Interest in quantitative interpretation (QI) of seismic data in the Abu Dhabi region continues to steadily increase, and the objective of creating inversion-ready seismic data is driving evolution of the surface seismic data processing workflows to focus on more detailed and thorough handling of the amplitude and phase throughout processing (pre-, during, and post-imaging). To achieve close well ties across the survey and to ensure the data is suitable for interpretation purposes, zero-phasing and wavelet stability (along with using well information during earth model building) are key stages in the depth imaging seismic processing workflow. Accurate amplitude with offset and azimuth handling is also required for inversion studies. In this paper, we propose a workflow where a geophysically and geologically credible, 3D variable Q-field is built into the earth model early in the processing flow, allowing a more complete approach to handling the Q-effects of the subsurface without increasing project turnaround time. This case study shows that a data-driven spatially variable Q-field combined with Kirchhoff Pre-Stack Depth migration compensates effectively for both amplitude and phase effects, providing a broadband image with improved event continuity and better handling of noise compared with applying a constant pre-migration Q-compensation (which was previously thought to be suitable for this low-relief region). By calibrating the variable Q-field to available well logs and near surface information, and ensuring that the different geophysical parameters in the earth model are all suitably coupled, an enhanced image is achieved which then requires minimal spectral shaping or residual phase corrections post migration. Ray-based Q-tomography workflows allow iterative 3D updates alongside coupled subsurface properties like anisotropy and velocity, within a high-resolution Earth model suitable for depth imaging. Reliable phase stability, higher resolution, broader useable bandwidth and improved amplitude preservation are key targets of this holistic approach.
Decline curve analysis is widely used in industry to perform production forecasting and to estimate reserves volumes. A useful technique in verifying the validity of a decline model is to estimate the Arps decline parameters, the loss ratio and the b-factor, with respect to time. This is used to check the model fit and to determine the flow regimes under which the reservoir produces. Existing methods to estimate the b-factor are heavily impacted by noise in production data. In this work, we introduce a new method to estimate the Arps decline parameters.
We treat the loss ratio and the b-factor over time as parameters to be estimated in a Bayesian framework. We include prior information on the parameters in the model. This serves to regularize the solution and prevent noise in the data from being amplified. We then fit the parameters to the model using Markov chain Monte Carlo methods to obtain probability distributions of the parameters. These distributions characterize the uncertainty in the parameters being estimated. We then compare our method with existing methods using simulated and field data.
We show that our method produces smooth loss ratio and b-factor estimates over time. Estimates using the three-point derivative method are not matched with data, and results in biased estimates of the Arps parameters. This can lead to misleading fits in decline curve analysis and unreliable estimates of reserves. We show that our technique helps in identification of end of linear flow and start of boundary dominated flow. We use our method on simulated data, with and without noise. Finally, we demonstrate the validity of our method on field cases.
Fitting a decline curve using the loss ratio and b-factor plots is a powerful technique that can highlight important features in the data and the possible points of failure of a model. Calculating these plots using the Bourdet three-point derivative induces bias and magnifies noise. Our analysis ensures that this estimation is robust and repeatable by adding prior information on the parameters to the model and by calibrating the estimates to the data.
Horizontal wells with hydraulic fractures enable economical hydrocarbon extraction from unconventional reservoirs, and the associated transient production data is a reliable source for reservoir characterization. However, the complicated convolution of rate-pressure-time history leads to a less informative analysis of true reservoir characteristics. This paper presents a novel data-driven deconvolution approach using physics-based superposition to reconstruct constant-rate-drawdown pressure responses, which are further translated into diagnostic plots for efficient production analysis.
Traditional deconvolution in pressure transient analysis is usually an ill-conditioned "inverse" process that requires systematic curve-fitting, and the deconvolution response is highly sensitive to noise. Our proposed approach uses superposition equations as training features to honor the transient physics, and further projects them into higher dimensional ‘reservoir’ space (kernel-space) for the purpose of rigorous regression. Additionally, by implementing Laplacian eigenmaps, our algorithm is relatively insensitive to noise owing to its locality-preserving character. After training, the constant-rate-drawdown pressure response is reconstructed and a diagnostic plot is generated to identify key reservoir characteristics such as flow regimes.
