Extraction of Interference from Long Term Transient Pressure Using Multi-Well Deconvolution Algorithm for Well Test Analysis

2010 ◽  
Author(s):  
Shi-yi Zheng ◽  
Fei Wang
Keyword(s):  
Well Test ◽  
Transient Pressure ◽  
Well Test Analysis ◽  
Test Analysis ◽  
Deconvolution Algorithm

Practical Application of Pressure-Rate Deconvolution to Analysis of Real Well Tests

2005 ◽  
Vol 8 (02) ◽  
pp. 113-121 ◽  
Author(s):  
Michael M. Levitan
Keyword(s):  
Test Data ◽  
Rate Data ◽  
Well Test ◽  
Pressure Data ◽  
Well Test Analysis ◽  
Test Analysis ◽  
Deconvolution Algorithm ◽  
Constant Rate ◽  
Test Pressure ◽  
Real Test

Summary Pressure/rate deconvolution is a long-standing problem of well-test analysis that has been the subject of research by a number of authors. A variety of different deconvolution algorithms have been proposed in the literature. However, none of them is robust enough to be implemented in the commercial well-test-analysis software used most widely in the industry. Recently, vonSchroeter et al.1,2 published a deconvolution algorithm that has been shown to work even when a reasonable level of noise is present in the test pressure and rate data. In our independent evaluation of the algorithm, we have found that it works well on consistent sets of pressure and rate data. It fails, however, when used with inconsistent data. Some degree of inconsistency is normally present in real test data. In this paper, we describe the enhancements of the deconvolution algorithm that allow it to be used reliably with real test data. We demonstrate the application of pressure/rate deconvolution analysis to several real test examples. Introduction The well bottomhole-pressure behavior in response to a constant-rate flow test is a characteristic response function of the reservoir/well system. The constant-rate pressure-transient response depends on such reservoir and well properties as permeability, large-scale reservoir heterogeneities, and well damage (skin factor). It also depends on the reservoir flow geometry defined by the geometry of well completion and by reservoir boundaries. Hence, these reservoir and well characteristics are reflected in the system's constant-rate drawdown pressure-transient response, and some of these reservoir and well characteristics may potentially be recovered from the response function by conventional methods of well-test analysis. Direct measurement of constant-rate transient-pressure response does not normally yield good-quality data because of our inability to accurately control rates and because the well pressure is very sensitive to rate variations. For this reason, typical well tests are not single-rate, but variable-rate, tests. A well-test sequence normally includes several flow periods. During one or more of these flow periods, the well is shut in. Often, only the pressure data acquired during shut-in periods have the quality required for pressure-transient analysis. The pressure behavior during the individual flow period of a multirate test sequence depends on the flow history before this flow period. Hence, it is not the same as a constant-rate system-response function. The well-test-analysis theory that evolved over the past 50 years has been built around the idea of applying a special time transform to the test pressure data so that the pressure behavior during individual flow periods would be similar in some way to constant-rate drawdown-pressure behavior. The superposition-time transform commonly used for this purpose does not completely remove all effects of previous rate variation. There are sometimes residual superposition effects left, and this often complicates test analysis. An alternative approach is to convert the pressure data acquired during a variable-rate test to equivalent pressure data that would have been obtained if the well flowed at constant rate for the duration of the whole test. This is the pressure/rate deconvolution problem. Pressure/rate deconvolution has been a subject of research by a number of authors over the past 40 years. Pressure/rate deconvolution reduces to the solution of an integral equation. The kernel and the right side of the equation are given by the rate and the pressure data acquired during a test. This problem is ill conditioned, meaning that small changes in input (test pressure and rates) lead to large changes in output result—a deconvolved constant-rate pressure response. The ill-conditioned nature of the pressure/rate deconvolution problem, combined with errors always present in the test rate and pressure data, makes the problem highly unstable. A variety of different deconvolution algorithms have been proposed in the literature.3–8 However, none of them is robust enough to be implemented in the commercial well-test-analysis software used most widely in the industry. Recently, von Schroeter et al.1,2 published a deconvolution algorithm that has been shown to work when a reasonable level of noise is present in test pressure and rate data. In our independent implementation and evaluation of the algorithm, we have found that it works well on consistent sets of pressure and rate data. It fails, however, when used with inconsistent data. Examples of such inconsistencies include wellbore storage or skin factor changing during a well-test sequence. Some degree of inconsistency is almost always present in real test data. Therefore, the deconvolution algorithm in the form described in the references cited cannot work reliably with real test data. In this paper, we describe the enhancements of the deconvolution algorithm that allow it to be used reliably with real test data. We demonstrate application of the pressure/rate deconvolution analysis to several real test examples.

