1,721,100 research outputs found
Using well log data and statistical Gaussian simulations to estimate the crack density value within a geothermal reservoir located in fractured hard rocks
No full textTo identify the most promising targets when exploring fractured geothermal reservoirs it is crucial to infer the crack density value (the fracture density per volume) in the subsurface. In this work we use statistical simulations to estimate the crack density value within fractured portions of the Larderello–Travale area where deep intrusive/metamorphic rocks constitute the main drilling targets of geothermal exploration. Waveform sonic recording and circumferential borehole imager log acquired in the investigated area, evidence the presence of several vertically aligned fractures with a preferential orientation NNW-SSE at the depth of the productive levels, whereas the encasing rocks appear to be quite isotropic. This characteristic allows us to approximate the target level as a transverse isotropic medium with a horizontal axis of symmetry (HTI medium). Then, basing on the well data and by using a statistical technique, we develop several models that keep the encasing medium and the strike of the fractures within the target constant, but change the crack density from 0 (no fractures) to 0.1 (highly fractured).
More specifically, in our approach the statistical characteristics (covariance matrix, and autocorrelations) derived on velocity logs in the tight rock are supposed to be stationary and equal to those in the fractured interval. These statistical properties will serve us to generate mutually and vertically coupled velocities within the target interval in the following statistical simulation. The average P-wave, S-wave velocity and density values computed from the logs in the tight encasing rock are used to derive the average Lamé parameters of the isotropic rock. Then, by assuming a given value for the crack density in the target, fractured, level we compute the associated elasticity tensor following Aleardi et al. (2015). This elasticity tensor is used to derive the average Thomsen anisotropic parameters and the average P-wave and S-wave velocities for the simulated HTI fractured zone. Finally, these average velocities values, together with the autocorrelation and the covariance matrix previously computed are used to perform a statistical simulation, in which, by assuming Gaussian distributed properties we generate vertically and mutually correlated P-wave, S-wave velocities for the fractured zone for each given crack density value. After each simulation the match between the simulated P-wave and S-wave velocities with the actual logs in the fractured interval is used to determine the most likely crack density. The proposed methodology applied to different wells returns plausible results for the crack density value and together with reflection seismic observations may bring to predict fracture orientation and density
The importance of the Vp/Vs ratio in determining the error propagation, the stability and the resolution of linear AVA inversion: A theoretical demonstration
Full text linkThe linear Amplitude-Versus-Angle (AVA) inversion has become a standard tool in deep-sediments hydrocarbon exploration since its introduction in the oil and gas industry. However, in the last decades, with the increase of offshore construction activity, applications of this method have been also extended to predict overpressured zones and/or to evaluate the geotechnical properties of shallow sea bottom layers. Among the input parameters requested by linear AVA inversion there is the background Vp/Vs ratio across the reflecting interface and a Vp/Vs ratio of two is frequently assumed. This value is usually very close to the true ratio in case of deep, compacted sediments but it can be a gross underestimation of the true value in case of shallow or overpressured sediments. Despite that, the importance of the background Vp/Vs ratio in AVA inversion is frequently underrated and thus I consider two frequently used approximations of the Zoeppritz equations to study their impact on the outcomes of linear AVA inversion: the three-term Aki and Richards equation and the two-term Ursenbach and Stewart formula. These equations are then analysed, varying the Vp/Vs value, using tools frequently applied in sensitivity analysis. It turns out that the background Vp/Vs ratio controls the error propagation from data to model space and determines the cross-talk between the inverted parameters. Moreover, an increasing Vp/Vs ratio causes a decrease of stability of the AVA inversion and worsens the estimate of the Vs contrast at the reflecting interface
Seismic velocity estimation from well log data with genetic algorithms in comparison to neural networks and multilinear approaches
