Time-rate analysis and time-rate-pressure analysis methods are available to estimate reserves and study flow performance of wells in unconventional gas reservoirs. However, these tools are often incorrectly used or the analysis can become difficult because of the complex nature of the reservoir system. Conventional methods (e.g., Arps' time-rate relations) are often used incorrectly to estimate reserves from such reservoirs. It was only recently that a serious study was conducted to outline the limitations of these relations and to set guidelines for their correct application. New time-rate relations, particularly the Duong and logistic growth model, were introduced to estimate reserves and forecast production from unconventional reservoirs. These new models are being used with limited understanding of their characteristics and limitations. Moreover, well performance analyses using analytical/semi-analytical solutions (time-rate-pressure) are often complicated from non-uniqueness that arises when estimating well/formation properties. In this work, we present a detailed study of the Duong model and logistic growth model to investigate the behaviors and limitations of these models when analyzing production data from unconventional reservoirs. We consider production data generated from numerical simulation cases and data obtained from unconventional gas reservoirs to study the quality of match to specific flow regimes and compare accuracy of the reserve estimates. We use the power-law exponential model (PLE), which has been shown to model transient, transition and boundary-dominated flow regimes reliably, as a benchmark to study performance of Duong and logistic growth models. Moreover, we use the "continuous EUR" approach to compare these models during reserve estimation. Finally, we develop four new time-rate relations, based on characteristics of the time-rate data on diagnostic plots. Using diagnostic plots we show that the new time-rate relations provide a quality match to the production data across all flow regimes, leading to a reliable reserve estimate. In a preliminary study, we integrated time-rate model parameters with fundamental reservoir properties (i.e., fracture conductivity (Fc) and 30 year EUR (EUR30yr)), by studying 15 numerical simulation cases to yield parametric correlations. We have demonstrated a methodology to integrate time-rate model parameters and reservoir properties. This method avoids the non-uniqueness issues often associated with model-based production data analysis. This study provides theoretical basis for further demonstration of the methodology using field cases.

There is a huge demand in the industry to forecast production in shale gas reservoirs accurately. There are many methods including volumetric, Decline Curve Analysis (DCA), analytical simulation and numerical simulation. Each one of these methods has its advantages and disadvantages, but only the DCA technique can use readily available production data to forecast rapidly and to an extent accurately. The DCA methods in use in the industry such as the Arps method had originally been developed for Boundary dominated flow (BDF) wells but it has been observed in shale reservoirs the predominant flow regime is transient flow. Therefore it was imperative to develop newer models to match and forecast transient flow regimes. The SEDM/SEPD, the Duong model and the Arps with a minimum decline rate are models that have the ability to match and forecast wells with transient flow followed by boundary flow. I have revised the Duong model to forecast better than the original model. I have also observed a certain variation of the Duong model proves to be a robust model for most of the well cases and flow regimes. The modified Duong has been shown to work best compared to other deterministic models in most cases. For grouped datasets the SPED & Duong models forecast accurately while the Modified Arps does a poor job.

This study compares four recently developed decline curve methods and the traditional Arps or Fetkovich approach. The four methods which are empirically formulated for shale and tight gas wells are: 1. Power Law Exponential Decline (PLE). 2. Stretched Exponential Decline (SEPD). 3. Duong Method. 4. Logistic Growth Model (LGM). Each method has different tuning parameters and equation forms. The main objective of this work is to determine the best method(s) in terms of Estimated Ultimate Recovery (EUR) accuracy, goodness of fit, and ease of matching. In addition, these methods are compared against each other at different production times in order to understand the effect of production time on forecasts. As a part of validation process, all methods are benchmarked against simulation. This study compares the decline methods to four simulation cases which represent the common shale declines observed in the field. Shale wells, which are completed with horizontal wells and multiple traverse highly-conductive hydraulic fractures, exhibit long transient linear flow. Based on certain models, linear flow is preceded by bilinear flow if natural fractures are present. In addition to this, linear flow is succeeded by Boundary Dominated Flow (BDF) decline when pressure wave reaches boundary. This means four declines are possible, hence four simulation cases are required for comparison. To facilitate automatic data fitting, a non-linear regression program was developed using excel VBA. The program optimizes the Least-Square (LS) objective function to find the best fit. The used optimization algorithm is the Levenberg-Marquardt Algorithm (LMA) and it is used because of its robustness and ease of use. This work shows that all methods forecast different EURs and some fit certain simulation cases better than others. In addition, no method can forecast EUR accurately without reaching BDF. Using this work, engineers can choose the best method to forecast EUR after identifying the simulation case that is most analogous to their field wells. The VBA program and the matching procedure presented here can help engineers automate these methods into their forecasting sheets.