Condensate Bank Characterization from Well Test Data and Fluid PVT Properties

2006 ◽  
Vol 9 (05) ◽  
pp. 596-611 ◽  
Author(s):  
Manijeh Bozorgzadeh ◽  
Alain C. Gringarten
Keyword(s):  
Capillary Number ◽  
Gas Condensate ◽  
Test Interpretation ◽  
Well Test ◽  
Transient Pressure ◽  
Compositional Simulation ◽  
Well Test Analysis ◽  
Test Analysis ◽  
Inertia Effects ◽  
The North

Summary Published well-test analyses in gas/condensate reservoirs in which the pressure has dropped below the dewpoint are usually based on a two- or three-region radial composite well-test interpretation model to represent condensate dropout around the wellbore and initial gas in place away from the well. Gas/condensate-specific results from well-test analysis are the mobility and storativity ratios between the regions and the condensate-bank radius. For a given region, however, well-test analysis cannot uncouple the storativity ratio from the region radius, and the storativity ratio must be estimated independently to obtain the correct bank radius. In most cases, the storativity ratio is calculated incorrectly, which explains why condensate bank radii from well-test analysis often differ greatly from those obtained by numerical compositional simulation. In this study, a new method is introduced to estimate the storativity ratios between the different zones from buildup data when the saturation profile does not change during the buildup. Application of the method is illustrated with the analysis of a transient-pressure test in a gas/condensate field in the North Sea. The analysis uses single-phase pseudo pressures and two- and three-zone radial composite well-test interpretation models to yield the condensate-bank radius. The calculated condensate-bank radius is validated by verifying analytical well-test analyses with compositional simulations that include capillary number and inertia effects. Introduction and Background When the bottomhole flowing pressure falls below the dewpoint in a gas/condensate reservoir, retrograde condensation occurs, and a bank of condensate builds up around the producing well. This process creates concentric zones with different liquid saturations around the well (Fevang and Whitson 1996; Kniazeff and Nvaille 1965; Economides et al. 1987). The zone away from the well, where the reservoir pressure is still above the dewpoint, contains the original gas. The condensate bank around the wellbore contains two phases, reservoir gas and liquid condensate, and has a reduced gas mobility, except in the immediate vicinity of the well at high production rates, where the relative permeability to gas is greater than in the bank because of capillary number effects (Danesh et al. 1994; Boom et al. 1995; Henderson et al. 1998; Mott et al. 1999).

Determination of Average Reservoir Pressure from Pressure Buildup Tests

1972 ◽  
Author(s):  
Hossein Kazemi
Keyword(s):  
Reservoir Pressure ◽  
Well Test ◽  
Well Test Analysis ◽  
Test Analysis ◽  
Gas Well ◽  
Pressure Buildup ◽  
Production History ◽  
Calculated Average

Abstract Two simple and equivalent procedures are suggested for improving the calculated average reservoir pressure from pressure buildup tests of liquid or gas wells in developed reservoirs. These procedures are particularly useful in gas well test analysis irrespective of gas composition, in reservoirs with pressure-dependent permeability and porosity, and in oil reservoirs where substantial gas saturation has been developed. Long-term production history need not be known. Introduction For analyzing pressure buildup data with constant flowrate before shut in, two plotting procedures are mostly used: The Miller-Dyes-Hutchinson (MDH) plot (1,8) and the Horner plot (2,8). The Miller-Dyes-Hutchinson plot is a plot of pws vs log Δt. The Horner plot consists of plotting the bottom hole shut-in pressure, pws vs log [(tp + Δt)/Δt]. Δt is the shut-in time and tp is a pseudo-production time equal to the ratio of total produced fluid and the last stabilized flowrate prior to shut in. This method was first used by Theis (3) in the water industry.

scholarly journals A mathematical model and semi-analytical solution for transient pressure of vertical fracture with varying conductivity in three crossflow rectangular layers

2018 ◽  
Vol 37 (1) ◽  
pp. 230-250 ◽  
Author(s):  
Jie Liu ◽  
Pengcheng Liu ◽  
Shunming Li ◽  
Xiaodong Wang
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Flow Characteristics ◽  
Well Test ◽  
Transient Pressure ◽  
Well Test Analysis ◽  
Test Analysis ◽  
Fracture Conductivity ◽  
Vertical Fracture ◽  
Flow Phase

