spe 56419 processing and interpretation of long-term data ... · the installation of permanent...

Copyright 1999, Society of Petroleum Engineers Inc.

This paper was prepared for presentation at the 1999 SPE Annual Technical Conference andExhibition held in Houston, Texas, 3–6 October 1999.

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AbstractLong-term data from permanent gauges have the potential toprovide more information about a reservoir than data fromtraditional pressure transient tests that last for a relativelysmall duration. Besides reducing ambiguity and uncertaintiesin the interpretation, long-term data also provide an insight onhow reservoir properties may change as the reservoir isproduced. This type of long-term surveillance provides theopportunity to look at the reservoir information in fourdimensions rather than obtaining a glimpse or snapshot intime. However, the installation of permanent downhole gaugesis only a recent phenomenon, and a methodology for theinterpretation of the data has yet to be developed. The use oflong-term data requires special handling and interpretationtechniques due to the instability of in-situ permanent dataacquisition systems, extremely large volume of data,incomplete flow rate history caused by unmeasured anduncertain rate changes, and dynamic changes in reservoirconditions and properties throughout the life of the reservoir.

This study developed a multistep procedure for theprocessing and interpretation of long-term pressure data. Theprocedure was tested with several sets of simulated and actualfield data. It was found to be an effective approach for theanalysis of long-term pressure data from permanent gauges.

IntroductionReservoir pressure is probably the most important type of dataused to monitor reservoir conditions, obtain reservoirdescriptions, develop recovery schemes, and forecast reservoirperformance. The changes in reservoir pressure due to

alteration of production conditions are characteristic ofreservoir properties themselves. Therefore, the reservoirproperties can be inferred by matching the pressure responseto a reservoir model. The inferred reservoir model can then beused for future reservoir management.

To monitor the well condition in real time, many recentlycompleted wells have been equipped with permanentdownhole pressure gauges. Continuous measurement ofpressure enables engineers to observe ongoing changes in thewell and make operating adjustments to optimize recovery.The installation of permanent downhole pressure gauges hasproven to be cost-effective even for the use of well monitoringalone, not to mention the additional reservoir informationobtained from the analysis of pressure data1. Although theinstallation of permanent downhole gauges has been aphenomenon of the 1990s, their use has been discussed sincemuch earlier 2-7.

Long-term data are prone to different types of errorscompared to data from a short test. In a traditional well test,the pressure response of the reservoir is carefully measuredwhile the well undergoes flow rate changes. The test is under astrictly controlled environment. By design, there are no otherdynamic changes in the system except the flow rate alteration.In the case of long-term monitoring, the well and the reservoirmay undergo dynamic changes throughout their lives. Thewell may be stimulated, worked over due to failure in thewellbore, etc. Due to these changes the data may containextraneous measurements. Abrupt changes in flowingtemperature can also cause erroneous recordings. Besidesphysical changes in the reservoir, the permanent gauge dataacquisition system itself may pose a problem. In some cases,pressure data are stored with low precision, creatingsuperfluous outliers and noise. Therefore, one part in theanalysis of long-term data is to remove outliers and noise fromthe data. These steps may be referred to as outlier removaland denoising process.

The amount of data collected by permanent downholegauges is tremendous. In some cases, pressure is measured at10-second interval for a period of several years. One year ofdata consists of over three million measurements. It isimpossible to include the entire data in the interpretation dueto limited computer resources. Therefore, it is essential to

SPE 56419

Processing and Interpretation of Long-term Data from Permanent Downhole PressureGaugesSuwat Athichanagorn, SPE, Stanford University, Roland N. Horne, SPE, Stanford University, and Jitendra Kikani, SPE,Chevron Petroleum Technology Company

2 S. ATHICHANAGORN, R. N. HORNE, AND J. KIKANI SPE 56419

reduce the number of data to a manageable size by eliminatingdata that provide redundant information. This process may bereferred to as data reduction.

In most cases of long-term monitoring, a complete recordof well activities and flow rate history is not available. Theflow rate may be measured only once a week while there areunmeasured rate changes in between. First, the times at whichthe flow rate changes occur have to be located. This step maybe referred to as transient identification. Then unknown flowrate changes need to be estimated. The reconstruction of flowrate history may be necessary in the interpretation of pressuredata. Unknown and uncertain flow rates can be reconstructedduring regression on pressure by parameterizing them asunknown parameters constrained to existing ratemeasurements and production data. This process may bereferred to as flow history reconstruction.

Since the long-term monitoring is under an uncontrolledenvironment, the pressure may not be consistent betweentransients for the reasons mentioned before. Aberrant pressurebehavior during a transient may lead to large uncertainties inparameter estimates or even a wrong interpretation. To correctthis, aberrant sections of the data need to be removed from theinterpretation. The variances between the regression matchand the data can be used to determine which transients areinconsistent with the rest of the data. This process may bereferred to as behavioral filtering.

Changes in reservoir properties and conditions that mayoccur when interpreting long-term data have to be accountedfor. Since the properties may change, it is not appropriate tointerpret the entire data at once. A procedure is thereforeneeded to analyze pressure response due to changing reservoirproperties. This process may be referred to as datainterpretation.

The proposed approach to analyze long-term data can besummarized in a seven-step procedure as follows:

• outlier removal• denoising• transient identification• data reduction• flow history reconstruction• behavioral filtering• data interpretation

Although permanent downhole pressure gauges have beeninstalled in over a thousand wells worldwide, there have beenonly a few studies on the subject of data processing andinterpretation1,7-8. Most of these studies touch on a single or acouple of subjects related with long-term data. Kikani and He7

deal with issues associated with the processing of pressuredata using wavelet techniques. Unneland et al.8 use the rateconvolution integral to determine the flow rates that wouldoccur if the well were kept at a constant flowing pressure.These rates are then used in the decline curve analysis todetermine reservoir properties. Landa and Horne9 use long-term pressure history from multiple wells to estimate the

distributions of permeability and porosity in heterogeneousreservoirs.

In this study, a methodology is developed to process andinterpret the long-term pressure data. Wavelet-basedalgorithms were developed for most of the data processingsteps such as outlier removal, denoising, transientidentification, and data reduction. Flow history reconstruction,behavioral filtering, and data interpretation are performed withthe use of nonlinear regression analysis. A brief backgroundon the wavelet analysis is given in the following section.

