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- Dwivedi, P.. (1)
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- Viberti, Dario (1)
- Wang, HanYi (1)
- Whitson, C.H. (1)
- Whittle, Tim (1)

**Concept Tag**

- analyze simultaneous transient pressure (1)
- application (2)
- approximation (1)
- Artificial Intelligence (1)
- bottom-hole pressure (1)
- bottomhole pressure (1)
- build-up (1)
- buildup data (1)
- calculation (1)
- cartesian plot (1)
- closure pressure (1)
- closure time (1)
- complex reservoir (2)
- conductivity case (1)
- convolution derivative (1)
- convolution integral (1)
- convolution plot (1)
- convolution time (1)
- decline curve (1)
- Decline Model (1)
- deconvolution (1)
- derivative (2)
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- Drillstem Testing (4)
- drillstem/well testing (4)
- dt log-log plot (1)
- equation (3)
- Exhibition (1)
- flow in porous media (1)
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- flow regime (1)
- Fluid Dynamics (1)
- fluid property (1)
- forecast (1)
- formation linear-flow (1)
- forward simulation (1)
- fracture (1)
- fracture properties (1)
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- good fit (1)
- graphical procedure (1)
- Horner analysis (1)
- hydraulic fracturing (2)
- identify flow pattern transition (1)
- infinite shut-in time (1)
- inflow performance (1)
- information (1)
- initial pressure (2)
- interpretation (1)
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- pressure transient testing (3)
- procedure (1)
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- production forecasting (1)
- production monitoring (3)
- production rate (2)
- production stage 1 (1)
- pseudo pressure (1)
- radial flow (2)
- reservoir pressure (2)
- Reservoir Surveillance (3)
- SFRC (1)
- SPE Formation Evaluation (1)
- straight line (4)
- superposition (2)
- superposition function (2)
**superposition plot (8)**- superposition time (2)
- Time Function (2)
- Upstream Oil & Gas (8)
- Van Everdingen (1)
- Well Performance Model (1)

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Abstract Market-induced production shut-downs and restarts offer us an opportunity to gather step-rate and shut-in data for pressure transient analysis (PTA) and rate transient analysis (RTA). In this study, we present a unified transient analysis (UTA) to combine PTA and RTA in a single framework. In this new approach continuous production data, step-rate data, shut-in data and re-start data can be visualized and analyzed in a single superposition plot, which can be used to estimate both and infer formation pore pressure in a holistic manner by utilizing all available data. Most importantly, we show that traditional log-log and square root of time plots can lead to false interpretation of the termination of linear-flow or power-law behavior. Field cases are presented to demonstrate the superiority of the newly introduced superposition plot, along with discussion on the calibration of long-term bottom-hole pressure with short-term measurements.

bottom-hole pressure, cartesian plot, convolution time, Drillstem Testing, drillstem/well testing, formation linear-flow, pore pressure, power-law behavior, pressure transient analysis, pressure transient testing, production rate, production stage 1, rate transient analysis, reservoir, shut-in data, square root, straight line, superposition plot, surface pressure, time plot, Upstream Oil & Gas, uta superposition plot

Oilfield Places:

- North America > United States > Texas > Permian Basin (0.98)
- North America > United States > New Mexico > Permian Basin (0.98)

SPE Disciplines:

Whittle, Tim (Politecnico di Torino and Imperial College) | Viberti, Dario (Politecnico di Torino) | Salina Borello, Eloisa (Politecnico di Torino) | Verga, Francesca (Politecnico di Torino)

