Application of the Delta Transient Method to Multi-Rate Tests: A Method for Calculating Individual Layer Permeability and Skin in a Multilayered Reservoir using Production Logging Data

Abstract

The method proposed in this work calculates the permeability and wellbore skin factor for each individual layer in a multilayered reservoir, fully addressing the superposition principle for the multi-rate test scenario. The method provides an explicit solution for the inverse problem, where the main inputs are downhole pressure data, production logging data and the surface rate schedule, as well as other commonly known parameters. The Method has a strong operational drive, which consists of demanding only few hours of rig time to acquire the necessary data. The main contribution of this work is to allow the application of the method to multi-rate schedules, providing more flexibility for the data acquisition scheme. Regarding production logging data, only two flow profiles at distinct times are required for full application of the Method. No stationary data are needed. The calculations for each layer are performed with a set of algebraic equations, which can be easily modeled in any ordinary spreadsheet software. No graph analyses are required. The resulting skin distribution has a great impact on acid job designing techniques, enabling the assessment of diversion effectiveness across the wellbore, especially on carbonate reservoirs, where acidizing procedures are largely employed. The individual layer permeabilities provide more accurate data for geological modeling, potentially resulting in more reliable production curves and reserves estimates. As a final step to the Method, once permeability and skin for each layer are obtained, a reasonableness check is provided. The purpose of this check is to guarantee reliability on the resulting outcomes. A successful case study is presented, where it took 9 hours to acquire all necessary data.

Pressure Transient Analysis for Injectivity Tests in Multilayer Reservoirs

“…However, flow-rate profiles computed using the analytical solution developed by Barreto et al [16] diverged from the other methods in layers 1 and 3. This result is particularly interesting, since accurate knowledge over layer flow-rate data is crucial for parameter estimation techniques [5,13,56,57].…”

“…3.15 evidence that both the formulation proposed in Section 3.2 and the solution presented by Mastbaum et al [48] exhibited a great agreement with the numerical data. As mentioned earlier, accurate evaluation of flow-rates in each layer is helpful to some interpretation techniques that aim to estimate individual layer properties [5,13,56,57].…”

“…Pressure and layer flow-rate profiles displayed in Figs. 3.10 to 3.15 were employed to estimate layer permeabilities using the Delta Transient Method [56,57]. This procedure demands pressure and flow-rate data from only two distinct time steps, which is a significant operational advantage [56,57].…”

“…We also provide a brief discussion regarding the radial flow regime that may be observed during an injectivity test. Furthermore, the Delta Transient Method [56,57] was applied to estimate layer permeabilities in the multilayer cases.…”

“…Thus, the analytical models developed by Barreto et al [16], Bela et al [12] and in Chapter 2 present an inconsistency, as they are based on the Thompson and Reynolds' [15] steady-state theory. Moreover, the Delta Transient Method [56,57] was successfully applied to estimate individual layer permeabilities.…”