Wavelet AnalysisWavelet analysis has a wide range of applications in dataanalysis such as signal processing, data compression,statistical analysis, etc. In the past few years, wavelet analysishas appeared several times in the petroleum literature indifferent applications such as in data denoising, upscaling ofreservoir properties, and solving partial differential equationgoverning fluid flow in reservoirs 7,10-13. The most attractivefeature of the wavelet analysis is its ability to separate highfrequency contents that represent small-scale information fromlow frequency components that represent large-scale or trendinformation. Kikani and He7 used the wavelet analysis todenoise data and for event detection.

A wavelet is a function ψ(x) that waves through the x-axissuch that:

∫∞

∞−= 0)( dxxψ (1)

The function ψ(x) is constructed to have certain mathematicalproperties so that they can be used as basis functions totransform functions or data. The wavelet transform of afunction f(x) at location b and scale a is defined as:

dxa

bxxf

abaWf )()(

1),( ∫

∞

∞−

−= ψ (2)

The window width of the wavelet transform depends on thescaling parameter (a). By changing the scaling parameter, wecan analyze different frequencies of the data independently. Anarrow time window may be used to analyze high frequencydata while a broader window may be used to analyze lowfrequency data. In order to relate across scales or frequencies,another transform referred to as the scaling function φ(x) isused:

dxa

bxxf

abaC f )()(

1),( ∫

∞

∞−

−= φ (3)

The mathematical details about the wavelet transform havebeen described in the literature (see Refs. 14-15). Therefore,we will focus on the implementation of the wavelet technique.Roughly speaking, the method consists of performing a band-unlimited low-pass and high-pass filtering of the data. Thelow-pass filter (Eq. 3) can be viewed as an approximation tothe signal while the high-pass filter which is the wavelettransform itself (Eq. 2) can be seen as the local detail in thesignal. Since the original signal is passed through two filters

SPE 56419 PROCESSING AND INTERPRETATION OF LONG-TERM DATA FROM PERMANENT DOWNHOLE PRESSURE GAUGES 3

yielding approximated and detailed components, this processis called wavelet decomposition.

There are two types of wavelet decomposition algorithms:(1) the pyramidal algorithm for orthogonal wavelet bases15 and(2) the a trous (redundant) algorithm for nonorthogonalwavelets 16,17. In the pyramidal algorithm, the number of datain the signal is reduced in half after each filtering. As we moveto larger scales (higher levels of transform), the resolution ofthe data becomes coarser. This means we are approximatingthe signal to a higher degree. The pyramidal algorithm is veryuseful in up-scaling applications, and is sometimes used toapproximate signals where the exact locations of theapproximated data and the number of data points are notimportant but computational time and storage are of a greatconcern.

Spline Wavelet for Singularity DetectionBased on the Lipschitz exponent analysis which measureslocal regularity of functions, Mallat and Hwang18 and Mallatand Zhong19 developed a new type of nonorthogonal wavelet -a quadratic spline, suitable for detecting singularity in the data.The spline wavelet is defined as20:

1

2/1

0

2/1

2/1

0

2/1

1

2)1(2

22)1(4

22)1(4

2)1(2

)(

−

<<<<

≤≤≤≤

−−

−−+−−−+−

+

=

x

x

x

x

x

xxx

xxx

x

xψ (4)

Since the spline wavelet is nonorthogonal, the a trousalgorithm can be used to compute approximated and detailsignals. Thus, the data are sampled on the same grid acrossscales. Figs. 1 and 2 illustrate the approximated and detailsignals of a set of data obtained from wavelet decompositionusing the spline wavelet. As seen in the figures, theapproximate signal provides information on the overallfeatures in the original data while the signal details describechanges in the signal at local scales. As the level ofdecomposition increases, the approximated signal gives higherdegrees of approximation. Similarly, the detail signalcharacterizes change on coarser scales with the increasinglevel of decomposition.

From Fig. 2, we can see that the detail signal reaches anextremum when there is a sudden change (singularity) in theoriginal signal itself. To pinpoint the location of a singularity,Mallat and Hwang18 defined a wavelet modulus maximum at ascale a0 as a point (a0, x0) such that |Wf(a0,x)| < |Wf(a0,x0)|where x belongs to the left or right neighborhood of x0. Inother words, the wavelet modulus maximum is basically thehighest or lowest point in its neighborhood. The waveletmaxima can therefore be used to locate singularities in thesignal. Fig. 3 depicts the locations of the wavelet maxima andthe values of the detail signal at the corresponding positionsfor the original data shown in Fig. 1. At different levels ofdecomposition, the wavelet modulus maxima provide differenttypes of information concerning singularities. The waveletmodulus maxima at low levels of decomposition (levels 1-2)

represent both signal singularities and noise singularities. Inthe regions where there are obvious singularities such as thefirst two jumps in the data signal, these singularities can beidentified by the high magnitude of wavelet maxima. On theother hand, gradual singularities in the second half of thesignal are mixed with noise singularities. Small values ofwavelet maxima at low levels are characteristics of both noiseand small changes in the data. Consequently, it is difficult todistinguish one from the other. As the signal resolutionbecomes coarser in levels 3-4(intermediate levels), the noisesingularities gradually diminish revealing the gradualsingularities in the second half of the signal while the obvioussingularities can still be identified by the wavelet modulusmaxima. At high levels of decomposition such as levels 5-6,the wavelet modulus maxima now correspond to singularitiesof very coarse data features. Some singularities such as thefirst two jumps in the data signal are now grouped into onesingularity representing an overall trend in the neighborhood.

The proposed processing and interpretation methodologyis discussed step by step as follows:

Step 1: Outlier RemovalThere are, in general, two types of measurement errors: noiseand outliers. “Noise” is a group of data points that scatteraround the trend of the overall data, but lie in the sameneighborhood as the true data. “Outliers”, on the other hand,are data points that lie away from the trend of the data. Theycan be identified from their misalignment with the rest of thedata.

Since an outlier is isolated and lies away from the rest ofthe data, it causes discontinuities in the data stream creatingtwo consecutive singularities. For example, an outlier that liesabove the trend of the data departs from the data trend,creating the first singularity. The second singularity is a resultof a sudden decrease from the outlier back to the trend of thesignal. This characteristic can be exploited using a singularitydetection framework with wavelets. When there exists anoutlier, the detail signal will first change sharply in onedirection, either increasing or decreasing, and then changeagain in the opposite direction. Therefore, the singularitiescreated by the outliers can be detected by screening for twolarge magnitudes of the detail signal with opposite signs.

