Browsing by Subject "Well Testing"
Now showing 1 - 3 of 3
Results Per Page
Sort Options
Item A New Series of Rate Decline Relations Based on the Diagnosis of Rate-Time Data(2010-01-14) Boulis, AnastasiosThe 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.Item Deconvolution of variable rate reservoir performance data using B-splines(Texas A&M University, 2007-04-25) Ilk, DilhanThis 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.Item Explicit deconvolution of wellbore storage distorted well test data(Texas A&M University, 2007-04-25) Bahabanian, OlivierThe 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.