Full text linkPredicting missing log data is a useful capability for geophysicists. Geophysical measurements in boreholes are frequently affected by gaps in the recording of one or more logs. In particular, sonic and shear sonic logs are often recorded over limited intervals along the well path, but the information these logs contain is crucial for many geophysical applications. Estimating missing log intervals from a set of recorded logs is therefore of great interest. In this work, I propose to estimate the data in missing parts of velocity logs using a genetic algorithm (GA) optimisation and I demonstrate that this method is capable of extracting linear or exponential relations that link the velocity to other available logs. The technique was tested on different sets of logs (gamma ray, resistivity, density, neutron, sonic and shear sonic) from three wells drilled in different geological settings and through different lithologies (sedimentary and intrusive rocks). The effectiveness of this methodology is demonstrated by a series of blind tests and by evaluating the correlation coefficients between the true versus predicted velocity values. The combination of GA optimisation with a Gibbs sampler (GS) and subsequent Monte Carlo simulations allows the uncertainties in the final predicted velocities to be reliably quantified. The GA method is also compared with the neural networks (NN) approach and classical multilinear regression. The comparisons show that the GA, NN and multilinear methods provide velocity estimates with the same predictive capability when the relation between the input logs and the seismic velocity is approximately linear. The GA and NN approaches are more robust when the relations are non-linear. However, in all cases, the main advantages of the GA optimisation procedure over the NN approach is that it directly provides an interpretable and simple equation that relates the input and predicted logs. Moreover, the GA method is not affected by the disadvantages that characterise gradient descent techniques such as the NN method
Progetto Overpressure: report 2014
No full textQuest'anno l'attività di ricerca sul progetto overpressure ha riguardato essenzialmente lo sviluppo di un metodo per l'individuazione di livelli in sovrappressione tramite l'analisi di diversi campi di velocità derivati in fase di elaborazione del dato sismico. L'esempio che seguirà riguarda il dato sismico nelle immediate vicinanze del pozzo XX2.
La fase iniziale del lavoro si è concentrata sul dato sismico, sul quale sono state applicate una serie di operazioni di elaborazione finalizzate all’ottenimento di un campo di velocità ottimale ai fini della stima della pressione. Il dato sismico fornitoci riguardava essenzialmente 21 In-Line e Cross-Line ritagliate dal più ampio volume 3D e centrate rispetto alla posizione del pozzo. In questa prima fase l’attenzione, quindi, si è orientata su quelle operazioni che permettono di ricavare il campo di velocità, quali l’analisi di velocità e la migrazione. L’analisi di velocità è stata effettuata, oltre che con l’algoritmo standard della Semblance, con altre tecniche che producono una maggiore risoluzione nel calcolo delle misure di coerenza, quali il Complex Matched Filter [Spagnolini et al, 1993] e l’algoritmo Eigenstructure [Key e Smithson, 1990]. Queste funzioni di velocità sono state affiancate da quella ottenuta con la tecnica della migrazione pre stack in profondità (PSDM), una delle metodologie più affidabili nel fornire un profilo di velocità che si avvicina a quello reale del sottosuolo (condizione fondamentale per una stima affidabile della pressione).
La fase successiva del lavoro ha riguardato la stima della pressione nel sottosuolo, in corrispondenza della posizione del pozzo, a partire dalle velocità sismiche ottenute dall’elaborazione del dato. Questo compito è stato affrontato supponendo di non avere alcuna informazione geologica dell’area circostante, e si è cercato di valutare la pore pressure esclusivamente dalle velocità sismiche. A tal fine, è stata scelta una strada che prevede il confronto tra le velocità così ricavate e un trend normale di velocità, costruito tramite relazioni empiriche, che rappresenta quella velocità che si avrebbe in condizioni di pressione normale. Gli eventuali discostamenti della velocità sismica da questo trend normale sono considerati indice della presenza di sovrapressione. In particolare, si è scelto di calcolare il trend normale tramite due diverse formule, quella di Bowers [Bowers, 1995] e quella di Miller [Miller, 2002], con lo scopo di confrontarle e valutarne le differenze; i discostamenti tra le velocità sismiche ed i trend costruiti, invece, sono stati trasformati in pressione tramite la formula di Eaton [Eaton, 1975], utilizzando diversi valori per l’esponente caratteristico di tale formula. La valutazione del valore più adatto per l’esponente è stata effettuata confrontando le curve di pressione con le misure puntuali di pressione in pozzo. Tutte le operazioni descritte in precedenza verranno discusse nei capitoli 2 e 3.
