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This work presents the development, validation and application of a novel deconvolution method based on B-splines for analyzing variable-rate reservoir performance data. Variable-rate deconvolution is a mathematically unstable problem which has been under investigation by many researchers over the last 35 years. While many deconvolution methods have been developed, few of these methods perform well in practice - and the importance of variable-rate deconvolution is increasing due to applications of permanent downhole gauges and large-scale processing/analysis of production data. Under these circumstances, our objective is to create a robust and practical tool which can tolerate reasonable variability and relatively large errors in rate and pressure data without generating instability in the deconvolution process. We propose representing the derivative of unknown unit rate drawdown pressure as a weighted sum of Bsplines (with logarithmically distributed knots). We then apply the convolution theorem in the Laplace domain with the input rate and obtain the sensitivities of the pressure response with respect to individual B-splines after numerical inversion of the Laplace transform. The sensitivity matrix is then used in a regularized least-squares procedure to obtain the unknown coefficients of the B-spline representation of the unit rate response or the well testing pressure derivative function. We have also implemented a physically sound regularization scheme into our deconvolution procedure for handling higher levels of noise and systematic errors. We validate our method with synthetic examples generated with and without errors. The new method can recover the unit rate drawdown pressure response and its derivative to a considerable extent, even when high levels of noise are present in both the rate and pressure observations. We also demonstrate the use of regularization and provide examples of under and over-regularization, and we discuss procedures for ensuring proper regularization. Upon validation, we then demonstrate our deconvolution method using a variety of field cases. Ultimately, the results of our new variable-rate deconvolution technique suggest that this technique has a broad applicability in pressure transient/production data analysis. The goal of this thesis is to demonstrate that the combined approach of B-splines, Laplace domain convolution, least-squares error reduction, and regularization are innovative and robust; therefore, the proposed technique has potential utility in the analysis and interpretation of reservoir performance data.

The analysis/interpretation of wellbore storage distorted pressure transient test data remains one of the most significant challenges in well test analysis. Deconvolution (i.e., the "conversion" of a variable-rate distorted pressure profile into the pressure profile for an equivalent constant rate production sequence) has been in limited use as a "conversion" mechanism for the last 25 years. Unfortunately, standard deconvolution techniques require accurate measurements of flow-rate and pressure — at downhole (or sandface) conditions. While accurate pressure measurements are commonplace, the measurement of sandface flowrates is rare, essentially non-existent in practice. As such, the "deconvolution" of wellbore storage distorted pressure test data is problematic. In theory, this process is possible, but in practice, without accurate measurements of flowrates, this process can not be employed. In this work we provide explicit (direct) deconvolution of wellbore storage distorted pressure test data using only those pressure data. The underlying equations associated with each deconvolution scheme are derived in the Appendices and implemented via a computational module. The value of this work is that we provide explicit tools for the analysis of wellbore storage distorted pressure data; specifically, we utilize the following techniques: * Russell method (1966) (very approximate approach), * "Beta" deconvolution (1950s and 1980s), * "Material Balance" deconvolution (1990s). Each method has been validated using both synthetic data and literature field cases and each method should be considered valid for practical applications. Our primary technical contribution in this work is the adaptation of various deconvolution methods for the explicit analysis of an arbitrary set of pressure transient test data which are distorted by wellbore storage — without the requirement of having measured sandface flowrates.

This thesis presents new productivity and well testing formulae of horizontal wells. Taking a horizontal well as a uniform line source, this thesis finds velocity potential formula and the productivity formulae for a horizontal well in an ellipsoid of revolution drainage volume by solving analytically the involved three-dimensional partial differential equations. These formulae can account for the advantages of horizontal wells, and they are more accurate than other formulae which are based on two-dimensional hypotheses. This thesis also presents new well testing formulae of horizontal wells in a single porosity system and a double porosity system. Compared with the formulae published in the literature, our formulae, which do not use the sum of infinite series, are more reasonable and easy to be used in well testing analysis. / Master of Science

