The Ensemble Kalman Filter(EnKF),as the most popular sequential data assimilation algorithm for history matching,has the intrinsic problem of high computational cost and the potential inconsistency of state variables ...The Ensemble Kalman Filter(EnKF),as the most popular sequential data assimilation algorithm for history matching,has the intrinsic problem of high computational cost and the potential inconsistency of state variables updated at each loop of data assimilation and its corresponding reservoir simulated result.This problem forbids the reservoir engineers to make the best use of the 4D seismic data,which provides valuable information about the fluid change inside the reservoir.Moreover,only matching the production data in the past is not enough to accurately forecast the future,and the development plan based on the false forecast is very likely to be suboptimal.To solve this problem,we developed a workflow for geophysical and production data history matching by modifying ensemble smoother with multiple data assimilation(ESMDA).In this work,we derived the mathematical expressions of ESMDA and discussed its scope of applications.The geophysical data we used is P-wave impedance,which is typically included in a basic seismic interpretation,and it directly reflects the saturation change in the reservoir.Full resolution of the seismic data is not necessary,we subsampled the P-wave impedance data to further reduce the computational cost.With our case studies on a benchmark synthetic reservoir model,we also showed the supremacy of matching both geophysical and production data,than the traditional reservoir history matching merely on the production data:the overall percentage error of the observed data is halved,and the variances of the updated forecasts are reduced by two orders of the magnitude.展开更多
Simulation of reservoir flow processes at the finest scale is computationally expensive and in some cases impractical.Consequently,upscaling of several fine-scale grid blocks into fewer coarse-scale grids has become a...Simulation of reservoir flow processes at the finest scale is computationally expensive and in some cases impractical.Consequently,upscaling of several fine-scale grid blocks into fewer coarse-scale grids has become an integral part of reservoir simulation for most reservoirs.This is because as the number of grid blocks increases,the number of flow equations increases and this increases,in large proportion,the time required for solving flow problems.Although we can adopt parallel computation to share the load,a large number of grid blocks still pose significant computational challenges.Thus,upscaling acts as a bridge between the reservoir scale and the simulation scale.However as the upscaling ratio is increased,the accuracy of the numerical simulation is reduced;hence,there is a need to keep a balance between the two.In this work,we present a sensitivity-based upscaling technique that is applicable during history matching.This method involves partial homogenization of the reservoir model based on the model reduction pattern obtained from analysis of the sensitivity matrix.The technique is based on wavelet transformation and reduction of the data and model spaces as presented in the 2Dwp-wk approach.In the 2Dwp-wk approach,a set of wavelets of measured data is first selected and then a reduced model space composed of important wavelets is gradually built during the first few iterations of nonlinear regression.The building of the reduced model space is done by thresholding the full wavelet sensitivity matrix.The pattern of permeability distribution in the reservoir resulting from the thresholding of the full wavelet sensitivity matrix is used to determine the neighboring grids that are upscaled.In essence,neighboring grid blocks having the same permeability values due to model space reduction are combined into a single grid block in the simulation model,thus integrating upscaling with wavelet multiscale inverse modeling.We apply the method to estimate the parameters of two synthetic reservoirs.The history matching results obtained using this sensitivity-based upscaling are in very close agreement with the match provided by fine-scale inverse analysis.The reliability of the technique is evaluated using various scenarios and almost all the cases considered have shown very good results.The technique speeds up the history matching process without seriously compromising the accuracy of the estimates.展开更多
Vibration failure of piping is a serious problem and a matter of concern for safety and reliability of plant operations. Fatigue is the main cause of such failures. Due to the complexity of the phenomenon no closed fo...Vibration failure of piping is a serious problem and a matter of concern for safety and reliability of plant operations. Fatigue is the main cause of such failures. Due to the complexity of the phenomenon no closed form design solutions are available. In our study an analytical technique based on the theory of vibrations in the time domain has been presented. Using the inverse theory, the problem has been reduced to a system of Volterra Integral equations to be solved simultaneously at every time step. The solution of the inverse problem may be used in the conventional method to calculate stresses and end reactions which are important from the perspective of engineering design and condition monitoring. The method is robust, simple and can be easily adopted by practicing engineers.展开更多
基金supported by Chinese National Science and Technology Major Project(2016ZX05015-005).