Abstract Objectives/Scope Rate and pressure transient analysis is considered a routine process that has been developed and refined over many years. The underlying assumptions of linearity justify the use of superposition (in time and space), convolution and deconvolution. The reality of non-linearities are handled on a case by case basis depending on their source (fluid, well or reservoir). Shale gas wells are subject to significant non-linearity over their producing life. We review some of the fundamental equations that govern pressure and rate transient behavior, introduce several new techniques which are suited to the analysis of data from producing wells and apply them to a synthetic example of a shale gas well. Methods, Procedures, Process First, we use simple calculus to show how the convolution integral is derived from standard multi-rate superposition. Then, from the convolution integral, we derive an equation that describes the pressure response due to a step-ramp rate (i.e. an instantaneous rate change from initial conditions followed by a linear variation in rate). It results in a combination of the pressure change due to a constant rate and it's integral. Applying superposition to this equation allows any rate variation to be approximated by a sequence of ramps with far fewer points than those required to achieve the same level of accuracy using standard constant step rate superposition. Second, we re-write multi-rate superposition functions allowing for stepwise linear variable rate which, when applied to flowing data and used to calculate the pressure derivative, can result in a much smoother response and hence an overall improvement in the analysis of rate and pressure transients recorded from producing wells. Third, we review the use of the Laplace transform and how it can be applied to discrete data with a view to deconvolving rate transient data. Finally, we demonstrate how data de-trending can remove the impact of long term non-linearities and apply the methods mentioned above to a synthetic dataset based on a typical shale gas well production profile. Results, Observations, Conclusions We illustrate the advantages of the newly introduced superposition functions compared to conventional analysis methods when applied to the pressure transients of wells flowing at variable rate. As an example, we have simulated the production of two shale gas wells over twenty years. Both have the same production profile, but one includes pressure dependent permeability. At various intervals during the life of the well, we introduce a relatively short well test which imposes a small variation in rate but does not include a shut-in. We de-trend the rate transients and then apply the techniques described above to analyse the resulting data. The interpretation allows us to identify non-linearities that may be influencing well productivity over time and to obtain a better understanding of the physics of shale gas production. The mathematics documented in the paper provides a useful overview of how convolution, superposition, deconvolution and Laplace transforms provide the means to analyse pressure and rate transients for linear systems. Data de-trending removes the impact of long term non-linearities on shorter transient test periods. Novel/Additive Information We develop and demonstrate some new and improved techniques for rate and pressure transient analysis, and we illustrate how these can provide insight into the non-linearities affecting shale gas production.

complex reservoir, convolution integral, deconvolution, derivative, equation, laplace deconvolution, Laplace space, Laplace transform, linear flow, Petroleum Engineer, pressure change, pressure response, pressure transient analysis, pressure transient testing, sequence, shale gas, straight line, superposition, superposition function, superposition plot, Upstream Oil & Gas, variable rate

SPE Disciplines:

Abstract The challenge facing reservoir and production engineers remains ensuring continued production from a well, including additional recovery with artificial lift methods. To accomplish this, means to determine the production performance of a well until the end of its life is desired. This challenge is even greater when dealing with production from unconventional formations. This paper presents a methodology to model the production performance of a well producing from an unconventional oil or gas formation. Emphasis is placed on the use of readily-available information to production engineers for the day-to-day analysis and optimization of production from the field. For developing the model, traditional flow regimes observed during the production of a well are utilized. Using this information as well as superposition principle, a working model is developed, tested and validated. Technical contributions of this paper include a procedure to implement this solution in any producing oil or gas well from an unconventional formation, and an Inflow Performance Relationship (IPR) framework for visualizing productivity changes with time of a particular well.

application, complex reservoir, equation, fluid property, forecast, inflow performance, information, oil saturation, Petroleum Engineer, pressure response, pressure transformation, production control, production monitoring, production rate, pseudo pressure, Reservoir Surveillance, superposition plot, superposition time, Time Function, unconventional formation, Upstream Oil & Gas, well performance, Well Performance Model

