WO2006116088A1

WO2006116088A1 - A method and apparatus for estimating of fluid contamination downhole

Info

Publication number: WO2006116088A1
Application number: PCT/US2006/015096
Authority: WO
Inventors: Rocco Difoggio; Bernardo Pohl
Original assignee: Baker Hughes Incorporated
Priority date: 2005-04-22
Filing date: 2006-04-21
Publication date: 2006-11-02
Also published as: NO20075256L; EP1875399A1; EP1875399A4

Abstract

The present invention provides a system and method for estimating a characteristic of a formation fluid, including terminal purity, in real time. The system provides for taking a plurality of measurements of a parameter of the extracted formation fluid over time and fitting a non-asymptotic curve to the measurements to estimate the characteristics of the formation fluid.

Description

TITLE: A METHOD AND APPARATUS FOR

ESTIMATING A FLUID CHARACTERISTIC

INVENTORS: ROCCO DIFOGGIO; BERNARDO POHL

BACKGROUND OF THE INVENTION

1. Field of the Invention

[0001] The invention relates generally to a method and apparatus for quantifying fluid contamination as an indication of sample cleanup in real time in a wellbore environment. Specifically, the invention is a method and apparatus for measurement of physical properties of fluid being pumped from a formation surrounding a wellbore by a wireline or monitoring while drilling tool to estimate sample cleanup or to predict the time at which a sample having a desired purity can be obtained.

2. Summary of the Related Art

[0002] In wellbore exploration, typically drilling muds such as oil-based muds, synthetic material-based muds or water-based muds are used. The filtrates from these muds generally invade the formation through the borehole wall to an extent, meaning that this filtrate must be removed from the formation in order to access the formation fluids. Open hole sampling is an effective way to acquire representative reservoir fluids. Sample acquisition allows determination of critical information for assessing the economic value of reserves. In addition, optimal production strategies can be designed to handle these complex fluids. In openhole sampling, initially, the flow from the formation contains considerable filtrate, but as the filtrate is drained from the formation, the flow increasingly becomes richer in formation fluid. That is, the sampled flow from the formation contains a higher percentage of formation fluid as pumping continues.

[0003] It is well known that fluid being pumped from a wellbore undergoes a clean-up process in which the purity of the sample increases over time as filtrate is gradually removed from the formation and less filtrate appears in the sample. Herein, f_p is defined to be the fraction of purity and f_c to be the fraction of contamination, where f_p + f_c = 1. As the composition of the sampled formation fluid changes, so do the optical and physical properties of the sampled fluid, such as optical absorption, fluorescence, refractive index, viscosity, density, sound speed, and bulk modulus. A number of different measurements are used to determine various optical and physical properties of a fluid downhole in real time. Measuring these properties of the fluid therefore provides qualitative insight into a fluid sample's purity but does not provide a quantitative value, f_p, for the fluid sample. Even after pumping fluid for a long time, the fraction of fluid contamination does not necessarily drop to zero. In many cases where after pumping for a long time period, an optical or a physical property stops to substantially change the fraction of contamination (as subsequently determined in a surface lab) can be far from zero and in some cases can be as high as 45%. In that case, the terminal purity maybe of the order of 55%.

[0004] At long pumping times, a dynamic equilibrium can be reached in which a fluid sample being withdrawn from a tapped zone cleans up at the same rate that it is being recontaminated from the zones above and below the tapped zone. Thus, even though a downhole measured property (such as optical density or "OD") has substantially stopped changing, the sample still may not be at 100% purity. This dynamic equilibrium depends on various factors such as the ratio of the vertical to horizontal permeability. Therefore, for the purpose of this disclosure, ft_p is defined as the fraction of the terminal purity, where the terminal purity is the purity achieved at very long pumping times and which is usually less than 100%. Thus, what can be estimated by monitoring changes in OD or some other property over time (or over volume pumped) is the fraction of the terminal purity, f_tp, but not the fraction of formation-fluid purity, f_p.

[0005] When extracting fluids from a formation, it is desirable to quantify the progress of the cleanup, that is, the degree of filtrate contamination or purity in real time. If it is known that there is too much filtrate contamination in the sample (more than about 5% or 10%), then there is no reason to collect the formation fluid sample in a sample tank until the contamination level drops to an acceptable level. On the other hand, if by pumping for a very long time, it is possible to achieve only slightly lower contamination level, then there may not be any need to continue pumping. Thus, there is a need to determine how long it will be necessary to pump to obtain a sample from the formation.

[0006] When pumping first begins, the fluid being pumped contains a large amount of mud filtrate contamination and then the fluid filtrate percentage starts to decrease at a fast rate. This process of decreasing fluid filtrate contamination is referred to as sample clean up process. Later, the pumped fluid contains less contamination and the fluid filtrate percentage decreases at a slower rate. Mullins, et. al. published paper on curve fitting of a sample's absorbance versus time to monitor clean up in real time, entitled "Real Time Determination of Filtrate Contamination During Openhole Wireline Sampling by Optical Spectroscopy," SPWLA, 41^st Annual Meeting, Dallas, TX, June 2000. The U.S. patents 6,274,865 and 6,350,986 also discuss certain curve fittings.

