The proposed work provides a new definition of the pressure derivative function [that is the β-derivative function, Δp βd(t)], which is defined as the derivative of the logarithm of pressure drop data with respect to the logarithm of time This formulation is based on the "power-law" concept. This is not a trivial definition, but rather a definition that provides a unique characterization of "power-law" flow regimes which are uniquely defined by the Δp βd(t) function [that is a constant Δp βd(t) behavior]. The Δp βd(t) function represents a new application of the traditional pressure derivative function, the "power-law" differentiation method (that is computing the dln(Δp)/dln(t) derivative) provides an accurate and consistent mechanism for computing the primary pressure derivative (that is the Cartesian derivative, dΔp/dt) as well as the "Bourdet" well testing derivative [that is the "semilog" derivative, Δpd(t)=dΔp/dln(t)]. The Cartesian and semilog derivatives can be extracted directly from the power-law derivative (and vice-versa) using the definition given above.

Shale gas has become increasingly important to United States energy supply. During recent decades, the mechanisms of shale gas storage and transport were gradually recognized. Gas desorption was also realized and quantitatively described. Models and approaches special for estimating rate decline and recovery of shale gas wells were developed. As the strategy of the horizontal well with multiple transverse fractures (MTFHW) was discovered and its significance to economic shale gas production was understood, rate decline and pressure transient analysis models for this type of well were developed to reveal the well behavior. In this thesis, we considered a “Triple-porosity/Dual-permeability” model and performed sensitivity studies to understand long term pressure drawdown behavior of MTFHWs. A key observation from this study is that the early linear flow regime before interfracture interference gives a relationship between summed fracture half-length and permeability, from which we can estimate either when the other is known. We studied the impact of gas desorption on the time when the pressure perturbation caused by production from adjacent transference fractures (fracture interference time) and programmed an empirical method to calculate a time shift that can be used to qualify the gas desorption impact on long term production behavior. We focused on the field case Well A in New Albany Shale. We estimated the EUR for 33 wells, including Well A, using an existing analysis approach. We applied a unified BU-RNP method to process the one-year production/pressure transient data and performed PTA to the resulting virtual constant-rate pressure drawdown. Production analysis was performed meanwhile. Diagnosis plots for PTA and RNP analysis revealed that only the early linear flow regime was visible in the data, and permeability was estimated both from a model match and from the relationship between fracture halflength and permeability. Considering gas desorption, the fracture interference will occur only after several centuries. Based on this result, we recommend a well design strategy to increase the gas recovery factor by decreasing the facture spacing. The higher EUR of Well A compared to the vertical wells encourages drilling more MTFHWs in New Albany Shale.

In practice today, pressure transient analysis (PTA) and production data analysis (PDA) are done separately and differently by different interpreters in different companies using different analysis techniques, different interpreter-dependent inputs, on pressure and production rate data from the same well, with different software packages. This has led to different analyses outputs and characterizations of the same reservoir. To avoid inconsistent results from different interpretations, this study presents a new way to integrate PTA and PDA on a single diagnostic plot to account for and see the early time and mid-time responses (from the transient tests) and late time (boundary affected/PSS) responses achievable with production analysis, on the same plot; thereby unifying short and long-term analyses and improving the reservoir characterization. The rate normalized pressure (RNP) technique was combined with conventional pressure buildup PTA technique. Data processing algorithms were formulated to improve plot presentation and a stepwise analysis procedure is presented to apply the new technique. The new technique is simple to use and the same conventional interpretation techniques as PTA apply. We have applied the technique to a simulated well case and two field cases. Finally, this new technique represents improvements over previous PDA methods and can help give a long term dynamic description of the well’s drainage area.

