6
Applied Well Test Interpretation
Well test interpretation is an inverse problem. The two central problems of well testing are (1) to identify the unknown reservoir model, and (2) to estimate the unknown parameters of that model. Although we often focus on parameter estimation, correct model identification is an essential component of any interpretation. If the model is wrong, the resulting parameter estimates are useless. Correct model identification is an essential component of well test interpretation. If the model is wrong, the resulting parameter estimates are useless.
1.5 Well Test Interpretation Methods Virtually, all quantitative well test interpretation methods fall into one of three categories: straight-line analysis, type-curve analysis, and simulation/history matching. Each of these categories has certain strengths and weaknesses. In our preferred workflow, type-curve and straight-line methods are used to identify the reservoir model and obtain preliminary estimates of reservoir properties, while history matching with an analytical or numerical model is used to verify and, if necessary, fine-tune the preliminary interpretation. 1.5.1 Straight-Line Methods. In straight-line analysis methods, the analysis must first identify data that exhibit a specific type of flow or flow regime, such as infinite-acting radial flow. The data are then graphed, perhaps after transforming pressure and time variables to account for non-ideal phenomena or flow conditions. Finally, a straight line is drawn through the data exhibiting the desired flow regime. From the slope and intercept of the straight line, the analyst then calculates reservoir properties, such as permeability, and/or well properties, such as skin factor. Straight-line methods were historically the first methods to be used in the petroleum industry. They are easy to perform by hand or implement in a spreadsheet. When the desired flow regimes are present and can be correctly identified, straight-line analysis methods give excellent results. Unfortunately, straight-line methods often require the pressure and time data be transformed. Another, more significant disadvantage of straight-line methods is that specific flow regimes must be present to determine certain reservoir properties. Finally, because straight-line methods use only data within a single flow regime, there is no guarantee that the resulting parameter estimates will be consistent with the rest of the pressure data. 1.5.2 Type-Curve Methods. In type-curve analysis methods, the analyst graphs the pressure and time data, perhaps after transforming to account for non-ideal phenomena, on a log-log scale. This field data graph is then matched to the pressure response (or type curve) from an ideal reservoir model. The shape and position of the field data relative to the type curve are used to estimate formation and/or well properties such as permeability, skin factor, and wellbore storage. Type-curve methods honor more of the data than straight-line methods and are thus less likely to give results that are inconsistent with the rest of the data. Type-curve methods may be used manually with paper type curves. However, the procedure is tedious and time-consuming, and paper type curves are available for only a limited number of different reservoir models. On-screen matching with computer-generated type curves is fast and flexible . However, some commercial well test software packages have limited type-curve matching capability. 1.5.3 Simulation and History Matching. In the simulation/history-matching approach, an analytical or numerical model is used to calculate the pressure response for known reservoir properties and assumed values for unknown reservoir properties. The values of the unknown properties are then adjusted until the calculated pressure response matches the observed field data. Matching may be conducted manually, or automatically using a nonlinear regression algorithm. The biggest advantage of history matching with a simulator is that more phenomena can be incorporated in the analysis, allowing most if not all of the data to be used in an integrated analysis, thereby ensuring consistency of the interpretation with the entire data set. However, history matching may be very time-consuming, unless good initial estimates of the unknown reservoir properties are available. In practice, we have found that the best workflow is to begin with type-curve and straight-line methods to get initial estimates of reservoir properties, then use simulation and history matching to verify or to fine-tune those initial estimates.
1.6 Rock and Fluid Properties A variety of rock and fluid property data are used as input data in well test interpretation. These data can be categorized as (1) rock property data, usually obtained from openhole logs, (2) fluid property data, usually obtained from correlations or lab measurements, and (3) other data.
Introduction to Applied Well Test Interpretation
Pore space
7
Grains
Fig. 1.3—Porosity is a measure of the capacity of the reservoir rock to store fluids.
1.6.1 Rock Properties. In this section, we will discuss the porosity, fluid saturations, permeability, pore volume compressibility, and net-pay thickness. Porosity. Porosity, φ , is a measure of the capacity of the reservoir rock to store fluids (see Fig. 1.3), defined as the ratio of the volume of the pore space to the total or bulk volume of the reservoir rock, Eq. 1.1: φ
=
pore volume bulk volume
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1.1)
When used in equations in well test interpretation, porosity is always expressed as a fraction. In reports, graphs, and tables, porosity is often given in %. Porosity may vary over a wide range, depending on the type of reservoir. Coalbed methane reservoirs may have porosity as low as 0.5%, while a diatomite may have a porosity as high as 60%. Table 1.1 gives typical ranges of porosity for a number of common rock types. Porosities estimated from openhole logs typically have an uncertainty of 5% to 15% (Spivey and Pursell 1998). Saturation. Fluid saturation is defined as the fraction of pore space occupied by a particular fluid (see Fig. 1.4), Eqs. 1.2, 1.3, and 1.4: S o
=
S g
=
S w
=
oil volume pore volume gas volume pore volume
, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1.2)
, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1.3)
water volume pore volume
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1.4)
TABLE 1.1—TYPICAL POROSITY VALUES FOR DIFFERENT LITHOLOGIES
Rock Type
Porosity Range
Diatomite
50–60%
Chalk
50–60%
Clean sandstone
25–30%
Typical sandstone
15–25%
Shaly sandstone
5–15%
Tight gas sand
5–12%
Limestone
2–15%
Fractured shale
0.5–8%
Coalbed methane
0.5–4%
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Disclaimer
This book was prepared by members of the Society of Petroleum Engineers and their well-qualified colleagues from material published in the recognized technical literature and from their own individual experience and expertise. While the material presented is believed believed to be based on sound technical knowledge, neither the Society of Petroleum Engineers nor any of the authors or editors herein provide a warranty either expressed or implied in its application. Correspondingly, the discussion of materials, methods, or techniques that may be covered by letters patents implies no freedom to use such materials, methods, or techniques without permission through appropriate licensing. Nothing described within this book should be construed to lessen the need to apply sound engineering judgment nor to carefully apply accepted engineering practices in the design, implementation, or application of the techniques described herein.
