This book provides an introduction to hardware and interpretation theory and methods for wireline formation testers (WFT). Naturally, methods fall within the pressure transient analysis purview, with nuances related to static and transient data acquired at multiple depths. In many ways, as demonstrated in this book, the gradient data from formation testers are the most in-depth information of the formation fluids.

Since the 1950s, formation testers have advanced substantially. Not only are they the mainstay for obtaining formation pressures, but they also provide initial samples of formation fluids and their first-pass compositional estimates, reservoir heterogeneity in the vicinity of the wellbore, fluid contacts, elemental analysis of formation wettability, and formation parting pressure through mini injection tests.

We use models to represent reservoirs and formations interchangeably because the investigation scale of WFT applies to both. Interval or interference pressure transient tests (IPTT) provide information up to a few hundred feet (approximately 100m) under favorable circumstances, with depth resolution varying with the density of station measurements.

Familiarity with transient testing and flow in porous media would help, though the necessary introductory material is given for each subtopic. Understanding of special functions is useful for the more mathematical chapters. The concept of mixed boundary value problems is quite prevalent in interpretation, and some readers may want to skip to the final results in these sections. In this regard, the book serves the needs of engineers desiring to evaluate reservoirs while being aware of the results’ scope. Similarly, in universities, this book may be suitably filtered for classroom instruction at undergraduate and applied graduate courses.

Many test examples to facilitate the understanding of each topic are provided. We hope that the book will help readers develop a better understanding of using commercial software; in particular, we expect them to recognize the limitations of numerical computations and accuracy limits of analytical solutions. Some of the solutions related to packer intervals are useful in well tests and hydrology.

Chapter 1 describes WFT hardware. Demarcated by flow geometry, WFT may be classified as either a dual packer or a probe tool or both. The dual packer or packer module contains two inflatable packer components set against the borehole wall to hydraulically isolate the volume between them (interval) from the rest of the wellbore. The probe module consists of a probe in tubular-shape coaxial with a packer element and is set against the borehole wall to hydraulically isolate it from the rest of the wellbore while communicating to the formation. The packer’s radius is smaller than the wellbore radius and is shaped to be almost flush with the curved wellbore. Probe geometry is also available in a casedhole version, in which the casing and the cement are drilled to establish flow communication between the tool and the formation and the hole plugged post-testing. Pressure gauge metrology and measurement errors are common to all these tools.

Chapter 2 outlines reservoir geology to the extent needed for improvising models for formation testers. The chapter covers structural, stratigraphic, and other traps. It introduces aquifers, carbonates and their porosity evolution, and naturally fractured reservoirs.

Chapter 3 presents the basics of porous media and rock and fluid properties. It covers pore size, porous media classification, representative elementary volume, macroscopic equations, heterogeneous media, distribution of reservoir fluids, connate and residual saturations, wettability, capillary pressure, hydrocarbon phase behavior, and properties of the reservoir fluids.

Chapter 4 presents single-phase fluid flow through porous media, Darcy’s law, and permeability. It covers pressure diffusion with and without gravity in nondeformable media and introduces deformable media. Modification of Darcy’s law, Klingenberg, and other nonlinear effects are given. Macroscopic and continuity equations for pressure diffusion in ideal porous media are also covered, along with some standard coordinate systems.

Chapter 5 presents the fundamentals of two-phase flow and extensions to Darcy’s law. It covers relative permeability and capillary pressure and governing equations for two-phase flow in nondeformable porous media. It also presents an example for estimating multiphase fluid properties, such as relative permeabilities, using array induction logs including enhancement with pressure and water-cut measurements from a packer-probe wireline formation tester.

Boundary and initial conditions are introduced in Chapter 6. These include prescribed pressure (Dirichlet), prescribed flux (Neumann), Robin, and mixed boundary conditions. By mixed, we mean that Dirichlet or Neumann conditions may apply to subsets of a coordinate surface. Additional material on skin and storage are also given. Components necessary to develop generalized impulse responses, including multilayer formations, are also presented.

Differential equations with boundary and initial conditions applicable to formation testing for several sink and observation probes are given in Chapter 7. Probe geometries include circular, rectangular, elliptical, ring, and guarded coaxial. Transient and steady-state solutions for mixed boundary value problems are stated here. For complicated probe geometries, acceptable and computationally efficient solutions are given. Efficient computable solutions are essential for nonlinear parameter estimation—a topic addressed in Chapter 10.

Chapter 8 presents differential equations with boundary and initial conditions and their analytical solutions dual-packer and slotted-packer modules with observations probes in vertical, horizontal, and deviated wells.

Pressure-rate and pressure-pressure convolution and deconvolution techniques are in Chapter 9. Solving convolution integrals is known to be an ill-posed problem and presents challenges in system identification. This chapter introduces some techniques to reconstruct stable and physically acceptable solutions. Several examples are given for both pressure-rate and pressure-pressure deconvolution.

Most of the nonlinear regression algorithms presented in the well-test literature are based on minimizing a simple sum of squares. Chapter 10 presents the maximum-likelihood-based evaluation (MLE). The MLE treats observations as random variables with specified probability distributions and is more appropriate for statistical inference. Procedures using MLE are illustrated using several synthetic and field WFT pressure and rate data sets.

Chapter 11 introduces pretests, examines pressure profiles and gradients with uncertainties and validation, and presents illustrative examples. Fluid contact determination from pressure profiles is also given in this chapter.

Geological model building for interpretation of WFT pressure and rate data, quality assurance, and data processing are given in Chapter 12. A unified framework for interpreting WFT pressure and rate data from multiprobe and packer-probe modules is in Chapter 13. Model recognition and building, flow-regime identification, parameter estimation, and validation and consistency of results are discussed. Formation testing hardware and gauge selection for test design are introduced in this chapter.

Chapter 14 presents techniques for obtaining formation mobility (permeability/viscosity) from pretest drawdown data acquired by packer and probe modules. This chapter also presents the conventional flow regime analyses for drawdown and buildup tests, along with examples.

Chapter 15 is devoted to the application of the interpretation methodology given in Chapters 13 and 14 for interpretation of many field and synthetic examples. A key aspect is the radius of investigation in formation testing. In particular, likelihood estimators of formation anomalies are given in Chapter 16.

Chapter 17 discusses downhole-sampling-formation fluid. This chapter covers flowline resistivity, optical fluid analyzer, and in situ measurements of downhole viscosity, density, and refractive index, along with mixture models for these properties. Chapter 18 presents stress testing with a field example.

In this book, all equations and definitions are given in any consistent unit system, such as SI or CGS. However, when we use the oilfield [American Petroleum Institute (API)] units, we state them explicitly. Furthermore, the flow rate q is assumed to be at downhole conditions (this the case for WFTs). Therefore, the formation volume factor B is omitted in all equations. Abbrevations are given in Appendix B.