We first validated our approach with two synthetic cases, a horizontal well with single and multiple transverse fractures (MTFW), and the drawdown pressure responses were obtained through simulation using a highly variable flow rate history. Additionally, we added artificial white Gaussian noise to the simulation output to mimic measured signals collected in the field, and we input this data into our model for deconvolution. The model-reconstructed constant-rate-drawdown pressure responses were used to determine flow regimes and reservoir properties such as permeability and stimulated reservoir volume (SRV) using traditional transient testing diagnostic tools and specialized plots. The deconvolved responses for each case were in alignment with the fractured-basement reservoir model proposed by
This study showed that our proposed methodology is a reliable diagnostic tool to interpret pressure-rate data using traditional pressure transient analysis for unconventional reservoirs. Rapid and accurate deconvolved pressure responses greatly enhance the analysis of data with moderate noise and highly variable production histories, enabling engineers to recognize flow patterns and estimate reservoir properties. We demonstrated the versatility and applicability of our proposed approach with synthetic and field cases.
This paper uses pseudo-time to extend the application of constrained multiwell deconvolution algorithm to gas reservoirs with significant pressure depletion. Multiwell deconvolution is the extension of single well deconvolution to multiple interfering wells. Constraints are added to account for a-priori knowledge on the expected deconvolved derivative behaviors and to eliminate non-physical solutions.
Multiwell deconvolution converts pressure and rate histories from interfering wells into constant-rate pressure responses for each well as if it were producing alone in the reservoir. It also extracts the interference responses observed at each of the other wells due to this single well production. The deconvolved responses have the same duration as the pressure history. This allows to identify reservoir features not visible during individual build ups.
Deconvolution techniques can only be applied to pressure and rate data when flow can be represented by linear equations. In strongly depleted gas reservoirs, fluid properties, and gas compressibility in particular, are pressure dependent, which makes the flow problem non-linear. The paper uses pseudo-pressure and pseudo-time transforms to linearize the problem in such conditions.
The pseudo-time method developed by
The paper extends the application of constrained multiwell deconvolution to strongly depleted gas reservoirs. Constrained multiwell deconvolution is an efficient way to exploit data recorded by permanent downhole pressure gauges and provides information not otherwise available. It can help to identify field heterogeneities and compartmentalization early in field life, making it possible to modify the field development plan and to improve locations of future wells. It can accelerate history-matching with the reservoir model by doing it on the constant rate pressure responses rather than on the actual, usually complex, production history. An added advantage is that comparison between the pressure derivatives of the model and the actual deconvolved derivatives allows identification of mismatch causes.
Content of PetroWiki is intended for personal use only and to supplement, not replace, engineering judgment. SPE disclaims any and all liability for your use of such content. In a seismic context, deconvolution is an automated profile-based depth estimation method derived from analysis of magnetic anomalies in sheet-like bodies. Polynomials can be simultaneously solved to estimate the depth, dip, horizontal location and susceptibility (magnetic) of the surface or structure.
Tamar is a high permeability clastic gas reservoir that behaves like a well-connected tank, in many respects. At the same time, it has a significant level of complexity. The reservoir is comprised of three sand intervals, which are separated vertically by shales and broken into a number of fault blocks. While the degree of aquifer support has been an uncertainty, it is believed that the field demonstrates components of both bottom water and edge water drive. All Tamar wells were equipped with permanent downhole pressure and temperature gauges, and the surveillance of these pressure and rate data over the five-year production history has provided an unusually comprehensive data set.
Rate and pressure transient analysis is considered a routine process that has been developed and refined over many years. The underlying assumptions of linearity justify the use of superposition (in time and space), convolution and deconvolution. The reality of non-linearities are handled on a case by case basis depending on their source (fluid, well or reservoir). Shale gas wells are subject to significant non-linearity over their producing life.
We review some of the fundamental equations that govern pressure and rate transient behavior, introduce several new techniques which are suited to the analysis of data from producing wells and apply them to a synthetic example of a shale gas well.
