Probabilistic decline curve analysis (PDCA) methods have been developed to quantify uncertainty in production forecasts and reserves estimates. However, the application of PDCA in shale gas reservoirs is relatively new. Limited work has been done on the performance of PDCA methods when the available production data are limited. In addition, PDCA methods have often been coupled with Arp’s equations, which might not be the optimum decline curve analysis model (DCA) to use, as new DCA models for shale reservoirs have been developed. Also, decline curve methods are based on production data only and do not by themselves incorporate other types of information, such as volumetric data. My research objective was to integrate volumetric information with PDCA methods and DCA models to reliably quantify the uncertainty in production forecasts from hydraulically fractured horizontal shale gas wells, regardless of the stage of depletion. In this work, hindcasts of multiple DCA models coupled to different probabilistic methods were performed to determine the reliability of the probabilistic DCA methods. In a hindcast, only a portion of the historical data is matched; predictions are made for the remainder of the historical period and compared to the actual historical production. Most of the DCA models were well calibrated visually when used with an appropriate probabilistic method, regardless of the amount of production data available to match. Volumetric assessments, used as prior information, were incorporated to further enhance the calibration of production forecasts and reserves estimates when using the Markov Chain Monte Carlo (MCMC) as the PDCA method and the logistic growth DCA model. The proposed combination of the MCMC PDCA method, the logistic growth DCA model, and use of volumetric data provides an integrated procedure to reliably quantify the uncertainty in production forecasts and reserves estimates in shale gas reservoirs. Reliable quantification of uncertainty should yield more reliable expected values of reserves estimates, as well as more reliable assessment of upside and downside potential. This can be particularly valuable early in the development of a play, because decisions regarding continued development are based to a large degree on production forecasts and reserves estimates for early wells in the play.

Proved reserves estimation is a crucial process since it impacts aspects of the petroleum business. By definition of the Society of Petroleum Engineers, the proved reserves must be estimated by reliable methods that must have a chance of at least a 90 percent probability (P90) that the actual quantities recovered will equal or exceed the estimates. Decline curve analysis, DCA, is a commonly used method; which a trend is fitted to a production history and extrapolated to an economic limit for the reserves estimation. The trend is the “best estimate” line that represents the well performance, which corresponds to the 50th percentile value (P50). This practice, therefore, conflicts with the proved reserves definition. An exponential decline model is used as a base case because it forms a straight line in a rate-cum coordinate scale. Two straight line fitting methods, i.e. ordinary least square and error-in-variables are compared. The least square method works better in that the result is consistent with the Gauss-Markov theorem. In compliance with the definition, the proved reserves can be estimated by determining the 90th percentile value of the descending order data from the variance. A conventional estimation using a principal of confidence intervals is first introduced to quantify the spread, a difference between P50 and P90, from the variability of a cumulative production. Because of the spread overestimation of the conventional method, the analytical formula is derived for estimating the variance of the cumulative production. The formula is from an integration of production of rate over a period of time and an error model. The variance estimations agree with Monte Carlo simulation (MCS) results. The variance is then used further to quantify the spread with the assumption that the ultimate cumulative production is normally distributed. Hyperbolic and harmonic models are also studied. The spread discrepancy between the analytics and the MCS is acceptable. However, the results depend on the accuracy of the decline model and error used. If the decline curve changes during the estimation period the estimated spread will be inaccurate. In sensitivity analysis, the trend of the spread is similar to how uncertainty changes as the parameter changes. For instance, the spread reduces if uncertainty reduces with the changing parameter, and vice versa. The field application of the analytical solution is consistent to the assumed model. The spread depends on how much uncertainty in the data is; the higher uncertainty we assume in the data, the higher spread. / text

This study examined science achievement growth across elementary and middle school and parent school involvement using the Early Childhood Longitudinal Study – Kindergarten Class of 1998 – 1999 (ECLS-K). The ECLS-K is a nationally representative kindergarten cohort of students from public and private schools who attended full-day or half-day kindergarten class in 1998 – 1999. The present study’s sample (N = 8,070) was based on students that had a sampling weight available from the public-use data file. Students were assessed in science achievement at third, fifth, and eighth grades and parents of the students were surveyed at the same time points. Analyses using latent growth curve modeling with time invariant and varying covariates in an SEM framework revealed a positive relationship between science achievement and parent involvement at eighth grade. Furthermore, there were gender and racial/ethnic differences in parents’ school involvement as a predictor of science achievement. Findings indicated that students with lower initial science achievement scores had a faster rate of growth across time. The achievement gap between low and high achievers in earth, space and life sciences lessened from elementary to middle school. Parents’ involvement with school usually tapers off after elementary school, but due to parent school involvement being a significant predictor of eighth grade science achievement, later school involvement may need to be supported and better implemented in secondary schooling.