Abstract In many companies, production forecasting using multiple segments is gaining traction. Theoretically, the multiple segments are used to capture the different flow regimes in the reservoir over a period of time. A three-segment Arps decline model has been prevalently used, where, in early time, an Arps b parameter of 2 is used to denote transient flow;, during middle time, an b parameter of 0.2 to 1 is used; and, during late time, a b parameter of 0 to 0.2 is used to denote the boundary dominated effects. Choosing the segments and the b parameters was usually based on an educated guess about the reservoir and the visual observation of the changing slopes of decline. The three-segment model presupposes a reservoir behavior that may not be happening in the field, and varying operating conditions can skew the production rate slope and can mask the flow regimes observed in the reservoir, This, in turn, can lead to misleading forecasts. We are proposing a way to remove the guesswork from flow transition, the presupposition of flow regimes in the reservoir, and the masking effects of pressure using rate transient analysis.

decline curve, Decline Model, flow pattern transition, flow regime, fracture, good fit, identify flow pattern transition, Modeling & Simulation, pattern transition, Petroleum Engineer, presented, production control, production forecasting, production monitoring, Reservoir Surveillance, rta superposition plot, slope change, superposition plot, transient flow, transition, unconventional reservoir, Upstream Oil & Gas, workflow

Oilfield Places:

- North America > United States > West Virginia > Appalachian Basin > Marcellus Shale (0.98)
- North America > United States > Virginia > Appalachian Basin > Marcellus Shale (0.98)
- North America > United States > Pennsylvania > Appalachian Basin > Marcellus Shale (0.98)
- (4 more...)

SPE Disciplines:

Abstract Pre-fracture injection tests have been commonly used, across the industry, in order to estimate the required hydraulic fracture design parameters and associated reservoir pressure. However, evidence would suggest that industry approaches to both the injection execution and the post-injection analyses are not as equally consistent. The result could potentially be an erroneous and inaccurate interpretation, which could lead to over estimation of these reservoir characteristics and subsequent inefficient fracture design and placement. This paper demonstrates how a unified approach to the analysis of pre-frac injection tests can lead to the valid application of this technique in obtaining reliable estimates of both the reservoir pressure and the matrix permeability in a tight unconventional shale play (Utica play fairway). Analyses of the pressure fall off data, from pre-frac injection tests that were performed in a number of wells, will be discussed here. These analyses included the use of a conventional log-log diagnostic plot, as well as Pressure Decline Analysis using the SQRT (square root time), G function and G dP/dG plots. Finally, the results were also interpreted utilizing the ACA (after closure analysis) approach by employing type curves and flow regime time functions. The results of the formation permeability, the initial reservoir pressure, the closure time and the closure pressure from three of these field tests will be presented in this paper. Two of these tests achieved pseudo-radial flow, whilst one test failed to reach either pseudo-linear or pseudo-radial flow, resulting in a demonstrable overestimation of the reservoir parameters. The paper will present the injection test execution and analysis, as well as confirming the importance of achieving pseudo radial flow in order to obtain reliable and consistent test results.

closure pressure, closure time, derivative, diagnostic plot, Drillstem Testing, drillstem/well testing, dt log-log plot, Exhibition, hydraulic fracturing, log-log diagnostic plot, permeability, pre-frac injection test analysis, radial flow, reservoir parameter, reservoir pressure, spe annual technical conference, superposition function, superposition plot, Upstream Oil & Gas, well 2, well 3

SPE Disciplines:

