Application of well log tomography to the Dundee and Rogers City Limestones, Michigan Basin, USA

The Michigan Basin is located in the upper Midwest region of the United States and is centered geographically over the Lower Peninsula of Michigan. It is filled primarily with Paleozoic carbonates and clastics, overlying Precambrian basement rocks and covered by Pleistocene glacial drift. In Michigan, more than 46,000 wells have been drilled in the basin, many producing significant quantities of oil and gas since the 1920s in addition to providing a wealth of data for subsurface visualization. Well log tomography, formerly log-curve amplitude slicing, is a visualization method recently developed at Michigan Technological University to correlate subsurface data by utilizing the high vertical resolution of well log curves. The well log tomography method was first successfully applied to the Middle Devonian Traverse Group within the Michigan Basin using gamma ray log curves. The purpose of this study is to prepare a digital data set for the Middle Devonian Dundee and Rogers City Limestones, apply the well log tomography method to this data and from this application, interpret paleogeographic trends in the natural radioactivity. Both the Dundee and Rogers City intervals directly underlie the Traverse Group and combined are the most prolific reservoir within the Michigan Basin. Differences between this study and the Traverse Group include increased well control and “slicing” of a more uniform lithology. Gamma ray log curves for the Dundee and Rogers City Limestones were obtained from 295 vertical wells distributed over the Lower Peninsula of Michigan, converted to Log ASCII Standard files, and input into the well log tomography program. The “slicing” contour results indicate that during the formation of the Dundee and Rogers City intervals, carbonates and evaporites with low natural radioactive signatures on gamma ray logs were deposited. This contrasts the higher gamma ray amplitudes from siliciclastic deltas that cyclically entered the basin during Traverse Group deposition. Additionally, a subtle north-south, low natural radioactive trend in the center of the basin may correlate with previously published Dundee facies tracts. Prominent trends associated with the distribution of limestone and dolomite are not observed because the regional range of gamma ray values for both carbonates are equivalent in the Michigan Basin and additional log curves are needed to separate these lithologies.

Sonic log prediction in carbonates

This work is conducted to study the complications associated with the sonic log prediction in carbonate logs and to investigate the possible solutions to accurately predict the sonic logs in Traverse Limestone. Well logs from fifty different wells were analyzed to define the mineralogy of the Traverse Limestone by using conventional 4-mineral and 3-mineral identification approaches. We modified the conventional 3-mineral identification approach (that completely neglects the gamma ray response) to correct the shale effects on the basis of gamma ray log before employing the 3-mineral identification. This modification helped to get the meaningful insight of the data when a plot was made between DGA (dry grain density) and UMA (Photoelectric Volumetric Cross-section) with the characteristic ternary diagram of the quartz, calcite and dolomite. The results were then compared with the 4-mineral identification approach. Contour maps of the average mineral fractions present in the Traverse Limestone were prepared to see the basin wide mineralogy of Traverse Limestone. In the second part, sonic response of Traverse Limestone was predicted in fifty randomly distributed wells. We used the modified time average equation that accounts for the shale effects on the basis of gamma ray log, and used it to predict the sonic behavior from density porosity and average porosity. To account for the secondary porosity of dolomite, we subtracted the dolomitic fraction of clean porosity from the total porosity. The pseudo-sonic logs were then compared with the measured sonic logs on the root mean square (RMS) basis. Addition of dolomite correction in modified time average equation improved the results of sonic prediction from neutron porosity and average porosity. The results demonstrated that sonic logs could be predicted in carbonate rocks with a root mean square error of about 4μsec/ft. We also attempted the use of individual mineral components for sonic log prediction but the ambiguities in mineral fractions and in the sonic properties of the minerals limited the accuracy of the results.