With the increase in energy consumption, new oil and gas extraction methods in unconventional resources have been explored. Hydraulic fracturing creates fractures to produce and make low permeability reservoirs economically profitable. Hydraulic fractures are also caused unintentionally by the uncontrolled injection in secondary recovery projects or CO2 geological storage. During proppant placement and CO2 injection, the permeability is reduced near the wellbore region due to pore clogging and mineral precipitation. The generated fractures act as high conductivity conduits that increase the capacity of flow in the reservoir. The fracture conductivity is strictly related to its geometry and hydraulic properties. However, these tend to degrade as pressure decreases. The current models do not consider fracture width change in the diffusivity inside the fracture. Additionally, the effect of fracture face skin in fracture closure has not been incorporated. This work focuses on the identification of fracture closure in fractured wells using Pressure Transient data. A semi-analytical model was developed for including the effects of fracture closure, fracture face skin, and complex fracture geometries. The matrix and fracture systems are coupled by pressure continuity at the interface. Fracture face skin is added, assuming a thin layer surrounding the fracture. The model is solved in Laplace space using a semi-analytical approach. The results are validated using a commercial simulator (CMG) and previous models. The pressure response in fractured wells with stress-sensitive fractures is analyzed at early, middle, and late times. In each time period, we identify pressure signals to detect fracture closure by incorporating effective fracture compressibility and fracture conductivity reduction. By incorporating the effective fracture compressibility, the model can reproduce a high storage capacity fracture signal. This signal occurs at early times and can help in post-fracture analysis. The fracture face skin creates an additional pressure drop in the fracture system, triggering conductivity reduction earlier than an undamaged fracture. We proposed a semi-log approach to identify fracture closure for slow rates of fracture closure and the pseudo-radial simplification to generate late time response curves instead of the complete solution for the model.

[pt] Este trabalho apresenta um novo modelo térmico analítico que acopla poço e reservatório, constituído por um sistema combinado de reservatório, revestimento e coluna de produção. As soluções analíticas consideram fluxo monofásico de fluido pouco compressível em um reservatório homogêneo e infinito e fornecem dados transitórios de temperatura e pressão ao longo do poço para testes de fluxo e de crescimento de pressão, considerando efeitos Joule-Thomson, de expansão adiabática, de condução e convecção. A massa específica do fluido é modelada como função da temperatura e a solução analítica faz uso da transformada de Laplace para resolver a equação diferencial de fluxo de calor transiente, assumindo o termo aT⁄az totalmente transiente. Com relação à análise de transientes de pressão (PTA), dados de pressão impactados por variações térmicas podem levar à interpretação de falsas heterogeneidades geológicas, pois a perda de calor durante a estática proporciona um aumento da pressão exercida pela coluna de fluido, devido ao incremento de sua massa específica, além de uma contração da coluna de produção, provocando uma mudança na posição do registrador. Esses efeitos podem fazer com que um reservatório homogêneo seja erroneamente interpretado como um reservatório de dupla porosidade, resultando em conclusões inválidas para a modelagem geológica. Os resultados deste trabalho são comparados com a resposta de um simulador comercial não-isotérmico e impactos nas interpretações são extensivamente investigados. Adicionalmente, um estudo de caso de campo é fornecido para validar as soluções analíticas propostas. Comparado à Literatura, o modelo proposto fornece perfis transientes de temperatura mais acurados. / [en] This work presents a new coupled transient-wellbore/reservoir thermal analytical model, consisting of a reservoir/casing/tubing combined system. The analytical solutions consider flow of a slightly compressible, single-phase fluid in a homogeneous infinite-acting reservoir system and provide temperature- and pressure-transient data for drawdown and buildup tests at any gauge location along the wellbore, accounting for Joule-Thomson, adiabatic fluid-expansion, conduction and convection effects. The wellbore fluid mass density is modeled as a function of temperature and the analytical solution makes use of the Laplace transformation to solve the transient heat-flow differential equation, accounting for a rigorous transient wellbore-temperature gradient aT⁄az. Regarding pressure transient analysis (PTA), thermal impacted pressure data may lead to the interpretation of false geological heterogeneities, since the heat loss during the buildup period provides an increase in the pressure exerted by the wellbore-fluid column, due to an increase in the oil mass density, and a change in tubing length, consequently causing a change in the gauge location. These effects can make a homogeneous reservoir be wrongly interpreted as a double-porosity reservoir, yielding invalid conclusions to geological modeling. Results are compared to the response of a commercial non-isothermal simulator and thermal impacts on PTA interpretations are thoroughly investigated. In addition, a field case study is also provided to verify the proposed analytical solutions. The proposed model provides more accurate transient temperature flow profiles along the wellbore when compared to previous models in Literature.

