Production forecasting in shale (ultra-low permeability) gas reservoirs is of great interest due to the advent of multi-stage fracturing and horizontal drilling. The well renowned production forecasting model, Arps? Hyperbolic Decline Model, is widely used in industry to forecast shale gas wells. Left unconstrained, the model often overestimates reserves by a great deal. A minimum decline rate is imposed to prevent overestimation of reserves but with less than ten years of production history available to analyze, an accurate minimum decline rate is currently unknown; an educated guess of 5% minimum decline is often imposed. Other decline curve models have been proposed with the theoretical advantage of being able to match linear flow followed by a transition to boundary dominated flow. This thesis investigates the applicability of the Stretched Exponential Production Decline Model (SEPD) and compares it to the industry standard, Arps' with a minimum decline rate. When possible, we investigate an SEPD type curve. Simulated data is analyzed to show advantages of the SEPD model and provide a comparison to Arps' model with an imposed minimum decline rate of 5% where the full production history is known. Long-term production behavior is provided by an analytical solution for a homogenous reservoir with homogenous hydraulic fractures. Various simulations from short-term linear flow (~1 year) to long-term linear flow (~20 years) show the ability of the models to handle onset of boundary dominated flow at various times during production history. SEPD provides more accurate reserves estimates when linear flow ends at 5 years or earlier. Both models provide sufficient reserves estimates for longer-term linear flow scenarios. Barnett Shale production data demonstrates the ability of the models to forecast field data. Denton and Tarrant County wells are analyzed as groups and individually. SEPD type curves generated with 2004 well groups provide forecasts for wells drilled in subsequent years. This study suggests a type curve is most useful when 24 months or less is available to forecast. The SEPD model generally provides more conservative forecasts and EUR estimates than Arps' model with a minimum decline rate of 5%.

Today everyone seems to agree that ultra-low permeability and shale reservoirs have become the potentials to transform North America's oil and gas industry to a new phase. Unfortunately, transient flow is of long duration (perhaps life of the well) in ultra-low permeability reservoirs, and traditional decline curve analysis (DCA) models can lead to significantly over-optimistic production forecasts without additional safeguards. Stretched Exponential decline model (SEDM) gives considerably more stabilized production forecast than traditional DCA models and in this work it is shown that it produces unchanging EUR forecasts after only two-three years of production data are available in selected reservoirs, notably the Barnett Shale. For an individual well, the SEDM model parameters, can be determined by the method of least squares in various ways, but the inherent nonlinear character of the least squares problem cannot be bypassed. To assure a unique solution to the parameter estimation problem, this work suggests a physics-based regularization approach, based on critical velocity concept. Applied to selected Barnett Shale gas wells, the suggested method leads to reliable and consistent EURs. To further understand the interaction of the different fracture properties on reservoir response and production decline curve behavior, a series of Discrete Fracture Network (DFN) simulations were performed. Results show that at least a 3-layer model is required to reproduce the decline behavior as captured in the published SEDM parameters for Barnett Shale. Further, DFN modeling implies a large number of parameters like fracture density and fracture length are in such a way that their effect can be compensated by the other one. The results of DFN modeling of several Barnett Shale horizontal wells, with numerous fracture stages, showed a very good agreement with the estimated SEDM model for the same wells. Estimation of P90 reserves that meet SEC criteria is required by law for all companies that raise capital in the United States. Estimation of P50 and P10 reserves that meet SPE/WPC/AAPG/SPEE Petroleum Resources Management System (PRMS) criteria is important for internal resource inventories for most companies. In this work a systematic methodology was developed to quantify the range of uncertainty in production forecast using SEDM. This methodology can be used as a probabilistic tool to quantify P90, P50, and P10 reserves and hence might provide one possible way to satisfy the various legal and technical-society-suggested criteria.

