Ranaee, Ehsan (Dipartimento di Energia Politecnico di Milano, Via Lambruschini 4, 20156 Milano) | Inzoli, Fabio (Dipartimento di Energia Politecnico di Milano, Via Lambruschini 4, 20156 Milano) | Riva, Monica (Dipartimento di Ingegneria Civile e Ambientale, Politecnico di Milano, Piazza L. Da Vinci 32, 20133 Milano) | Cominelli, Alberto (Eni - S.p.A. Via Emilia 1, 20097 San Donato Milanese, Milano) | Guadagnini, Alberto (Dipartimento di Ingegneria Civile e Ambientale, Politecnico di Milano, Piazza L. Da Vinci 32, 20133 Milano)
We study the way uncertainty associated with estimates of parameters of three-phase relative permeability models, including hysteresis, propagates to responses of reservoir simulations under Water Alternating Gas (WAG) conditions. We model three-phase relative permeabilities by: (i) joint calibration (on threephase data) of a recent oil relative permeability model (Ranaee et al., 2015) and of the Larsen and Skauge (1998) gas relative permeability hysteretic model; and (ii) the common practice of relying on three-phase oil relative permeability models that are characterized solely on the basis of two-phase information (e.g., Stone, 1970 and Baker, 1988) in conjunction with the formulation of Larsen and Skauge (1998) for threephase gas relative permeability. While model parameters associated with the former approach are linked to an estimation uncertainty, those of the models relying only on two-phase data are not. A numerical Monte Carlo (MC) framework is employed to estimate propagation to reservoir simulation outputs of uncertainty of parameters estimated through model calibration on three-phase data. Our findings suggest that evaluation of oil relative permeability through a saturation-weighted interpolation Baker model, even in combination with a three-phase gas relative permeability hysteresis model, yields the lowest values of field oil recovery. These are seen to lie outside uncertainty bounds evaluated via the above mentioned MCbased analysis. Relying on the Stone formulations together with the Larsen and Skauge (1998) gas relative permeability model yields (a) values of ultimate field oil recovery comprised within MC uncertainty bound and (b) values of field gas-oil ratio (GOR) which are smaller than those obtained through the Baker model in conjunction with the Larsen and Skauge (1998) formulation, both results falling markedly outside the MCbased confidence interval. Our results document the effect that propagation of uncertainties from calibrating three-phase relative permeability model parameters can have on field-scale simulation outputs, such as ultimate oil recovery and field GOR. They also serve as a baseline against which simulation results based on typical procedures to model three-phase relative permeabilities can be assessed.
AbstractThis work is focused on exploring the applicability of intelligent methods in assessing porosity and permeability in the context of reservoir characterization. The main motivation underlying our study is that appropriate estimation of reservoir petrophysical parameters such as porosity and/or permeability is a key step for in-situ hydrocarbon reservoir evaluation. We ground our analysis on information on log-depth, caliper, conductivity, sonic logging, natural gamma, density and neutron porosity, water saturation, percentage of shale volume, and type of lithology collected from well loggings in an oil field in the middle-east (a total number of 11 exploratory wells are considered). Data also include porosities and permeabilities evaluated on core samples from the same wells. All these data are embedded in a neural network-based approach which enables us to establish input-output relationships in terms of an optimized number of input variables. Three diverse intelligent techniques are tested. These include: (i) classical artificial neural networks; (ii) artificial neural networks based on principal component analysis (PCA) transformation; and (iii) statistical neural networks based on a bagging approach. Our results suggest that the statistical neural network is most effective for the field setting considered. The application of this neural network with 9 input parameters provides reliable performances in 94% and 81% of the cases, respectively in the training and validation phases, for the estimation of porosity. A trained network with 10 input parameters leads to successfull reproduction of permeability values in 85% and 79.5% of the cases, respectively during training and validation of the network. Results from this study are expected to be transferable to applications involving evaluation of petrophysical properties of a target reservoir in the presence of incomplete well log datasets.