When implementing wavelet decomposition, the input datamust be sampled uniformly. In many cases, the pressure datafrom permanent gauges are unevenly spaced. At first glance, itmay seem desirable to interpolate between data points toobtain an evenly sampled set of data. However, interpolationfrom data that contain outliers may give a poor approximationto the signal. Also, outliers are members of the original dataand not the interpolated data. If interpolated data are used inwavelet decomposition, the outliers determined by thesingularity detection algorithm are the interpolated points.This has to be mapped back to the original points to determinethe location of the actual outliers. Mapping back to theoriginal data may result in misidentifying the exact points. Forthese reasons, the data should be looked at as a sequenceinstead of pressure versus time. The time scale should be


replaced by the rank of the data collected. For example, therank of the first data point is 1, and the rank of the secondpoint is 2, and so on. In other words, we pretend that thespacings between data points are equal. The singularitycharacteristics of the outliers using rank representation are stillpreserved.

Due to its nature, the order of pressure transient data playsa very important role in outlier analysis. During each transient,the magnitude of the pressure change at late times is generallylower than that of the pressure change at early times. A smalldeparture of the data from its trend at late times is easier toidentify than a departure of the same magnitude at early time.Consequently, it is easier to identify outliers at late times thanearly times. The data then should be analyzed from the end tothe beginning in a reverse order. Fig. 4 plots the pressure datausing reverse rank order of the data. The wavelet transform ofthis new representation is shown in Fig. 5.

In order to determine the outliers, a threshold is set up forthe magnitude of the detailed signal. A rule of thumb inchoosing a threshold is to ask oneself how far does a pointhave to be from the general trend to be considered an outlier.The magnitude of the threshold generally depends on themagnitude of changes in the pressure and/or the resolution ofthe measuring instrument. In general, 5 psi may be used as athreshold for outliers. Since pressure data may be spuriouswith outliers of different magnitudes, the obvious outliersshould be eliminated first, thus revealing the main structure ofthe signal, and the less obvious ones are eliminated iteratively.In such an implementation, the outliers whose magnitudes inthe detail signal are higher than 20 psi should be removedfirst. Then, the threshold is reduced to 15 psi, 10 psi, and 5 psisuccessively. The result of applying the iterative thresholdingmethod to field data is shown in Fig. 6. This method separatesoutliers from the data effectively.

Step 2: DenoisingDenoising is a procedure that is applied to the data to reducethe scattering and the fluctuations in the data values in order toextract the most representative features from the data. One ofthe most effective ways to denoise data without making priorassumptions about their behavior is the wavelet thresholdingmethod. While most denoising methods tend to smear outsharp features in the data, the wavelet thresholding methodgenerally preserves most of these features. In any case, thesmearing effect cannot be avoided when data spacings arelarge. The denoising process, thus, may be used when the dataare collected at high sampling frequencies.

To reduce the noise level, the wavelet detail signals whosemagnitudes are smaller than a certain threshold are set to zeroand the denoised signal is constructed using the smootherdetail signals. This process is sometimes called waveletshrinkage since the detail signals are shrunk towards zero.Donoho and Johnstone 21,22 introduced the use of hard and softthresholding methods to screen for significant details in thedetail signal. The criterion for the hard thresholding method is:

otherwise

ddd kjkjhard

kj 0

|| ,,,

λ>= (5)

where dj,k is the detail signal, and λ is the threshold. Thecriterion for the soft thresholding method is:

λλλλλ

≤−<+

>−=

|,|0,,,,

,kjd

kjdkjdkjdkjd

softkjd (6)

To investigate the robustness of the hard and softthresholding methods, a test function whose behavior followsa pressure transient response from a closed circular boundaryreservoir is used. Normally distributed random noise with anoise level of 0.5 psi [N (0,0.5)], were added to the data. Avalue of 2.5 was selected as a threshold. The results for bothhard and soft thresholding methods are shown in Figs. 7 and 8,respectively. The differences between the original noise-freesignal and the estimates are shown in Figs. 9 and 10. The hardthresholding method outperforms the soft thresholding methodaround the vicinity of discontinuities in the signal. However,the hard thresholding method is unable to suppress a few noisypoints in the continuous regions of the data while the softthresholding method can. Kikani and He7 came to the sameconclusion but chose to use the soft-thresholding methodexclusively.

Recognizing the benefit of the hard thresholding method inpreserving signal sharpness and the advantage of the softthresholding method in smoothing noisy features, a hybridcriterion was developed. In the hybrid thresholding method,the soft thresholding criterion is used in the continuous dataregions and the hard thresholding criterion is applied to thedata located in the vicinities of the discontinuities. Thelocations of the discontinuities can be found by checkingwhether the detail signals at higher levels of decompositionexceed the noise threshold. In general, it is sufficient to checkonly the level of decomposition in which the detail signalcorresponding to feature changes exceeds the detail signal ofthe noise. In this work, level 5 was used. Mathematically, thehybrid thresholding criterion can be written as:

λλλλλλλλλ

≤<−<+

<>−

>>

=

||0||

||

||||

,

,,,

,,,

,,,

,

kj

klkjkj

klkjkj

klkjkj

hybridkj

ddanddd

danddd

danddd

d (7)

where l is the level of decomposition used to check sharpfeature changes.

Results using the hybrid criterion are shown in Figs. 11and 12. The advantages of hard and soft thresholding arecombined in this method. The noisy points left by the hardthresholding method now disappear, and at the same time thedifferences between the denoised pressure and the originalnoise-free signal in the vicinity of the discontinuities areminimal.

In practice, the data may not be collected at a uniforminterval while the wavelet decomposition requires the input to


be uniformly spaced. To obtain an evenly sampled set of data,one may use a linear interpolation scheme to interpolatebetween data points. Other types of interpolation may notwork as well as the linear interpolation method since they tendto smear out the regions where there are rapid changes. Thehybrid thresholding method was applied to actual field datawhich were collected at an interval of 10 seconds using athreshold value of 1.5. Several samples were recorded at largerintervals creating nonuniformity in the sample spacing. Thelinear interpolation scheme was used to interpolate betweendata points to obtain data at 10-second spacing. Fig. 13displays the estimates from the denoising process reflectingthe success of the procedure in suppressing the noise whilepreserving the data features.

Step 3: Transient IdentificationGenerally a complete record of times at which the well flowrate changes is not available. Fortunately, the times at whichthe flow rates change can be determined by identifying suddenchanges in pressure data. These changes can be viewed assingularities in the data. Therefore, the wavelet modulusmaxima which indicate the neighborhoods of singularities canbe used to determine the times at which flow rate changes.

