Determination of thermal properties and formation temperature from borehole thermal recovery data

Geophysics ◽  
2003 ◽  
Vol 68 (6) ◽  
pp. 1835-1846 ◽  
Author(s):  
Tien‐Chang Lee ◽  
A. D. Duchkov ◽  
S. G. Morozov
Keyword(s):  
Synthetic Data ◽  
Thermal Recovery ◽  
Model Parameters ◽  
Formation Temperature ◽  
Drilling Mud ◽  
Borehole Data ◽  
Linear Inversion ◽  
Element Simulation ◽  
Model Formation ◽  
Parameter Values

Thermal recovery in boreholes cooled by circulation of drilling mud has been modeled for estimating formation temperature and thermal conductivity. Coupled with a finite‐element simulation of heat conduction, inverse modeling for the desired parameters starts with a genetic algorithm that feeds initial estimates of model parameters to an iterative quasi‐linear inversion scheme. In addition to using the rms misfit between the computed and observed borehole temperatures, the results are assessed by comparing or constraining the model formation temperature with a value obtained conventionally from an asymptotic temperature–time relation for a steady line source. The model conductivity is further evaluated for equality with a conductivity value, which is estimated through simulation of heat exchange between the formation and circulating mud. Test results on synthetic data and two sets of highly noisy borehole data from Lake Baikal in Russia indicate that the two equality criteria in temperature and conductivity are achievable. Multiple runs of GA‐IM are used to find mean parameter values and their uncertainties. The resultant model conductivity values are consistent with those measured in cores with a needle‐probe method.

Formation temperature estimation by inversion of borehole measurements

Geophysics ◽  
1988 ◽  
Vol 53 (7) ◽  
pp. 979-988 ◽  
Author(s):  
Song Cao ◽  
Ian Lerche ◽  
Christian Hermanrud
Keyword(s):  
Thermal Conductivity ◽  
Input Data ◽  
Synthetic Data ◽  
Thermal Stabilization ◽  
Efficiency Factor ◽  
Temperature Measurements ◽  
Quality Data ◽  
Formation Temperature ◽  
Drilling Mud ◽  
Specific Heats

We describe a new numerical method that uses inverse methods to model thermal stabilization of a borehole after drilling mud circulation has stopped. The following five geophysical parameters can be estimated from the method: (1) true formation temperature [Formula: see text] (2) mud temperature [Formula: see text] at the time the mud circulation stops; (3) thermal invasion distance (R) into the formation before the formation is at the true formation temperature[Formula: see text]; (4) formation thermal conductivity (K) perpendicular to the borehole; and (5) efficiency factor (F) for heating mud in the borehole after mud circulation has stopped. Crucial input data for the model are the temperature measurements with shut‐in time taken at a fixed depth, more than two measurements being required, and the mud temperature at the surface at the time circulation stops. Other input data include the radius of the borehole, and the densities and specific heats of the drilling mud and of the formation on which the temperature measurements are made. Applications of the new inverse procedure to both synthetic data and field data show that the true formation temperature in many cases can be estimated precisely (to within about 0.4 percent); that the mud temperature can be estimated with acceptable accuracy (5 percent or so); while the thermal conductivity (K), the thermal invasion distance (R), and the efficiency factor (F) can be roughly estimated, provided high‐quality data are available.

Modeling Heart Rate Dynamics in Response to Changes in Exercise Intensity

2015 ◽  
Author(s):  
Michael J. Mazzoleni ◽  
Claudio L. Battaglini ◽  
Brian P. Mann
Keyword(s):  
Genetic Algorithm ◽  
Mathematical Model ◽  
Heart Rate ◽  
Heart Rate Response ◽  
Synthetic Data ◽  
Model Parameters ◽  
Nonlinear Mathematical Model ◽  
Heart Rate Dynamics ◽  
Parameter Values ◽  
Good Agreement

This paper develops a nonlinear mathematical model to describe the heart rate response of an individual during cycling. The model is able to account for the fluctuations of an individual’s heart rate while they participate in exercise that varies in intensity. A method for estimating the model parameters using a genetic algorithm is presented and implemented, and the results show good agreement between the actual parameter values and the estimated values when tested using synthetic data.

Improvement in MRS parameter estimation by joint and laterally constrained inversion of MRS and TEM data

Geophysics ◽  
2012 ◽  
Vol 77 (4) ◽  
pp. WB191-WB200 ◽  
Author(s):  
Ahmad A. Behroozmand ◽  
Esben Auken ◽  
Gianluca Fiandaca ◽  
Anders Vest Christiansen
Keyword(s):  
Water Content ◽  
Joint Inversion ◽  
Synthetic Data ◽  
Clear Correlation ◽  
Model Parameters ◽  
Dc Resistivity ◽  
Borehole Data ◽  
Simultaneous Inversion ◽  
Transient Electromagnetic ◽  
Magnetic Resonance Sounding

