Interpretation of Pressure Buildup Test Using In-Situ Measurement of Afterflow
Authors: Meunier Denis , Wittmann M.J. , Stewart George 
Published: December 2007

Summary
The influence of after flow on transient pressure responsehas long been recognized in well test analysis. The type-curve approach based on the simplified model of aconstant wellbore storage coefficient has attempted to assessafterflow effects from pressure data alone. Theintroduction of a new generation of production logging tools thatcan measure bottomhole flow (BHF) and pressure (BHP)simultaneously allows the afterflow in the well to bemonitored at the surface. Consequently, the well test canbe more rigorously interpreted by using a new form ofvariable rate analysis, and the shut-in time required toallow the detection of a straight line on the appropriatesemilog plot [e.g., Homer, or Miller-Dyes-Hutchison(MDH)] is much reduced. The analysis of the pressureand flow data transmitted from the production loggingdevice may be carried out at the wellsite in real time so that the test can be continued until the desired objectives are achieved. A field example shows how continuous BHF measurement during the wellbore storage period can improve the interpretation of a short-duration build up test.

Introduction
The constant rate solution of the flow equation in aninfinite reservoir is the basis of the conventional analysisof well tests. Even if the reservoir is bounded, the analysis applies while the reservoir is infinite acting-i.e., untilthe pressure change reaches the outer boundary. For the conventional analysis, it is essential to maintain constantrate, and it is well known that this is difficult to achieve. The best way to maintain constant rate is to make it zero, hence the wide use of buildup tests. Because of the compressibility of the fluid in thewellbore, the BHF does not adjust instantly to thesurface flow after a change of rate is imposed at the wellhead. This phenomenon is called "afterflow" in a buildup testor, more generally, "wellbore storage effect. "Duringthis time, the sandface rate is not constant, and early datacannot be used in the conventional (i.e., Homer or MDH)analysis. Furthermore, outer boundary effects maydevelop before the wellbore storage effect disappears, inwhich case the conventional analysis does not apply. Hence, the necessity of interpreting early data. This interpretation is possible through a more generalsolution of the flow equation, with a variable sandfacerate as inner boundary condition. The rate can be obtainedfrom a direct measurement or by other means. The firstattempt known to us of direct measurement in a builduptest was presented by Gladfelter et al. The afterflow ratewas obtained by measuring the rise of the liquid level inthe wellbore. The analysis used a semilog plot of the"corrected pressure," which is the ratio of the pressure dropto the sandface rate variation. Another method is to estimate the sandface rate froma mathematical model. Van Everdingen and Hurstpresented an exponential function of time as an presented an exponential function of time as an approximation of the sandface rate. In the currently acceptedtype-curve analysis, it is estimated from the derivative ofpressure with respect to time, on the assumption that the pressure with respect to time, on the assumption that the wellbore storage coefficient and the surface rate areconstant. A comprehensive review of this technique ispresented in Ref. 4. presented in Ref. 4. Recently, wireline tools capable of simultaneousmeasurement of sandface rate and pressure (as well asfluid temperature and density) were introduced. The firstbuildup tests recorded with these tools in oil and gas wellsalmost invariably revealed abnormal situations such asvery long afterflow or backflow and phase segregationin the wellbore. Such observations justifiably may leadus to question the validity of sandface rate estimated frompressure data alone. We present an analysis of the pressure data alone. We present an analysis of the wellbore storage concept and show briefly how a direct sandface measurement could improve the type-curve analysis. Our main purpose is to propose a new analysis basedon simultaneously measured sandface rate and pressure. The technique makes use of a rate-convolved time function similar to the superposition time function of Odehand Jones. The wireline aspect of the measurement offers the possibility of analysis in real time. We presentthis analysis for a buildup test in a homogeneous reservoir. Shortly after the original presentation of this work, several authors presented more comprehensive applications of direct sandface rate measurements. Fetkovich andVienot introduced their rate-normalized type curves, Kucuk and Ayestaran used a deconvolution process toidentify the reservoir model, and Stewart et al. appliedthe rate-convolved time function in nonhomogeneous reservoirs.
JPT
P. 143