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Certain hydrogel forming de novo proteins that utilize different crosslinking methods are studied experimentally on a rheometer. The stress reaxation modulus of CRC, a telechelic, triblock protein, is shown to be that of a stretched exponential function with a value of β ≅ 0.5. The insertion of an integrin binding domain and changes in pH within the range 6.5–8.5 are shown not to significantly affect the resulting rheological behavior. A selective chemical crosslinker is used on CRC hydrogel systems and is shown to change the rheological behavior of the system to that of a combination of a chemically and physically crosslinked system. Chemically crosslinked hydrogels composed of W6, a wheat gluten-based protein, demonstrate a storage modulus weakly dependent on the angular frequency that is much greater than the loss modulus, with a modulus concentration dependence of c^9/4.

Certain hydrogel forming de novo proteins that utilize different crosslinking methods are studied experimentally on a rheometer. The stress reaxation modulus of CRC, a telechelic, triblock protein, is shown to be that of a stretched exponential function with a value of β ≅ 0.5. The insertion of an integrin binding domain and changes in pH within the range 6.5–8.5 are shown not to significantly affect the resulting rheological behavior. A selective chemical crosslinker is used on CRC hydrogel systems and is shown to change the rheological behavior of the system to that of a combination of a chemically and physically crosslinked system. Chemically crosslinked hydrogels composed of W6, a wheat gluten-based protein, demonstrate a storage modulus weakly dependent on the angular frequency that is much greater than the loss modulus, with a modulus concentration dependence of c^9/4.

Reserves estimation in an unconventional-reservoir setting is a daunting task because of geologic uncertainty and complex flow patterns evolving in a long-stimulated horizontal well, among other variables. To tackle this complex problem, we present a reserves-evaluation workflow that couples the traditional decline-curve analysis with a probabilistic forecasting frame. The stretched-exponential production decline model (SEPD) underpins the production behavior. Our recovery appraisal workflow has two different applications: forecasting probabilistic future performance of wells that have production history; and forecasting production from new wells without production data. For the new field case, numerical model runs are made in accord with the statistical design of experiments for a range of design variables pertinent to the field of interest. In contrast, for the producing wells the early-time data often need adjustments owing to restimulation, installation of artificial-lift, etc. to focus on the decline trend. Thereafter, production data of either new or existing wells are grouped in accord with initial rates to obtain common SEPD parameters for similar wells. After determining the distribution of model parameters using well grouping, the methodology establishes a probabilistic forecast for individual wells. We present a probabilistic performance forecasting methodology in unconventional reservoirs for wells with and without production history. Unlike other probabilistic forecasting tools, grouping wells with similar production character allows estimation of self-consistent SEPD parameters and alleviates the burden of having to define uncertainties associated with reservoir and well-completion parameters.

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.

Certain hydrogel forming de novo proteins that utilize different crosslinking methods are studied experimentally on a rheometer. The stress reaxation modulus of CRC, a telechelic, triblock protein, is shown to be that of a stretched exponential function with a value of β ≅ 0.5. The insertion of an integrin binding domain and changes in pH within the range 6.5–8.5 are shown not to significantly affect the resulting rheological behavior. A selective chemical crosslinker is used on CRC hydrogel systems and is shown to change the rheological behavior of the system to that of a combination of a chemically and physically crosslinked system. Chemically crosslinked hydrogels composed of W6, a wheat gluten-based protein, demonstrate a storage modulus weakly dependent on the angular frequency that is much greater than the loss modulus, with a modulus concentration dependence of c^9/4.

Certain hydrogel forming de novo proteins that utilize different crosslinking methods are studied experimentally on a rheometer. The stress reaxation modulus of CRC, a telechelic, triblock protein, is shown to be that of a stretched exponential function with a value of β ≅ 0.5. The insertion of an integrin binding domain and changes in pH within the range 6.5–8.5 are shown not to significantly affect the resulting rheological behavior. A selective chemical crosslinker is used on CRC hydrogel systems and is shown to change the rheological behavior of the system to that of a combination of a chemically and physically crosslinked system. Chemically crosslinked hydrogels composed of W6, a wheat gluten-based protein, demonstrate a storage modulus weakly dependent on the angular frequency that is much greater than the loss modulus, with a modulus concentration dependence of c^9/4.

No description available.