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**File Type**

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.

Artificial Intelligence, compressibility, constraint, deconvolution, Drillstem Testing, drillstem/well testing, Exhibition, gas reservoir, Gringarten, interference, material balance pseudo-time, multiwell deconvolution, reservoir, reservoir pressure, significant pressure depletion, society of petroleum engineers, spe annual technical conference, Upstream Oil & Gas

SPE Disciplines: Reservoir Description and Dynamics > Formation Evaluation & Management > Drillstem/well testing (1.00)

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.

algorithm, Artificial Intelligence, constant rate, constraint, deconvolution, deconvolved derivative, Drillstem Testing, drillstem/well testing, Gringarten, History, initial pressure, interference, multiwell, multiwell deconvolution, multiwell deconvolution algorithm, pressure match, reservoir, Simulation, simulation model, society of petroleum engineers, spe annual technical conference, Upstream Oil & Gas

SPE Disciplines: Reservoir Description and Dynamics > Formation Evaluation & Management > Drillstem/well testing (1.00)

Nandi Formentin, Helena (Durham University and University of Campinas) | Vernon, Ian (Durham University) | Avansi, Guilherme Daniel (University of Campinas) | Caiado, Camila (Durham University) | Maschio, Célio (University of Campinas) | Goldstein, Michael (Durham University) | Schiozer, Denis José (University of Campinas)

Reservoir simulation models incorporate physical laws and reservoir characteristics. They represent our understanding of sub-surface structures based on the available information. Emulators are statistical representations of simulation models, offering fast evaluations of a sufficiently large number of reservoir scenarios, to enable a full uncertainty analysis. Bayesian History Matching (BHM) aims to find the range of reservoir scenarios that are consistent with the historical data, in order to provide comprehensive evaluation of reservoir performance and consistent, unbiased predictions incorporating realistic levels of uncertainty, required for full asset management. We describe a systematic approach for uncertainty quantification that combines reservoir simulation and emulation techniques within a coherent Bayesian framework for uncertainty quantification.

Our systematic procedure is an alternative and more rigorous tool for reservoir studies dealing with probabilistic uncertainty reduction. It comprises the design of sets of simulation scenarios to facilitate the construction of emulators, capable of accurately mimicking the simulator with known levels of uncertainty. Emulators can be used to accelerate the steps requiring large numbers of evaluations of the input space in order to be valid from a statistical perspective. Via implausibility measures, we compare emulated outputs with historical data incorporating major process uncertainties. Then, we iteratively identify regions of input parameter space unlikely to provide acceptable matches, performing more runs and reconstructing more accurate emulators at each wave, an approach that benefits from several efficiency improvements. We provide a workflow covering each stage of this procedure.

The procedure was applied to reduce uncertainty in a complex reservoir case study with 25 injection and production wells. The case study contains 26 uncertain attributes representing petrophysical, rock-fluid and fluid properties. We selected phases of evaluation considering specific events during the reservoir management, improving the efficiency of simulation resources use. We identified and addressed data patterns untracked in previous studies: simulator targets, ^{−11}%). The systematic procedure showed that uncertainty reduction using iterative Bayesian History Matching has the potential to be used in a large class of reservoir studies with a high number of uncertain parameters.

We advance the applicability of Bayesian History Matching for reservoir studies with four deliveries: (a) a general workflow for systematic BHM, (b) the use of phases to progressively evaluate the historical data; and (c) the integration of two-class emulators in the BHM formulation. Finally, we demonstrate the internal discrepancy as a source of error in the reservoir model.

application, Artificial Intelligence, Bayesian, calibration, discrepancy, emulator, evaluation, historical data, implausibility, implausibility measure, information, Information Index, machine learning, procedure, quantity, reservoir simulation, Scenario, search space, simulator, uncertainty reduction, Upstream Oil & Gas

SPE Disciplines:

Technology: Information Technology > Artificial Intelligence > Machine Learning > Statistical Learning (1.00)