Prior research demonstrates that military service disconnects men from past social and personal disadvantages and thus potentially alters normal life-course patterns of development. Much of this research, however, has been conducted only with World War II veterans. Relatively few studies have examined the influence of military service in Vietnam and its impact on altering individual trajectories of development. Through latent growth curve models, the authors examine the impact of military service in Vietnam on drug use and arrests across the life-course. Longitudinal data collected by the Marion County Youth study (1964-1979) were used to track a sample of men over a 15-year period. Analyses of these data revealed substantial nonrandom selection effects associated with service in Vietnam. Lower-class youths with already established delinquent patterns were significantly more likely to have served in Vietnam. It also appears, however, that service in Vietnam significantly increased individual drug use and, hence, offending rates.

Unconventional reservoir systems can best be described as petroleum (oil and/or gas) accumulations which are difficult to be characterized and produced by conventional technologies. In this work we present the development of a systematic procedure to evaluate well performance in unconventional (i.e., low to ultra-low permeability) reservoir systems. The specific tasks achieved in this work include the following: ● Integrated Diagnostics and Analysis of Production Data in Unconventional Reservoirs: We identify the challenges and common pitfalls of production analysis and provide guidelines for the analysis of production data. We provide a comprehensive workflow which consists of model-based production analysis (i.e., rate-transient or model matching approaches) complemented by traditional decline curve analysis to estimate reserves in unconventional reservoirs. In particular, we use analytical solutions (e.g., elliptical flow, horizontal well with multiple fractures solution, etc.) which are applicable to wells produced in unconventional reservoirs. ● Deconvolution: We propose to use deconvolution to identify the correlation between pressure and rate data. For our purposes we modify the B-spline deconvolution algorithm to obtain the constantpressure rate solution using cumulative production and bottomhole pressure data in real time domain. It is shown that constant-pressure rate and constant-rate pressure solutions obtained by deconvolution could identify the correlation between measured rate and pressure data when used in conjunction. ● Series of Rate-Time Relations: We develop three new main rate-time relations and five supplementary rate-time relations which utilize power-law, hyperbolic, stretched exponential, and exponential components to properly model the behavior of a given set of rate-time data. These relations are well-suited for the estimation of ultimate recovery as well as for extrapolating production into the future. While our proposed models can be used for any system, we provide application almost exclusively for wells completed in unconventional reservoirs as a means of providing estimates of time-dependent reserves. We attempt to correlate the rate-time relation model parameters versus model-based production analysis results. As example applications, we present a variety of field examples using production data acquired from tight gas, shale gas reservoir systems.

Current models used to forecast production in unconventional oil and gas formations are often not producing valid results. When traditional decline curve analysis models are used in shale formations, Arps b-values greater than 1 are commonly obtained, and these values yield infinite cumulative production, which is non-physical.. Additional methods have been developed to prevent the unrealistic values produced, like truncating hyperbolic declines with exponential declines when a minimum production rate is reached. Truncating a hyperbolic decline with an exponential decline solves some of the problems associated with decline curve analysis, but it is not an ideal solution. The exponential decline rate used is arbitrary, and the value picked greatly effects the results of the forecast. A new empirical model has been developed and used as an alternative to traditional decline curve analysis with the Arps equation. The new model is based on the concept of logistic growth models. Logistic growth models were originally developed in the 1830s by Belgian mathematician, Pierre Verhulst, to model population growth. The new logistic model for production forecasting in ultra-tight reservoirs uses the concept of a carrying capacity. The carrying capacity provides the maximum recoverable oil or gas from a single well, and it causes all forecasts produced with this model to be within a reasonable range of known volumetrically available oil. Additionally the carrying capacity causes the production rate forecast to eventually terminate as the cumulative production approaches the carrying capacity. The new model provides a more realistic method for forecasting reserves in unconventional formations than the traditional Arps model. The typical problems encountered when using conventional decline curve analysis are not present when using the logistic model. Predictions of the future are always difficult and often subject to factors such as operating conditions, which can never be predicted. The logistic growth model is well established, robust, and flexible. It provides a method to forecast reserves, which has been shown to accurately trend to existing production data and provide a realistic forecast based on known hydrocarbon volumes. / text

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Ongoing work in the laboratory of Professor Chris Backhouse is aimed at developing a portable and inexpensive lab on a chip instrument. A system capable of molecular biology protocols including sample preparation (SP), polymerase chain reaction (PCR), and melting curve analysis (MCA) would meet the requirements for point of care genetic analysis. The SP, PCR, and MCA modules were designed and tested on a standalone basis and then integrated for analysis of raw clinical samples. An automated XY stage was developed for magnetic bead-based DNA purification. In addition, a LED/CCD-based optical detection module was employed for real time PCR and MCA. Data analysis algorithms and protocols were implemented to remove noise and interpret data. This work culminated in proof of principle on-chip SP-PCR-MCA to detect ß2m DNA from human buccal cells in a modular and inexpensive system. / Biomedical Engineering

Thesis (M.S. Ed.)--Virginia Polytechnic Institute and State University, 1992. / Vita. Abstract. Includes bibliographical references (leaves 56-59). Also available via the Internet.