[0007] In this paper, Mullins et al. assume that the rate of sample cleanup as measured by observing optical density progresses as f⁵¹¹² where / is time. This clean up rate is based on empirical experience in the Gulf of Mexico and elsewhere. However, Mullins et al. also states that, for extended pumping durations, the sample cleanup rate for shallow invasion progresses as f^1/3 and that the cleanup rate for deeper invasions progresses as f^2β . One assumption of a sample clean rate off^5/12 can be rigid and inapplicable to real time situations. Moreover, using time as a fitting parameter necessarily assumes a constant pumping rate. Another problem with monitoring sample clean up over time by looking at optical absorption over time is that sand particles and other particulates can cause considerable scattering, which causes the absorption values measured over time to "jump" and appear noisy. Thus, there is a need for a more flexible system and method for obtaining the estimation of formation cleanup based on fluid properties and characteristics for downhole pumping in real time.

SUMMARY OF THE INVENTION

[0008] The present invention provides a method and apparatus of quantifying sample clean up in real time from measurement data over time (or over volume) of some optical or physical properties of fluid samples taken from a formation surrounding a borehole. Sample fluid is extracted from the formation surrounding the borehole. As fluid continues to be extracted from the formation, the composition of the sampled fluid changes, altering the measured values of an optical or physical property for the sampled fluid.

[0009] In a first aspect of the present invention, a method and apparatus are provided that fit fluid measurement data to a non-asymptotic curve. One example of a non-asymptotic curve is a curve (e.g., a power series approximation), which provides an improved fit to the data over the typical pumping time and, which can also be successfully extrapolated to several times that pumping time, but which approaches plus or minus infinity at infinite times. Another example of a non-asymptotic curve is an equation that has an oscillatory component, such as a sine wave, which never reaches a fixed limit. The sine wave can be adjusted in frequency, phase and amplitude to provide an improved fit. In a third aspect of the invention, a method and apparatus are provided that perform pattern recognition of a straight line to a best fit of the measured data in log-log space.

[0010] For best performance, spikes in the data are removed first. The remaining data are piecewise smoothed over a rolling interval of 100 or more neighboring points using a smoothing function. For example, a fit can be performed for absorbance over a rolling time segment using a non-asymptotic fitting equation such as, A = b₀ + b_\ t + b₂ t². Then, by calculus, A¹ = dA/dt = bi + 2 b₂1 and AV A = (bi + 2 b₂ t) / (b₀ + bit + b₂ t²) can be determined. Then, for an equation of the form, A(t) = Ao - Ai t^"p, one can do a linear regression of ln(dA/dt) against ln(t) to obtain the slope and intercept and from these calculate, -p = (1+Slope) and -Ai = exp(Intercept-ln(l+Slope)). In this way, there is not an assumption of a value of -5/12, of -2/3 (as suggested by Mullins), or of any other fixed value for -p. Instead, one can estimate f_tp=A/Ao from the best-fit values for p and Ai, and from twice the average of A(t) and Ait^"p at a plurality of times.

[0011] Also, the method and apparatus of the present invention can use a data- fitting equation such as log (1-f_tp) = (-p) log (t) + log (A₁ZAo), which is the equation of a straight line that has no (Y=constant) asymptote, except for the meaningless case of p=0. The method and apparatus perform a series of regressions using different estimates of Ao but do not actually calculate Ao, itself. For example, one can start with the current value, A, at a time t, as the first estimate of A₀, then proceed to a slightly higher value of A + ε, then to an even higher value of A + 2ε, and so on. The A₀ value for which the fit to the measured data is closest to the shape of a straight line (based on the highest coefficient of determination, or i?-squared value) then becomes the best estimate of an Ao value. In a third aspect the method and apparatus of the present invention a method and apparatus are provided that fit a differentiable curve to measurement data or physical property data derived from the measurement data. The present invention then estimates f_tp from the ratio of (dA/dt) to A. [0012] Another aspect of the present invention, a method and apparatus are provided that fit an asymptotic curve to difference of two responses such as the difference of two absorbances associated with different wavelengths (optical channels) rather than to an absorbance itself. Using an absorbance difference removes the baseline offsets caused by passing sand particles or bubbles.

BRIEF DESCRIPTION OF THE FIGURES

[0013] Other objects and advantages of the invention will become apparent upon reading the following detailed description and upon reference to the accompanying drawings, in which:

Figure 1 is a diagram of the Fluid Characterization Module;

Figure 2 is an illustration of an embodiment of the present invention deployed in a borehole using a plurality of sources and sensors;

Figures 3-10 are charts of functions performed in embodiments of the invention;

Figure 11 is an illustration of an embodiment of the invention using an acoustic transducer;

Figure 12 is an illustration of an embodiment of the invention using a pyroelectric array; and

Figure 13 is an illustration of a function performed according to another embodiment of the invention.

BRIEF DESCRIPTION OF THE INVENTION

[0014] Fig. 1 illustrates a schematic representation for a downhole fluid characterization module 100 for obtaining and analyzing optical measurement data. A light source 101 (e.g. tungsten light bulb) emits light toward a fluid 110. The light can be collimated by a collimating lens device 103 lying between the light source 101 and the fluid 110. The collimated light 111 is incident generally perpendicular to a first sapphire window 301 adjacent sample 110. Sapphire windows 301 and 303 lie generally perpendicular to the collimated beam of light and are separated by a gap or channel 304 enabling a fluid 110 to flow between them. An optical property of the fluid, for example, including but not limited to reflectance, absorbance and fluorescence of light from the fluid is measured over time by an optical sensor, such as but not limited to a spectrometer 105. A processor 113 is provided to estimate fluid properties from the optical measurements. The existing tools (Figure 1) can be fitted with a UV or infrared light source 112, which can be turned on when the tungsten light source 101 is turned off. The same spectrometer, for example, comprising single wavelength filters over photodiodes, enables collecting the crude oil fluorescence and infrared spectra. The processor 113 includes memory and performs calculations using equations to estimate fluid characteristics or properties, such as percent contamination, from the optical measurements for the fluid as described herein. Power to the various components of the module 100 is provided by a power supply.

