Toward a Unified Theory of Well Testing for Nonlinear-Radial-Flow Problems With Application to Interference Tests

1990 ◽  
Vol 5 (02) ◽  
pp. 151-160 ◽  
Author(s):  
Alvaro M.M. Peres ◽  
Kelson V. Serra ◽  
Albert C. Reynolds
Keyword(s):  
Radial Flow ◽  
Well Testing ◽  
Unified Theory ◽  
Flow Problems ◽  
Interference Tests

An Approximate Method for Transient Radial Flow

1962 ◽  
Vol 2 (03) ◽  
pp. 225-256 ◽  
Author(s):  
G. Rowan ◽  
M.W. Clegg
Keyword(s):  
Infinite Series ◽  
Analytical Solutions ◽  
Radial Flow ◽  
Numerical Solutions ◽  
Basic Theory ◽  
Variable Pressure ◽  
Flow Problems ◽  
Disturbed Zone ◽  
Approximate Analytical Solutions ◽  
Wide Range

Abstract The basic equations for the flow of gases, compressible liquids and incompressible liquids are derived and the full implications of linearising then discussed. Approximate solutions of these equations are obtained by introducing the concept of a disturbed zone around the well, which expands outwards into the reservoir as fluid is produced. Many important and well-established results are deduced in terms of simple functions rather than the infinite series, or numerical solutions normally associated with these problems. The wide range of application of this approach to transient radial flow problems is illustrated with many examples including; gravity drainage of depletion-type reservoirs; multiple well systems; well interference. Introduction A large number of problems concerning the flow of fluids in oil reservoirs have been solved by both analytical and numerical methods but in almost all cases these solutions have some disadvantages - the analytical ones usually involve rather complex functions (infinite series or infinite integrals) which are difficult to handle, and the numerical ones tend to mask the physical principles underlying the problem. It would seem appropriate, therefore, to try to find approximate analytical solutions to these problems without introducing any further appreciable errors, so that the physical nature of the problem is retained and solutions of comparable accuracy are obtained. One class of problems will be considered in this paper, namely, transient radial flow problems, and it will be shown that approximate analytical solutions of the equations governing radial flow can be obtained, and that these solutions yield comparable results to those calculated numerically and those obtained from "exact" solutions. It will also be shown that the restrictions imposed upon the dependent variable (pressure) are just those which have to be assumed in deriving the usual diffusion-type equations. The method was originally suggested by Guseinov, whopostulated a disturbed zone in the reservoir, the radius of which increases with time, andreplaced the time derivatives in the basic differential equation by its mean value in the disturbed zone. In this paper it is proposed to review the basic theory leading to the equations governing the flow of homogeneous fluids in porous media and to consider the full implications of the approximation introduced in linearising them. The Guseinov-type approximation will then be applied to these equations and the solutions for the flow of compressible and incompressible fluids, and gases in bounded and infinite reservoirs obtained. As an example of the application of this type of approximation, solutions to such problems as production from stratified reservoirs, radial permeability discontinuities; multiple-well systems, and well interference will be given. These solutions agree with many other published results, and in some cases they may be extended to more complex problems without the computational difficulties experienced by other authors. THEORY In order to review the basic theory from a fairly general standpoint it is proposed to limit the idealising assumptions to the minimum necessary for analytical convenience. The assumptions to be made are the following:That the flow is irrotational.That the formation is of constant thickness.Darcy's Law is valid.The formation is saturated with a single homogeneous fluid. SPEJ P. 225^

The Integrated Technology of Residual Reserves Localization and Profit Increase on Brownfields

2021 ◽  
Author(s):  
Artur Aslanyan ◽  
Bulat Ganiev ◽  
Azat Lutfullin ◽  
Ildar Z. Farhutdinov ◽  
Danila Gulyaev ◽  
...  
Keyword(s):  
Well Testing ◽  
Test Results ◽  
Reservoir Model ◽  
Digital Twin ◽  
Integrated Technology ◽  
History Analysis ◽  
Production History ◽  
Production Increase ◽  
Interference Tests ◽  
Advanced Production