Well testing has long been used to determine the dynamic characteristics of a reservoir. However due to the increase in interest in exploring deep offshore reservoirs and the expense associated with performing well tests of sufficient duration, alternative methods for retrieving reservoir specific information from tests of limited duration are necessary. This thesis presents analysis of derivative plots from well tests in different locations along a heterogeneous channelized environment and the information that can be derived the shape of these plots. The viability of calibrating a multiple point proxy that captures the reservoir flow connectivity information contained in well test data is explored. Such a proxy can provide useful insight into the nature of reservoir heterogeneity in the vicinity of the well. The behavior of the log-log derivative plot gives invaluable information about the nature of the reservoir surrounding the penetrating wells. Based on the change in slope of the derivative plot one can tell if a flow conduit or a low permeability zone is close to the well. Proximity to these features is also indicated in the curvature of the derivative plot with the test plot showing increasing symmetry as flow boundaries are approached. This was found to be true in both systematic simulations as well as in real build up test data. The calibration of the multiple point permeability proxy also provides information about the connectivity of the reservoir. Single point statistics provide the best estimate for wells either inside a channel or very close to the channel boundary. This is because of the relative homogeneity of permeability values within the spatial template used for averaging. The further the well gets from the channel fewer high permeability blocks will be picked up by the template and thus multiple point models provide the best estimate for effective permeability, Keff. Three point models were found to be the most accurate when the template exhibited complex permeability transition from the mudstone to the channel facies. / text

The so-called "Arps" rate decline relations are by far the most widely used tool for assessing oil and gas reserves from rate performance. These relations (i.e., the exponential and hyperbolic decline relations) are empirical where the starting point for their derivation is given by the definitions of the "loss ratio" and the "derivative of the loss ratio", where the "loss ratio" is the ratio of rate data to derivative of rate data, and the "derivative of the loss ratio" is the "b-parameter" as defined by Arps [1945]. The primary goal of this work is the interpretation of the b-parameter continuously over time and thus the better understanding of its character. As is shown below we propose "monotonically decreasing functional forms" for the characterization of the b-parameter, in addition to the exponential and hyperbolic rate decline relations, where the b-parameter is assumed to be zero and constant, respectively. The proposed equations are as follow: b(t)=constant (Arps' hyperbolic rate-decline relation), []tbbtb10exp)(-bt= (exponential function), (power-law function), 10)(btbtb=)/(1)(10tbbtb+= (rational function). The corresponding rate decline relation for each case is obtained by solving the differential equation associated with the selected functional for the b-parameter. The next step of this procedure is to test and validate each of the rate decline relations by applying them to various numerical simulation cases (for gas), as well as for field data cases obtained from tight/shale gas reservoirs. Our results indicate that b-parameter is never constant but it changes continuously with time. The ultimate objective of this work is to establish each model as a potential analysis/diagnostic relation. Most of the proposed models yield more realistic estimations of gas reserves in comparison to the traditional Arps' rate decline relations (i.e., the hyperbolic decline) where the reserves estimates are inconsistent and over-estimated. As an example, the rational b-parameter model seems to be the most accurate model in terms of representing the character of rate data; and therefore, should yield more realistic reserves estimates. Illustrative examples are provided for better understanding of each b-parameter rate decline model. The proposed family of rate decline relations was based on the character of the b-parameter computed from the rate-time data and they can be applied to a wide range of data sets, as dictated by the character of rate data.

This thesis describes two novel Bayesian methods: the Iterative Ensemble Square Filter (IEnSRF) and the Warp Ensemble Square Root Filter (WEnSRF) for solving the barcode detection problem, the deconvolution problem in well testing and the history matching problem of facies patterns. For the barcode detection problem, at the expanse of overestimating the posterior uncertainty, the IEnSRF efficiently achieves successful detections with very challenging real barcode images which the other considered methods and commercial software fail to detect. It also performs reliable detection on low-resolution images under poor ambient light conditions. For the deconvolution problem in well testing, the IEnSRF is capable of quantifying estimation uncertainty, incorporating the cumulative production data and estimating the initial pressure, which were thought to be unachievable in the existing well testing literature. The estimation results for the considered real benchmark data using the IEnSRF significantly outperform the existing methods in the commercial software. The WEnSRF is utilised for solving the history matching problem of facies patterns. Through the warping transformation, the WEnSRF performs adjustment on the reservoir features directly and is thus superior in estimating the large-scale complicated facies patterns. It is able to provide accurate estimates of the reservoir properties robustly and efficiently with reasonably reliable prior reservoir structural information.

[pt] O principal objetivo deste trabalho é preencher canais turbidíticos com alguma propriedade petrofísica, como a permeabilidade. Estes canais são geometricamente limitados por lobos turbidíticos, gerando a simulação de um sistema deposicional. Simulações numéricas são usadas para tentar ajustar a permeabilidade a um caso de referência por meio de uma função objetivo. Um simulador convencional de diferenças finitas foi usado para comparar os dados de referência com as simulações, obtendo resultados próximos. / [en] The main objective of this work is to populate turbidite channels with some petrophysical property such as permeability. These channels are geometrically constrained by turbidite lobes creating a simulated depositional system. Numerical simulations are used to try to fit the permeability field to a reference case through an objective function. A conventional finite difference simulator was used to compare the reference data to the simulations, obtaining close results.

