Conditional Statistical Moment Equations for Dynamic Data Integration in Heterogeneous Reservoirs

2005 ◽  
Author(s):  
L. Li ◽  
H.A. Tchelepi
Keyword(s):  
Data Integration ◽  
Statistical Moment ◽  
Moment Equations ◽  
Dynamic Data ◽  
Heterogeneous Reservoirs

Dynamic Data Integration and Quantification of Prediction Uncertainty Using Statistical-Moment Equations

SPE Journal ◽  
2011 ◽  
Vol 17 (01) ◽  
pp. 98-111 ◽  
Author(s):  
P.. Likanapaisal ◽  
L.. Li ◽  
H.A.. A. Tchelepi
Keyword(s):  
Data Integration ◽  
History Matching ◽  
Dynamic Properties ◽  
Statistical Moment ◽  
Statistical Moments ◽  
Moment Equations ◽  
Inversion Algorithm ◽  
Reservoir Properties ◽  
Dynamic Data ◽  
Prediction Uncertainty

Summary The use of a probabilistic framework for dynamic data integration (history matching) has become accepted practice. In this framework, one constructs an ensemble of reservoir models, in which each realization honors the available (static and dynamic) information. The variations in the flow performance across the ensemble provide an assessment of the prediction uncertainty due to incomplete knowledge of the reservoir properties (e.g., permeability distribution). Methods based on Monte Carlo simulation (MCS) are widely used because of the generality and simplicity of MCS. As a black-box approach, only pre- and post-processing of conventional flow simulations are needed. To achieve reasonable accuracy in estimating the statistical moments of flow-performance predictions, however, large numbers of realizations are usually necessary. Here, we use a different, and direct, approach for model calibration and uncertainty quantification. Specifically, we describe a statistical-moment-equations (SMEs) framework for both the forward and inverse problems associated with immiscible two-phase flow. In the SME method, the equations governing the statistical moments of the quantities of interest (e.g., pressure and saturation) are derived and solved directly. We assume that statistical information and a few measurements are available for the permeability field. As for the dynamic properties, we assume that measurements of pressure, saturation, and flow rate are available at a few locations and at several times. For the forward problem, the flow (pressure and total-velocity) SMEs are solved on a regular grid, while a streamline-based strategy is used to solve the transport SMEs. We use a kriging-based inversion algorithm, in which the first two statistical moments of permeability are conditioned directly using the available dynamic data. We analyze the behaviors of the saturation moments and their evolution as they are conditioned on measurements, in both space and time. Moreover, we discuss the relationship between the widely used MCS-based Kalman-filter approach and our SME inversion scheme.

Conditional Statistical Moment Equations for Dynamic Data Integration in Heterogeneous Reservoirs

2006 ◽  
Vol 9 (03) ◽  
pp. 280-288 ◽  
Author(s):  
Liyong Li ◽  
Hamdi A. Tchelepi
Keyword(s):  
Statistical Moment ◽  
Limited Data ◽  
Pressure Data ◽  
Moment Equations ◽  
Reservoir Properties ◽  
Incomplete Knowledge ◽  
Heterogeneous Reservoirs ◽  
Knowledge Uncertainty ◽  
Available Information ◽  
Permeability Field

Summary An inversion method for the integration of dynamic (pressure) data directly into statistical moment equations (SMEs) is presented. The method is demonstrated for incompressible flow in heterogeneous reservoirs. In addition to information about the mean, variance, and correlation structure of the permeability, few permeability measurements are assumed available. Moreover, few measurements of the dependent variable are available. The first two statistical moments of the dependent variable (pressure) are conditioned on all available information directly. An iterative inversion scheme is used to integrate the pressure data into the conditional statistical moment equations (CSMEs). That is, the available information is used to condition, or improve the estimates of, the first two moments of permeability, pressure, and velocity directly. This is different from Monte Carlo (MC) -based geostatistical inversion techniques, where conditioning on dynamic data is performed for one realization of the permeability field at a time. In the MC approach, estimates of the prediction uncertainty are obtained from statistical post-processing of a large number of inversions, one per realization. Several examples of flow in heterogeneous domains in a quarter-five-spot setting are used to demonstrate the CSME-based method. We found that as the number of pressure measurements increases, the conditional mean pressure becomes more spatially variable, while the conditional pressure variance gets smaller. Iteration of the CSME inversion loop is necessary only when the number of pressure measurements is large. Use of the CSME simulator to assess the value of information in terms of its impact on prediction uncertainty is also presented. Introduction The properties of natural geologic formations (e.g., permeability) rarely display uniformity or smoothness. Instead, they usually show significant variability and complex patterns of correlation. The detailed spatial distributions of reservoir properties, such as permeability, are needed to make performance predictions using numerical reservoir simulation. Unfortunately, only limited data are available for the construction of these detailed reservoir-description models. Consequently, our incomplete knowledge (uncertainty) about the property distributions in these highly complex natural geologic systems means that significant uncertainty accompanies predictions of reservoir flow performance. To deal with the problem of characterizing reservoir properties that exhibit such variability and complexity of spatial correlation patterns when only limited data are available, a probabilistic framework is commonly used. In this framework, the reservoir properties (e.g., permeability) are assumed to be a random space function. As a result, flow-related properties such as pressure, velocity, and saturations are random functions. We assume that the available information about the permeability field includes a few measurements in addition to the spatial correlation structure, which we take here as the two-point covariance. This incomplete knowledge (uncertainty) about the detailed spatial distribution of permeability is the only source of uncertainty in our problem. Uncertainty about the detailed distribution of the permeability field in the reservoir leads to uncertainty in the computed predictions of the flow field (e.g., pressure).

scholarly journals Dynamic Data Integration for Resilience to Sensor Attacks in Multi-Agent Systems

IEEE Access ◽  
2021 ◽  
Vol 9 ◽  
pp. 31236-31245
Author(s):  
Luis Burbano ◽  
Luis Francisco Combita ◽  
Nicanor Quijano ◽  
Sandra Rueda
Keyword(s):  
Data Integration ◽  
Multi Agent Systems ◽  
Dynamic Data ◽  
Agent Systems ◽  
Multi Agent

Dynamic data integration using Web services

2004 ◽  
Author(s):  
Fujun Zhu ◽  
M. Turner ◽  
I. Kotsiopoulos ◽  
K. Bennett ◽  
M. Russell ◽  
...  
Keyword(s):  
Web Services ◽  
Data Integration ◽  
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Modified Markov Chain Monte Carlo Method for Dynamic Data Integration Using Streamline Approach

2008 ◽  
Vol 40 (2) ◽  
pp. 213-232 ◽  
Author(s):  
Yalchin Efendiev ◽  
Akhil Datta-Gupta ◽  
Xianlin Ma ◽  
Bani Mallick
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Monte Carlo Method ◽  
Data Integration ◽  
Dynamic Data
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