Abstract Brown fields that are currently experiencing production decline can benefit a lot from production enhancement operations based on localization of residual reserves and geology clarification. The set of solutions includes targeted recommendations for additional well surveys followed by producers and injectors workovers, like whole wellbore or selective stimulation, polymer flow conformance, hydraulic fracturing and side tracking. As a result, previously poorly drained areas are involved in production, which increases current rates and ultimate recovery. The integrated technology of residual reserves localization and production increase includes: Primary analysis of the production history for reservoir blocks ranking by production increase potential. Advanced bottom-hole pressures and production history analysis by multiwell deconvolution for pressure maintenance system optimization and production enhancement. Advanced production logging for flow profile and production layer-by-layer allocation. Conducting pulse-code interference testing for average saturation between wells estimation. 3D reservoir dynamic model calibration on advanced tests findings. Multi-scenario development planning for the scenario with biggest NPV regarding surface infrastructure. The presented integrated technology is carried stage by stage. Based on the data analysis at the first stage (the Prime analysis) it is possible to get three types of results. The top-level assessment of the current development opportunities of the area, evaluation of current residual reserves on base of displacement sweep efficiency estimation, and evaluation of the potential production increase for various blocks of the field. Results of the second stage were obtained for the block deemed with the highest potential for production increase. Those results may reveal possible complications, and relevant workovers can be advised along with additional surveys that can further help to locate current reserves. The last stage of Prime analysis provides the most suitable choice was to perform an advanced logging and well-testing, as they include both single-well and multi-well tests. Pulse-code interference tests, multi-well retrospective tests and reservoir-oriented production logging make it possible to scan the reservoir laterally and vertically, which is especially important for multi-layered fields. The reservoir parameters obtained from the test results are used to calibrate the dynamic reservoir model. The effects of production enhancement operations are calculated from the 3D model. The set of possible activities is evaluated in terms of their financial efficiency based on the economic model of the operator company using multi-scenario approach on a specifically created digital twin of the field. The unique feature of this approach lies in an integrated usage of advanced production history analysis, advanced logging and well-testing technologies, as well as further calibration of the dynamic reservoir model based on test results and used-friendly interface for field digital twin interaction. This paper demonstrates on how to use the field tests results to calibrate the reservoir model and increase the accuracy of production forecasting by reducing the model uncertainty, with intent to increase profit of brownfields.

CSG well testing—Santos' experience in Queensland

2013 ◽  
Vol 53 (1) ◽  
pp. 227
Author(s):  
Czek Hoong Tan ◽  
Guncel Demircan ◽  
Mathias Satyagraha
Keyword(s):  
Radial Flow ◽  
Test Methods ◽  
Well Testing ◽  
Test Results ◽  
Well Test ◽  
Well Performance ◽  
Validity Of Results ◽  
Transient Behaviour ◽  
Key Factor ◽  
Primary Porosity

Permeability of the cleat system is a key factor controlling the productivity of CSG reservoirs and, therefore, the commerciality of development projects. Well testing is routinely used to provide representative values of coal permeability. The authors’ experience has shown pressure transient behaviour in coal reservoirs to be similar to those in primary porosity systems, with pseudo radial flow frequently observed, and the dual-porosity signature largely absent. Despite the authors’ best efforts in test design, large permeability variation and extremely high skin factors have been seen. The authors have run variations of drill stem tests (DSTs), injection tests, and wireline tests to understand the dependency of results to test methods, and the validity of results obtained. Pertinent examples of each type of test are discussed. Finally, recommendations to reconcile well test results to actual well performance are presented.

