1. INTRODUCTION - Tullow Oil Ghana acquired the first 4D monitor survey on the Jubilee field in Feb-March 2017 based on the results of 4D feasibility studies using core calibrated stress sensitivity measurements and conventional elastic 4D rock physics analysis. The observed 4D responses (AI, GI and time shifts) proved significantly larger than those predicted from the 4D feasibility study. Interpreting 4D seismic responses due to reservoir production and water injection can be challenging due to the effect of changes in both reservoir pore pressure and saturation on reservoir rock properties. The 4D signal at Jubilee showed a dominant effect from the pressure increase due to water flood and production changes. A study to understand these changes and update the field rock physics models was commissioned with Ikon Science, to allow the 4D responses to be linked to the reservoir models.

2. PATCHY CEMENT WORKFLOW - A rock physics workflow based on the patchy cement rock physics model [1] was applied to model the 4D changes at each well. The patchy cement model predicts stress sensitivity in poorly to moderately consolidated sandstones using a multiple nested Hashin-Shtrikman approach combined with contact cementation theory. The key parameter in the model is the fstep, which is interpreted to be the fraction of cement vs uncemented ‘patches’ in the sandstone.
The patchy cement model was calibrated to the pre-production wireline logs and stress to determine a baseline ‘f-step’ for the reservoir at pre-production conditions. The patchy cement model was then run for a range of f-step values given estimates of the maximum pore pressure due to injection at each well, and for each model the 4D changes in acoustic impedance (AI) and gradient impedance (GI) and time shift was calculated. The model therefore represents the inelastic effect of production on sandstone consolidation. The predicted 4D changes which best matched the observed 4D changes were then chosen and used to derive an empirical relationship between the maximum delta pore pressure (max. ΔPpore) and the reservoir f-step, the idea being that the maximum ΔPpore results in a reduction on the fraction of cemented grain contacts in the sandstone. This results in a 4D model with baseline f-step at pre-production conditions and a maximum ΔPpore dependent f-step for the monitor survey. At wells in the water leg, the increase in reservoir pressure due to injection has relaxed the rock frame and lowered the P and S-wave velocity of the rock: overall the AI decreases and GI increases. The modelled change in P-wave velocity due to the reduction in vertical effective stress is shown in Figure 1 and compared to the pre-production stress sensitivity from laboratory core measurements.

Modelling saturation was done using Gassmann’s equations using the appropriate dry frame rock properties for baseline and monitor. The 4D predictions of AI, GI and time shift were inspected across the reservoir at both production and injection wells and had a good match to the observed 4D signals at the wells.

3. 2D MODELLING - The workflow was then used to model a cross-section though the reservoir which intersects a down dip injector and an up-dip producer, and with a change in oil-water contact between the baseline and monitor surveys. The predicted 4D synthetics showed a good match to the observed 4D differences across section.

4. CONCLUSIONS - This interpretation approach to 4D signals using a patchy cement workflow has provided a simple workflow to understand 4D signals due to pressure increases and saturation changes across the reservoir wells and allows 4D modelled predictions to be built in 3D and compared in detail to the observed 4D signals. Further improvements by integrating this workflow with both pressure models from a reservoir simulator and with the 4D difference volumes across the reservoir would further refine how to interpret 4D signals through the life of the field.

5. REFERENCES
[1] Avseth, P., Skjei, N., and Mavko, G., 2016, Rock-physics modeling of stress sensitivity and 4D time shifts in patchy cemented sandstones – application to the Visund field, North Sea: The Leading Edge, 35, issue 10, 868-878.
[2] Dvorkin, J., and Nur, A., 1996, Elasticity of high-porosity sandstones: Theory for two North Sea datasets: Geophysics, 61, no. 5, 1363-1370.
[3] Saul, M., and D. Lumley, 2015, The combined effects of pressure and cementation on 4D seismic data: Geophysics, 80, no. 2,WA135–WA148, http://dx.doi.org/10.1190/geo2014-0226.