Simulated annealing technique in discrete fracture network inversion: optimizing the optimization

Tran, Nam H.

doi:10.1007/s10596-007-9049-7

Cited by 16 publications

(3 citation statements)

References 28 publications

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“…SA is in fact such a stochastic optimization method that has been used in variety of problems that involve finding global optimum values of a function consisting of large number of independent variables (e.g. Tran 2007). Below we outline our implementation of SA for the estimation of fracture distributions.…”

Section: E T H O D F O R M O D E L L I N G F R a C T U R E D I S T mentioning

confidence: 99%

Generation of spatially correlated fracture models for seismic simulations

Shekhar¹,

Gibson²

2011

Geophysical Journal International

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S U M M A R YThe critical geometrical parameters that quantify the spatial distribution of natural fractures are the orientation, length and position of fractures. Knowledge of their spatial distribution is important as they control the movement of subsurface fluids and also influence seismic waves propagating in the subsurface. However, generating realistic models of all of these geometrical parameters to use in forward seismic modelling or inversion applications can become very difficult, especially when constraints are available only at a few sparse well locations. Hence, this provides strong motivation for applying seismic data to estimate these quantities in field settings, and reliable seismic modelling provides important constraints for interpretation and inversion. The Discrete Fracture Network (DFN) approach has been used frequently to generate models with stochastic distributions of fractures based on sparse well and seismic data. However, most of these studies lack any constraint from physical models of the behaviour of fractured media. In this paper, we implement and extend an alternative modelling technique to generate several realizations of a fracture model beginning with theoretical results for the strain energy of a fractured material and propose ways to better incorporate geological field observations. The method utilizes an elastic energy function that sums the interactions of all pairs of fractures present in the model. The energy for each pair depends on the distance between the two fractures, their orientations, lengths and some material properties. This energy function also serves as an objective function for a simulated annealing (SA) algorithm used to obtain multiple realizations of correlated fracture networks. We improve earlier versions of this technique by incorporating periodic boundary conditions, including criteria to limit the maximum range of pair-wise calculations and suggesting methods to constrain models to match field data. Assuming that the host rock is isotropic and homogeneous, this method produces orthogonal sets of fractures, a pattern that is commonly observed during basin formation or subsidence. This shows how the method can be utilized to provide constraints with a physical basis to facilitate the development of fracture models. We also outline how the fracture model can be converted into an anisotropic seismic velocity model to compute synthetic seismograms for reservoir characterization applications.

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Section: E T H O D F O R M O D E L L I N G F R a C T U R E D I S T mentioning

confidence: 99%

Generation of spatially correlated fracture models for seismic simulations

Shekhar¹,

Gibson²

2011

Geophysical Journal International

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“…Solving for spatially varying reservoir properties of geothermal fields have required about 10 3 [ Vogt et al ., ] and 10 4 iterations [ Cui et al ., ; Vogt et al ., ], while net present value optimization of petroleum production also needed 10 4 iterations [ Isebor et al ., ]. Tran [] employed simulated annealing to solve for a discrete fracture network using over 10 6 iterations. Given the large number of function evaluations, relying exclusively on a numerical code may not be practical.…”

Section: Introductionmentioning

confidence: 99%

An analytical thermohydraulic model for discretely fractured geothermal reservoirs

Fox

Koch

Tester

2016

Water Resources Research

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In discretely fractured reservoirs such as those found in Enhanced/Engineered Geothermal Systems (EGS), knowledge of the fracture network is important in understanding the thermal hydraulics, i.e., how the fluid flows and the resulting temporal evolution of the subsurface temperature. The purpose of this study was to develop an analytical model of the fluid flow and heat transport in a discretely fractured network that can be used for a wide range of modeling applications and serve as an alternative analysis tool to more computationally intensive numerical codes. Given the connectivity and structure of a fracture network, the flow in the system was solved using a linear system of algebraic equations for the pressure at the nodes of the network. With the flow determined, the temperature in the fracture was solved by coupling convective heat transport in the fracture with one‐dimensional heat conduction perpendicular to the fracture, employing the Green's function derived solution for a single discrete fracture. The predicted temperatures along the fracture surfaces from the analytical solution were compared to numerical simulations using the TOUGH2 reservoir code. Through two case studies, we showed the capabilities of the analytical model and explored the effect of uncertainty in the fracture apertures and network structure on thermal performance. While both sources of uncertainty independently produce large variations in production temperature, uncertainty in the network structure, whenever present, had a predominant influence on thermal performance.

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“…One of the main features of the particular problem is that obstacles are concentrated inside some relatively small volume (layer), and there is no need to describe extremely precisely the shape of each single obstacle but rather their distribution within a given volume. Note that typically, the models of fractured reservoirs are derived by means of a statistical simulation [34], and they are provided on some sufficiently fine regular grid [35]. So, we admit that the Galerkin-type approaches on irregular adaptive meshes are suitable for the simulation of wave propagation with a few small-scale obstacles [36,37].…”

Section: Introductionmentioning

confidence: 99%