Abstract Pressure transient tests are routinely performed on wells that have been hydraulically fractured. During the build-up, wells typically exhibit linear or bilinear flow, depending on the fracture conductivity. For high permeability wells radial flow may also be evident. For low permeability gas wells, the time to radial flow can often be impractically long. As a result many pressure transient analysis (PTA) tests end before radial flow happens. Without radial flow a unique value for reservoir permeability cannot be determined. To compound the problem low permeability wells often do not flow before being stimulated, so that pre-fracture tests require very specialized testing procedures and are not always possible. Unfortunately permeability dominates the productivity index calculation and without a reasonable value for permeability, the resultant production forecast will be significantly off. Furthermore, the ability to diagnose the success or failure of the actual stimulation treatment without prior knowledge of permeability will be diminished. This paper will show a technique, called the matrix method, which significantly reduces the uncertainty in permeability estimation for such cases. The essence of the technique is to generate a plausible set of matches considering the build-up data only. Then one takes this group of solutions and utilizes additional data, namely the pressure and rate history during the drawdown period, to determine the best possible match of the drawdown data. Introduction For oil and gas wells, the proper sizing and proppant selection for hydraulic fracture treatments requires knowledge of reservoir permeability. For moderate to high permeability reservoirs, a properly conducted pre-fracture flow and build-up test will allow the reservoir permeability to be determined. A stimulation treatment design methodology such as Unified Fracture Design 1,2 can then be used to optimize the design for propped length and fracture conductivity. Following treatment, a post-fracture flow and build-up test and PTA analysis can determine fracture properties to see if the design achieved actual results. Long-term production forecasts can then be made. After sufficient production data has been acquired, further refinements to the reservoir and fracture properties can be done utilizing modern production analysis techniques 3. In an ideal world all of these techniques will be used in some combination to refine the process of designing and obtaining optimal hydraulic fracture treatments. Low permeability (tight) gas reservoirs are increasingly being developed throughout the world; these wells typically will not flow prior to being stimulated. Using conventional pre-fracture tests to determine permeability is not possible for these wells. To circumvent the inability to flow, modifications of closed chamber tests first proposed by Alexander 4 are now being performed with increasing regularity. The modern application of this test is to use the whole wellbore or a portion of it as the closed chamber and to perform underbalance perforating, with surface measurement of pressures. Various interpretation models have been proposed 5,6,7, and initial pressure and permeability can be determined from an ideally conducted test, after which the previously described design methodology can be performed.

Artificial Intelligence, build-up, conductivity case, derivative plot, drawdown, flow in porous media, Fluid Dynamics, forward simulation, fracture properties, fracture property, hydraulic fracturing, initial pressure, interpretation, log-log derivative plot, matrix, permeability, radial flow, spe 113325, superposition plot, Upstream Oil & Gas

SPE Disciplines:

Summary

This paper discusses application of superposition to pressure-transient analysis when rate varies significantly before and pressure-transient analysis when rate varies significantly before and during pressure measurements. To apply rigorous superposition, use of conventional pressure-transient and rate-time methods is recommended to estimate permeability, skin, and in some cases, drainage area. These properties allow calculation of the dimensionless time constant used in properties allow calculation of the dimensionless time constant used in superposition calculations on the basis of rate change and dimensionless pressure. As van Everdingen and Meyer proposed, the time constant is varied until a linear fit of the pressure variable is made vs. superposition time. An important step is to use all available rate data, even though pressures may not be measured during periods of rate change. Our work shows the use of full superposition to check the consistency of standard well-test analysis based on the constant-rate or constant-pressure assumption. Data from two gas wells and results from a gas-well simulator provide the basis for our discussion. Problems covered are choosing provide the basis for our discussion. Problems covered are choosing the dimensionless pressure solution, estimating initial pressure by extrapolation of the superposition plot, and analyzing rate-dependent effects.

Introduction

Well-test analysis based on rate and pressure data is an important tool to the petroleum engineer. It allows estimation of such reservoir properties as permeability, skin, initial or average pressure, and drainage area. Many methods aid the analysis of rate and pressure data, perhaps the most important being the Horner plot for pressure data, perhaps the most important being the Horner plot for buildup analysis, type-curve matching for drawdown and buildup analysis, and the square-root-of-time plot for vertically fractured wells. The results of these analyses are used to determine the need for well treatment, to forecast production, to estimate reserves, and to define well properties for reservoir simulation.

Most well-testing methods use only part of the available pressure and rate data to determine reservoir properties. They often pressure and rate data to determine reservoir properties. They often are based on the constant-rate or constant-flowing-pressure assumption, neither of which is the case for typical oil and gas wells. Well tests may contain several periods of variable rate and shut-in. A given method (e.g., Horner analysis) commonly is applied separately to each buildup period during a multirate test. The permeability and skin from each analysis may be (and usually are) different, leaving the engineer with the problem of assigning an average set of properties to the well.