[0015] As shown in Fig. 2, additional measurements from additional sources and sensors can be added, including but not limited to a flexural mechanical resonator, acoustic transducer, pyroelectric array, infrared light source, and sensors to measure retroactive index. More detailed schematics of the acoustic transducer and the pyroelectric array are shown in Figs. 11 and 12. These additional sources and sensors can be provided for measurements of fluid parameters including but not limited to viscosity, density, sound speed, fluorescence, attenuated, total reflectance, refractive index, bulk modulus and resistivity. These measurements can be monitored over time to estimate a characteristic of the fluid, including fractional terminal purity or fractional terminal contamination as discussed below.

[0016] Fig. 2 illustrates an embodiment of a system deployed in a borehole 12 drilled from the surface 15 and formed in a formation 16 that can be used to perform the methods of the invention. A probe 14 is provided for extraction of fluid from the formation. The measurement sensors, such as sensor 100 or other sensors of the present invention are contained in a downhole tool 20. The downhole tool is deployed from a wireline or drill string 18. The tool 20 also includes a controller that controls the operation of the downhole tool. The controller includes memory and programs, including algorithms described herein to execute the methods described herein. During operation, the tool 20 is lowered into the wellbore and set to obtain fluid samples from the formation 16. The sensor 100 measures a desired property or characteristic of the fluid over time. The controller in the tool 20 or another controller at the surface utilizing the programs performs the methods described herein below and provides the desired estimates and other results as described herein.

[0017] Prior systems used the functional form for the cleanup approximated by In(OD) = C - D / t ^p. Some prior systems calculated the percentage of contamination by assuming that, upon reaching asymptotic optical absorbance, the sample had achieved zero contamination. Other prior systems, however, assumed that a dynamic equilibrium can be reached between fluid clean up and continued filtrate incursion, depending on the ratio of vertical to horizontal permeability and other factors. Thus, the contamination may not drop to zero, but only to some minimum value, even after very long pumping times. That is, the terminal contamination level represents the minimum contamination but, not necessarily, zero contamination.

[0018] As the composition of the sampled formation fluid properties change, so do the optical and physical properties of the sampled fluid, such as optical absorption, fluorescence, refractive index, viscosity, density, sound speed, and bulk modulus. These properties can be monitored to estimate the fraction of terminal purity, which is the degree of formation fluid clean up. Different measurements can be used based on the actual conditions. For example in certain cases with monitoring the cleanup over time by looking at the optical absorption over time (over a 2mm path length) may be less desirable because sand particles and other particulates can cause considerable scattering, which makes the absorption over time "jump" a lot and look very noisy. On the other hand, monitoring cleanup over time by monitoring refractive index (which is an interface-based technique) is less sensitive to particulates in the fluid stream because one is only looking at a thin layer of fluid that is in direct contact (at the interface) with the sapphire window. Similarly, for crude oils, fluorescence only sees a thin layer of crude oil near the window and therefore, it is very insensitive to particulates in the stream. However, measurements of any suitable parameter or characteristic of the fluid may be used for the purpose of this invention.

[0019] As an example of formation fluid clean-up, simulation results and actual field data for optical density can be fitted to forms such as, Y = m X^'p + b or In(Y) = mX^'p + b. Using the sample contamination concentration as Y and the pumping time as X, simulation results fit these forms well, especially the logarithmic form. Because the optical density (OD) is an indicator of clean-up, the OD data can be used as 7 and the pumping time can be used as X. If the pumping speed changes many times during the course of clean-up, the cumulative volume pumped is used as X instead of time.

[0020] A small p value indicates that clean-up process is slow and it will take longer to obtain a quality sample, while a large p value indicates that the clean-up process will be faster and the chance for obtaining a sample of the desired purity is high. The value of b is used as an indicator for clean-up to the best sample quality achievable (the asymptotic value). By comparing the current OD value with the b value, the current sample contamination percentage is obtained. The future sample quality is estimated using the fitted values of m, p, and b, and a decision can be made as to whether to continue or to stop the pumping process if the estimated future sample quality is deemed insufficient.

[0021] The power of X , which is -p, (where p is a positive number) can be used as an indicator of the rapidity of the clean-up process. Consequently, when the p value is small, and the calculated current contamination is high, there will be little chance of obtaining a high quality sample and it will take a long time, perhaps too long to obtain the desired sample purity.

[0022] When the invasion profile is gradual, meaning a transition zone is present instead of sharp invasion boundary, the value ofp decreases below 1.0. The value of p depends on the thickness of the transition zone between the region of filtrate and region of formation fluid. The thicker the transition zone, the lower the p value. This gradual transition has a similar effect to that of deep invasion. When the invasion is deep, then the clean fluid from the fresh zone will be mixed with the filtrate while it flows toward the probe. Hence a deep invasion will have a thick transition zone, and clean-up for that zone will take a long time.

[0023] Formation damage can also affect the clean-up process. The clean-up can be improved when the formation near the wellbore is damaged or when the near wellbore formation permeability is less than the true formation permeability due to the small particle invasion.