Reservoir testing and analysis are fundamental tools in understanding reservoir hydraulics and hence forecasting reservoir responses. The quality of the analysis is very dependent on the conceptual model used in investigating the responses under different flowing conditions. The use of reservoir testing in the characterization and derivation of reservoir parameters is widely established, especially in conventional oil and gas reservoirs. However, with depleting conventional reserves, the quest for unconventional reservoirs to secure the increasing demand for energy is increasing; which has triggered intensive research in the fields of reservoir characterization. Gas hydrate reservoirs, being one of the unconventional gas reservoirs with huge energy potential, is still in the juvenile stage with reservoir testing as compared to the other unconventional reservoirs. The endothermic dissociation hydrates to gas and water requires addressing multiphase flow and heat energy balance, which has made efforts to develop reservoir testing models in this field difficult. As of now, analytically quantifying the effect on hydrate dissociation on rate and pressure transient responses are till date a huge challenge. During depressurization, the heat energy stored in the reservoir is used up and due to the endothermic nature of the dissociation; heat flux begins from the confining layers. For Class 3 gas hydrates, just heat conduction would be responsible for the heat influx and further hydrate dissociation; however, the moving boundary problem could also be an issue to address in this reservoir, depending on the equilibrium pressure. To address heat flux problem, a proper definition of the inner boundary condition for temperature propagation using a Clausius-Clapeyron type hydrate equilibrium model is required. In Class 1 and 2, crossflow problems would occur and depending on the layer of production, convective heat influx from the free fluid layer and heat conduction from the cap rock of the hydrate layer would be further issues to address. All these phenomena make the derivation of a suitable reservoir testing model very complex. However, with a strong combination of heat energy and mass balance techniques, a representative diffusivity equation can be derived. Reservoir testing models have been developed and responses investigated for different boundary conditions in normally pressured Class 3 gas hydrates, over-pressured Class 3 gas hydrates (moving boundary problem) and Class 1 and 2 gas hydrates (crossflow problem). The effects of heat flux on the reservoir responses have been addressed in detail.

Reservoir testing and analysis are fundamental tools in understanding reservoir hydraulics and hence forecasting reservoir responses. The quality of the analysis is very dependent on the conceptual model used in investigating the responses under different flowing conditions. The use of reservoir testing in the characterization and derivation of reservoir parameters is widely established, especially in conventional oil and gas reservoirs. However, with depleting conventional reserves, the quest for unconventional reservoirs to secure the increasing demand for energy is increasing; which has triggered intensive research in the fields of reservoir characterization. Gas hydrate reservoirs, being one of the unconventional gas reservoirs with huge energy potential, is still in the juvenile stage with reservoir testing as compared to the other unconventional reservoirs. The endothermic dissociation hydrates to gas and water requires addressing multiphase flow and heat energy balance, which has made efforts to develop reservoir testing models in this field difficult. As of now, analytically quantifying the effect on hydrate dissociation on rate and pressure transient responses are till date a huge challenge. During depressurization, the heat energy stored in the reservoir is used up and due to the endothermic nature of the dissociation; heat flux begins from the confining layers. For Class 3 gas hydrates, just heat conduction would be responsible for the heat influx and further hydrate dissociation; however, the moving boundary problem could also be an issue to address in this reservoir, depending on the equilibrium pressure. To address heat flux problem, a proper definition of the inner boundary condition for temperature propagation using a Clausius-Clapeyron type hydrate equilibrium model is required. In Class 1 and 2, crossflow problems would occur and depending on the layer of production, convective heat influx from the free fluid layer and heat conduction from the cap rock of the hydrate layer would be further issues to address. All these phenomena make the derivation of a suitable reservoir testing model very complex. However, with a strong combination of heat energy and mass balance techniques, a representative diffusivity equation can be derived. Reservoir testing models have been developed and responses investigated for different boundary conditions in normally pressured Class 3 gas hydrates, over-pressured Class 3 gas hydrates (moving boundary problem) and Class 1 and 2 gas hydrates (crossflow problem). The effects of heat flux on the reservoir responses have been addressed in detail.