As discussed before, the wavelet modulus maxima atdifferent levels of decomposition provide different types ofinformation. Specifically, at intermediate levels, thesingularities caused by noise disappear while the signalsingularities are still present. From this characteristic, thebeginning of a new transient could be detected at anintermediate level of decomposition.

The question is then what should be considered anintermediate level. An appropriate level to be used actuallydepends on the spacing of the data. In fact, when decidingwhat level should be used, we are choosing the resolution ofthe data. First, the length of the shortest transient to bedetected (∆tmin) has to be chosen. The highest level at whichthe shortest transient can be detected is the level at which itsresolution is lower than or equal to ∆tmin. Since the dyadicwavelet decomposition is used, the resolution takes the formof 2j, where j is the level of decomposition (j = 0, 1, 2, ...). Let∆t be the original spacing between data points and l be thehighest level of wavelet decomposition that can be used todetect the shortest transient. The level l can be determined bysolving the following constraints:

(2l) ∆t < ∆tmin < (2l+1 ) ∆t ………………..(8)As in detecting outliers, a threshold has to be chosen for

the detail signal in order to determine which change is actuallya singularity. The rule of thumb in choosing the threshold is todetermine how much pressure difference between two datapoints is considered the beginning of a new transient. Thethreshold then depends on the spacing between the data points.Once a pressure threshold is chosen for the original dataspacing, the threshold at any decomposition level j can becomputed by multiplying 2j-1 to the threshold in the originalspacing. Note that the multiplier is 2j-1 not 2j because thedetail signal at level j contains the high-frequency content of

the approximated signal at level j-1. It may be more intuitivefor us to choose a threshold in terms of a rate of pressurechange per unit time (slope of pressure data) instead of anabsolute pressure change. However, in terms of computation,it is more efficient to use the absolute pressure threshold toavoid computing the slopes for the detail signal at the desiredresolution. Here, the pressure threshold and the slopethreshold are referred to interchangeably. In order todetermine small pressure changes that are responses of smallvariations in flow rate, the slope threshold should also besmall. However, the threshold should not be too small.Otherwise, all minor variations such as noise may bemisinterpreted as new transients.

After choosing a decomposition level and a slopethreshold, possible locations for starting positions of newtransients may be identified from wavelet modulus maximawhose detail signals are higher than the threshold. The waveletmaxima at the chosen scale only provide indications ofsingularities not the exact locations of singularities for tworeasons. First of all, the detail signal at the chosen scale hasless resolution than the original signal. Therefore, the waveletmaxima are determined at a coarser resolution rather than theoriginal data. Secondly, a singularity at the beginning of a newtransient is not necessarily an extremum, but is actually thefirst point that departs from a prior trend in the signal. Sincethe decomposition at level 1 uses the data in their originalresolution, the location of each singularity can be determinedby finding the first point whose detail signal at level 1 ishigher than the pressure threshold.

To make sure that the singularities detected arecharacteristic of new transients instead of local variations, weneed to check the slope of the data in the neighborhood ofsingularities. First, the forward slope extending from the pointof singularity needs to be higher than the slope threshold.Secondly, the absolute difference between the forward slopeand the slope of the data prior to the point of singularityshould be big enough to demonstrate a discontinuity in thedata trend. In this study, if the difference between the twoslopes is higher than half of the slope threshold, the detectedpoint is considered a point of singularity. Each slope can becomputed by running a simple straight line regression throughthe data in its neighborhood.

Even at the original resolution, the exact location of a flowrate change does not necessarily lie on the discretization grid.They can be determined by finding the intersection between astraight line passing through the last two points before asudden change in pressure and another line that passes the firsttwo points right after the point of singularity. Since the dataare subject to noise, the computed intersection may lie outsidethe interval between the two middle points. If this happens, thepoint of singularity on the discretized grid itself may be usedas the starting time for the new transient.

To study the effect of noise in transient detection, thealgorithm was applied noisy field data and denoised data. Thespacing between data points was chosen to be 0.01 hours inboth cases. The length of the shortest transient ∆tmin was set to


be 0.1 hour. Using the formula given in Eq. 8, thedecomposition level used in the detection was computed as 3.The slope threshold was chosen to be 10 psi/hour. Theresolution at this level is then 23 x 0.01 = 0.08 hours. Thepressure threshold at level 3 is 10 x 22 x 0.01 = 0.4 psi. Thepoints of singularities corresponding to new transientsdetected from the original data and denoised data are plottedas vertical lines in Figs. 14 and 15, respectively. As seen fromthe figures, the denoised data provide better results than theoriginal noisy data. Therefore, data should be denoised beforeusing them for transient identification. Denoising may not beneeded when the associated noise is minimal since denoisingmay smear sharp features in the data to a certain degree.

The transient identification algorithm was then applied toanother set of field data. In this example, the pressure datawere recorded at variable frequencies with a minimumrecording interval of 1.728 seconds and a maximum spacingof 1.5 hours (excluding large gaps caused by operationalproblems). There are a few series of several short transientsembedded in a decreasing trend that seems like a singledrawdown. This type of response calls for a small value of∆tmin. In this example, ∆tmin was set to be 0.1 hour. Beforeapplying the detection algorithm, outliers were removed fromthe data using the procedure described earlier. Linearinterpolation was then applied to the original data to obtain anew uniform sample spacing of 10 seconds. When examinedclosely, the data are quite noisy. Therefore, the hybriddenoising algorithm with a threshold of 1.5 was used tosuppress the noise. The denoised data were then used in thedetection algorithm with a slope threshold of 10 psi/hour.

The starting points of new transients detected from thealgorithm are shown as vertical lines in Fig. 16. A close-upview is illustrated in Fig. 17. The algorithm did well indetecting the singularities caused by flow rate changes.However, a few singularities caused by noise and smallchanges were also detected. The singularity at time t=123.796is due to noise. Since the noise level is quite high at thislocation, the noise was mistaken as signal singularity. Thedetection t=126.678 reflects the recognition of a small changein the pressure signal. The slope of this change is higher thanthe slope threshold of 10 psi/hour. Thus, this microtrend wasmisidentified as a new transient.

The results from the detection algorithm revealedsingularities corresponding to changes in flow rates and a fewsingularities corresponding to unconventional behaviors in thedata. The detection of the latter is, in fact, beneficial to ussince it helps us determine problematic regions in the data.Results from the detection algorithm should be reviewed toscreen for abnormalities in the data before being used forinterpretation. In any case, the detection algorithm greatlyreduces the task that otherwise would have to be performedmanually even though it may still call for a certain degree ofhuman intervention.

