Summary
The formation-rate-analysis (FRASM) technique is introduced. The technique is based on the calculated formation rate by correcting the piston rate with fluid compressibility. A geometric factor is used to account for irregular flow geometry caused by probe drawdown. The technique focuses on the flow from formation, is applicable to both drawdown and buildup data simultaneously, does not require long buildup periods, and can be implemented with a multilinear regression, from which near-wellbore permeability, p * and formation fluid compressibility are readily determined. The field data applications indicate that FRA is much less amenable to data quality because it utilizes the entire data set.
Introduction
A wireline formation test (WFT) is initiated when a probe from the tool is set against the formation. A measured volume of fluid is then withdrawn from the formation through the probe. The test continues with a buildup period until pressure in the tool reaches formation pressure.
WFTs provide formation fluid samples and produce high-precision vertical pressure profiles, which, in turn, can be used to identify formation fluid types and locate fluid contacts. Wireline formation testing is much faster compared with the regular pressure transient testing. Total drawdown time for a formation test is just a few seconds and buildup times vary from less than a second (for permeability of hundreds of millidarcy) to half a minute (for permeability of less than 0.1 md), depending on system volume, drawdown rate, and formation permeability. Because WFT tested volume can be small (a few cubic centimeters), the details of reservoir heterogeneity on a fine scale are given with better spatial resolution than is possible with conventional pressure transient tests. Furthermore, WFTs may be preferable to laboratory core permeability measurements since WFTs are conducted at in-situ reservoir stress and temperature.
Various conventional analysis techniques are used in the industry. Spherical-flow analysis utilizes early-time buildup data and usually gives permeability that is within an order of magnitude of the true permeability. For p* determination, cylindrical-flow analysis is preferred because it focuses on late-time buildup data. However, both the cylindrical- and spherical-flow analyses have their drawbacks. Early-time data in spherical-flow analysis results in erroneous p* estimation. Late-time data are obtained after long testing times, especially in low-permeability formations; however, long testing periods are not desirable because of potential tool "sticking" problems. Even after extended testing times, the cylindrical-flow period may not occur or may not be detectable on WFTs. When it does occur, permeability estimates derived from the cylindrical-flow period may be incorrect and their validity is difficult to judge.
New concepts and analysis techniques, combined with 3-D numerical studies, have recently been reported in the literature.1–7 Three-dimensional numerical simulation studies1–6 have contributed to the diagnosis of WFT-related problems and the improved analysis of WFT data. The experimental studies7 showed that the geometric factor concept is valid for unsteady state probe pressure tests.
This study presents the FRA technique8 that can be applied to the entire WFT where a plot for both drawdown and buildup periods renders straight lines with identical slopes. Numerical simulation studies were used to generate data to test both the conventional and the FRA techniques. The numerical simulation data are ideally suited for such studies because the correct answer is known (e.g., the input data). The new technique and the conventional analysis techniques are also applied to the field data and the results are compared. We first review the theory of conventional analysis techniques, then present the FRA technique for combined drawdown and buildup data. A discussion of the numerical results and the field data applications are followed by the conclusions.
Analysis Techniques
It has been industry practice to use three conventional techniques, i.e., pseudo-steady-state drawdown (PSSDD), spherical and cylindrical-flow analyses, to calculate permeability and p*
Conventional Techniques
Pseudo-Steady-State Drawdown (PSSDD).
When drawdown data are analyzed, it is assumed that late in the drawdown period the pressure drop stabilizes and the system approaches to a pseudo-steady state when the formation flow rate is equal to the drawdown rate. PSSDD permeability is calculated from Darcy's equation with the stabilized (maximum) pressure drop and the flowrate resulting from the piston withdrawal:9–11 $$k {d}=1754.5\left({q\mu \over r {i}\Delta p {{\rm max}}}\right),\eqno ({\rm 1})$$where kd=PSSDD permeability, md. The other parameters are given in Nomenclature.
Late time acceleration of the 3-space in a higher dimensional steady state universe in dilaton gravity