[0024] A functional form that can be best fit to simulation data regardless of invasion depth or formation damage is OD = exp(mf^p+b), so that at longer times, the OD stops changing because the time-dependent term goes to zero as time goes to infinity. That form is equivalent to the form, In(OD) = C - D/t^Λp where C = b, m = - D, and p is a positive number. Curve fitting of sample clean-up using the form of In(Y) = mX^"p + B where Y= optical or physical properties such as absorbance or fluorescence at some wavelength as the sample as it cleans up, X=Time since started pumping sample or, more correctly, the cumulative volume pumped, when the volumetric flow rate is not constant.

[0025] Applying the functional form In(OD) = A * 1 / Time" + B to simulation results, shows that: a) In a simple system with no permeability damage and a sharply-defined filtration zone (100% filtrate zone followed by 0 % zone), the n value is 1.1; b) Adding permeability damage to system, speeds up the cleaning process, and the n value is 1.3; c) Using a gradual filtrate contamination, in which contamination decreases as moving away from wellbore (that is 100, 80, 60 .. and 0 %) then the n value is 0.75; d) Adding damage to the system (c), then the n value is 1.0; and e) Adding a permeability change due to formation damage, then the n value can vary from 0.25 to 0.5. Fitting formation clean-up simulation results and some field data (optical density) to the above functional form, the following findings are provided.

[0026] Using the sample contamination concentration as Y and the cumulative pump-volume as X, simulation results fit the form very well. Because the optical density (OD) is an indicator of clean-up, the OD data can be used as Y and pump-time can be used as X. If the pumping speed changes many times during the course of clean-up, the cumulative volume pumped should be used as X instead of time. The power of X, which is -p (where p is a positive number), can be used as an indicator for the clean-up process. For a nominal invasion of 6 inches or less, p is near 1.0 - 1.1. When the invasion profile is gradual, this indicates that there is a transition zone instead of a sharp invasion boundary, and p decreases below 1.0. The p value will depend on the thickness of the transition zone, the thicker the zone, the lower the p value. A similar effect is found for deep invasion. When the invasion is deep, then the clean fluid from the fresh zone will be mixed with the filtrate while it flows toward the probe. Hence the deep invasion will have a thick transition zone, and it will take a longer time to clean-up that zone.

[0027] When the formation near the wellbore is damaged, that is the near wellbore formation permeability is less than the true formation permeability due to the small particle invasion, the clean-up can be improved as discussed in papers in the Society for Petroleum Engineers, papers SPE 39817 and SPE 48958. The formation anisotropy also helps the clean-up process (see SPE papers, SPE 39817 and SPE 48958). When there is a damage or a formation anisotropy, the p value increases above 1.0 - 1.1 up to 1.3 - 1.4. Hence a small p value indicates that the clean-up process will be slow and will take longer to get a quality sample of the desired purity. [0028] It is primarily the aromatic and polynuclear aromatics molecules that fluoresce. That is why, crude oil usually fluoresces much more than does the filtrate of oil based mud (OBM). For environmental reasons, synthetic OBMs are designed to be as aromatic free as possible but they may pick up some aromatic contamination from drilling or they may have small amounts of aromatic emulsifiers or fluid loss control materials added to them. Also, the filtrate of water-based mud has little or no fluorescence because water itself is non-fluorescing. Some compounds that dissolve in water may fluoresce. Furthermore, one could deliberately add fluorescent compounds to water based or oil based mud as fluorescent tracers.

[0029] In the specific case where the property being fit is a function of the optical absorption, certain particularly useful functions can be selected for the absorption. One such function is the ratio of a baseline-adjusted oil peak to a baseline-adjusted water peak or its inverse. This function is particularly useful in monitoring the cleanup from water based mud filtrate to native crude oil. Its inverse is particularly useful in monitoring the cleanup from oil based much filtrate to connate water, when it is desired to collect a sample of water.

[0030] The baseline-adjusted oil peak is an oil peak channel (near 1740 nm) minus a nearby low-absorbance "baseline reference" channel (e.g. channels at 1300 or 1600 nm). The baseline-adjusted water peak is a water peak channel (near 1420 or 1935 ran) minus a nearby low-absorbance "baseline reference" channel (e.g. channels at 1300 or 1600 nm). Substituting time equals infinity into our forecasting model enables estimation of the limiting value of property, P, at infinite time. Dividing the current value of property, P, by its forecasted terminal value yields the fraction of terminal purity. [0031] In a first embodiment of the present invention, the method and apparatus of the present invention fit fluid measurement data to a non-asymptotic curve. One example of a non-asymptotic curve is a curve which provides an improved fit to the data over the typical pumping time and, which can also be successfully extrapolated to several times that pumping time, but which approaches plus or minus infinity at infinite times, such as a power series approximation. Another example of a non-asymptotic curve is an equation that has an oscillatory component such as a sine wave, which never reaches a fixed limit. The sine wave can be adjusted in frequency, phase and amplitude to provide an improved fit to pulses in the monitored response that are associated with each stroke of the pump.

[0032] In a second embodiment, the method and apparatus use pattern recognition. That is, the method and apparatus of the present invention use an equation such as log (1-f_tp) = (-p) log (t) + log (A₁ZAo). The method and apparatus then perform a series of different estimates of the terminal purity or terminal value for a physical property of the fluid is represented by Ao, where A₀ starting with A₁, A + ε, A + 2ε, etc. The Ao value for which the fit to the data is closest to the shape of a straight line (based on the i?-squared value) becomes the best estimate of A₀. In a third embodiment the method and apparatus of the present invention fit a differentiable curve to measurement data or physical property data derived from the measurement data. The present invention then estimates AZA₀ from the ratio of (dA/dt) to A. In a fourth embodiment, the present invention fits an asymptotic curve to absorbance differences of nearby optical channels (wavelengths) rather than to absorbance itself. The absorbance differences remove baseline offsets caused by passing sand particles or bubbles. [0033] In the conventional approach to formation contamination, equations 1 and 3 are applicable.

