Cross-diameter flow measurements can be used as a measure of permeability of a core to complement conventional axial permeability. Conformal mapping is used to derive appropriate two-dimensional equations to calculate cross-diameter permeability from the measured flow rate and differential pressure. In some cases, particularly in pre-test measurements for API RP 43 standard perforation flow test, the flow measurement is performed along only a portion of the core length. Axial flow components allow some fluid to penetrate beyond the test segment. This results in artificially high flow rates and leads to errors in calculation permeability. The extent of the error depends on test geometry, core orientation and permeability anisotropy. In this paper, we use a finite difference numerical model to calculate correction factors which can be used to obtain correct values of cross-diameter permeability using the two-dimensional analytical equation.
This note addresses the measurement of whole-core permeability using cross-diameter flow as applied in API RP 43 recommended procedures.(1) The procedure discussed here complements an accompanying paper(2) which discusses the basis and use of the perforation flow test procedures.
FIGURE 1: Basic cross-diameter flow measurement.(Available in full paper)
The method of cross-diameter permeability measurement is not new. Figure 1 illustrates the method in which differential pressure is applied across opposing segments of the core's external surface. A two-dimensional solution of Darcy's law for these boundary conditions can be obtained using conformal mapping techniques: Equation (1) (Available in full paper)
Equation (2) (Available in full paper)
FIGURE 2: Cross-diameter flow arrangement as used in API RP 43 perforation flow tests. (Available in full paper)
FIGURE 3: illustration of extra flow beyond the test region due to axial flow. (Available in full paper)
The perforation flow performance test in Section 4 of RP 43 uses Equation (2). This measurement, combined with conventional axial permeability, comprise the pre-test data used to interpret subsequent perforation flow data. However, the test procedures introduce an additional complication in that cross-diameter flow should be measured only over the partial length of the core that corresponds to the expected perforation depth. The test arrangement is shown in Figure 2. In using Equation (2), the open flow length Li is used in place of the total core length L. This geometry results in an additional axial flow component (Figure 3) causing Q to be greater than in the simple 2D case [Equation (2)]. The difference depends on the axial permeability (K2) and the sample dimensions.
Morita(4) illustrated the effect for a specific case by calculating flow rates with finite difference modeling. In this note we present similar calculations and provide graphical correction factors for use in determining Kd for perforation flow tests.
FIGURE 4: Correction factors for samples with LIR = 4. (Available in full paper)
FIGURE 5: Correction factors for samples with LIR=5. (Available in full paper)
Initial calculations were done using commercial software. The results presented here were obtained using our own unsteady-state model with anisotropy and non-Darcy flow options.