This paper first describes a mathematical model of a vertical fracture with constant conductivity in three crossflow rectangular layers. Then, three forms of vertical fracture (linear, logarithmic, and exponential variations) with varying conductivity are introduced to this mathematical model. A novel mathematical model and its semi-analytical solution of a vertical fracture with varying conductivity intercepting a three-separate-layered crossflow reservoir is developed and executed. Results show that the transient pressures are divided into three stages: the linear-flow phase, the medium unsteady-flow stage, and the later pseudo-steady-flow phase. The parameters of the fracture, reservoir, and the multi-permeability medium directly influence the direction, transition, and shape of the transient pressure. Meanwhile, the fracture conductivity is higher near the well bottom and is smaller at the tip of the fracture for the varying conductivity. Therefore, there are many more differences between varying conductivity and constant conductivity. Varying conductivity can correctly reflect the flow characteristics of a vertical fractured well during well-test analysis.

Analysis of Horizontal-Well Responses: Contemporary vs. Conventional

2001 ◽  
Vol 4 (04) ◽  
pp. 260-269 ◽  
Author(s):  
Erdal Ozkan
Keyword(s):  
Horizontal Well ◽  
Horizontal Wells ◽  
Well Test ◽  
Transient Pressure ◽  
Vertical Wells ◽  
Well Test Analysis ◽  
Test Analysis ◽  
Response Models ◽  
In The Beginning ◽  
Well Models

Summary Most of the conventional horizontal-well transient-response models were developed during the 1980's. These models visualized horizontal wells as vertical wells rotated 90°. In the beginning of the 1990's, it was realized that horizontal wells deserve genuine models and concepts. Wellbore conductivity, nonuniform skin effect, selective completion, and multiple laterals are a few of the new concepts. Although well-established analysis procedures are yet to be developed, some contemporary horizontal-well models are now available. The contemporary models, however, are generally sophisticated. The basic objective of this paper is to answer two important questions:When should we use the contemporary models? andHow much error do we make by using the conventional models? This objective is accomplished by considering examples and comparing the results of the contemporary and conventional approaches. Introduction Since the early 1980's, horizontal wells have been extremely popular in the oil industry and have gained an impeccable standing among the conventional well completions. The rapid increase in the applications of horizontal-well technology brought an impetuous development of the procedures to evaluate the performances of horizontal wells. These procedures, however, used the vertical-well concepts almost indiscriminately to analyze the horizontal-well transient-pressure responses.1–14 Among these concepts were 1) the assumptions of a line-source well and an infinite-conductivity wellbore, 2) a single lateral withdrawing fluids along its entire length, and 3) a skin region that is uniformly distributed along the well. It should be realized that for the lengths, production rates, and configurations of horizontal wells drilled in the 1980's, these concepts were usually justifiable. The increased lengths of horizontal wells, high production rates, sectional and multilateral completions, and the vast variety of other new applications toward the end of the 1980's made us question the validity of the horizontal-well models and the well-test concepts adopted from vertical wells. The interest in improved horizontal-well models also flourished on the grounds of high productivities of horizontal wells. It was realized that, in many cases, a few percent of the production rate of a reasonably long horizontal well could amount to the cumulative production rate of a few vertical wells. In addition, the productivity-reducing effects were additive; that is, a slight reduction in the productivity here and there could add up to a sizeable loss of the well's production capacity. Furthermore, the low oil prices also created an economic environment where the marginal gains and losses in the productivity may decisively affect the economics of many projects. In the beginning of the 1990's, a new wave of developing horizontal-well solutions under more realistic conditions gained impetus.15–25 As a result, some contemporary models are available today for those who want to challenge the limitations of the conventional horizontal-well models. Unfortunately, the rigor is accomplished at the expense of complexity. Furthermore, even when a rigorous model is available, well-established analysis procedures are usually yet to be developed. This paper presents a critique of the conventional and contemporary horizontal well-test-analysis procedures. The main objective of this assessment is to answer the two fundamental questions horizontal-well-test analysts are currently facing:When is the use of contemporary analysis methods essential? andIf the conventional analysis methods are used, what are the margins of error? Background: The Conventional Methods The standard models of horizontal-well-test analysis have been developed mostly during the 1980's.1-4,8,9 Despite the differences in the development of these models, the basic assumptions and the final solutions are similar. Fig. 1 is a sketch of the horizontal well-reservoir system considered in the pressure-transient-response models. A horizontal well of length Lh is assumed to be located in an infinite slab reservoir of thickness h. The elevation of the horizontal well from the bottom boundary of the formation (well eccentricity) is denoted by zw. The top and bottom reservoir boundaries are usually assumed to be impermeable, although some models consider constant-pressure boundaries.14,15 Before discussing the characteristic features of the conventional horizontal-well transient-pressure-response models, we must first define the dimensionless variables to be used in our discussion. We define the dimensionless pressure, time, and distance in the conventional manner except that we use the horizontal-well half-length, Lh/2, as the reference length in the system. These variables are defined, respectively, by the following expressions.Equation 1Equation 2Equation 3Equation 4 In Eqs. 1 through 3, k=the harmonic average of the principal permeabilities that are assumed to be in the directions of the coordinate axes (). We also define the dimensionless horizontal-well length, wellbore radius, and well eccentricity (distance from the bottom boundary of the formation) as follows.Equation 5Equation 6Equation 7 In Eq. 6, rw, eq=the equivalent radius of the horizontal well in an anisotropic reservoir.26