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Introduction
The objective of this textbook is to introduce the reader to the fundamentals of applied well test interpretation. The text focuses on the most basic well testing scenario: a single-well test on a well producing a single-phase fluid, from a single-layer single-layer,, homogeneous reservoir. Although Although simple, this scenario illustrates most of the elements required for interpretation in more complex scenarios. Chapter 1—Introducti 1 —Introduction on to Applied Well Test Test Analysis opens Analysis opens with an overview of different types of well tests, common applications and objectives in well testing, and alternati alternatives ves to conventional testing. The chapter continues with a review of reservoir rock and fluid properties and ends with a brief discussion of the effects of graphical scales on data presentation. Chapter 2—Fluid Flow in Porous Media covers Media covers the assumptions on which the diffusivity equation is based, then introduces the concepts of superposition in space, superposition in time, and radius of investigation. The remainder of the chapter focuses on the applied topics of wellbore damage and stimulation, pseudosteady-state flow, and wellbore storage. Chapter 3—Radial Flow Semilog Analysis introduces Analysis introduces semilog methods for estimating permeability and skin factor from data in infinite-acting radial flow for both drawdown and buildup tests. The chapter also discusses classical methods of estimating average reservoir pressure using the semilog plot. Chapter 4—Log-Log Type Curve Analysis discusses Analysis discusses the Gringarten-Bour Gringarten-Bourdet det pressure and pressure derivative derivative type curves and the log-log field data plot. The chapter discusses use of the log-log plot to qualitatively evaluate evaluate whether or not a well is damaged or stimulated, and to identify wellbore storage and the infinite-acting radial flow period. The chapter covers estimation of permeability, permeability, skin factor, and wellbore storage coefficient from the loglog field data plot without using type curves. The chapter closes with a discussion of some common methods used to calculate the logarithmic derivative derivative from field data. Chapter 5—Pressure Transient Testing for Gas Wells introduces Wells introduces the real-gas pseudopressure and pseudotime transforms and their normalized counterparts, adjusted pressure and adjusted time, to allow the use of methods developed for slightly compressible compressible liquids to be used for analysis of gas well test data. Chapter 6—Flow Regimes and the Diagnostic Plot introduces Plot introduces the common flow regimes and the use of the standard log-log and flow-regime specific diagnostic plots for flow-regime identification. For each flow regime, examples of one or more reservoir models that exhibit the flow regime are given. behavior. Chapter 7—Bounded Reservoir Behavior covers Behavior covers the most common models of single-layer reservoir behavior. For each model, the flow regimes that may be exhibited and the order in which they occur are discussed. Chapter 8—Variable Flow Rate History discusses History discusses various methods for treating a variable flow-rate history, from ignoring prior history for short buildups following long drawdowns to deconvolution. deconvolution. The chapter discusses the effects of some common types of boundaries on the shape of the log-log buildup test for different ways of plotting the data. The chapter then provides a spatial interpretation of a variable rate history as a pressure profile in the reservoir. reservoir. The effects of rate history on a subsequent buildup are discussed, as are the differences between the drawdown drawdow n and buildup responses for a well in a closed reservoir, reservoir, a reservoir with a constant-pressure boundary, and a radial composite reservoir. reservoir. A method for graphing the rate history preceding a buildup along with the pressure response during the buildup is introduced to help distinguish rate-history-induced features in the derivative derivative from those caused by boundaries. Chapter 9—Wellbore Phenomena addresses Phenomena addresses an issue that impacts any well test to one degree or another, yet has received only sporadic attention in the well testing literature. A number of different wellbore phenomena that
may affect the shape of the pressure response, such as changing wellbore storage, a rising or falling fluid interface, and completion cleanup, are discussed. In addition, other phenomena that affect the pressure response but have no impact on well productivit productivity y (such as pressure fluctuations from earth tides or daily changes in wellhead temperature, gauge problems, or data processing artifacts) are also addressed. Chapter 10—Near-Wellbore Phenomena covers Phenomena covers phenomena present in the near-wellbore area that do impact the well performance, including geometric skin factor for a perforated completion, a limited-entry or partial penetration completion, or a deviated well, and non-Darcy skin factor for both drawdown and buildup. Chapter 11—Well Test Interpretation Workflow presents Workflow presents a recommended workflow (more accurately, accurately, a workflow framework or checklist) for well test interpretation. The major steps are the same for virtually any well test interpretation: collect the data, QC the data, identify flow regimes, select a reservoir model, estimate model parameters, and validate the results. Chapter 12—Well Test Design Workflow presents Workflow presents a recommended workflow for well test design. As with well test interpretation, the major steps in well test design are the same for most situations: define the test objectives, collect data, estimate unknown reservoir properties, estimate test duration, estimate test flow rate, and determine flow rate sequence Disclaimer. The phrases “recommended procedure,” “recommended practice,” or other similar phrases refer to Disclaimer. The procedures or practices recommended by the authors and do not imply endorsement by the Society of Petroleum Engineers.