Parallelamente a questa attività sono stati sviluppati 2 codici di inversione sismica. Il primo è un codice di inversione della risposta AVA del fondale al fine di ricavarne le proprietà elastiche. Il secondo è un codice parallelo di inversione FWI elastica 1D. Di questi codici verranno forniti assieme al presente rapporto i due tutorial a cui si rimanda per più dettagliate informazioni sulla loro struttura e sul loro utilizzo. Tali codici, ed i rispettivi tutorial, sono già stati consegnati ad ENI e sperimentati nei laboratori ENI il giorno 4 Dicembre 2014
The limits of narrow and wide-angle AVA inversions for high Vp/Vs ratios: An application to elastic seabed characterization
Full text linkSince its introduction in the oil and gas industry, amplitude versus angle (AVA) inversion has become a standard tool in deep hydrocarbon exploration. However, with the intensification of offshore construction activity, applications of this method have been extended to evaluate the elastic properties of seabed sediments and of the shallowest part of the subsurface. These regions are often characterized by undercompacted sediments with very low S-wave velocities (Vs) and high P-wave velocity to S-wave velocity (Vp/Vs) ratios. However, the importance of the Vp/Vs ratio is usually underrated in AVA inversion. In this study, we analyse the limits of the AVA method in cases of high Vp/Vs ratios and the benefits introduced by wide-angle reflections in constraining the inversion results. A simplified seabed model that is characterized by a high Vp/Vs ratio is used to study the influence of the elastic and viscoelastic parameters on the P-wave reflection coefficients and to compute the error function of the AVA inversion. In addition, a synthetic AVA inversion is performed on this simplified model, which enables us to apply the sensitivity analysis tools to the inversion kernel. These theoretical analyses show that in the case of high Vp/Vs ratios, the Vs contrast at the reflecting interface plays a very minor role in determining the P-wave reflection coefficients and that the viscoelastic effects can be neglected when only pre-critical angles are considered in the inversion. In addition, wide-angle reflections are essential to reducing both the cross-talk between the inverted elastic parameters and the uncertainties in the Vp and density estimations, but they are not sufficient to better constrain the Vs estimation. As an application to field data, we derive the elastic properties of the seabed interface by applying AVA inversion to a 2D seismic dataset from a well-site survey acquisition. The limited water depth, the maximum available source-to-receiver offset, and the high frequency content of the data allow two different ranges of incidence angles to be considered: 0-30° and 0-60°. The results of the field data inversion confirm the conclusions from the theoretical analysis
Progetto Overpressure e Caratterizzazione Fondale Marino - report 2013
No full textNel presente report verranno discusse in dettaglio le attività svolte nell'anno 2013 dall'Università di Pisa nell'ambito dei progetti ENI sull'individuazione di zone in sovrappressione e sulla caratterizzazione del fondale marino.
Data la relativa indipendenza degli argomenti trattati il report verrà diviso in due arti distinte: la prima riguardante il progetto sulla caratterizzazione fondale marino, la seconda rivolta invece al progetto sovrappressioni.
Per quanto riguarda quest'ultimo durante l'anno 2013 si sono ulteriormente sviluppati alcuni argomenti già affrontati nell'anno precedente oltre ad introdurre nuove tematiche di ricerca che, in parte, sono state testate anche su dati reali.
Come è noto una sovrappressione può presentarsi o come brusco salto da una condizione idrostatica ad una in sovrappressione (da noi per brevità chiamato gradino di pressione) o come un aumento graduale della pressione dei pori rispetto alla pressione idrostatica (brevemente chiamato in seguito gradiente di pressione). Tali diversità avevano già distinto il nostro lavoro dell'anno 2012. Nell'ambito della prima casistica era stata sviluppata un'inversione non lineare AVA petrofisica che permettesse una stima della pressione effettiva. Purtroppo per la mancanza di dati opportuni tale metodo attende ancora di essere testato su dati reali. Per quanto concerne il gradiente di pressione nello scorso anno si erano sviluppati una serie di modelli di rockphysics che potessero spiegare delle anomalie di velocità P riscontrate in log reali acquisiti in un area dove si registrava un aumento progressivo della pressione del fluido interstiziale. Tali modelli portavano alla conclusione che almeno dal punto di vista teorico tali anomalie potessero influenzare la pendenza del background trend dell'AVA. Nel corso del 2013 è stata approfondita questa tematica con test su alcuni dati analitici e sintetici. Infine l'analisi del dato sismico 3D estratto attorno al pozzo Oberan2 è stata ostacolata da problemi riscontrati durante l'analisi dello stesso.