Sanford, Oliver G. (Durham University) | Hobbs, Richard W. (Durham University) | Schofield, Nick (University of Aberdeen) | Brown, Richard J. (Durham University)

Summary Sub-sill seismic imaging is a current exploration challenge, ranging from detection to the impact on deeper imaging. Limited studies have been undertaken as to understand these issues. Here we present new results using constrained models of intrusions and full-waveform seismic modelling techniques to better understand the wave propagation processes, specifically focusing on the causes of reduced imaging. A significant amount of primary energy is lost to refractions, conversions and interbed multiples, however, unlike extrusive basalt, scattering and the associated rapid attenuation of all but the lowest frequency signal is not the significant problem. Introduction Hydrocarbon exploration is increasingly focused on regions containing extensive igneous intrusion (sill/dyke) complexes (e.g.

amplitude, annual meeting 10, conversion, exploration, finite difference, Imaging, international exposition, intrusion, reflection, Reservoir Characterization, Schofield, sediment, seg seg international, seismic data, seismic imaging, sill, sill complex, University, Upstream Oil & Gas, wave propagation

SPE Disciplines: Reservoir Description and Dynamics > Reservoir Characterization > Seismic processing and interpretation (1.00)

Ferreira, Carla J. (Unicamp) | Davolio, Alessandra (Unicamp) | Schiozer, Denis J. (Unicamp) | Vernon, Ian (Durham University) | Goldstein, Michael (Durham University)

In petroleum engineering, simulation models are used in reservoir performance prediction and in the decision-making process. These models are complex systems, typically characterized by a vast number of input parameters. Typically, the physical state of the reservoir is highly uncertain and, thus, the appropriate parameters of the input choices are also highly uncertain. 4D seismic data can reduce significantly the uncertainty of the reservoir because it has a high area resolution, as opposed to the observed well rates and pressure. However, two main challenges are faced to calibrate the simulation model using 4D seismic data. The process can be time consuming because most models go through a series of iterations before being considered sufficiently accurate to give an adequate representation of the physical system. The consideration of 4D seismic data as an observed parameter in the form of maps would lead to an unfeasibly large number of variables to be matched. To overcome such issues, the construction of an emulator that represents the simulation model and the use of the canonical correlation technique to incorporate 4D seismic data can be used. The present study constructed a stochastic representation of the computer model called an emulator to quantify the reduction in the parameter input space. 4D seismic data was incorporated in the procedure through the canonical correlation technique. The water saturation map derived from seismic data was converted into seven canonical functions. Such functions represent the observable characteristics to be matched in the uncertainty reduction process. A high number of evaluations was necessary to identify the range of input parameters whose outputs matched the historical data (4D seismic data). The large number of evaluations justifies the use of an emulator and the reduction of uncertainties with areal characteristics shows that 4D seismic data was successfully incorporated. The emulator methodology represents a powerful tool in the analysis of complex physical problems such as history matching. The incorporation of 4D seismic data as an observable output to be matched leads to a difficult problem to be solved. However, the canonical correlation permitted a successful incorporation of such data into the problem.

Artificial Intelligence, canonical correlation, canonical correlation technique, canonical function, correlation, emulator, grid cell, implausibility, input parameter, input space, machine learning, reduction, Reservoir Characterization, reservoir simulation, Scenario, seismic data, uncertainty reduction, Upstream Oil & Gas, water saturation, water saturation map

Oilfield Places: Africa > Angola > Angola Offshore > Lower Congo Basin > Block 17 > Girassol Field (0.99)

SPE Disciplines:

Technology: Information Technology > Artificial Intelligence > Machine Learning > Statistical Learning (0.70)

Single-well deconvolution is now commonly used in well test analysis. Within a reservoir, the pressure drop as a function of time is equal to the convoluted product of the rate and the reservoir response at that time. To obtain the reservoir response, inverse convolution – or deconvolution - must take place. This technique, until recently, could only be applied to single-well reservoirs since the deconvolution algorithms assumed zero interference from surrounding wells.

