Theory and Analysis of Injectivity Tests on Horizontal Wells
- Alvaro M.M. Peres (Petrobras) | Albert C. Reynolds (U. of Tulsa)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- June 2003
- Document Type
- Journal Paper
- 147 - 159
- 2003. Society of Petroleum Engineers
- 1.8 Formation Damage, 5.2.1 Phase Behavior and PVT Measurements, 5.6.3 Pressure Transient Testing, 5.6.4 Drillstem/Well Testing, 5.2 Reservoir Fluid Dynamics, 4.1.2 Separation and Treating, 4.6 Natural Gas, 2 Well Completion, 5.8.8 Gas-condensate reservoirs, 5.5 Reservoir Simulation, 5.3.4 Reduction of Residual Oil Saturation, 5.4.1 Waterflooding, 5.3.2 Multiphase Flow, 6.5.2 Water use, produced water discharge and disposal
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This work presents information on the pressure behavior at a horizontal water-injection well completed in an oil reservoir. We show that, quite remarkably, the pressure and pressure derivative behavior is similar to that of the single-phase solution calculated with oil properties evaluated at initial water saturation. This behavior is quite different from the injectivity solution for a vertical well where, except at early times, the injectivity solution is similar to the single-phase solution based on water properties. It is shown that flow regimes can be identified with the standard log-log diagnostic plots. The Thompson-Reynolds steady-state theory for multiphase-flow well testing is applied to derive a simple accurate approximate analytical solution for the wellbore pressure during injection for both the horizontal and vertical well cases. The horizontal well solution is completely new. Unlike the previous solutions for the vertical well case, we have incorporated a skin zone based on Hawkins' formula. The analytical solution, verified by reservoir simulation results using hybrid grids and local grid refinement, shows that the movement of injected water in a damaged zone has a strong and distinctive effect on both the pressure and pressure-derivative behavior at early times. Based on the analytical solution, we propose procedures for analyzing pressure data from injectivity tests.
For many decades, injection and falloff tests have been conducted on vertical water injection wells upon completion and throughout the life of the waterflooding project. These tests can provide estimates of reservoir pressure, effective permeability, and formation damage (mechanical skin factor). The injectivity index, obtained from the test data, is frequently used to monitor injectivity loss on injection wells. With the current focus on protecting the environment, injection/falloff tests provide an emissions-free alternative to traditional drawdown/buildup tests.
Early work1-4 on the analysis of falloff data considered solutions based on a two-zone (composite) reservoir model, in which the injected water displaces the original reservoir fluid in a piston-like fashion.
According to Abbaszadeh and Kamal,5 Verigin6 presented the first analytical solution for the injection pressure response for piston displacement. Abbaszadeh and Kamal5 and Bratvold and Horne7 derived an analytical solution for the pressure response during the injection and falloff periods. Their solutions assume radial flow from a vertical injection well. Their falloff solutions are based on a radially composite reservoir.
Thompson and Reynolds8 presented a theory for pressure behavior in radially heterogeneous reservoirs under multiphase flow conditions. They found that derivative data reflect a weighted average of permeability-mobility over the reservoir. The averaging process gives large weights to regions where total rate and total mobility change most rapidly with time. The Thompson-Reynolds steady-state theory is a convenient way to understand the effect of multiphase flow on pressure transient tests, because it allows one to identify the part of the total pressure derivative response that is caused by multiphase flow effects. The theory can also be used to construct analytical solutions (see Refs. 9 and 10 and the solutions presented in this work).
Banerjee et al.10 applied the Thompson-Reynolds steady-state theory ideas of Ref. 8 to injectivity and falloff tests for vertical wells in heterogeneous reservoirs and provided simple equations for the mechanical skin factor. However, because they neglected a term that they assumed to be small, their solution indicates that, in the homogenous case, the derivative of injection pressure reflects the total mobility at the waterfront. As discussed later, if the integral term they neglected is included, then it can be shown that the derivative of injection pressure reflects the water mobility at the sandface. This latter result is consistent with the "long-time" solution of Bratvold-Horne, as well as earlier results for the piston displacement case6,11 and the results of Serra et al.12 who showed that when the Boltzmann transform applies, the derivative of wellbore pressure with respect to logarithm of time reflects the mobility at the wellbore.
Field development using horizontal wells has become widespread. For single-phase flow problems, analytical solutions for the flow/shut-in pressure response at a horizontal well have been presented by several authors (e.g., Refs. 13 through 15). The industry has shown an increasing interest in the technological and economical aspects of horizontal injection wells, which are especially attractive in offshore waterflooding projects. However, to the best of our knowledge, no paper prior to ours has presented an analytical solution of the injection or falloff response at a horizontal water-injection well. In this work, the Thompson-Reynolds steady-state theory is applied to construct an analytical solution for injection pressure at a water injection well.
We also propose a procedure to analyze pressure data from a horizontal water injection well. The procedure, which requires that relative permeabilities are known, is based on removing multiphase flow effects to construct an equivalent single-phase solution based on oil properties. Analysis of pressure falloff tests is not considered.
The first part of this section deals with water injection into an oil reservoir via a vertical well water-injection well. In the second part, the horizontal well pressure behavior under single-phase flow conditions is reviewed.
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