Eq. 1 A = A₀ - Ai t^~5/n where A₀X)₅ Ai>0, Hm A = A₀

Instead of time, t, volume, V could be used. One could also generalize to the case where the best fitting power, p, is calculated instead of assumed. Eq. 2 A = A₀ - Ai t^~p where Ao>O, Ai>O, p>O Um A = A₀ t — > oo

Eq. 3 f_tp = A / A₀ = fraction of terminal absorbance, A₀, which is achieved when absorbance is A.

Only in those cases where A₀ is the absorbance of pure crude oil does f_tp = fraction of terminal purity also equal f_p = fraction of purity.

Eq. 4 1- f_tp = [ 1 - ( A / A₀ ) ] = fraction away from terminal absorbance. For Eq. 1, the conventional approach finds best A₀, Ai using a linear least squares fit to the Ndata points, (A_/, t,^"5/12), where i = 1, N. For Eq. 2, one finds best A₀, A₁ using a linear least squares fit to the N data points, (A₁-, t,- ^~p ), where i = 1, N after one assumes or finds a best fit value for p as described elsewhere in this invention.

[0034] Turning now to Figs. 3-10, various functions performed in embodiments for the invention are depicted. As shown in Fig. 3, in one example of the present invention fluid is extracted from a formation 310. A property of the fluid is measured 320 from which an estimate of fluid contamination is made from a fit of the property with a non-asymptotic curve including fits performed to obtain data slope 330. [0035] Although the discussion below uses elapsed time as the dependent variable, it is understood that the volume of pumped fluid or some other parameter could also be used. As shown in Fig. 4, in an embodiment of the present invention the present invention performs a piecewise non-asymptotic curve fit to data to determine smoothed values and data slopes at centers of each segment. A regression is performed on the logarithm of the derivative of the data over time against the logarithm of time to obtain a straight-line regression slope and intercept. A value for fractional terminal purity ftp is estimated from the straight-line regression slope and intercept and from averages of A(t) and Ait^"p at a plurality of times. For example, a method and apparatus are provided to fit absorbance over a rolling time segment using a non-asymptotic equation such as the power series, A = b₀ + b_\ t + b₂1². Then, by calculus, A¹ = dA/dt = bi + 2 b₂1 and AV A = (bi + 2 b₂ t) / (b₀ + bit + b₂1²). For an equation of the form, A(t) = Ao - A₁ f ^p, one can perform a straight-line regression of ln(dA/dt) against ln(t) to obtain the best-fit line's slope and intercept and calculate best-fit values, -p = (1+Slope) and -A₁ = exp(Intercept-ln(l+Slope)). In this way, one does not need to assume a value of -5/12, or -2/3, or of any other fixed value for -p. Instead, one can estimate f_tp=A/Ao from the best-fit values for p and A₁, and from twice the average of A(t) and A₁^ at a plurality of times 410.

[0036] As shown in Fig. 5, in the second embodiment of the present invention, a method and apparatus are provided that use a non-asymptotic curve to fit the data 510. In this embodiment, the method and apparatus fit a modified version of Eq. 1 to data, wherein the modified equation does not approach an asymptote at infinite time such as the examples shown in Equations 8 and 9 below, using the form A = A₀ - h(t) where t -» ∞ and h(t) does not go to zero. Eq. 8 A = A₀ - A₁ Σ t^x, where x = -n to +m.

Eq. 9 A = A₀ - Ai [t^~p + Ic^-1Sm (ωt)].

[0037] The sin(ωt) term can provide a better fit to data that has periodic spikes in response that commonly occur with every pump stroke as particulates are stirred up. Of course, this oscillating term prevents the curve from ever stabilizing to a fixed value no matter how long the time so it is not an asymptotic curve. The value of ω can be chosen to coincide with the pump-stroke frequency. For Eq. 9, the present invention finds best Ao, Ai using a linear least squares fit to the N data points, (A₁-, t,^~ ^5/12+ k^~1sin (ωt)).

[0038] As shown in Fig. 6, in a third embodiment, the present invention provides for a pattern recognition 610. As shown in Fig. 6, the present invention performs a pattern recognition for a trial-and-error estimate of A₀, rather than a direct calculation of Ao. In this embodiment, the pattern to be observed is the closest resemblance to a straight line as determined by the highest correlation coefficient, R, for a linear least squares fit. The method and apparatus performs a series of linear least squares fits to the absorbance data using a series of different estimates of Ao starting with, A + ε, A + 2 ε, up to A + Ν ε, where A + Ν ε < 3.5 OD, where 3.5 is used as an example for the upper dynamic range limit of the tool. The Ao value for which the fit is closest to a straight line in log-log space then becomes the best estimate of A₀. Closeness of the fit to a straight-line shape is determined by the closeness of R² to unity, where R² is the correlation coefficient squared that ranges from 0 (no correlation) to 1 (perfect correlation). That is, for a series of Ao guesses, find the best Ao based on the best R² in a linear least squares fit to N measured data points, (log[t;], log[l-(A(t/)/A₀)]).

[0039] An example of the slope of such as line would be (-pAi / Ao ), which for any fixed value of p, also allows immediate determination of Ai. One can assume a fixed value for p or one can calculate a best-fit value for p from the slope of the straight-line regression of ln(dA/dt) versus ln(t). Note that Ao is not calculated here.