Semianalytical Modeling of Complex-Geometry Reservoirs

2002 ◽  
Vol 5 (06) ◽  
pp. 437-446 ◽  
Author(s):  
Gang Zhao ◽  
Leslie G. Thompson
Keyword(s):  
Analytical Solutions ◽  
Complex Geometry ◽  
Well Test ◽  
Transient Pressure ◽  
Well Test Analysis ◽  
Test Analysis ◽  
Simple Geometry ◽  
Reservoir Systems ◽  
Fluid Transfer ◽  
Source Sink

Summary Complex geometry reservoirs can be encountered in the field for a variety of depositional and tectonic processes. For example, fluvial depositional environments may produce interbranching channel reservoirs or reservoirs consisting of relatively high-permeability channels in communication with low-permeability splays. This paper presents a general methodology for computing pressure responses and flow characteristics in complex geometry reservoirs. The proposed method consists of decomposing the original complex-geometry reservoir into a set of simple-geometry reservoirs, which interact with each other by transfer of fluid and equality of pressure over the regions where they are in hydraulic contact. Analytical solutions are written for each of the simple reservoir components in terms of the unknown pressures and fluxes at their boundaries, and the coupled systems are solved for the desired wellbore pressure responses. The method of sources and sinks is used to compute the pressure response in the Laplace domain, and the results are inverted numerically with the Stehfest Inversion algorithm.1 We present fast, accurate methods of taking numerical Laplace transforms of the source/sink solutions that make the computations reasonably fast and efficient. The proposed methodology can be extended to any system (infinite or bounded) in which the Laplace-space solution can be written easily in terms of integrals of real-space source/sink functions, including production at constant bottomhole pressure, wellbore storage effects, or naturally fractured systems. We demonstrate the applicability of the method by modeling branching channels and channel/splay systems. Introduction Classical well-test analysis has long been used as a valuable tool in characterizing reservoirs using transient pressure vs. time behavior. In most classical well-test models, the reservoir is idealized as a homogeneous single- or dual-porosity system with a simple reservoir and well geometry. This is done to facilitate generation of analytical solutions to the reservoir problem. In fluvial-deltaic reservoir systems, however, the complex geometry precludes idealizing the reservoir as a simple-shaped homogeneous system and, in general, the transient pressure responses do not resemble those of classical simple-geometry systems. Fluvial-deltaic reservoir systems are one example of general complex-geometry reservoirs for which classical well-test analysis models may not be applicable. Except for work presented by Larsen2,3 on a network of interconnected linear reservoirs, there appears to have been very little presented in the literature on modeling or describing the pressure transient pressure behavior of these types of reservoirs. Larsen's work was concerned primarily with the long-time productivity of a network of intersecting linear reservoirs, with no special consideration given to the geometry at the regions of intersection. Larsen's work indicated that proper understanding of reservoir type is critical in situations in which extrapolation of short-time test data to possible late-time production characteristics is attempted. Reservoirs with sealing or partially sealing faults are another type of complex-geometry reservoirs that has received attention in the literature.4–9 Both numerical and analytical solutions have been presented to model the pressure behavior in faulted reservoirs; however, the focus of these studies has been on the effect of the sealing and/or nonsealing faults, with little attention given to the physics of the fluid transfer between the communicating reservoirs. In this work, we attempt to rigorously account for the effects of the hydraulic contact between the connected reservoir components. Modeling Philosophy and Methodology In this section, we illustrate our general modeling approach by applying it to a simple reservoir system. The physical model considered in Fig. 1 consists of two semi-infinite reservoirs separated over most of their extent by a hydraulically sealing barrier. One has flow properties of a "channel," which we will refer to as Region 1, while the other has properties of a "splay" (Region 2). The reservoirs are in hydraulic contact only over a small area. A well is producing from one of the reservoirs. The first step in the modeling procedure is to identify simplegeometry homogeneous reservoir components that make up the complex system. In the preceding example, the complex reservoir is composed of two semi-infinite reservoirs: Region 1 and Region 2. Considering Region 1 only, the reservoir behaves as if it contains two wells: the original producer and a planar injection well at the area of communication between the two reservoirs. Similarly, considering Region 2 only, it behaves as if there were a single producing planar fractured well at the area of communication between the two reservoirs. Because all the fluid leaving Region 2 is entering Region 1, the production and injection rates of the apparent planar "fractured" wells in each of the regions must be the same. The second step in the modeling process involves separating the various reservoir components from one another at their junction(s) by applying no-flow boundaries. For simple reservoir systems that contain wells, this is achieved by creating a mirror image to the no-flow boundary; that is, the inserted no-flow boundary becomes a plane of symmetry for the extended system. For the problem under consideration, Region 1 and Region 2 are each reflected using the fault as a mirror (see Figs. 2 and 3). Planar injection or production wells are added along the plane of symmetry to account for fluid transfer from one system to the other. The separate systems are then coupled by equating rates and pressures at the junctions and solving (in Laplace space) for the unknown flux distributions along the introduced planar wells. Finally, the flux profiles from the preceding step are substituted into the pressure equation for the well of interest to obtain the desired pressure response. We illustrate the procedure in more detail for the simple problem under consideration.