Nuovi temi di ricerca sono stati introdotti per quanto riguarda la tematica del gradino di pressione. Innanzi tutto è stato testato un nuovo attributo AVA che potenzialmente è in grado di evidenziare anomalie di pressione. L'efficacia di tale attributo è stato validata sia su dati sintetici che reali. Inoltre si sono messi in luce i problemi connessi con l'individuazione di zone in sovrappressione confinate servendosi unicamente di un inversione AVA lineare. A tal fine è stato sviluppato un codice di Full-Waveform Inversion (FWI) elastica 1D che, utilizzano l'intera informazione di ampiezza e fase contenuta nel dato, offre una stima più affidabile delle proprietà elastiche del sottosuolo.
La tematica fondale marino ha ovviamente tratto beneficio da alcune metodologie sviluppate parallelamente nell'ambito del progetto overpressure. In questo caso si sono pertanto analizzate le potenzialità dell'inversione AVA lineare, AVA linearizzata con Gauss-Newton, AVA+PVA long-offset e FWI elastica. In aggiunta sono state evidenziate le potenzialità, ma soprattutto i limiti, di una caratterizzazione del fondale mediante il metodo di sismica a rifrazione
The importance of the Vp/Vs ratio in determining the error propagation and the resolution in linear AVA inversion
No full textThe Amplitude-Versus-Angle (AVA) method exploits the variation in seismic reflection amplitude with increasing incidence angle to infer the contrast in seismic velocities and densities at the reflecting interfaces (Castagna, 1998). For this characteristic the AVA technique has been extensively used worldwide for lithology and fluid prediction in deep hydrocarbon exploration (e.g., Ostrander, 1984; Rutherford and Williams, 1989; Mazzotti, 1990; Mazzotti, 1991).
The AVA method is based on the Zoeppritz equations (Zoeppritz, 1919) which describe the variation in seismic amplitude with increasing angle of incidence for a plane wave incident on an idealized interface separating two semi-infinite half spaces. The system of equation formulated by Zoeppritz is so algebraically complex that many different approximated formulas have been derived to simplify and linearise the inversion process. These simplified equations, valid under certain assumptions, are those frequently used in AVA inversion and interpretation (Ursenbach and Stewart, 2008; Wang, 1999).
Performing linear AVA inversion a Vp/Vs ratio equal to two is usually assumed (Castagna, 1998). This ratio is a good approximation of the true value in case of classical deep sediments exploration (hydrocarbon exploration), but generally it is an underestimation of the true ratio in case of shallow or seabed sediments. This may constitute a problem because, in addition to the classical deep exploration, the AVA inversion can also be useful for characterizing shallow layers (Riedel and Theilen, 2001) and, thus can be of help for shallow hazard assessment and well site analysis.