Only R² is calculated for different guesses (estimates) of Ao. That is, different estimates of Ao = A + nε, are tried and the one that produces the best R² is used. To estimate Ao to a finer resolution than ε, one could use binary convergence to iteratively test Ao values between the best two previously-determined A₀ values.

Eq. 10 log (1-ftp) = (-p) log (t) + log (A₁ZA₀)

I

For Eq. 10, for a series of different Ao guesses, the present invention finds the best R² using a linear least squares fit to the N data points.

[0040] In a fourth embodiment, the method and apparatus of the present invention fits a differentiable curve to the measured data. The present invention estimates ftp from (dA/dt)/A by fitting a continuously differentiable curve to the absorbance data (or smoothed absorbance data). A piecewise fit to various segments of the data can also be performed. Note that this fitting curve need not approach a terminal value itself. Its purpose is simply to provide a smooth fitting function over a large enough time interval of data points so that fitted values of both A(t) and dA(t)/dt can be calculated for any time, t, within the interval and then substituted into equations 14 - 16. [0041] As shown in equations 14 - 16, the terminal absorbance value can now be determined from the ratio of the current slope, dA(t)/dt, to the current value, A(t). The local fitting and smoothing functions used for calculating dA(t)/dt and A(t) do not need to have terminal values themselves. They can even tend to plus or minus infinity, at infinite time, as would occur with a power series fit or a group of power series fits.

[0042] Therefore, as shown in Figs. 7, 8 and 9, without ever calculating A₀ or fitting an asymptotic curve to the absorbance data, it is possible to determine the fraction of terminal purity, f_tp, that is achieved at time, t from ratio of the rate of change of the absorbance to the absorbance. For example, let

Eq. 11 A = A₀ - A₁ h(t) where Hm h(t) = 0 ^{t → ∞}

Take first derivative with respect to time,

Eq. 12 (dA/dt) = - Aj (dh/dt) therefore A₁ = - (dA/dt) / (dh/dt) Eq. 13 ftp = A / [ A + A₁ h(t) ] = 1 / [ 1 + A₁ h(t) / A] = 1 / [ 1 - (dA/dt) (dh/dt)-¹ h(t) A-¹] so 710 Eq. 14 f_tp = [ 1 - A^dA/ht) g(t) (dh/dt) ^Λ ] ^{~ ι}

Example: Let h(t) = f^p so that dh/dt = -p f^p t^"1 Then,

810 Eq. 15 f_tp = [ l + A-^dAZdO tP^-1 ] - ¹

For the special case where p = 5/12, 910 Eq. 16 f_tp = [ 1 + (12/5) A^dA/dt) t ] ^{~ l}

[0043] In a fifth embodiment, as shown in Fig. 10, the method and apparatus of the present invention , finds terminal values of absorbance differences data rather than of absorbance itself. Absorbance differences of neighboring channels are plotted to remove baseline offsets caused by sand particles or bubbles 1010. The method and apparatus of the present invention perform a fit to absorbance differences rather than to absorbances themselves. The channel differences are forecast, for example, the difference between optical channels, OD 16-OD 15, corresponding to different optical wavelengths out to their terminal values, rather than forecasting a single OD channel out to its terminal value. The absorbance difference data is used independently or in conjunction with the approaches described in figures 3-9 to determine fractional terminal purity, ftp.

[0044] In a sixth embodiment, as shown in Fig. 13, the present invention fits a continuously-differentiable, non-asymptotic curve 1302 to the raw data which may be measured values of any suitable parameter relating to the fluid or data derived from such measured values. The fit can be to the elapsed time or fit to the volume of fluid pumped. The present invention uses, for example, but is not limited to, fitting a non- asymptotic curve to the raw data points such as A(t) = cj + C₂ t ^1/2 + C₃ 1 ^1/3 + C₄ t ^m. Using calculus, analytically calculate the first derivative as dA/dt = (c₂/2) t ^~m + (c₃/3) t ^"2/3 + (cV4) t ^"3/4 to estimate the "terminal" value of the parameter such as absorbance, refractive index, resistivity, etc. at some very long time (e.g., 24 hours) which is much longer than a time (2 hours) at which one would normally terminate pumping to achieve sample cleanup. As time progresses, both (A₀ - A) and t (dA/dt) decrease, where A is absorbance at time t. Assuming that they decrease at the same rate, then they are proportional, which means (A₀ - A) = m t (dA/dt) where "m" is a constant. The present invention tries various guesses for A₀ until it finds a guess that produces the best linear, least-squares fit between y = (A - A₀ ) and x = [ t (dA/dt) ]. The best fit is given by y = m x + b where the intercept, b, is closest to zero, which we found to be more sensitive than finding the maximum R² for linear fits between two variables that are directly proportional. The present invention selects a raw data point at some time, t, (preferably, the latest time, t) at which the actual data intersects (or gets closest to) the best fit line. To forecast absorbance at a slightly later time, t+Δt, we use ΔA = (Ao - A ) / [ l + m ( l + t / Δt ) ] which is obtained by replacing dA/dt by ΔA/Δt, replacing t by t+Δt, and replacing A by A+ΔA in (A₀ - A) = m t (dA/dt). We recursively apply this ΔA formula to forecast the absorbance at t + Δt and then use our newly-calculated absorbance to compute the absorbance at some slightly later time, t + 2Δt, and so on, for all future times.