Inferring Interwell Connectivity from Well Bottomhole-Pressure Fluctuations in Waterfloods

2008 ◽  
Vol 11 (05) ◽  
pp. 874-881 ◽  
Author(s):  
Djebbar Tiab ◽  
Anh V. Dinh
Keyword(s):  
Pressure Fluctuations ◽  
The Other ◽  
Time Interval ◽  
Well Testing ◽  
Production Rates ◽  
Data Points ◽  
Interwell Connectivity ◽  
Reservoir Simulator ◽  
Interference Tests ◽  
Bottomhole Pressure

Summary This paper presents a new procedure to determine interwell connectivity in a reservoir on the basis of fluctuations of bottomhole pressure of both injectors and producers in a waterflood. The method uses a constrained multivariate linear-regression (MLR) analysis to obtain information about permeability trends, channels, and barriers. Previous authors applied the same analysis to injection and production rates to infer connectivity between wells. In order to obtain good results, however, they applied various diffusivity filters to the flow-rate data to account for the time lags and the attenuation. This was a tedious process that requires subjective judgment. Shut-in periods in the data, usually unavoidable when a large number of data points were used, created significant errors in the results and were often eliminated from the analysis. This new method yielded better results compared with the results obtained when production data were used. Its advantages include:no diffusivity filters needed for the analysis,minimal number of data points required to obtain good results,and flexible plan to collect data because all constraints can be controlled at the surface. The new procedure was tested by use of a numerical reservoir simulator. Thus, different cases were run on two fields, one with five injectors and four producers and the other with 25 injectors and 16 producers. For a large waterflood system, multiple wells are present and most of them are active at the same time. In this case, pulse tests or interference tests between two wells are difficult to conduct because the signal can be distorted by other active wells in the reservoir. In the proposed method, interwell connectivity can be obtained quantitatively from multiwell pressure fluctuations without running interference tests. Introduction Well testing is a common and important tool of reservoir characterization. Many well-testing methods have been developed in order to obtain various reservoir properties. Interference tests and pulse tests are used to quantify communication between wells. These methods are often applied to two wells such that one well sending the signals (by changing flow rates) and the other is receiving them (Lee et al. 2003). For a large field such as a waterflood system, however, multiple wells are present, and most of them are active at the same time. In that case, pulse tests or interference tests between two wells are difficult to conduct because the signal can be distorted by other active wells in the reservoir. In this method, data can be obtained from multiwell pressure tests that resemble interference tests. Thus, we can have several wells sending signals and the others receiving the signals at the same time. The wells that are receiving the signal, however, can either be shut in or kept at constant producing rates. The pressures at all wells are recorded simultaneously within a constant time interval. The length of the test will depend on the length of the time interval and the number of data points. Results of this method can be used to optimize operations and economics and enhance oil recovery of existing waterfloods by changing well patterns, changing injection rates, recompletion of wells, and infill drilling. This work is based on previous work conducted by Albertoni and Lake (2003) by use of injection and production rates. In their work, Albertoni and Lake developed and tested different approaches by use of constrained MLR analysis with a numerical simulator and then applied it to a waterflooded field in Argentina. They used diffusivity filters to account for the time lag and attenuation of the data. In his thesis, Dinh (2003) verified the method by use of a different reservoir simulator and applied it to a waterflooded field in Nowata, Oklahoma. He also investigated the effect of shut-in periods and vertical distances on the results. The main objectives of this work are to verify the results obtained from pressure data with results from flow-rate data to propose a new method to determine interwell connectivity and to suggest further research and study on the method. Similar to the method that uses production rates, we will concentrate on a waterflood system only. The reservoir is considered as a system that processes a stimulus (i.e., a well that is sending signals) and returns a response (i.e., a well that is receiving the signals). The effect of the reservoir on the input signal will depend on the location and the orientation of each stimulus/response pair. Because the total pressure changes at active and observation wells are not equal, only the MLR (Albertoni and Lake 2003; Dinh 2003; Albertoni 2002) was used. The effect of diffusion was not significant, thus the diffusivity filters were not used. The method was applied to two synthetic fields, one with five injectors and four producers and the other with 25 injectors and 16 producers.