Step 4: Data ReductionThe size of data sets acquired with permanent pressure gaugesis enormous. A gauge system with a 10-second recordinginterval registers more than three million data points a year. Itis cumbersome even to plot the data to see the generalbehavior, not to mention analyzing them. Therefore, it isnecessary to reduce the number of data to a representative set.

One of the methods for reducing the number of data is thepressure thresholding method. In this method, the data aresampled only when a certain change in pressure is reached.However, using a threshold on pressure alone is not sufficientas the pressure may stay relatively constant over long periodsof time. The pressure threshold criterion may produce largegaps in data. A time limit should thus, be imposed on thesampling space. The pressure should be recorded when thechange in pressure is higher than a maximum preset pressurevalue (∆pmax) and whenever the time span between samplesbecomes higher than a maximum preset time threshold (∆tmax).

For noisy data that are collected at high frequency, it maybe necessary to denoise the data before undertaking the datareduction step so that it is easier to pick out representativepoints from the data set. To illustrate how denoising can helpreduce the size of data, the pressure/time threshold criteriadescribed above was applied to both original and denoiseddata using a data set of 18,000 points from a field test. ∆pmax

was chosen to be 0.5 psi, and ∆tmax was set to be one hour.Figs. 18 and 19 display the pressure data after the reductionprocess using original data and denoised data, respectively.When the original data was used, the data size was reducedfrom 18,000 to 3,258. On the other hand, the number of datawas reduced to 99 when using denoised data.

Step 5: Flow History ReconstructionIn order to solve the problem of incomplete flow rate historyand uncertainty in flow rate measurement, the unknown flowrates themselves may be included as model parameters in anonlinear regression model n. The objective function to is thesum of the squares of the differences between themeasurements and the model response:

∑ −==

n

iixFiyE

1

2)),(( Θ (9)

where Θ is a vector of unknown model parameters. The theoryof nonlinear regression is well documented in the literature23,24. The Gauss-Newton method is used in this study. In thismethod, the model function and the first partial derivatives ofthe model function with respect to unknown parameters needto be evaluated. The reservoir model function for a multiplerate test can be written as:

11

11 ,)()(2.141

)( −=

−− >−−−= ∑ j

nq

jDjDjji ttttpqq

hk

Bptp

µ (10)

where nq is the number of flow periods. The derivatives canbe computed by taking the first partial derivative with respectto each model parameter. The evaluation of the derivatives


with respect to model parameters is discussed in Rosa andHorne25. The partial derivative with respect to unknown flowrate qk can be expressed as:

))()((2.141)(

1 DkDDkDk

ttpttpkh

B

q

tp −−−= −µ

∂∂

(11)

From Eq. 10, it is clear that permeability and flow rates arelinearly dependent. If all the flow rates are unknown, therewill be nonuniqueness in solutions due to the strongcorrelation between permeability and flow rates. To avoid this,some flow rates need to be known in order to constrain theregression match. Theoretically, if at least one flow rate isknown with absolute certainty, the model parameters can bedetermined uniquely. This known flow rate fixes the level ofpermeability and other parameters in the regression.

A simulated pressure response from a channel reservoir isused in the regression to estimate the reservoir parameters andunknown flow rates. Fig. 20 depicts the simulated pressureresponse generated with the model parameters and flow ratehistory shown in Table 1. Only 4 out of 13 flow rates areassumed known. The initial guesses for the unknown reservoirparameters and unknown flow rates are also shown Table 1along with the parameters estimated from the regression. Theestimates for model parameters and unknown flow rates areclose to the true values reflecting the effectiveness of theprocedure in retrieving the unknown flow rates.

Another approach to eliminate nonuniqueness in thesolution is to match the cumulative production in addition tothe pressure match. The objective function for nonlinearregression then becomes:

∑∑=

−+=

−=nQ

iivQiz

n

iixFiyE

1

2)),((

1

2)),(( qΘ (12)

where

data production cumulative ofnumber unknown) and known (both ratesflow

function production cumulative to1 timefrom production

(time) variabledependent

===

−==

nQ

Qiviviz

iv

q

The cumulative production function is simply a linearcombination of flow rates:

)(...)()()( 1111 −++− −++−+−= liljjjijji uvquuqvuqvQ (13)

where

1,...,2,1 , to timeduring rateflow ends when time

to timeduring rateflow last ends when time

to timeduring rateflow first

1

11

1

1

−++=−−−

−

−

==

===

ljjkuuqqu

vvqqu

vvq

kk

ll

iil

jj

iij

Since the cumulative production function (Q) is only afunction of flow rates, not a function of reservoir parameters,the derivatives of the cumulative production function with

respect to reservoir parameters are zero. The derivatives withrespect to the unknown flow rates can be expressed as:

1

1

1

)(

,)(

)(

1,...,2,1

−

−

−

−=∂

∂

=−=∂

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−=∂

∂

−++

lil

i

kkk

i

ijj

i

uvq

vQ

kuuq

vQ

vuq

vQ

ljj (14)

The same set of data as in the previous example was usedto test the validity of this approach. All the flow rates are nowunknown but the cumulative production is known. Thecumulative production history is shown in Table 2. The truevalues and the initial guesses of the reservoir and flow rateparameters are shown in Table 3. The regression wasperformed using the cumulative production data as constraints.The estimates of unknown parameters from the constrainedregression are also shown in Table 3. Again, the estimates ofthe reservoir parameters and unknown flow rates agree wellwith the true values. The cumulative production history waseffective in constraining the regression to converge to the rightsolution.

Step 6: Behavioral FilteringOccasionally the pressure data may show strange behavior thatdoes not follow the general trend. These aberrant behaviorsmay be caused by sudden changes in conditions in the welland/or reservoir. The pressure gauge may record incorrectvalues during these sudden changes. Excluding thesetransients from the analysis should reduce the uncertainty ofthe regression match and provide better estimates of thereservoir parameters.

One measure that can be used to determine the goodness offit of each transient is the variance between the regressionmatch and the data. The variances of the aberrant transientsare generally unusually high due to the fact that they are notwell matched by the regression. To determine these aberranttransients, first, the variance is calculated for each transient.The transient with the maximum variance is excluded from thecalculation of the average variance of the overall data.. Then,the variance of each transient including the one with themaximum variance is compared with the average variance. Inthis study, the transients whose variances are at least threetimes higher than the average variance are considered aberranttransients and hence excluded from the analysis. After theaberrant transients are eliminated, the data is regressed again.The new variances for the transients are then compared againwith the new average variance. Generally, the quality of thesecond match is better than the previous one, i.e., the newaverage variance is less than the previous average variance.Using the same variance criteria, more aberrant transients maybe eliminated in this second iteration. This process may berepeated until there are no more transients to eliminate.