A multi-well deconvolution algorithm was recently presented by

The deconvolved derivatives for four individual wells were analysed for permeability and boundary effects, and the results were in agreement with pre-existing seismic interpretation and geological knowledge of the area. The reliability of the deconvolved derivatives produced by the multiwell algorithm was confirmed by using the algorithm to perform single-well deconvolution and then comparing the results to the outputs from a well-trusted single-well deconvolution tool.

The algorithm also outputs an interference response for each pair of deconvolved wells. Interpreting the interference responses allows to identify relative strengths of communication between wells and to obtain storativity and permeability-thickness of the reservoir between a pair of wells.

It was determined that the run-times of the algorithm were reasonable, and a study of computer run-times is found at the end of this paper whereby some typical multiwell deconvolutions have been run on two different specifications of computer.

algorithm, boundary, deconvolution, deconvolution algorithm, Deconvolution method, deconvolution response, deconvolution result, deconvolution tool, deconvolved derivative, derivative, Drillstem Testing, drillstem/well testing, interference, interference response, interpretation, multiwell, multiwell algorithm, multiwell deconvolution, pressure drop, reservoir, single-well deconvolution, Upstream Oil & Gas

SPE Disciplines: Reservoir Description and Dynamics > Formation Evaluation & Management > Drillstem/well testing (1.00)

Cumming, Jonathan (Durham University) | Wooff, David (Durham University) | Whittle, Tim (BG Group) | Gringarten, Alain C. (Imperial College)

In well-test analysis, deconvolution is used to transform variablerate-pressure data into a single constant-rate drawdown suitable for interpretation. It is becoming part of a standard workflow for exploration and appraisal well-test analyses and in production-test analysis in which there are no interference effects from nearby wells. This paper develops and extends the single-well deconvolution algorithm of von Schroeter et al. (2004) to the larger and more-complex multiwell deconvolution problem. To validate the algorithm, it is applied to a synthetic example with known solution, and an uncertainty analysis is performed to quantify the impact of nonuniqueness on multiwell deconvolution. The use of the algorithm is illustrated further with a field example.

Ferreira, C. (Universidade Estadual De Campinas) | Vernon, I. (Durham University) | Schiozer, D.J. (Universidade Estadual De Campinas) | Goldstein, M. (Durham University)

In petroleum engineering, simulation models are used in the reservoir performance prediction and in the decision making process. These models are complex systems, typically characterized by a vast number of input parameters. Usually the physical state of the reservoir is highly uncertain, and thus the appropriate parameters of the input choices. The uncertainty analysis often proceeds by first calibrating the simulator against observed production history and then using the calibrated model to forecast future well production. Most models go through a series of iterations before being judged to give an adequate representation of the physical system. This can be a difficult task since the input space to be searched may be high dimensional, the collection of outputs to be matched may be very large, and each single evaluation may take a long time. As the uncertainty analysis is complex and time consuming; in this paper, a stochastic representation of the computer model was constructed, called an emulator, to quantify the reduction in the parameter input space due to production data over different production periods. The emulator methodology used represents a powerful and general tool in the analysis of complex physical models such as reservoir simulators. Such emulation techniques have been successfully applied across a large number of scientific disciplines. The emulator methodology was applied to evaluate the production data capacity to identify uncertain reservoir physical features over the production period for a synthetic reservoir simulation model. The synthetic model was built to represent a region of an injector and related producers. In the case studied; thousands of realizations were required to identify certain physical reservoir features. This justifies the use of emulation and shows the importance of this technique for the identification of regions of feasible input parameters. Moreover, the impact on the input space reduction due to different production periods was determined. The emulator methodology used assists in carrying out tasks that require computationally expensive objective function evaluation, such as identifying regions of feasible input parameters; making predictions for future behavior of the physical system and investigating the reservoir behavior.

