Afterflow Measurement and Deconvolution in Well Test Analysis

Abstract

ABSTRACT The introduction of new production logging devices which simultaneously measure and record bottom-hole flow and pressure allows improved identification of reservoir parameters from well test analysis. In particular the detection of sandface flow resulting from the location of the logging tool just above the formation top means that the actual mechanics of wellbore storage phenomena can be excluded from consideration. In the case of pressure buildup or falloff tests the afterflow is directly measured and the amount of information available for interpretation at early time is essentially doubled in comparison to the situation where only pressure is recorded and flow is deduced from a simplified model based on a constant wellbore storage coefficient. The monitoring device continuously transmits the instantaneous pressure, p(t), and sandface flowrate, q(t), throughout the test and methods of well test analysis for a general, known rate schedule are considered. For the purposes of deconvolution the measured rate schedule, q(t), is replaced by a piecewise linear approximation comprising a series of pulses in which flow is a linear function of time. The convolution integral has an analytical solution for this case which shows that, for radial flow, a plot of p(t)/q(t) versus a modified logarithmic time function is a straight line of slope μ/(4πkh) with an intercept which is dependent on the skin factor. Simultaneous pressure and flow data taken during the afterflow period can therefore be analysed in terms of kh and S using a semilog plot in a manner analogous to the constant rate case; this gives much greater precision than type curve analysis of pressure data alone. The deconvolution method is based on homogeneous, radial flow theory and its performance when applied to simultaneous, transient pressure and flow data from heterogeneous systems is considered. It is shown that in the case of drawdown in which the rate schedule is monatonic the variable-rate semilog plot based on homogeneous deconvolution exhibits the same characteristics as the constant-rate semilog plot. This is demonstrated for two types of heterogeneity - the single sealing fault and a dual porosity or layered system. Thus in the drawdown case, analysis methods based on constant-rate theory can be employed on the generalised variable-rate semilog plot to define heterogeneity parameters such as the distance to a fault. Buildup tests should be analysed using drawdown theory on the basis of the pressure difference pws - pwfex. The elimination of the influence of afterflow means that any deviation from the initial semilog straight line is better defined.