We developed a new scheme for joint and laterally constrained inversion (LCI) of magnetic resonance sounding (MRS) data and transient electromagnetic (TEM) data, which greatly improves the estimation of the MRS model parameters. During the last few decades, electrical and electromagnetic methods have been widely used for groundwater investigation, but they suffer from some inherent limitations; for example, equivalent layer sequences. Furthermore, the water content information is only empirically correlated to resistivity of the formation. MRS is a noninvasive geophysical technique that directly quantifies the water content distribution from surface measurements. The resistivity information of the subsurface is obtained from a complementary geophysical method such as TEM or DC resistivity methods. The conventional inversion of MRS data assumes the resulting resistivity structure to be correct and considers a constant MRS kernel through the inversion. We found that this assumption may introduce an error to the forward modeling and consequently could result in erroneous parameter estimations in the inversion process. We investigated the advantage of TEM for the joint inversion compared to DC resistivity. A fast and numerically efficient MRS forward routine made it possible to invert the MRS and TEM data sets simultaneously along profiles. Furthermore, by application of lateral constraints on the model parameters, lateral smooth 2D model sections could be be obtained. The simultaneous inversion for resistivity and MRS parameters led to a more reliable and robust estimation of all parameters, and the MRS data diminished the range of equivalent resistivity models. We examined the approach through synthetic data and a field example in Denmark where good agreement with borehole data was demonstrated with clear correlation between the relaxation time [Formula: see text] and the grain size distribution of a sandy aquifer.

scholarly journals Assimilation of Dynamic Combined Finite Discrete Element Methods Using the Ensemble Kalman Filter

2021 ◽  
Vol 11 (7) ◽  
pp. 2898
Author(s):  
Humberto C. Godinez ◽  
Esteban Rougier
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Failure Modes ◽  
Split Hopkinson Pressure Bar ◽  
Peak Stress ◽  
Discrete Element ◽  
Material Behavior ◽  
Model Parameters ◽  
Hopkinson Pressure Bar ◽  
Parameter Values

Simulation of fracture initiation, propagation, and arrest is a problem of interest for many applications in the scientific community. There are a number of numerical methods used for this purpose, and among the most widely accepted is the combined finite-discrete element method (FDEM). To model fracture with FDEM, material behavior is described by specifying a combination of elastic properties, strengths (in the normal and tangential directions), and energy dissipated in failure modes I and II, which are modeled by incorporating a parameterized softening curve defining a post-peak stress-displacement relationship unique to each material. In this work, we implement a data assimilation method to estimate key model parameter values with the objective of improving the calibration processes for FDEM fracture simulations. Specifically, we implement the ensemble Kalman filter assimilation method to the Hybrid Optimization Software Suite (HOSS), a FDEM-based code which was developed for the simulation of fracture and fragmentation behavior. We present a set of assimilation experiments to match the numerical results obtained for a Split Hopkinson Pressure Bar (SHPB) model with experimental observations for granite. We achieved this by calibrating a subset of model parameters. The results show a steady convergence of the assimilated parameter values towards observed time/stress curves from the SHPB observations. In particular, both tensile and shear strengths seem to be converging faster than the other parameters considered.

scholarly journals A flexible framework for sequential estimation of model parameters in computational hemodynamics

2020 ◽  
Vol 7 (1) ◽  
Author(s):  
Christopher J. Arthurs ◽  
Nan Xiao ◽  
Philippe Moireau ◽  
Tobias Schaeffter ◽  
C. Alberto Figueroa
Keyword(s):  
Unscented Kalman Filter ◽  
Three Dimensional ◽  
Synthetic Data ◽  
Sequential Estimation ◽  
Wall Material ◽  
Patient Specific ◽  
Model Parameters ◽  
Computational Framework ◽  
Lumped Parameter ◽  
Estimation Of Model Parameters

AbstractA major challenge in constructing three dimensional patient specific hemodynamic models is the calibration of model parameters to match patient data on flow, pressure, wall motion, etc. acquired in the clinic. Current workflows are manual and time-consuming. This work presents a flexible computational framework for model parameter estimation in cardiovascular flows that relies on the following fundamental contributions. (i) A Reduced-Order Unscented Kalman Filter (ROUKF) model for data assimilation for wall material and simple lumped parameter network (LPN) boundary condition model parameters. (ii) A constrained least squares augmentation (ROUKF-CLS) for more complex LPNs. (iii) A “Netlist” implementation, supporting easy filtering of parameters in such complex LPNs. The ROUKF algorithm is demonstrated using non-invasive patient-specific data on anatomy, flow and pressure from a healthy volunteer. The ROUKF-CLS algorithm is demonstrated using synthetic data on a coronary LPN. The methods described in this paper have been implemented as part of the CRIMSON hemodynamics software package.

scholarly journals An enhanced set of displacement parameter restraints in CRYSTALS

2018 ◽  
Vol 51 (4) ◽  
pp. 1059-1068 ◽  
Author(s):  
Pascal Parois ◽  
James Arnold ◽  
Richard Cooper
Keyword(s):  
Structural Model ◽  
Rigid Bodies ◽  
Model Parameters ◽  
Coordinate Systems ◽  
Principal Axes ◽  
Anisotropic Displacement Parameters ◽  
Set Up ◽  
Meaningful Relationships ◽  
Parameter Values ◽  
Total Model