Artificial Intelligence, emulator, history matching, hypothetical reality, implausibility, implausibility value, input parameter, input parameter space, input space, Modeling & Simulation, optimization problem, permeability, production control, Production data Management, production monitoring, production period, reservoir, reservoir model, reservoir simulation, reservoir simulation model, Reservoir Surveillance, simulation model, uncertainty reduction, Upstream Oil & Gas, vector

SPE Disciplines:

Technology:

Cumming, J.A. (Durham University) | Wooff, D.A. (Durham University) | Whittle, T.M. (BG Group) | Gringarten, A.C. (Imperial College)

Copyright 2013, Society of Petroleum Engineers This paper was prepared for presentation at the SPE Annual Technical Conference and Exhibition held in New Orleans, Louisiana, USA, 30 September-2 October 2013. This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied.

algorithm, Artificial Intelligence, deconvolution, deconvolution error function, deconvolved derivative, derivative, error function, hyperparameter, initial pressure, interference, interference effect, multi-well deconvolution, multiple well, pressure data, pressure drop, pressure match, pressure transient analysis, pressure transient testing, response function, Upstream Oil & Gas, vector, von Schroeter, weight hyperparameter

SPE Disciplines: Reservoir Description and Dynamics > Formation Evaluation & Management > Pressure transient analysis (1.00)

Cumming, J. A. (Durham University) | Wooff, D. A. (Durham University) | Whittle, T. (BG Group) | Crossman, R. J (Warwick Medical School) | Gringarten, A. C. (Imperial College)

**Abstract**

Uncertainty in well test analysis results from errors in pressure and rate measurements, from uncertainties

in basic well and reservoir parameters; from the quality of the match with the interpretation model; and

from the non-uniqueness of the interpretation model.

These various uncertainties, except the non-uniqueness of the interpretation model, were examined in

SPE 113888. It was concluded that the permeability-product kh is generally known within 15%; the

permeability k, within 20% (because of the uncertainty on the thickness h); and the skin effect S, within

8% for high S values and within ±0.5 for low S values. Distances (half-fracture lengths, horizontal well

lengths, and distances to reservoir boundaries) are usually known within 25%.

The issue of non-uniqueness of the interpretation model is more complex: not only may there be a

multitude of possible models for any one derivative response (the usual inverse problem), but there may

be also a multitude of derivative responses, due to the uncertainty inherent in the observed data.

This paper presents a methodology for assessing the derivative response uncertainty using

deconvolution. It is shown that the uncertainty depends mainly on the error bounds for initial pressure

and flow rates, which yield a range of possible shapes for the deconvolved pressure derivative and

therefore different possible interpretation models. In some cases, the non-uniqueness of deconvolution

can be reduced using knowledge of the expected model response, for instance from geology or seismic. In

the absence of differentiating information, however, alternative interpretation models have to be

considered, which may lead to completely different development options.

The methodology is illustrated with three field examples.

**Introduction**

Uncertainty in well test analysis results from errors in pressure and rate measurements; from

uncertainties in basic well and reservoir parameters; from the quality of the match with the interpretation

model; and from the non-uniqueness of the interpretation model.

These various uncertainties, except the non-uniqueness of the interpretation model, were examined by

Ali, *et al.* (2008). It was concluded that the permeability-product kh is generally known within 15%; the

permeability k, within 20% (because of the uncertainty on the thickness h); and the skin effect S, within

8% for high S values and within ±0.5 for low S values. Distances (half-fracture lengths, horizontal well

lengths, and distances to reservoir boundaries) are usually known within 25%.

The issue of non-uniqueness of the interpretation model is more complex: not only there may be a

multitude of possible models for any one derivative response (the usual inverse problem), but there may

also be a multitude of possible derivative responses, due to the uncertainty inherent in the observed data.

Artificial Intelligence, buildup, deconvolution, deconvolved derivative, Drillstem Testing, drillstem/well testing, estimation, Gringarten, initial pressure, interpretation model, Monte Carlo, observational, pressure data, pressure match, representation, reservoir, response function, uncertainty analysis, Upstream Oil & Gas, vector

Thank you!