement tool that acquires dielectric measurements of formations surrounding a borehole, and a porosity measurement tool that acquires total porosity measurements of the formations. The system further having a processor that determines and logs water-filled porosity of the formation as a function of the temperature, dielectric, and porosity measurements.
Each of embodiments A and B may have one or more of the following additional elements in any combination: Element 1: presenting a log of the water-filled porosity to a user. Element 2: where the temperature, total porosity, and dielectric measurements are acquired as a function of depth or position along a borehole, and the determining a water-filled porosity includes creating a log of the water-filled porosity as a function of depth or position along a borehole. Element 3: where determining a water salinity includes relating the real and imaginary components of water's dielectric constant. Element 4: where determining the water salinity and determining the water-filled porosity are performed by a processor in real-time. Element 5: determining a hydrocarbon porosity of the formation based on the water-filled porosity. Element 6: where determining a water salinity includes obtaining temperature-dependent function coefficients expressing a dependence of real and imaginary components of water's dielectric constant on salinity. Element 7: where determining the function coefficients includes implementing a piecewise polynomial fit. Element 8: further including determining real and imaginary components of a refractive index of the formation from the dielectric measurement. Element 9: calculating a constant based on the refractive index, the porosity, a dielectric constant of hydrocarbons, and a dielectric constant of the matrix. Element 10: calculating a dielectric constant of water based at least in part on the water salinity. Element 11: calculating a refractive index of water based at least in part on the water salinity. Element 12: storing the coefficients in a memory.
Element 13: a user interface coupled to the processor, where the user interface displays the log of water-filled porosity. Element 14: where the processor further determines a water salinity of the formation as a function of the temperature, dielectric, and porosity measurements. Element 15: where the processor further determines the water-filled porosity based at least in part on salinity and temperature. Element 16: a memory that stores temperature dependent function coefficients expressing dependence of water's dielectric constant on salinity. Element 17: where the dielectric measurement tool is a high frequency dielectric measurement tool (HFDT) operating at a frequency of 1 GHz or greater.
Filing Document | Filing Date | Country | Kind |
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PCT/US14/17738 | 2/21/2014 | WO | 00 |