Geophysical Journal International, v. 169, n. 2, p. 667-674, 2007. http://dx.doi.org/10.1111/j.1365-246X.2007.03359.xInternational audienc

No abstract

Summary Rock composition can be related to conventional well logs through theoretical equations and petrophysical endpoints. Multimineral analysis is a formation evaluation tool that uses inversions to quantify rock composition from well logs. However, because of data errors and the multivariate selection of petrophysical endpoints, solutions from the multimineral analysis are nonunique. Many plausible realizations exhibit comparable data misfits. Therefore, the uncertainties in rock composition and petrophysical endpoints must be quantified but cannot be fulfilled by deterministic solvers. Stochastic Bayesian methods have been applied to assess the uncertainties, but the high run time, tedious parameter tuning, and need for specific prior information hinder their practical use. We implement Markov chain Monte Carlo with ensemble samplers (MCMCES) to assess the uncertainties of rock composition or petrophysical endpoints in the Bayesian framework. The resultant posterior probability density functions (PDFs) quantify the uncertainties. Our method has fewer tuning parameters and is more efficient in convergence than the conventional random walk Markov chain Monte Carlo (MCMC) methods in high-dimensional problems. We present two independent applications of MCMCES in multimineral analysis. We first apply MCMCES to assess the uncertainties in volume fractions with a suite of well logs and petrophysical endpoints. However, defining the petrophysical endpoints can be challenging in complex geological settings because the values of standard endpoints may not be optimal. Next, we use MCMCES to estimate petrophysical endpoints’ posterior PDFs when the endpoints are uncertain. Our methods provide posterior volume-fraction or petrophysical-endpoint realizations for interpreters to evaluate multimineral solutions. We demonstrate our approach with synthetic and field examples. Reproducible results are supplemented with the paper.

Multimineral log analysis is a quantitative formation evaluation tool for geological and petrophysical reservoir characterization. Rock composition can be estimated by solving equations that relate log measurements to the petrophysical endpoints of minerals and fluids. Due to errors in log data and uncertainties in petrophysical endpoints of constituents, we propose using effective medium models from rock physics as additional independent information to validate or constrain the results. In this paper, we examine the Voigt-Reuss (VR) bound model, self-consistent approximation (SCA), and differential effective medium (DEM). The VR bound model provides the first-order quality control of multimineral results. We first show a conventional carbonate reservoir study with intervals where the predicted effective medium models from multimineral results are inconsistent with the measured elastic properties. We use the VR bound model as an inequality constraint in multimineral analysis for plausible alternative solutions. SCA and DEM models provide good estimates in low porosity intervals and imply geological information for the porous intervals. Then, we show a field case of the Bakken and Three Forks formations. A linear interpolation of the VR bound model helps validate multimineral results and approximate the elastic moduli of clay. There are two major advantages to use our new method (a) rock physics effective medium models provide independent quality control of petrophysical multimineral results, and (b) multimineral information leads to realistic rock physics models.

An Improved Particle Swarm Optimization-Based Fuzzy PID Control Algorithm(IPSO-PID) is used to address the problem of poor CFRP molding quality caused by the inadequate adaptive capability and slow response time of the induction heating temperature control system during the curing process of carbon fiber reinforced polymer (CFRP) by electromagnetic induction heating. The three PID parameters are optimized and self-adjusted using the improved algorithm. This algorithm combines the advantages of PSO and Fuzzy-PID algorithms. It guarantees the control accuracy and search performance of the improved algorithm during the iterative process and prevents the improved algorithm from settling for the local optimal solution. The outcomes of simulation and experimentation demonstrate that the algorithm significantly improves the controller’s capacity for adaptation and shortens the adjustment period. In contrast to the conventional PID algorithm, this algorithm is better suited for controlling the temperature of electromagnetic induction heating CFRP because it reduces overshoot and steady-state error more than it does.