Summary This paper presents new analytical and semianalytical solutions derived from a coupled transient-wellbore/reservoir thermal model to investigate the information content of transient-temperature measurement made within the vertical wellbore across from the producing horizon or at a gauge depth above it during drawdown and buildup tests. The solutions consider flow of a slightly compressible, single-phase fluid in a homogeneous infinite-acting reservoir system with skin modeled as a composite zone adjacent to the wellbore and account for the Joule-Thomson (J-T) heating/cooling, adiabatic-fluid expansion, conduction and convection effects both in the wellbore and reservoir. They are developed depending on the assumption that the effects of temperature changes on wellbore and reservoir-pressure-transient data can be neglected so that the mass-, momentum-, and energy-balance equations in the wellbore and reservoir can be decoupled. The semianalytical solution for predicting sandface temperatures is verified by use of a general-purpose thermal simulator. Wellbore temperatures at a certain gauge depth are evaluated through the analytical steady-state and transient-wellbore-temperature equations coupled with a semianalytical reservoir-temperature model accounting for conservation of momentum in the wellbore. Results show that drawdown- and buildup-sandface-temperature data may exhibit two semilog straight lines: one at early times reflecting the effects of adiabatic-fluid expansion in the skin zone near the wellbore, and the other, the late-time semilog straight line, reflecting the J-T effects and exhibiting the nonskin-zone properties. However, the wellbore-temperature measurements made at locations above the producing horizon may not exhibit these semilog straight lines because they are strongly dependent upon distance above the producing horizon, geothermal gradient, and radial-heat losses from the wellbore fluid to the formation on the way to gauge. It is found that the skin-zone properties are very difficult to be estimated from drawdown- and buildup-wellbore temperatures unless the gauge location is not far from the producing zone. Specifically, we found that buildup-wellbore temperature is mostly dominated by wellbore-heat losses compared with drawdown-wellbore-temperature data, and hence may not be useful to estimate the formation properties, including skin-zone properties.

This paper presents a new spherical-flow cubic-analysis procedure for estimating horizontal and vertical permeabilities solely from pressure transient data acquired at an observation probe of the dual-packer-probe wireline formation testers (WFTs) for all inclination angles of the wellbore. The procedure is based on the analytical spherical-flow equation that Onur et al. (2004a) previously presented, and the conventional spherical-flow analysis plot of drawdown or buildup observation probe pressures. This procedure now makes it possible for one to estimate both horizontal and vertical permeabilities from observation- probe pressure data exhibiting spherical flow for packer-probe interval pressure transient tests (IPTTs). The new analysis procedure does not require one to know the formation thickness or to observe the radial flow regime at the dual-packer and/or observation probe. The procedure provides unique estimates of horizontal and vertical permeabilities from observation-probe pressure data obtained along both vertical and horizontal wellbores. However, for slanted well cases, the analysis procedure yields two possible solutions for the horizontal and vertical permeabilities. Therefore, one must use a priori information on permeabilities, from sources such as core data or pretests, to eliminate one of the solutions and identify the appropriate solution for the slanted well cases. For IPTTs that have transitional data from the spherical flow regime to late-radial flow regime, nonlinear regression analysis based on history matching of dual-packer- and/or observation-probe pressure measurements from slanted wells may also help one to estimate correct values of horizontal and vertical permeabilities. We illustrate the applicability of the proposed analysis procedure by considering two synthetic and two field packer-probe IPTT data sets from vertical and slanted wellbores. Introduction Over the last four decades, wireline formation testing has become quite attractive for reservoir pressure profiling, sampling/fluid identification, IPTTs, and in-situ stress testing. IPTTs conducted with packer-probe formation testers provide dynamic permeability and anisotropy information with high vertical resolution along the wellbore (Zimmerman et al. 1990; Pop et al. 1990; Goode and Thambynayagam 1992; Kuchuk et al. 1994). Permeability is one of the most important parameters for both reservoir management and well performance. Permeability and permeability anisotropy, the ratio kv/kh, strongly affect all reservoir displacement processes. Thus, it is becoming increasingly important to determine these values as operators shift their focus from primary to secondary and tertiary recovery. Fig. 1 shows a schematic diagram of a packer-probe interference test (usually referred to as an IPTT) in a deviated well in an anisotropic formation that is bounded vertically and infinite laterally. The schematic represents a general configuration that is valid for all inclination angles (qw) of the wellbore. For instance, if qw = 0o, then we consider an IPTT conducted in a vertical well, whereas if qw = 90o, we consider an IPTT conducted in a horizontal well. In these tests, a dual-packer is set against the formation to serve as a flow source. The pressure transients are measured at both the packer interval and observation probe. Any pressure change at the observation probe due to flow from the packer interval clearly indicates communication within the formation between the two locations. Interpretation of packer and probe data provides one with permeability values in both the vertical and horizontal direction. Furthermore, one can characterize the near-wellbore heterogeneity from IPTTs.

This paper presents a new infinite-acting radial-flow analysis procedure for estimating horizontal and vertical permeability solely from pressure transient data acquired at an observation probe during an interval pressure transient test (IPTT) conducted with a single-probe or dual-packer module. The procedure is based on new infinite-acting radial-flow equations that apply for all inclination angles of the wellbore in a single-layer, 3D anisotropic, homogeneous porous medium. The equations for 2D anisotropic cases are also presented and are derived from the general equations given for the 3D anisotropic case. It is shown that the radial-flow equation presented reduces to the Prats’ equation assuming infinite-acting radial flow at an observation point along a vertical wellbore in isotropic or 2D anisotropic formations of finite bed thickness. The applicability of the analysis procedure is demonstrated by considering synthetic and field probe-probe and packer-probe IPTT data. The results indicate that the procedure provides reliable estimates of horizontal and vertical permeability solely from observation-probe pressure data during radial flow for vertical, horizontal, and slanted wellbores. Most importantly, the analysis does not require that both spherical and radial flow prevail at the observation probe during the test.

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