While performing linear AVA inversion the importance of the Vp/Vs ratio is usually underrated and its value is set without worrying too much. Therefore, in this work we want to point out that the assumed Vp/Vs ratio plays a crucial role in determining the expected resolution and the uncertainties associated with each inverted parameter. To this end we have considered the well known three terms Aki and Richards (Aki and Richards, 1980) equation and the two terms Ursenbach and Stewart formula (Ursenbach and Stewart, 2008), which are analyzed making use of the sensitivity analysis tools applied to the inversion kernel. We have first studied how the Vp/Vs value influences the condition number, the amplitude of the eigenvalues (not shown here for the lack of space) and the orientation of associated eigenvectors in model space. Moreover, also applying the classical truncated SVD method and studying the resolution and the covariance matrices, we have analyzed how the Vp/Vs ratio determines both the expected resolution of each inverted parameter and the error propagation from data space to model space
Using well log data and statistical Gaussian simulations to estimate the crack density value within a geothermal reservoir located in hard rocks
No full textTo identify the most promising targets when exploring geothermal reservoirs it is crucial to infer the crack density value (the fracture density per volume) in the subsurface. In this work a geophysical forward modeling approach and statistical techniques were used to estimate the crack density within the deepest geothermal reservoir of the Larderello-Travale field where fractured intrusive/metamorphic rocks constitute the main drilling targets of geothermal exploration. Waveform sonic recording and circumferential borehole imager log, acquired in the investigated area, evidenced the presence of several vertically aligned fractures with a preferential orientation NNW-SSE at the depth of the productive levels, whereas the encasing rocks appeared to be quite isotropic. This characteristic permitted to approximate the target level as a transverse isotropic medium with a horizontal axis of symmetry (HTI medium). Then, basing on borehole data, several models were developed that keep the encasing medium and the strike of the fractures within the target constant, but change the crack density from 0 (no fractures) to 0.1 (highly fractured). For each given crack density value, the associated P-wave and S-wave velocity values within the fractured zone were derived. Then, comparing the probability distribution of the simulated velocities with the logged velocities it was possible to estimate the most likely crack density value. The proposed methodology applied to two wells returned plausible and similar results for the crack density valu
Applying a probabilistic seismic-petrophysical inversion and two different rock-physics models for reservoir characterization in offshore Nile Delta
No full textWe apply a two-step probabilistic seismic-petrophysical inversion for the characterization of a clastic, gas-saturated, reservoir located in offshore Nile Delta. In particular, we discuss and compare the results obtained when two different rock-physics models (RPMs) are employed in the inversion. The first RPM is an empirical, linear model directly derived from the available well log data by means of an optimization procedure. The second RPM is a theoretical, non-linear model based on the Hertz-Mindlin contact theory. The first step of the inversion procedure is a Bayesian linearized amplitude versus angle (AVA) inversion in which the elastic properties, and the associated uncertainties, are inferred from pre-stack seismic data. The estimated elastic properties constitute the input to the second step that is a probabilistic petrophysical inversion in which we account for the noise contaminating the recorded seismic data and the uncertainties affecting both the derived rock-physics models and the estimated elastic parameters. In particular, a Gaussian mixture a-priori distribution is used to properly take into account the facies-dependent behavior of petrophysical properties, related to the different fluid and rock properties of the different litho-fluid classes. In the synthetic and in the field data tests, the very minor differences between the results obtained by employing the two RPMs, and the good match between the estimated properties and well log information, confirm the applicability of the inversion approach and the suitability of the two different RPMs for reservoir characterization in the investigated area
Analysis of Different Statistical Models in Probabilistic Joint Estimation of Porosity and Litho-Fluid Facies from Acoustic Impedance Values
Full text linkWe discuss the influence of different statistical models in the prediction of porosity and
litho-fluid facies from logged and inverted acoustic impedance (Ip) values. We compare the inversion
and classification results that were obtained under three different statistical a-priori assumptions: an
analytical Gaussian distribution, an analytical Gaussian-mixture model, and a non-parametric mixtu
re distribution. The first model assumes Gaussian distributed porosity and Ip values, thus neglecting
their facies-dependent behaviour related to different lithologic and saturation conditions. Differently,
the other two statistical models relate each component of the mixture to a specific litho-fluid facies,
so that the facies-dependency of porosity and Ip values is taken into account. Blind well tests are
used to validate the final predictions, whereas the analysis of the maximum-a-posteriori (MAP)
solutions, the coverage ratio, and the contingency analysis tools are used to quantitatively compare
the inversion outcomes. This work points out that the correct choice of the statistical petrophysical
model could be crucial in reservoir characterization studies. Indeed, for the investigated zone, it turns
out that the simple Gaussian model constitutes an oversimplified assumption, while the two mixture
models provide more accurate estimates, although the non-parametric one yields slightly superior
predictions with respect to the Gaussian-mixture assumption
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