Application of Water Injection/Falloff Tests for Reservoir Appraisal: New Analytical Solution Method for Two-Phase Variable Rate Problems
- Michael M. Levitan (BP plc)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- December 2003
- Document Type
- Journal Paper
- 341 - 349
- 2003. Society of Petroleum Engineers
- 5.2 Reservoir Fluid Dynamics, 3.3 Well & Reservoir Surveillance and Monitoring, 5.2.1 Phase Behavior and PVT Measurements, 5.5 Reservoir Simulation, 1.6 Drilling Operations, 5.4.1 Waterflooding, 5.6.4 Drillstem/Well Testing, 5.6.3 Pressure Transient Testing, 6.5.2 Water use, produced water discharge and disposal, 5.3.4 Reduction of Residual Oil Saturation, 5.3.2 Multiphase Flow
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The challenges of reducing or eliminating emissions associated with well-testing operations during reservoir appraisal have revived interest in water injection/falloff tests. However, the two-phase flow and injection-induced temperature changes associated with injection/falloff tests complicate the problem of well-test analysis. Strictly speaking, these effects make the pressure transient problem nonlinear and preclude using conventional superposition technique to construct solutions for variable rate problems.
In this paper, we present a new analytical method for accurate solution of the pressure transient problem for two-phase flow associated with water injection/falloff tests. The solution algorithm allows one to compute the solution for any stepwise constant rate sequence that includes multiple injection and falloff periods. The method is general, and can be used for water injection governed by any physically meaningful relative permeabilities, as well as for pistonlike displacement.
Water injection/falloff tests are normally associated with waterflood projects. Recently, interest in this type of well test has developed in the area of reservoir appraisal. In the vast majority of situations associated with exploration activities, there is no infrastructure and equipment in place to collect and export the hydrocarbons produced during well tests. The common practice used in the industry is to burn the produced fluids. The demands to reduce emissions during well tests created enormous pressure to avoid these tests altogether. This brings large uncertainties to the reservoir appraisal, and increases the investment risk if a decision is made to sanction a project and to develop the field. In most cases, drilling additional wells to reduce appraisal risks is not an option in view of the enormous costs of wells in frontier and deepwater explorations areas.
Replacing a production/buildup test sequence by an injection/ falloff sequence solves the problem of emissions. However, this significantly complicates the problem of well-test analysis. First, the character of the system changes. Instead of single-phase flow, we are now faced with two-phase water/oil flow governed by relative permeabilities. Second, injection of cold water induces temperature changes in the formation and brings additional complications to pressure behavior through temperature effects on the oil and water viscosities. Third, injection of water may result in the formation fracturing and in coupling of rock mechanics and fluidflow problems. It is therefore critically important for successful test interpretation to avoid fracturing and to inject water at below the formation fracturing pressure.
Pressure transient behavior during water injection and falloff tests has been studied by a number of authors.1-11 Most of the efforts were concentrated on homogeneous reservoirs with radial flow geometry. Many original insights into this process came from numerical experiments.3 This opened the way for development of analytical models that are based on simplified flow equations that capture the leading order effects controlling transient pressure behavior. In one of the first studies on this subject, by Verigin,1 the two-phase flow during water injection was represented as a two-bank system in which injected water displaces formation fluid in a pistonlike manner. This model was later extended to pressure falloff tests.2,4,7 The two-bank model may be a reasonable approximation of the flow conditions for the case of very favorable mobility ratio when the mobility of injected water is much less than the mobility of reservoir fluid. Note that the two-bank model does not account for saturation variation within the water-invaded region. Numerical experiments, however, indicate that the saturation gradients that develop during water injection do have significant effects on transient pressure behavior. It has also been realized early on that the Buckley-Leverett12 model of oil-water displacement process provides an accurate approximation of the water saturation distribution within the water-invaded region. Abbaszadeh and Kamal4 developed a generalization of the two-bank model, the so-called multibank model, which is intended to account for water saturation variation within the water-invaded region. In a multibank model, the invaded region is divided into several banks with constant water saturation within each of the banks. The water saturation profile is thus approximated as a stepwise constant function. Bratvold and Horne5,6 were able to remove this restriction (stepwise constant saturation distribution) and developed an analytical solution for a constant rate injection problem that allows for continuous saturation variation within the water-invaded region.
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