[0045] If the slope 1304, m, of this fit is positive, it means a bad or undesirable section of raw data has been selected, which is curving upward or downward towards plus or minus infinity. Select a raw data point at some time, t, (preferably, the latest time, t) at which the actual data intersects (or gets closest to) the best fit line. The present invention then calculates the absorbance at some slightly later time, A(t+Δt) = A(t) +ΔA, in terms oft, A(t), A₀, and m using AA = (A₀ - A ) / [ 1 + m ( 1 + 1 / Δt ) ] . The present invention then recursively applies this ΔA formula forward to generate future forecasts, A(t), of the raw data. For data that is rising and leveling off over time, the fraction of terminal purity at any future time, t, is given by A(t) / Ao. For data that is falling and leveling off over time, the fraction of terminal purity at any future time, t, is given by [As - A(t)] / [As - A₀]. Here, As is the starting absorbance at the left edge (the earliest time) of the user-selected data window.

[0046] In a sixth embodiment, as shown in Fig. 13, it is not assumed that "m" is a negative number, which is why the recursion formula is written as [ 1 + m (1 + 1 / Δt) ] instead of being written as [ 1 - m (1 + t / Δt) ]. In the sixth embodiment, the closeness of the intercept "b" to zero is used. Closeness of the intercept to "b" is used because it is much more sensitive than the closeness of R ² to unity for finding a best fit line when it is known that the intercept of that line should be zero. Also a recursive formula for predicting absorbance at future times is used. For data that falls and levels off over time, we use the absorbance at the left edge of the user-selected window as the starting absorbance rather than using zero as the starting absorbance as is done when the data rises and levels off.

[0047] Turning now to Fig. 11, a more detailed schematic of the pyroelectric array for determining mid-infrared spectra for the fluid is illustrated. In one embodiment, the present invention provides a light source 402, such as an infrared light source which can be a steady state light source or a modulated or pulsed light source. In the case of a steady state light source a light modulator is provided. The modulator can be any suitable device which varies the intensity of the light source, including but not limited to an electronic pulser circuit, well known in the art, that varies the intensity of the light source or an electromechanical chopper 404 that interrupts the path of the light source to the downhole fluid. The modulator is provided to modulate the intensity of light from the light source that impinges on the fluid and the photodetector. A reflector or collimator 403 can be provided to focus and/or concentrate light from the light source 402. A chamber or conduit 406 is provided for presentation of a downhole fluid for exposure of the downhole fluid to light from the light source. An optical window 408 is provided, through which the downhole fluid 407 is exposed to the light. For purposes of the present application, the term "fluid" includes liquids, gases and solids that may precipitate from a fluid or a gas.

[0048] The present invention further includes a detector such as a pyroelectric detector 412. The pyroelectric detector 412 can also comprise a pyroelectric detector array. A spectrometer 414 and processor 422 are provided for analyzing signals from the pyroelectric detector to determine a property of the fluid 407 downhole. A mid- infrared linear variable filter 416 is provided and interposed between light radiating 440 from the downhole fluid and the pyroelectric detector 412. A high gain amplifier 420 is provided to amplify the signal from the pyroelectric detector 412 when desired. The spectrometer 414 includes a processor 422 with memory. The processor 422 includes programs that implement soft modeling techniques for applying a chemometric equation, neural network or other soft modeling programs to the measurements of infrared light detected by the pyroelectric detector to estimate other physical and chemical properties of the downhole fluid from the pyroelectric detector signal. The spectrometer output responsive to the pyroelectric signal is also input to the soft modeling program, neural network or chemometric equation to estimate properties of the downhole fluid.

[0049] Turning now to Fig. 12, a more detailed schematic of the acoustic transducer for determining sound speed in the fluid is illustrated. The present invention provides a transducer 701, a sample flow line 703 or sample flow path 705 containing a fluid sample for measuring fluid density and sound speed of the fluid 708 inside of the tube or sample flow path or sample tank 711. The thickness 707 of the flow line wall 706 is known. A processor 702 and pulsing electronics 704 are provided to send an acoustic pulse from pulser 701a through wall 706 into fluid 705 in flow path 705 or from pulse 701b through wall 706 of thickness 707b to sample chamber 711. The transducer 701 receives echoes from the acoustic pulse, which are monitored by the processor. The present invention further comprises a wall standoff, which is an acoustic spacer interposed between the transducer and the wall that is made of the same material as the wall. This spacer simply increases the round trip distance and corresponding travel time for pulse-echo reverberations within the combined standoff plus near- wall material. It serves to lengthen the time between successive decaying echo pulses and so it serves to improve pulse separation, to avoid overlap of pulses and to improve quantification of energy in each pulse.

[0050] The processor determines the density of the fluid in the sample flow line. The present invention captures a fluid sample in a flow line from the formation or the borehole. The present invention then sends an acoustic pulse into the fluid sample in the flow line or sample tank. The processor of the present invention then monitors the echo returns within the wall of the flow line or sample tank and integrates the energy of each acoustic echo pulse. The processor determines the slope of the decay of the integrated acoustic echo pulses bouncing inside of the wall of the flow line. The present invention then determines the reflection coefficient for the inner wall/fluid interface. The present invention determines the speed of sound in the fluid. The present invention determines the density of the fluid in the line as described above. The present invention determines the viscosity of the fluid in the flow line as described above. [0051] The present invention has been described as method and apparatus operating in a down hole environment in the preferred embodiment, however, the present invention may also be embodied as a set of instructions on a computer readable medium, comprising ROM, RAM, CD ROM, Flash or any other computer readable medium, now known or unknown that when executed cause a computer to implement the method of the present invention. While a preferred embodiment of the invention has been shown by the above invention, it is for purposes of example only and not intended to limit the scope of the invention, which is defined by the following claims.