文摘The Ensemble Kalman Filter(EnKF),as the most popular sequential data assimilation algorithm for history matching,has the intrinsic problem of high computational cost and the potential inconsistency of state variables updated at each loop of data assimilation and its corresponding reservoir simulated result.This problem forbids the reservoir engineers to make the best use of the 4D seismic data,which provides valuable information about the fluid change inside the reservoir.Moreover,only matching the production data in the past is not enough to accurately forecast the future,and the development plan based on the false forecast is very likely to be suboptimal.To solve this problem,we developed a workflow for geophysical and production data history matching by modifying ensemble smoother with multiple data assimilation(ESMDA).In this work,we derived the mathematical expressions of ESMDA and discussed its scope of applications.The geophysical data we used is P-wave impedance,which is typically included in a basic seismic interpretation,and it directly reflects the saturation change in the reservoir.Full resolution of the seismic data is not necessary,we subsampled the P-wave impedance data to further reduce the computational cost.With our case studies on a benchmark synthetic reservoir model,we also showed the supremacy of matching both geophysical and production data,than the traditional reservoir history matching merely on the production data:the overall percentage error of the observed data is halved,and the variances of the updated forecasts are reduced by two orders of the magnitude.
基金the support received from King Fahd University of Petroleum & Minerals through the DSR research Grant IN111046
文摘Simulation of reservoir flow processes at the finest scale is computationally expensive and in some cases impractical.Consequently,upscaling of several fine-scale grid blocks into fewer coarse-scale grids has become an integral part of reservoir simulation for most reservoirs.This is because as the number of grid blocks increases,the number of flow equations increases and this increases,in large proportion,the time required for solving flow problems.Although we can adopt parallel computation to share the load,a large number of grid blocks still pose significant computational challenges.Thus,upscaling acts as a bridge between the reservoir scale and the simulation scale.However as the upscaling ratio is increased,the accuracy of the numerical simulation is reduced;hence,there is a need to keep a balance between the two.In this work,we present a sensitivity-based upscaling technique that is applicable during history matching.This method involves partial homogenization of the reservoir model based on the model reduction pattern obtained from analysis of the sensitivity matrix.The technique is based on wavelet transformation and reduction of the data and model spaces as presented in the 2Dwp-wk approach.In the 2Dwp-wk approach,a set of wavelets of measured data is first selected and then a reduced model space composed of important wavelets is gradually built during the first few iterations of nonlinear regression.The building of the reduced model space is done by thresholding the full wavelet sensitivity matrix.The pattern of permeability distribution in the reservoir resulting from the thresholding of the full wavelet sensitivity matrix is used to determine the neighboring grids that are upscaled.In essence,neighboring grid blocks having the same permeability values due to model space reduction are combined into a single grid block in the simulation model,thus integrating upscaling with wavelet multiscale inverse modeling.We apply the method to estimate the parameters of two synthetic reservoirs.The history matching results obtained using this sensitivity-based upscaling are in very close agreement with the match provided by fine-scale inverse analysis.The reliability of the technique is evaluated using various scenarios and almost all the cases considered have shown very good results.The technique speeds up the history matching process without seriously compromising the accuracy of the estimates.
文摘Vibration failure of piping is a serious problem and a matter of concern for safety and reliability of plant operations. Fatigue is the main cause of such failures. Due to the complexity of the phenomenon no closed form design solutions are available. In our study an analytical technique based on the theory of vibrations in the time domain has been presented. Using the inverse theory, the problem has been reduced to a system of Volterra Integral equations to be solved simultaneously at every time step. The solution of the inverse problem may be used in the conventional method to calculate stresses and end reactions which are important from the perspective of engineering design and condition monitoring. The method is robust, simple and can be easily adopted by practicing engineers.