Fading pdf of free-space optical communication system with pointing error

A free-space optical (FSO) laser communication system with perfect fast-tracking experiences random power fading due to atmospheric turbulence. For a FSO communication system without fast-tracking or with imperfect fast-tracking, the fading probability density function (pdf) is also affected by the pointing error. In this thesis, the overall fading pdfs of FSO communication system with pointing errors are calculated using an analytical method based on the fast-tracked on-axis and off-axis fading pdfs and the fast-tracked beam profile of a turbulence channel. The overall fading pdf is firstly studied for the FSO communication system with collimated laser beam. Large-scale numerical wave-optics simulations are performed to verify the analytically calculated fading pdf with collimated beam under various turbulence channels and pointing errors. The calculated overall fading pdfs are almost identical to the directly simulated fading pdfs. The calculated overall fading pdfs are also compared with the gamma-gamma (GG) and the log-normal (LN) fading pdf models. They fit better than both the GG and LN fading pdf models under different receiver aperture sizes in all the studied cases. Further, the analytical method is expanded to the FSO communication system with beam diverging angle case. It is shown that the gamma pdf model is still valid for the fast-tracked on-axis and off-axis fading pdfs with point-like receiver aperture when the laser beam is propagated with beam diverging angle. Large-scale numerical wave-optics simulations prove that the analytically calculated fading pdfs perfectly fit the overall fading pdfs for both focused and diverged beam cases. The influence of the fast-tracked on-axis and off-axis fading pdfs, the fast-tracked beam profile, and the pointing error on the overall fading pdf is also discussed. At last, the analytical method is compared with the previous heuristic fading pdf models proposed since 1970s. Although some of previously proposed fading pdf models provide close fit to the experiment and simulation data, these close fits only exist under particular conditions. Only analytical method shows accurate fit to the directly simulated fading pdfs under different turbulence strength, propagation distances, receiver aperture sizes and pointing errors.

Effectiveness of a nondestructive evaluation technique for assessing standing timber quality

The research presented in this thesis was conducted to further the development of the stress wave method of nondestructively assessing the quality of wood in standing trees. The specific objective of this research was to examine, in the field, use of two stress wave nondestructive assessment techniques. The first technique examined utilizes a laboratory-built measurement system consisting of commercially available accelerometers and a digital storage oscilloscope. The second technique uses a commercially available tool that incorporates several technologies to determine speed of stress wave propagation in standing trees. Field measurements using both techniques were conducted on sixty red pine trees in south-central Wisconsin and 115 ponderosa pine trees in western Idaho. After in-situ measurements were taken, thirty tested red pine trees were felled and a 15-foot-long butt log was obtained from each tree, while all tested ponderosa pine trees were felled and an 8 1/2 -foot-long butt log was obtained, respectively. The butt logs were sent to the USDA Forest Products Laboratory and nondestructively tested using a resonance stress wave technique. Strong correlative relationships were observed between stress wave values obtained from both field measurement techniques. Excellent relationships were also observed between standing tree and log speed-of-sound values.

A PETROPHYSICAL EVALUATION OF THE TRENTON-BLACK RIVER FORMATION OF THE MICHIGAN BASIN

This work is conducted to study the geological and petrophysical features of the Trenton- Black River limestone formation. Log curves, crossplots and mineral identification methods using well-log data are used to determine the components and analyze changes in lithology. Thirty-five wells from the Michigan Basin are used to define the mineralogy of Trenton-Black River limestone. Using the different responses of a few log curves, especially gamma-ray, resistivity and neutron porosity, the formation tops for the Utica shale, the Trenton limestone, the Black River limestone and the Prairie du Chien sandstone are identified to confirm earlier authors’ work and provide a basis for my further work. From these, an isopach map showing the thickness of Trenton-Black River formation is created, indicating that its maximum thickness lies in the eastern basin and decreases gradually to the west. In order to obtain more detailed lithological information about the limestone formations at the thirty-five wells, (a) neutron-density and neutron-sonic crossplots, (b) mineral identification methods, including the M-N plot, MID plot, ϱmaa vs. Umaa MID plot, and the PEF plot, and (c) a modified mineral identification technique are applied to these wells. From this, compositions of the Trenton-Black River formation can be divided into three different rock types: pure limestone, partially dolomitized limestone, and shaly limestone. Maps showing the fraction of dolomite and shale indicate their geographic distribution, with dolomite present more in the western and southwestern basin, and shale more common in the north-central basin. Mineral identification is an independent check on the distribution found from other authors, who found similar distributions based on core descriptions. The Thomas Stieber method of analysis is best suited to sand-shale sequences, interpreting hree different distributions of shale within sand, including dispersed, laminated and structural. Since this method is commonly applied in clastic rocks, my work using the Thomas Stieber method is new, as an attempt to apply this technique, developed for clastics, to carbonate rocks. Based on the original assumption and equations with a corresponding change to the Trenton-Black River formation, feasibility of using the Thomas Stieber method in carbonates is tested. A graphical display of gamma-ray versus density porosity, using the properties of clean carbonate and pure shale, suggests the presence of laminated shale in fourteen wells in this study. Combined with Wilson’s study (2001), it is safe to conclude that when shale occurs in the Trenton-Black River formation, it tends to be laminated shale.