To show how the approach works, a test case wasconducted. In this exercise, errors were added to twotransients at times 100-160 hours and 400-450 hours. The flow


rate data are the same as the ones shown in Table 1. Most ofthe flow rates are not known. Cumulative production datawere assumed to be unavailable. The regression with thevariance test was run on the data. The parameters estimated inthe first regression are shown in column 3 in Table 4. Becauseof the two aberrant transients, the estimates of the modelparameters are quite poor. After running iterative regression toeliminate the aberrant transients, the quality of the matchbecomes better. Fig. 21 shows the final match. The estimatesof model parameters from the final regression match areshown in Table 4. The estimates of the final match areimproved considerably over those from the original matchreflecting the effectiveness of the behavioral filtering process.

Step 7: Data Interpretation Using Moving WindowAnalysisDue to the possibility that reservoir properties/conditions maychange, one constant-property model should not be fit to theentire data set. Sections of data should be analyzed todetermine local values of reservoir parameters by using amoving window technique26. If all the flow rates are known,each transient can be analyzed separately using local values ofreservoir and fluid properties. However, this traditionalpressure transient analysis cannot be used when some of theflow rates are unknown. A few transients need to be groupedtogether such that there is at least one known flow rate withinthe group. The known flow rates are used as constraints toreconstruct the flow rate history as described in Step 5.Cumulative production data can also be used to constraint theregression match in addition to the known rates.

The data in the transients that are grouped together form awindow of data. A regression can be run with theparameterization of flow rates as unknowns to concurrentlydetermine reservoir parameters, reconstruct flow rate history,and eliminate the aberrant transients using the approachdescribed in Step 6. After estimating the unknown parametersin the window, the analysis is moved forward to a newwindow. The starting point for the new window may lie withinthe span of the old window. Unknown flow rates are updatedbefore moving on to subsequent windows. Since theseunknowns cannot be inferred with high certainty from theresponse in later windows, they are estimated within thewindow of analysis and assumed known in subsequentwindows. This methodology is still being refined. The steps inthe moving window analysis are summarized as follows:

1. Choose a preliminary window size and translationlength, i.e., the number of hours of data to be analyzedand the time length to shift the window forward.

2. Run regression on the selected data window todetermine reservoir model parameters as well asunknown flow rates.

3. Eliminate the aberrant transients in the selected datawindow iteratively as described in Step 6.

4. Before moving to the next data window, update(unknown) flow rates that happen prior to the startingtime of the new window.

5. Interpret data in the new window. The new windowmay overlap the previous one.

Field ExampleApproximately 20,050 hours (28 months) of data werecollected generally at low frequencies except in a few regions.The raw data were first screened for outliers. Since most of thedata points have large spacings, the denoising routine was notimplemented to avoid smearing sharp features in the data. Thetransient identification methodology was applied to theoriginal data. The results were reexamined before using asinput data in the moving window analysis. Falseidentifications of transients were discarded, and undetectedtransients were added. Then, the data were resampled toreduce the redundancy.

Flow rates were measured quite infrequently. There were218 flow rate changes during the 28 months of data recording.However, only 58 flow rates were measured. This leaves uswith 160 unknown flow rates. The cumulative production datawere not recorded. Therefore, the constraints for theregression are the measured flow rates. A preliminary windowwidth was chosen to be 500 hours, and the translation lengthwas set to be 100 hours. In practice, the actual window widthis generally larger than the preselected value to avoid ending awindow in the middle of a transient. Another reason toincrease the window width is to constrain the regression matchby including at least one known flow rate in the window.Similar to the window width, the translation length may bechanged such that the beginning of each window coincideswith the beginning of a transient to avoid starting a window ofanalysis at the middle of a transient.

An analysis of pressure derivative and geologicalinformation indicates that the well may be placed in a channel.Fig. 22 shows the estimates of permeability, skin factor,distances to the boundaries as a function of time at the middleof each window. There does not appear to be uniform trends inthe parameter estimates. Instead, the variations illustrate theuncertainties associated with uncertainties in datameasurements (pressure and flow rate), instability in thewellbore and reservoir, uncertainty in the regressionprocedure, and uncertainty in the model. One way of reducingthe regression uncertainty is to limit the rate of change of eachparameter from one window to the next.

After experimenting with several rates of allowablechange, it was found that a rate of ±25 percent is mosteffective in minimizing the variations of parameter estimateswhile having a small effect on the average error between themeasurements and computed response. The new estimates ofreservoir parameters using limited search space are shown inFig. 23. The estimate of each model parameter has lessvariation than the estimate obtained from the regression withfree search space. The derivative plot of a long transient inwindow 72 is shown in Fig. 24. The matches to both thepressure and derivatives confirm that the chosen reservoirmodel and the estimates of the reservoir parameters aresuitable. Fig. 25 compares the average errors between themeasurements and computed response from the free search


space and limited search space case. The small difference inthe average errors between the two confirms that the resultsfrom both cases are equally good. Limited search spaceprocedure seems more robust to variations due to nonlinearregression procedure.

The parameter estimates are plotted as histograms in Fig.26. Only the estimates from windows with average error lessthan 5 psi were included in the histograms. The distributionsand statistics of the parameter estimates provide an insight intothe uncertainties of the estimation. These can perhaps be usedto assess uncertainties associated forecasting reservoirperformance, production scheduling, economic evaluation,and techniques that uses these reservoir parameters as inputdata. For this reason, a collection of estimates is more valuablethan a single set of parameter estimates.

ConclusionsA methodology to process and analyze data acquired withpermanent downhole pressure gauges has been developed. Anumber of sequential steps for semi-automatic processing andinterpretation of these data are proposed and demonstratedwith field data. Important learnings from this work can besummarized as follows:1) Wavelet decomposition analysis can be used effectively

to detect outliers in long-term data.2) The proposed hybrid wavelet thresholding method is

useful for data denoising. The transient identificationalgorithm developed in this study can be used effectivelyto locate the start of new transients. Although thetechnique is not perfect, it considerably reduces theamount of the task that is normally performed by hand. Itis recommended that noisy data may need to be denoisedprior to identifying the transients. Results using denoiseddata appear to be more reliable than from the ones withoriginal noisy data.