[pt] Modelos analíticos que descrevam o comportamento da pressão são de extrema utilidade na área de avaliação de formações e caracterização de reservatório, pois eles fornecem estimativas sobre diversos parâmetros do reservatório. Este trabalho tem dois objetivos principais: primeiro, estender a solução existente para testes de injetividade e falloff em reservatórios com uma camada e poços horizontais de modo que ela possa ser aplicada também em formações multicamadas com poços horizontais multirramificados. Além disso, este trabalho aplica funções impulso para obter uma formulação alternativa para testes de injetividade em reservatórios estratificados com poços verticais e formações com uma camada e poços horizontais. / [en] Analytical models that describe the pressure behavior are extremely useful for pressure transient analysis and reservoir characterization as they provide estimates of reservoir parameters. This work has two main goals: first, to extend the existing solutions for injectivity/falloff tests in single-layer formations with horizontal wells so that they can be applied to multilayer stratified reservoirs with multilateral horizontal wells. Furthermore, this work applies impulse functions to obtain an alternative formulation for injectivity tests in multilayer commingled formations with vertical wells and single-layer reservoirs with horizontal wells.

[pt] Teste de injetividade é uma técnica convencional em engenharia de reservatórios, utilizada para a recuperação de óleo em reservatórios e avaliação de formações. Geralmente utiliza-se água como fluido injetado, que resulta em um deslocamento do óleo presente devido ao aumento da pressão nos poros. Durante o teste, a resposta de pressão medida fornece diversas informações sobre os parâmetros do reservatório, tal como dados de permeabilidade. Desta forma, pesquisadores têm se dedicado em encontrar equações matemáticas que modelam a resposta de pressão desses testes com objetivo de gerenciamento e manutenção preditiva do reservatório. Neste trabalho, apresentamos uma nova solução analítica para a análise de testes de injetividade, que combina a técnica de convolução pressão-pressão com um modelo radial composto de duas zonas. Essa solução permite avaliar o teste de injetividade mesmo na ausência de dados precisos de vazão, uma vez que a convolução pressão-pressão utiliza exclusivamente os dados de pressão adquiridos em diferentes posições do reservatório. O modelo considerado consiste em dois poços, um injetor, localizado na zona interna do reservatório, e um observador, na zona externa. A validação da solução proposta foi realizada por meio da comparação dos resultados analíticos com aqueles obtidos em um simulador comercial baseado em diferenças finitas. / [en] The injectivity test is a conventional technique in reservoir engineering used for oil recovery and formation evaluation. Typically, water is injected to displace the existing oil by increasing the pressure in the pores. In this test, the pressure response measurement provides valuable information about the reservoir parameters, including permeability data. Therefore, researchers aim to develop mathematical equations that could accurately model pressure response during these tests for reservoir management and maintenance prediction purposes. This work introduces a new analytical solution for injectivity test analysis. The solution combines the pressure-pressure convolution technique with a two-zone radial model. It allows the evaluation of the injectivity test without precise flow rate data, as the pressure-pressure convolution exclusively uses the pressure data acquired at different positions in the reservoir. The reservoir model comprises an injector well in the inner zone of the reservoir and an observation well in the outer zone for measuring pressure response. The proposed solution was validated by comparing the analytical results with those obtained from a finite differences-based commercial simulator.