A Well-Testing Approach for Diagnostics of Fracture Complexity with Well Interference

2021 ◽  
Author(s):  
Zhiming Chen ◽  
Xinwei Liao ◽  
Pengfei Zhao ◽  
Biao Zhou ◽  
Duo Chen ◽  
...  
Keyword(s):  
Radial Flow ◽  
Flow Regimes ◽  
Well Testing ◽  
Pressure Derivative ◽  
Complex Fracture ◽  
Well Spacing ◽  
Fracture Complexity ◽  
Pressure Depletion ◽  
Testing Approach ◽  
The Impact

Abstract Owing to well interference, the fracture geometries of child wells are sometimes more complex than initially expected. Some approaches or methodologies have been developed to evaluate the complex fracture geometries, however, the fracture geometries are still poorly understood. This work uses the boundary element method to propose a new well testing approach to determine the complex fracture geometries of child wells with inter-well interference. It is found that the well interferences from Parent well on Child well mainly happen on the late stage, which can be physically expected. The flow regimes of Child well can be divided into: wellbore storage & skin effects, fracture bilinear flow, "fluid supply", formation linear flow, pseudo-boundary dominated flow, "well interferences", pseudo-radial flow, and boundary-dominated flow. The stage of "well interferences" occurs later with the increase in well spacing. The boundary-dominated flow is affected by the reservoir size and shape. When the reservoir size is fixed, the pressure curves in final stage of different-shape reservoirs overlap, which provides a tool to diagnose the reservoir size. While the reservoir size are variable, the occurrences of boundary-dominated flow are quite different. The smaller the reservoir, the quicker the boundary-dominated flow, which is in line with actual situations. It is also found that Parent-well rate mainly affects the flow regimes after pseudo-boundary dominated flow. That to say, after that flow regime, the performance of Child well is interfered by Parent well. The impact is more obvious with the increase in Parent-well rate, especially in pseudo-radial flow. In that flow stage, the horizontal value of pressure derivative also satisfies 0.5(qchd,D+qpar,D). In addition, when the Parent-well rate is negative, namely an injection well, the pressure derivatives of Child well decrease sharply, which means that the pressure depletion of Child well decreases and it is helpful to production of Child well. When the Parent-well rate is a positive and large value, the pressure depletion of Child well increase sharply and its production is harmed by the Parent well. Thus, there should be an optimized production strategies between Parent well and Child well. Finally, the model application on diagnostics of fracture complexity of an actual well is performed. This study provides a new way to identify the fracture geometries of child wells in unconventional plays.

Some Approximate Solutions of Radial Flow Problems Associated With Production at Constant Well Pressure

1967 ◽  
Vol 7 (01) ◽  
pp. 31-42 ◽  
Author(s):  
M.W. Clegg
Keyword(s):  
Porous Media ◽  
Infinite Series ◽  
Analytical Solutions ◽  
Laplace Transformation ◽  
Radial Flow ◽  
Approximate Solutions ◽  
Time Interval ◽  
Pressure Buildup ◽  
Flow Problems ◽  
The Times

Abstract The application of the Laplace transformation to problems in the flow of compressible fluids in porous media has provided a large number of exact solutions. For plane radial flow, however, these solutions are either complex integrals or infinite series and are of little value to the field engineer. !n the case of production at constant well pressure, the available approximate solutions are valid for large times only. In this paper it is shown that an approximate inversion formula for the Laplace transform, developed for the solution of viscoelastic problems, is applicable to radial flow problems and provides simple analytical solutions to constant terminal pressure problems. The method may be used to obtain approximate solutions to many problems, including media with radial permeability discontinuities, multi-layer formations and pressure buildup in wells after shut-in. The results are compared with the few available computer solutions as well as the large time solutions, and it is shown that this approximate method greatly extends the time interval over which a simple analytical solution is acceptable. INTRODUCTION The study of transient problems in the flow of fluids through porous media has benefited greatly from the application of transform methods. The use of the Laplace transformation for solving parabolic equations has been widely discussed in the field of heat conduction and diffusion as well as in the petroleum literature. Removal of the time variable with the Laplace transformation generally reduces the problem to a boundary value problem which may be solved by standard techniques. A much more formidable problem then faces the engineer, however, for frequently the transform does not possess a simple inverse. The result is that the general inversion integral must be used and this leads to either an infinite integral or an infinite series, both of which are difficult to handle from a computational standpoint. Asymptotic approximations for the inverse have been known for some time and these yield approximate inverse functions that are valid for very large or very small times - but frequently the times of interest lie somewhere between these two extremes. Therefore, some acceptable approximation valid over a larger interval of time is desirable. During the past few years a number of methods for achieving this have been developed and some of these are discussed briefly in this paper. The relative merits of the various methods are not evaluated here, but some general conclusions reached by other authors are given. One of these methods has been applied to problems associated with the radial flow of compressible liquids to producing wells. In the case of production at constant well pressure, the method leads to simple analytical solutions for a number of standard problems; e.g., homogeneous formation, permeability discontinuities, pressure buildup. These solutions greatly extend the range of validity of the asymptotic ones (valid for large times only) and should be of value in studying the behavior of wells producing under constant pressure conditions.