3) Flow rate history can be reconstructed by parameterizingthe unknown rates as unknown model parameters andmatching the pressure response constrained to knownflow rates and production data. Although the proceduredeveloped here was successful, it should be stressed thatthe continuous monitoring of flow rates downhole wouldbe a more desirable approach.

4) The behavioral filtering process to eliminate aberranttransients from the data using the variance criterion isvery effective in reducing the uncertainty in the solutionobtained from nonlinear regression.

5) The moving window analysis can account for changes inreservoir parameters given that the changes are gradual.If the changes are abrupt, the estimates of modelparameters in that data region may not be as accurate. Inany case, the estimates should improve in subsequentwindows due to the diminishing effect of time-superposition.

6) The moving window analysis provides parameterdistributions that capture some of the uncertainties in theinterpretation model and procedures. These distributions

may be useful in assessing uncertainties in subsequentanalysis and predictions.

The wavelet analysis has a high potential to be useful inseveral applications in the petroleum industry. The outlierdetection framework can be applied to any type of data toscreen for outliers such as in geostatistical data. The waveletmodulus maxima may be used to detect any type ofdiscontinuities such as the layering behaviors of well logsignals or a shock location in the numerical solution of theBuckley-Leverett equation. The denoising algorithm may beused to smooth the pressure derivatives in order to determinethe underlying characteristics hidden under noise.

The principle of moving window analysis may be appliedto reservoir characterization problems. The introduction of themoving window analysis into reservoir characterizationframework will give us distributions of realizations ofreservoir properties instead of a single set of answers.

Nomenclature B = formation volume factor d j,k = wavelet coefficient (discrete detail signal) E = Objective function F(θ, x) = Model function h = formation thickness, ft k = permeability, md nq = number of flow rate nQ = number of cumulative production data p = pressure, psi pi = initial reservoir pressure, psi q = flow rate, STB/D Q = Cumulative production function z = cumulative production, STB t = time, hour θ = vector of model parameters λ = wavelet denoising threshold µ = viscosity, cp φ (x) = scaling function ψ(x) = wavelet

AcknowledgementsThis research was supported by the member companies ofSUPRI-D Research Consortium for Innovation in WellTesting. We thank the management of Chevron PetroleumTechnology Company for permission to publish the paper andare grateful to Statoil, Chevron, and Shell for providing fielddata for this study.

References1. Unneland, T. and Haugland, T.: “Permanent Downhole Gauges

Used in Reservoir Management of Complex North Sea OilFields,” SPE Production and Facilities (August 1994) 195-203.

2. Nestlerode, W.A.: "The Use of Pressure Data from PermanentlyInstalled Bottom Hole Pressure Gauges," paper SPE 590presented at the Rocky Mountain Joint Regional Meeting,Denver, CO, May 27-28, 1963.


3. Gallivan, J.D., Kilvington, L.J., and Shere, A.J.: "ExperienceWith Permanent Bottomhole Pressure/Temperature Gauges in aNorth Sea Oil Field," paper SPE 13988 presented at the 1988SPE Annual Technical Conference and Exhibition, Oct. 8-11.

4. Shepherd, C.E., Neve, P. and Wilson, D.C.: "Use andApplication of Permanent Downhole Pressure Gauges in theBalmoral Field and Satellite Structures," SPE ProductionEngineering (August 1991) 6, No. 3, 271-276.

5. Baker, A., Gaskell, J., Jeffery, J., Thomas, A., Veneruso, T., andUnneland, T.: "Permanent Monitoring - Looking at LifetimeReservoir Dynamics," Oilfield Review (1995) 7, No. 4, 32-46.

6. Chalaturnyk, R. and Moffat, T.: "Permanent Instrumentation forProduction Optimization and Reservoir Management," paperSPE 30274 presented at the 1995 International Heavy OilSymposium, Calgary, Canada, June.

7. Kikani, K. and He, M.: “Multi-Resolution Analysis of PressureTransient Data Using Wavelet Methods,” paper SPE 48966presented at the 1998 SPE Annual Technical Conference andExhibition, October.

8. Unneland, T., Manin, Y. and Kuchuk, F: “Permanent GaugePressure and Rate Measurements for Reservoir Description andWell Monitoring: Field Cases,” paper SPE 38638 presented atthe 1997 Annual Technical Conference and Exhibition, SanAntonio, TX, October.

9. Panda, M.N., Mosher, C., and Chopra, A.K.: “Application ofWavelet Transforms to Reservoir Data Analysis and Scaling,”paper SPE 36516 presented at 1996 Annual TechnicalConference and Exhibition, Denver, CO, October.

10. Chu, L., Schatzinger, R.A. and Tham, M.K.: “Application ofWavelet Analysis to Upscaling of Rock Properties,” paper SPE36517 presented at 1996 Annual Technical Conference andExhibition, Denver, CO, October.

11. Moridis, G. J., Nikolaou, M. and You, Y.: “The Use of WaveletTransforms in the Solution of Two-Phase Flow Problems,” SPEJournal, (June 1996) 169-177.

12. Jansen, F.E. and Kelkar, M. G.: “Upscaling of ReservoirProperties Using Wavelets,” paper SPE 39495 presented at the1998 SPE India Oil and Gas Conference and Exhibition, NewDelhi, India, February.

13. Daubechies, I.: "Orthonormal Bases of Compactly SupportedWavelets," Com. on Pure and Appl. Math. (1988), 41, 909-996.

14. Mallat, S.: “A Theory for Multiresolution SignalDecomposition: The Wavelet Representation,” IEEE Trans.Pattern Analysis and Machine Intelligence (July 1989) 11, No.7, 674-693.

15. Holschneider, M., Kronland-Martinet, R., Morlet, J., andTchamitchian, P.: "A Real-Time Algorithm for Signal Analysiswith the Help of the Wavelet Transform," Wavelets, Time-Frequency Methods and Phase Space (1989), Springer-Verlag,Berlin, 289-297.

16. Shensa, M. J.: "The Discrete Wavelet Transform: Wedding theA Trous and Mallat Algorithms," IEEE Trans. on Sig.Processing (1992), 40, No. 10, 2464-2482.

17. Mallat, S. and Hwang, W. L.: “Singularity Detection andProcessing with Wavelets,” IEEE Trans. Infor. Theory (1992)38, No. 2, 617-643.

18. Mallat, S. and Zhong, S.: “Characterization of Signals fromMultiscale Edges,” IEEE Trans. Pattern Analysis and MachineIntelligence (July 1992) 14, No. 7, 710-732.