Claims

What is claimed is:

1. A method for estimating a characteristic of a downhole fluid comprising: receiving the fluid from a formation over time; making a plurality of measurements relating to a property of the fluid; fitting a non-asymptotic curve to the plurality of measurements; and estimating the characteristic of the fluid from the fitted curve.

2. The method of claim 1, further comprising: taking a first derivative of the fitted curve; and making estimates for a terminal value of the parameter, A₀, until an estimate is found that produces a substantially best least squares fit between y and x, wherein y = value of the parameter A at time t, minus the terminal value, Ao, and wherein x = t(dA/dt), and t=time.

3. The method of claim 2, wherein the best fit is given by y=mx + b, where intercept b is closest to zero and m is slope.

4. The method of claim 3, further comprising: selecting a data point which is close to the fitted curve; and using, A, and time, t, to forecast a future value of the parameter A at a later time, t + Δt.

5. The method of claim 4, wherein forecasting a future value of the parameter A further comprises: determining ΔA = (A₀-A)/ [1 + m (1 + t/Δt)].

6. The method of claim 5, further comprising: recursively determining ΔA to forecast the parameter A for a future time.

7. The method of claim 1 , wherein fitting a non-asymptotic curve comprises performing a piecewise non-asymptotic curve to obtain smoothed values and data slopes at centers of data segments, and the method further comprises: regressing logarithm of a derivative of data with respect to one of time or volume against logarithm of one of a set consisting of time and volume to obtain a straight-line regression slope and intercept.

8. The method of claim 7, further comprising: computing a fractional terminal purity, f_tp from a straight line regression slope and intercept and from averages of smoothed data values at a plurality of times.

9. The method of claim 1 , wherein the non-asymptotic curve is defined by the equation A = A₀ - A₁ Σ t ^x, where x = -n to + m.

10. The method of claim 1 , wherein the non-asymptotic curve is defined by the equation A = A₀ - A₁ [ t ^~p + k ^~l sin (ωt)] .

11. The method of claim 1 , wherein fitting a non-asymptotic curve comprises fitting a series of linear least square estimates of a terminal value, A₀ are fit to the equation, log f_c = log [1 - (A / A₀)] = (-5A₁ / 12A₀) log t, wherein the estimate having the fit closest to a straight line in log space is a best estimate OfA₀ at terminal fluid contamination.

12. The method of claim 1 , wherein the characteristic is one of a fractional terminal purity, f_tp and fractional terminal contamination f_tc.

13. The method of claim 1 , wherein the characteristic is fractional terminal purity that is estimated from f_tp from the equation ftp = [ 1 - A-¹CdAAIt) h(t) (dh/dt) ^"' ] ^" '•

14. The method of claim 1, wherein the characteristic is fractional terminal purity, fψ and is determined from the equation ftp = [ 1 + A^'^dA/dt) t p ^"1 ] ^{- 1}

15. The method of claim 1 , further comprising estimating fractional terminal purity, ftp and is determined from the equation f_φ = [ 1 + (12/5) A^"2(dA/dt) t ] ^~~ \

16. The method of claim 1 , wherein the property of the fluid comprises at least one of viscosity, density, sound speed, fluorescence, refractive index, bulk modulus, resistivity and optical property differences.

17. An apparatus for estimating a characteristic of formation fluid downhole, comprising: a probe in fluid communication with a formation; a sensor that makes a plurality of measurements of a property of the fluid over time; and a processor configured to fit the measurements of the property to a non- asymptotic curve to estimate the characteristic of the fluid.

18. The apparatus of claim 17, wherein the processor is further configured to take a first derivative of the fitted curve and make estimates for a terminal value, A₀, until an estimate of the terminal value is found that produces a substantially best least squares fit between y and x, wherein y = p value of property A at time t, minus the terminal value, A₀, and wherein x = t(dA/dt), and t=time.

19. The apparatus of claim 18, wherein the best fit is given by y=mx+b, where intercept, b is closest to zero and m is the slope.

20. The apparatus of claim 19, wherein the processor is further configured to select a data point which is close to the fitted curve and uses A, and time, t, to forecast a future absorbance at a later time, t + Δt.

21. The apparatus of claim 20, wherein to forecast the future value, the processor uses the equation ΔA = (A₀-A)/ [1 + m (1 + t/Δt)].

22. The apparatus of claim 21, wherein the processor is further configured to recursively determine ΔA to forecast the value of A.

23. A computer readable medium containing instructions that when executed by a computer perform a method for estimating a characteristic of a formation fluid comprising: receiving the fluid from a formation; making a plurality of measurements for a property of the fluid over time; and fitting a non-asymptotic curve to the measurements of the property to estimate the characteristic of the fluid.

24. The medium of claim 23, wherein the method further comprising: taking a first derivative of the curve; and making estimates for terminal values, A₀, until an estimate is found that produces a substantially best least squares fit between y and x, wherein y = terminal value A, at time t, minus the terminal value, A₀, and wherein x = t(dA/dt), and t=time.

25. The medium of claim 24, wherein the method the best fit is given by y= mx + b, where the intercept, b is closest to zero and m is the slope.

26. The medium of claim 25, wherein the method further comprises: selecting a data point which is close to the fitted curve and using A, and time, t, to forecast a future value at a later time, t + Δt.

27. The medium of claim 26, wherein in the method forecasting, A further comprises determining ΔA = (A₀-A)/ [1 + m (1 + t/Δt)].

28. The medium of claim 27, wherein the method further comprises: recursively determining ΔA to forecast the parameter A for a future time.