scholarly journals Numerical Well Testing Interpretation Model and Applications in Crossflow Double-Layer Reservoirs by Polymer Flooding

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Haiyang Yu ◽  
Hui Guo ◽  
Youwei He ◽  
Hainan Xu ◽  
Lei Li ◽  
...  
Keyword(s):  
Double Layer ◽  
Oil Recovery ◽  
Radial Flow ◽  
Polymer Flooding ◽  
Flow Section ◽  
Well Testing ◽  
Type Curves ◽  
Wellbore Storage ◽  
Numerical Well Testing ◽  
Interpretation Model

This work presents numerical well testing interpretation model and analysis techniques to evaluate formation by using pressure transient data acquired with logging tools in crossflow double-layer reservoirs by polymer flooding. A well testing model is established based on rheology experiments and by considering shear, diffusion, convection, inaccessible pore volume (IPV), permeability reduction, wellbore storage effect, and skin factors. The type curves were then developed based on this model, and parameter sensitivity is analyzed. Our research shows that the type curves have five segments with different flow status: (I) wellbore storage section, (II) intermediate flow section (transient section), (III) mid-radial flow section, (IV) crossflow section (from low permeability layer to high permeability layer), and (V) systematic radial flow section. The polymer flooding field tests prove that our model can accurately determine formation parameters in crossflow double-layer reservoirs by polymer flooding. Moreover, formation damage caused by polymer flooding can also be evaluated by comparison of the interpreted permeability with initial layered permeability before polymer flooding. Comparison of the analysis of numerical solution based on flow mechanism with observed polymer flooding field test data highlights the potential for the application of this interpretation method in formation evaluation and enhanced oil recovery (EOR).

Analysis of Thin Film Flows Using a Flux Vector Splitting1

2003 ◽  
Vol 125 (2) ◽  
pp. 365-374 ◽  
Author(s):  
J. Rafael Pacheco ◽  
Arturo Pacheco-Vega
Keyword(s):  
Thin Film ◽  
Shallow Water ◽  
Radial Flow ◽  
Computational Domain ◽  
Flux Vector ◽  
Thin Film Flow ◽  
Flow Problems ◽  
Shallow Water Approximation ◽  
Flux Vector Splitting ◽  
Film Flows

We propose a flux vector splitting (FVS) for the solution of film flows radially spreading on a flat surface created by an impinging jet using the shallow-water approximation. The governing equations along with the boundary conditions are transformed from the physical to the computational domain and solved in a rectangular grid. A first-order upwind finite difference scheme is used at the point of the shock while a second-order upwind differentiation is applied elsewhere. Higher-order spatial accuracy is achieved by introducing a MUSCL approach. Three thin film flow problems (1) one-dimensional dam break problem, (2) radial flow without jump, and (3) radial flow with jump, are investigated with emphasis in the prediction of hydraulic jumps. Results demonstrate that the method is useful and accurate in solving the shallow water equations for several flow conditions.

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