Crystallographic restraints are widely used during refinement of small-molecule and macromolecular crystal structures. They can be especially useful for introducing additional observations and information into structure refinements against low-quality or low-resolution data (e.g. data obtained at high pressure) or to retain physically meaningful parameter values in disordered or unstable refinements. However, despite the fact that the anisotropic displacement parameters (ADPs) often constitute more than half of the total model parameters determined in a structure analysis, there are relatively few useful restraints for them, examples being Hirshfeld rigid-bond restraints, direct equivalence of parameters and SHELXL RIGU-type restraints. Conversely, geometric parameters can be subject to a multitude of restraints (e.g. absolute or relative distance, angle, planarity, chiral volume, and geometric similarity). This article presents a series of new ADP restraints implemented in CRYSTALS [Parois, Cooper & Thompson (2015), Chem. Cent. J. 9, 30] to give more control over ADPs by restraining, in a variety of ways, the directions and magnitudes of the principal axes of the ellipsoids in locally defined coordinate systems. The use of these new ADPs results in more realistic models, as well as a better user experience, through restraints that are more efficient and faster to set up. The use of these restraints is recommended to preserve physically meaningful relationships between displacement parameters in a structural model for rigid bodies, rotationally disordered groups and low-completeness data.

FULL-WAVEFORM INVERSION WITH SOURCE AND RECEIVER COUPLING EFFECTS CORRECTION

Geophysics ◽  
2021 ◽  
pp. 1-37
Author(s):  
Xinhai Hu ◽  
Wei Guoqi ◽  
Jianyong Song ◽  
Zhifang Yang ◽  
Minghui Lu ◽  
...  
Keyword(s):  
Waveform Inversion ◽  
Nonlinear Least Squares ◽  
Real Data ◽  
Model Parameters ◽  
Full Waveform Inversion ◽  
Linear Inversion ◽  
Near Surface ◽  
Model Parameter ◽  
Full Waveform ◽  
Coupling Factors

Coupling factors of sources and receivers vary dramatically due to the strong heterogeneity of near surface, which are as important as the model parameters for the inversion success. We propose a full waveform inversion (FWI) scheme that corrects for variable coupling factors while updating the model parameter. A linear inversion is embedded into the scheme to estimate the source and receiver factors and compute the amplitude weights according to the acquisition geometry. After the weights are introduced in the objective function, the inversion falls into the category of separable nonlinear least-squares problems. Hence, we could use the variable projection technique widely used in source estimation problem to invert the model parameter without the knowledge of source and receiver factors. The efficacy of the inversion scheme is demonstrated with two synthetic examples and one real data test.

Modeling the crashes count using finite mixture models

2019 ◽  
Vol 7 (1) ◽  
pp. 13-27
Author(s):  
Safaa K. Kadhem ◽  
Sadeq A. Kadhim
Keyword(s):  
Bayesian Inference ◽  
Mixture Models ◽  
Gibbs Sampler ◽  
Simulation Study ◽  
Finite Mixture Models ◽  
Synthetic Data ◽  
Finite Mixture Model ◽  
Finite Mixture ◽  
Model Parameters ◽  
Mcmc Method

"This paper aims at the modeling the crashes count in Al Muthanna governance using finite mixture model. We use one of the most common MCMC method which is called the Gibbs sampler to implement the Bayesian inference for estimating the model parameters. We perform a simulation study, based on synthetic data, to check the ability of the sampler to find the best estimates of the model. We use the two well-known criteria, which are the AIC and BIC, to determine the best model fitted to the data. Finally, we apply our sampler to model the crashes count in Al Muthanna governance.

Explaining monotonic ranking functions

2020 ◽  
Vol 14 (4) ◽  
pp. 640-652
Author(s):  
Abraham Gale ◽  
Amélie Marian
Keyword(s):  
Decision Making ◽  
Selection Process ◽  
A Priori ◽  
Data Distribution ◽  
Synthetic Data ◽  
Decision Processes ◽  
Decision Makers ◽  
Ranking Functions ◽  
High School Admissions ◽  
Parameter Values

Ranking functions are commonly used to assist in decision-making in a wide variety of applications. As the general public realizes the significant societal impacts of the widespread use of algorithms in decision-making, there has been a push towards explainability and transparency in decision processes and results, as well as demands to justify the fairness of the processes. In this paper, we focus on providing metrics towards explainability and transparency of ranking functions, with a focus towards making the ranking process understandable, a priori , so that decision-makers can make informed choices when designing their ranking selection process. We propose transparent participation metrics to clarify the ranking process, by assessing the contribution of each parameter used in the ranking function in the creation of the final ranked outcome, using information about the ranking functions themselves, as well as observations of the underlying distributions of the parameter values involved in the ranking. To evaluate the outcome of the ranking process, we propose diversity and disparity metrics to measure how similar the selected objects are to each other, and to the underlying data distribution. We evaluate the behavior of our metrics on synthetic data, as well as on data and ranking functions on two real-world scenarios: high school admissions and decathlon scoring.

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