19. Gerritsen, M.: Designing an Efficient Solution Strategy for FluidFlows, PhD dissertation, Stanford University (December 1996).

20. Donoho, D.L. and Johnstone, I.M.: "Adapting to UnknownSmoothness Via Wavelet Shrinkage," J. of the Amer. Stat.Assoc. (1994), 90, No. 432, 1200-1224.

21. Donoho, D. L., Johnstone, I. M., Kerkyacharian, G., and Picard,D.: "Wavelet Shrinkage: Asymptopia?," J. of the Royal Stat.Soc., Series B (1995), 57, No. 2, 301-369.

22. Bard, Y.: Nonlinear Parameter Estimation, Academic Press Inc.Ltd., New York City (1974).

23. Horne, R.N.: “Advances in Computer-Aided Well TestInterpretation,” J. Pet. Tech. (July 1994) 595-606.

24. Rosa, A.J. and Horne, R.N.: “Automated Type-Curve Matchingin Well Test Analysis Using Laplace Space Determination ofParameter Gradients,” paper SPE 12131 presented at the 1983SPE Annual Technical Conference and Exhibition, SanFrancisco, CA, October.

25. Luo, W. and Billings, S. A.: "Adaptive Model Selection andEstimation for Nonlinear Systems Using A Sliding DataWindow," Signal Processing (1995), 46, 179-202.

TABLE 1 - COMPARISON BETWEEN EXACTPARAMETER VALUES AND THEIR ESTIMATESParameter True Value Initial Guess EstimatePermeability 100.00 50.00 100.98Skin 3.00 -3.00 3.09Storage 0.05 0.50 0.05re1 500.00 400.00 500.00re2 1000.00 900.00 1002.86q1 1000.00 known knownq2 1200.00 1300.00 1199.97q3 1100.00 1700.00 1099.96q4 800.00 known knownq5 1200.00 1400.00 1200.04q6 1100.00 1000.00 1099.99q7 500.00 700.00 499.81q8 900.00 known knownq9 1150.00 1000.00 1150.04q10 1100.00 1100.00 1100.00q11 1200.00 known knownq12 1000.00 700.00 1000.00q13 0.00 known known

TABLE 2 - CUMULATIVE PRODUCTIONHISTORY Time (hours) Cumulative Production (STB) 0 0.00 96 4275.00 192 8058.33 288 12091.66 384 16329.16 480 20812.49


TABLE 3 - COMPARISON BETWEEN EXACTPARAMETER VALUES AND THEIR ESTIMATESParameter True Value Initial Guess EstimatePermeability 100.00 50.00 100.91Skin 3.00 -3.00 3.08Storage 0.05 0.50 0.05re1 500.00 400.00 490.83re2 1000.00 900.00 1002.52q1 1000.00 800.00 1000.01q2 1200.00 1300.00 1199.97q3 1100.00 1700.00 1099.96q4 800.00 900.00 800.00q5 1200.00 1400.00 1200.01q6 1100.00 1000.00 1100.02q7 500.00 700.00 499.94q8 900.00 800.00 899.97q9 1150.00 1000.00 1150.02q10 1100.00 1300.00 1100.00q11 1200.00 1000.00 1200.01q12 1000.00 700.00 1000.00q13 0.00 0.00 0.10

TABLE 4 - ESTIMATES BEFORE AND AFTERBEHAVIORAL FILTERINGParameter True Value First Estimate Final EstimatePermeability 100.00 126.38 98.93Skin 3.00 5.14 2.91Storage 0.05 0.0555 0.0502re1 500.00 384.55 1028.67re2 1000.00 531.97 975.08

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Figure 1: Approximated signals from wavelet decomposition(after Mallat and Hwang17).

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Figure 2: signal details from wavelet decomposition (after Mallatand Hwang17).

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Figure 3: Wavelet modulus maxima (Mallat and Hwang17).

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aa

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c Outliera Acceptable

Figure 6: Results from the iterative outlier detection.

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a Noisy signalb Denoised signal

Figure 7: Denoising using the hard thresholding method.

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Figure 8: Denoising using the soft thresholding method.

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Figure 9: Difference between the denoised and original data usingthe hard thresholding method.

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Figure 10: Difference between the denoised and original datausing the soft thresholding method.


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Figure 11: Denoising using the hybrid thresholding method.

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Figure 12: Difference between the denoised and original datausing the hybrid thresholding method.

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Figure 13: Field example of data denoising using the hybridthresholding method.

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Figure 14: Transient identification using original data in waveletdecomposition.

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(ps

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Figure 15: Transient identification using denoised data in waveletdecomposition.

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Pres

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Figure 16: Field example of transient identification.


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a

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a aa a a

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aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaaaaaaaaaa a a a

Figure 17: Close-up view of transient identification.

4620

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4640

Pres

sure

(ps

ia)

4550 4560 4570 4580 4590 4600Time (hours)

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Figure 18: Data reduction using original data.

4620

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Pres

sure

(ps

ia)

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a a a a a a a a a a a aa a a a a a a a a a a a a a a

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Figure 19: Data reduction using denoised data.

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Figure 20: Simulated pressure response and flow history.

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Figure 21: Final regression match to pressure with aberranttransients.

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Figure 22: Estimates of reservoir parameters using free search space.

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Figure 23: Estimates of reservoir model parameters using limited search space.

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rror

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Figure 24: Comparison of errors from regression with free searchspace and regression with limited search space.

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Figure 25: Log-log plot of a transient in window 72.

Fre

quen

cy

Permeability (md)

0. 50. 100. 150. 200.

0.000

0.100

0.200

0.300

Number of Data 59

mean 63.18std. dev. 17.02

coef. of var 0.27

maximum 113.08upper quartile 67.71

median 60.45lower quartile 53.15

minimum 35.40

Fre

quen

cy

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-8.00 -7.00 -6.00 -5.00 -4.00 -3.00

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mean -5.92std. dev. 0.37

coef. of var undefined

maximum -4.98upper quartile -5.65

median -5.90lower quartile -6.16

minimum -6.98

Fre

quen

cy

Distance to the closer boundary

0. 200. 400. 600. 800. 1000.

0.000

0.050

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mean 427.80std. dev. 104.62

coef. of var 0.24



minimum 222.69

Fre

quen

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Number of Data 59

mean 3511.51std. dev. 1104.66

coef. of var 0.31



minimum 1308.30

Figure 26: Distribution of the estimates of reservoir model parameters using limited search space.

spe 56419 processing and interpretation of long-term data ... · the installation of permanent...

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