Several methods use variable-rate data from well tests and production history. The Odeh-Jones method applies superposition production history. The Odeh-Jones method applies superposition with the logarithmic approximation to analyze variable-rate drawdown tests. A limitation of this method is that buildup data with zero rate cannot be analyzed readily with drawdown data. Ridley suggests a unified method based on superposition to analyze drawdown and buildup data simultaneously that also uses log approximation. Fetkovich and Vienot modify the Odeh-Jones method to include the PD function instead of the log approximation. This improvement appears to be useful, particularly in analysis of low permeability, stimulated wells.

Bostic et al. proposed another superposition-based method to calculate a "unit function." This approach also was suggested by van Everdingen and Hurst (among others) for the study of aquifers and by Jargon and van Poollen for variable-rate, variable-pressure well tests.

application, approximation, buildup data, calculation, deviation, dimensionless time, Drillstem Testing, drillstem/well testing, equation, full superposition, gas well, Horner analysis, initial pressure, Modeling & Simulation, pressure transient analysis, pressure transient testing, psi 2, reservoir property, SPE Formation Evaluation, straight line, superposition, superposition plot, superposition time, Upstream Oil & Gas, Van Everdingen, wellbore pressure

SPE Disciplines:

Unsolicited. This document was submitted to SPE (or its predecessor organization) for consideration for publication in one of its technical journals. While not published, this paper has been included in the eLibrary with the permission of and transfer of copyright from the author.

**ABSTRACT**

A new presentation of sandface rate convolution has been devised which is compatible with the established Horner or superposition plots. The straight line on the new convolution plot provides the extrapolated reservoir pressure directly. Thus, the need for the current modified Horner plot is eliminated. The technique is based on a generalization of the existing convolution method to include any previous production rate history.

**INTRODUCTION**

Traditionally, the Horner plot or the more general superposition plot have been used to obtain reservoir parameters from buildup or multirate pressure transient tests. The procedure is based on fitting a straight line through the infinite-acting portion of the pressure buildup data and graphically extrapolating the line to infinite shut-in time to estimate *p**, the extrapolated reservoir pressure. When transient bottomhole pressure and downhole flow rate are measured simultaneously, the method of convolution^{1} may be used to analyse the test. The pressure and flow rate data ue convolved and then plotted on a cartesian graph referred to as the sandface rate convolution, SFRC. This technique yields a straight line whose slope gives the permeability of the reservoir in a manner analogous to the conventional superposition plot. The skin term is computed from the intercept. The extrapolated reservoir pressure, however, can not be obtained from the SFRO plot. Instead, another graph, the modified Horner plot,^{1} is prepared using the computed permeability and skin values. The extrapolation of the resulting straight line on the modified Horner plot gives *p**. Thus, a complete interpretation of simultaneous transient pressure and flow rate data requires several steps.

In this paper, a simple method is presented where the current SFRC plot is transformed into a new graph compatible with the conventional superposition plot. This allows for one-step interpretation of transient pressure and rate data in a manner similar to the establised Horner or superposition technique. The reservoir pressure is obtained from direct extrapolation of the infinite-acting straight line of the new transformed SFRC data. A modified Horner plot is no longer required. The method accounts for any previous surface flow rate history.

analyze simultaneous transient pressure, bottomhole pressure, convolution derivative, convolution plot, Drillstem Testing, drillstem/well testing, flow rate, graphical procedure, infinite shut-in time, normalized pressure change, presentation, pressure change, procedure, production control, production monitoring, rate data, reservoir pressure, Reservoir Surveillance, sandface rate data, SFRC, straight line, superposition plot, Time Function, Upstream Oil & Gas

SPE Disciplines:

Thank you!