First, we use simple calculus to show how the convolution integral is derived from standard multi-rate superposition. Then, from the convolution integral, we derive an equation that describes the pressure response due to a step-ramp rate (i.e. an instantaneous rate change from initial conditions followed by a linear variation in rate). It results in a combination of the pressure change due to a constant rate and it's integral. Applying superposition to this equation allows any rate variation to be approximated by a sequence of ramps with far fewer points than those required to achieve the same level of accuracy using standard constant step rate superposition.
Second, we re-write multi-rate superposition functions allowing for stepwise linear variable rate which, when applied to flowing data and used to calculate the pressure derivative, can result in a much smoother response and hence an overall improvement in the analysis of rate and pressure transients recorded from producing wells.
Third, we review the use of the Laplace transform and how it can be applied to discrete data with a view to deconvolving rate transient data.
Finally, we demonstrate how data de-trending can remove the impact of long term non-linearities and apply the methods mentioned above to a synthetic dataset based on a typical shale gas well production profile.
We illustrate the advantages of the newly introduced superposition functions compared to conventional analysis methods when applied to the pressure transients of wells flowing at variable rate.
As an example, we have simulated the production of two shale gas wells over twenty years. Both have the same production profile, but one includes pressure dependent permeability. At various intervals during the life of the well, we introduce a relatively short well test which imposes a small variation in rate but does not include a shut-in. We de-trend the rate transients and then apply the techniques described above to analyse the resulting data. The interpretation allows us to identify non-linearities that may be influencing well productivity over time and to obtain a better understanding of the physics of shale gas production.
The mathematics documented in the paper provides a useful overview of how convolution, superposition, deconvolution and Laplace transforms provide the means to analyse pressure and rate transients for linear systems.
Data de-trending removes the impact of long term non-linearities on shorter transient test periods.
We develop and demonstrate some new and improved techniques for rate and pressure transient analysis, and we illustrate how these can provide insight into the non-linearities affecting shale gas production.
This paper applies a new constrained multiwell deconvolution algorithm to two field cases: a gas reservoir with two producers, and an oil reservoir with three producers and one injector. Responses given by the constrained multiwell deconvolution are compared with simulations from history-matched reservoir models.
Permanent downhole pressure gauges are routinely installed in most new wells. The resulting large datasets are usually underexploited, however, because it is near impossible to extract information with conventional techniques in the case of well interferences. Multiwell deconvolution (
The published multiwell deconvolution algorithms are extensions of the single-well deconvolution algorithm from von Schroeter
By extracting well and interwell reservoir signatures, multiwell deconvolution allow identification of compartmentalization or unanticipated heterogeneities very early in field life, making it possible to adjust the field development plan and the locations of future wells. In addition, it can accelerate the history-matching process by doing it on constant rate pressure responses rather than on complex production histories. An added advantage is that the comparison between the model derivatives and the actual deconvolved derivatives enables identification of mismatch causes.
Aslanyan, Artur (Nafta College) | Grishko, Fedor (Salym Petroleum Development N.V.) | Krichevsky, Vladimir (Sofoil) | Gulyaev, Danila (Sofoil) | Panarina, Ekaterina (Sofoil) | Buyanov, Anton (Polykod)
A waterflood study has been performed on a heterogeneous oil deposit with a rising water-cut and production decline after 10 years of commercial production.
Aslanyan, Artur (Nafta College) | Asmadiyarov, Rustam (Gazpromneft STC) | Kaeshkov, Ilya (Gazpromneft STC) | Bikkulov, Marsel (Gazpromneft Khantos) | Farakhova, Rushana (Sofoil) | Krichevsky, Vladimir (Sofoil) | Gulyaev, Danila (Sofoil) | Musaleev, Kharis (Polykod)
A sandstone formation is showing accelerated production decline during the fully compensated waterflood development. The sporadic well tests suggested that liquid rate was following the nonuniform formation pressure decline, despite the full compensation of the offtakes. The paper presents a multiwell downhole pressure gauge deconvolution technique and associated study on the reasons of nonuniform area formation pressure decline and nonuniform injection water front propagation and resulted in recommendations which proved their efficiency after implementation.