Assessment of Optimal Operating Conditions in a SAGD Project by Design of Experiments and Response Surface Methodology

Prada, J.W. Vanegas; Cunha, L.B.

doi:10.1080/10916460701429399

Cited by 13 publications

(6 citation statements)

References 2 publications

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“…(12) Note that in this approach it is possible to perform the LU decomposition of the variogram matrix V and then find the vector…”

Section: Ordinary Kriging Proxy Modelmentioning

confidence: 99%

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Time-Dependent Proxy Modeling of SAGD Process

Fedutenko¹,

Yang²,

Card³

et al. 2013

All Days

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The present paper proposes the use of a time dependent proxy model with the goal of efficient prediction of the future production performance of SAGD operations from a limited number of reservoir simulations. The proposed model is shown to provide powerful means for developing learning functions from input-output relationships described by the reservoir dynamics entailed by multiple combinations of inputs and controls. A SAGD case with 3 well pairs is used to illustrate the approach. The workflow is organized as follows:1. The specified number of direct numerical simulations is run for the time horizon of ten years for the given reservoir. These simulations correspond to different combinations of the operational parameters sampled according to the Latin Hypercube Experimental Design (LHD).2. The time series of the simulated production performance (particularly: entire field Oil Production Rate SCTR, and entire field SOR Cumulative SCTR) are used to build the time-dependent proxy model which represents production performance as an output function of the operational parameters and time. This paper uses and compares the following interpolators in N+1dimensional space (operational parameters and time): a) anisotropic Ordinary Kriging, b) linear regression with regularization, c) Radial Basis Functions (RBF) Network method. Note that the extension of these methods to include time as the independent variable is one of the significant contributions of this paper.3. The proxy model is then used to predict the production data for the given reservoir for any time period (even longer than 10 years) and any combinations of the operational parameters.4. The predicted data are compared with the actual simulation results for the same time period and the same combinations of the operational parameters to evaluate the prediction quality. It is shown that all three proxy models can be used as a light version of simulator to get the production results for any combination of operational parameters and time horizon with much less computational efforts.

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“…(12) Note that in this approach it is possible to perform the LU decomposition of the variogram matrix V and then find the vector…”

Section: Ordinary Kriging Proxy Modelmentioning

confidence: 99%

“…(13) are fixed, whereas the variogram's coefficients in Eq. (12) are estimated from the training data fitting.…”

Section: Radial Basis Functions Network Interpolationmentioning

confidence: 99%

Time-Dependent Proxy Modeling of SAGD Process

Fedutenko¹,

Yang²,

Card³

et al. 2013

All Days

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“…Vanegas et al. discussed another strategy for assessing optimal operating conditions in the SAGD process using the design of experiments and polynomial response surface approach. However, these studies overlooked the geological uncertainties and real complexities of the SAGD model.…”

Section: Introductionmentioning

confidence: 99%

Application of polynomial chaos theory as an accurate and computationally efficient proxy model for heterogeneous steam‐assisted gravity drainage reservoirs

Jain

Patel

2017

Energy Science & Engineering

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Reservoir modeling and simulation have become important elements of reservoir management. However, high computational cost associated with the use of numerical simulators make them cumbersome, especially with large-scale simulation models and complex oil recovery processes like steam-assisted gravity drainage (SAGD). A data-driven proxy model can be an alternative to predict SAGD recovery performance in real heterogeneous reservoirs, however, computationally efficient proxy model which can handle large number of input variables while providing accurate results requires further attention. In this work, a proxy model based on polynomial chaos expansion (PCE) is developed to predict the production parameters of SAGD reservoir. Karhunen-Loeve (KL) expansion is used to parameterize input variables in terms of random variables using which PCE further calculates production data for the given reservoir. To calculate coefficients of PCE, probabilistic collocation method is used. To demonstrate the functionality of the proposed approach, case study of a SAGD reservoir located in northern Alberta, Canada is shown in this paper. Various production parameters predicted from the PCE proxy model are compared with the actual simulation results and other proxy models based on radial basis functions (RBF) and artificial neural networks (ANN). From the results, it can be said that PCE proxy model demonstrates good agreement with full-physics simulation results and outperforms other proxy methods in terms of training data required and accuracy of predictions. In addition, since proposed PCE proxy model greatly reduces the computing cost, it potentially paves the way for expedited and frequent execution of uncertainty quantification, assisted history matching, and optimization workflows, resulting into efficient reservoir management and significant monetary benefits.

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“…Three different strategies of proxy-models generation for SAGD projects have been identified in the literature: 1) static measures of the goodness of reservoir fitted to a reservoir simulation response, see for example [8]; 2) use of Design of Experiments (DOE) and Response Surface Methodology (RSM) to generate polynomials fitted to reservoir simulator responses, see for example [9,10]; and 3) physical-based proxies which are also adjusted to SAGD simulation responses, [11]. This paper is an extension of the work presented in [11].…”

Section: Introductionmentioning

confidence: 99%

Transference of Reservoir Uncertainty in Multi SAGD Well Pairs

2009

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Extensive computational time is required to predict SAGD production performance by thermal reservoir simulation. The common practice is to evaluate the performance of a single well pair and combine the results to pads and projects. Production forecasts for multiple SAGD well pairs simultaneously are computational expensive. At the same time, there is a need to make reservoir management decision in presence of reservoir uncertainty. Accounting for joint uncertainty across the reservoir requires simultaneous management of multiple realizations. Thermal simulators cannot be applied to the transference of such uncertainty to SAGD performance of many well pairs. A proxy model based on the Butler's SAGD theory has been developed to overcome this challenge. The proxy is able to account for reservoir heterogeneity. Modifying factors are included to fit the proxy results to simulation outcomes. The methodology for the transference of the reservoir uncertainty includes: generation of the reservoir uncertainty model using geostatistical tools; ranking the geologic realizations using the Cumulative Steam Oil Ratio (CSOR) calculated by the unfitted proxy. The ranking process is done in a reservoir volume representative of a single well pair: reservoir simulation for the P10 to P90 realizations, fitting the proxy model to simulation results, and assessment of the uncertainty of the SAGD performance by Monte Carlo Simulation (MCS). This methodology was applied to a synthetic example of a pad of eight SAGD well pairs, using 3D geometry and based on hard data from an Athabasca bitumen deposit. The results show the uncertainty in the dynamic performance of SAGD production variables for the entire pad. The results permit decision making under the uncertainty. It is shown that approximate models accounting for uncertainty are better than precise models that cannot be used in stochastic calculations. IntroductionAfter the success of the AOSTRA's Underground Test Facility (UTF) project [1-3], the Steam Assisted Gravity Drainage (SAGD) has become the standard recovery technology of oil sands industry to exploit the vast in-situ bitumen resources in Canada. Numerous commercial applications and pilot projects have been implemented since the UTF. As March 2008, eighteen commercial applications are being operated or approved by ERCB in Alberta [4].

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Assessment of Optimal Operating Conditions in a SAGD Project by Design of Experiments and Response Surface Methodology

Cited by 13 publications

References 2 publications

Time-Dependent Proxy Modeling of SAGD Process

Time-Dependent Proxy Modeling of SAGD Process

Application of polynomial chaos theory as an accurate and computationally efficient proxy model for heterogeneous steam‐assisted gravity drainage reservoirs

Transference of Reservoir Uncertainty in Multi SAGD Well Pairs

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