3‐D Magnetic data‐space inversion with sparseness constraints

2008 ◽  
Author(s):  
Mark Pilkington
Keyword(s):  
Magnetic Data ◽  
Data Space ◽  
Space Inversion

scholarly journals History Matching and Production Prediction of Steam Drive Reservoir Based on Data-Space Inversion Method

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
RuXiang Gong ◽  
JingSong Li ◽  
ZiJun Huang ◽  
Fei Wang ◽  
Hao Yang ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Simulation Model ◽  
History Matching ◽  
Production Optimization ◽  
Production Performance ◽  
Inversion Method ◽  
Data Space ◽  
Steam Flooding ◽  
Space Inversion ◽  
Production Prediction

Recently, a data-space inversion (DSI) method has been proposed and successfully applied for the history matching and production optimization for conventional waterflooding reservoir. Under Bayesian framework, DSI can directly and effectively obtain posterior flow predictions without inverting any geological parameters of reservoir model. In this paper, we integrate the numerical simulation model with DSI method for rapid history matching and production prediction for steam flooding reservoir. Based on the finite volume method, a numerical simulation model is established and it is used to provide production data samples for DSI by the simulation of ensemble geological models. DSI-based production prediction model is then established and get trained by the historical data through the random maximum likelihood principle. The posterior production estimation can be obtained fast by training the DSI-based model with history data, but without any posterior geological parameters. The proposed method is applied for history matching and estimating production performance prediction in some numerical examples and a field case, and the results prove its effectiveness and reliability.

scholarly journals Data-Space Inversion With a Recurrent Autoencoder for Naturally Fractured Systems

2021 ◽  
Vol 7 ◽  
Author(s):  
Su Jiang ◽  
Mun-Hong Hui ◽  
Louis J. Durlofsky
Keyword(s):  
Time Series ◽  
Data Assimilation ◽  
Time Series Data ◽  
Flow Simulation ◽  
Series Data ◽  
Model Parameters ◽  
Fractured Reservoir ◽  
Data Space ◽  
Naturally Fractured ◽  
Space Inversion

Data-space inversion (DSI) is a data assimilation procedure that directly generates posterior flow predictions, for time series of interest, without calibrating model parameters. No forward flow simulation is performed in the data assimilation process. DSI instead uses the prior data generated by performing O(1000) simulations on prior geomodel realizations. Data parameterization is useful in the DSI framework as it enables representation of the correlated time-series data quantities in terms of low-dimensional latent-space variables. In this work, a recently developed parameterization based on a recurrent autoencoder (RAE) is applied with DSI for a real naturally fractured reservoir. The parameterization, involving the use of a recurrent neural network and an autoencoder, is able to capture important correlations in the time-series data. RAE training is accomplished using flow simulation results for 1,350 prior model realizations. An ensemble smoother with multiple data assimilation (ESMDA) is applied to provide posterior DSI data samples. The modeling in this work is much more complex than that considered in previous DSI studies as it includes multiple 3D discrete fracture realizations, three-phase flow, tracer injection and production, and complicated field-management logic leading to frequent well shut-in and reopening. Results for the reconstruction of new simulation data (not seen in training), using both the RAE-based parameterization and a simpler approach based on principal component analysis (PCA) with histogram transformation, are presented. The RAE-based procedure is shown to provide better accuracy for these data reconstructions. Detailed posterior DSI results are then presented for a particular “true” model (which is outside the prior ensemble), and summary results are provided for five additional “true” models that are consistent with the prior ensemble. These results again demonstrate the advantages of DSI with RAE-based parameterization for this challenging fractured reservoir case.

scholarly journals Data-space inversion with ensemble smoother

2020 ◽  
Vol 24 (3) ◽  
pp. 1179-1200 ◽  
Author(s):  
Mateus M. Lima ◽  
Alexandre A. Emerick ◽  
Carlos E. P. Ortiz
Keyword(s):  
Data Space ◽  
Ensemble Smoother ◽  
Space Inversion

3D magnetic data-space inversion with sparseness constraints

Geophysics ◽  
2009 ◽  
Vol 74 (1) ◽  
pp. L7-L15 ◽  
Author(s):  
Mark Pilkington
Keyword(s):  
Least Squares ◽  
Synthetic Data ◽  
Model Space ◽  
Gradient Algorithm ◽  
Magnetic Data ◽  
Model Parameters ◽  
Linear System Of Equations ◽  
Data Space ◽  
System Versus ◽  
Sparse Inversion

I have developed an inversion approach that determines a 3D susceptibility distribution that produces a given magnetic anomaly. The subsurface model consists of a 3D, equally spaced array of dipoles. The inversion incorporates a model norm that enforces sparseness and depth weighting of the solution. Sparseness is imposed by using the Cauchy norm on model parameters. The inverse problem is posed in the data space, leading to a linear system of equations with dimensions based on the number of data, [Formula: see text]. This contrasts with the standard least-squares solution, derived through operations within the [Formula: see text]-dimensional model space ([Formula: see text] being the number of model parameters). Hence, the data-space method combined with a conjugate gradient algorithm leads to computational efficiency by dealing with an [Formula: see text] system versus an [Formula: see text] one, where [Formula: see text]. Tests on synthetic data show that sparse inversion produces a much more focused solution compared with a standard model-space, least-squares inversion. The inversion of aeromagnetic data collected over a Precambrian Shield area again shows that including the sparseness constraint leads to a simpler and better resolved solution. The degree of improvement in model resolution for the sparse case is quantified using the resolution matrix.

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