Deconvolution of Multiwell Test Data

SPE Journal ◽  
2007 ◽  
Vol 12 (04) ◽  
pp. 420-428 ◽  
Author(s):  
Michael M. Levitan
Keyword(s):  
Test Data ◽  
Rate Variation ◽  
Rate Data ◽  
Well Test ◽  
Well Test Analysis ◽  
Test Analysis ◽  
Deconvolution Analysis ◽  
Deconvolution Algorithm ◽  
Analysis Technique ◽  
Well Tests

Summary The deconvolution analysis technique that evolved with development of the deconvolution algorithms by von Schroeter et al. (2004), Levitan (2005), and Levitan et al. (2006) became a useful addition to the suite of techniques used in well-test analysis. This deconvolution algorithm, however, is limited to the pressure and rate data that originate from a single active well on the structure. It is ideally suited for analysis of the data from exploration and appraisal well tests. The previously mentioned deconvolution algorithm can not be used with the data that are acquired during startup and early field development that normally involve several producing wells. The paper describes a generalization of deconvolution to multiwell pressure and rate data. Several approaches and ideas for multiwell deconvolution are investigated and evaluated. The paper presents the results of this investigation and demonstrates performance of the deconvolution algorithm on synthetic multiwell test data. Introduction Pressure-rate deconvolution is a way of reconstructing the characteristic pressure transient behavior of a reservoir-well system hidden in the test data by well-rate variation during a test. The deconvolution analysis technique that evolved with development of the deconvolution algorithms by von Schroeter et al. (2004), Levitan (2005), and Levitan et al. (2006) became a useful addition to the suite of techniques used in well-test analysis. It has been implemented in commercial well-test analysis software and is routinely used for analysis of well tests. This deconvolution algorithm, however, is applicable only for the case when there is just one active well in the reservoir. It is ideally suited for analysis of exploration and appraisal well tests. The previously described deconvolution algorithm cannot be used for well-test analysis when there are several active wells operating in the field and the bottomhole pressure measured in one well during a well test is affected by the production from other wells operating in the same reservoir. The deconvolution algorithm has to be generalized so that it is possible to remove not only the effects of rate variation of the well itself but also the pressure interferences with other wells in the reservoir. As a result, we would be able to reconstruct the true characteristic well-pressure responses to unit-rate production of each producing well in the reservoir. These responses reflect the reservoir and well properties and could be used for recovering these properties by the techniques of pressure-transient analysis. Multiwell deconvolution thus becomes in a way a general technique for interference well-test analysis. The problem, however, is that the interference pressure signals produced by other wells are small compared to the pressure signal caused by the production of the well itself. These pressure interference signals are delayed in time and the time delay depends on the distance between respective wells. All this makes multiwell deconvolution an extremely difficult problem.

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