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Treatment evaluation leads to problem identification and to continuously improved treatments. The prime source of information on which to build an evaluation are the acid treatment report and the pressure and rate data during injection and falloff. Proper execution, quality control, and record keeping are prerequisites to the task of accurate evaluation. Evaluation of unsatisfactory treatments is essential to recommending changes in chemicals and/or treating techniques and procedures that will provide the best treatment for acidizing wells in the future. The most important measure of the treatment is the productivity of the well after treatment.
Hydraulic Impedance Testing (HIT) is an easily applied transient pressure response method that can be successfully employed in determining fracture closure. In addition pressure derivative analysis when applied to fracturing and/or falloff data can readily define the actual changing flow regimes that exist within the fracture at any given time. Knowledge of the proper flow regime is a critical component in selecting the most appropriate analysis methods that should be used to define the minimum in-situ stress ( min), i.e. techniques based on linear or bilinear flow analysis. The combined diagnostic methodology that employs HIT and improved pressure derivative analysis when used in conjunction with conventional microfracturing techniques can substantially reduce the error in defining min. The results of several field tests will be used to illustrate the power and simplicity of these techniques in assessing what can often appear to be ambiguous pressure falloff data.
Measurements of the in-situ stress magnitude and stress gradient are critical components in the design, execution and analysis of hydraulic stimulation treatments. Although a variety of testing methods that involve assessing rock properties through core or logging techniques have been advanced the use of microfracturing or in-situ stress testing remains the most direct technique in which to measure the magnitude of the earths compressive stresses.
In-situ stress testing whether performed in open hole or through cased hole perforations involves the injection of low rate, low viscosity fracturing fluids, generally water, to initiate and propagate a hydraulic fracture away from the adverse influence of the well bore. Although fracturing pressures are sometimes used in assessing confining stress, generally the analysis techniques rely on interpretation of the falloff pressure following injection when the pumps are shut down, the injection process diminishes and the fracture closes.
Various field testing practices and novel analysis techniques have been published in an attempt to define an accurate methodology from which to extract min from in-situ stress pressure data. However a valid interpretative routine depends on falloff pressure data that is "well behaved", that is to say that it fits the conjectured fracturing and reservoir interactive processes. Most often a simple elastic model is proposed that incorporates some basic assumptions that usually include the following,
- equivalency between the instantaneous shutin pressure (ISIP) and min,
- linear fluid loss (leakoff) leading up to fracture closure,
- simultaneous mechanical and hydraulic fracture closure, and
- little if any backstresses resulting from leakoff.
Unfortunately nature does not always fit such simple models and the falloff pressure records more often than not don't conform to the presumed wellbore, fracture and reservoir flow regimes but generally exhibit an ambiguous, ill defined smooth decay. As a consequence interpreted results can be subjective often providing poorly defined values of min.
This paper presents an interpretation methodology to estimate water and oil relative permeabilities from pressure transient analysis of water injection well data.
This study has been carried out in three related parts. In the first part, mathematical equations for injection, falloff and variable-rate injection solutions are derived based on the multicomposite and stepwise multicomposite systems.
In the second part, the effect of water and oil relative permeabilities was investigated using the mathematical models. The permeabilities was investigated using the mathematical models. The investigation showed that the characteristics of the relative permeabilities are reflected distinctly in the transient part between the early and late time ranges. part between the early and late time ranges. In the last part, the inverse problem of estimation of water and oil relative permeabilities from pressure transient data was discussed using the proposed interpretation system, which consisted of the multicomposite model and an improved nonlinear regression algorithm. The study showed that the power-law relative permeability curves can be determined uniquely from pressure falloff data. Interpretation of field examples supported the practicality of the developed approach.
Water and oil relative permeabilities are critical parameters in forecasting reservoir performances, particularly in water injection projects. Relative permeabilities obtained from projects. Relative permeabilities obtained from laboratory experiments may be different from reservoir relative permeabilities because the laboratory results can reflect only small pieces of reservoir rocks.
The use of well production data and numerical simulator, known as history matching, may be useful to estimate reservoir relative permeability. However, the procedure is only applicable after a long production history is obtained.
Recently, Al-Khalifah et al. presented a method which estimate three-phase relative permeabilities from multirate drawdown test data. However, the method is based on a pressure-saturation relationship which holds only during the depletion stage. Also the procedure was developed primarily to obtain oil and gas relative procedure was developed primarily to obtain oil and gas relative permeabilities and it can cover only a restricted range of water saturation permeabilities and it can cover only a restricted range of water saturation since the water saturation at the wellbore usually changes little during drawdown tests.
Several interpretation methods have been proposed for water injection wells based on the assumption that oil is displaced by water in a piston-like manner. Therefore, these methods do not consider the effect of water and oil relative permeabilities. permeabilities. Weinstein and Sosa et al. examined the effect of water and oil relative permeabilities on pressure transient behavior using numerical models. Abbaszadeh and Kamal and Bratvold and Horne presented analytical injection and falloff solutions in which the effects of relative permeabilities were considered. However, none of the works discussed permeabilities were considered. However, none of the works discussed the inverse problem of estimation of water and oil relative permeabilities from pressure transient data.
In this paper, first the mathematical solutions are examined. Next, the effect of relative permeabilities is investigated using the models. After the investigation, the inverse problem is discussed using the models and the improved problem is discussed using the models and the improved nonlinear regression algorithm presented previously by Nanba and Horne.
A superposition model was developed to study the effect of offset wells on pressure transient tests for vertically fractured wells. The principle of superposition was found to be a valid tool.
For the situation in which a vertically fractured well was surrounded by production wells, there was no difference in the portion of the data used for the analysis of pressure buildup data when the offset producers were shut-in and when they were left on during the buildup test. This result implies that for a fieldwide situation in which the offset wells are left on during the buildup test radial flow is not achieved and the formation flow capacity calculated from a semilog plot has to be corrected. There may be limitations to the accuracy of the correction factors in multilayer reservoirs.
Analysis of pressure buildup or falloff data for a pressure maintenance project with a vertically fractured well in the middle of a five-spot pattern can yield different results depending on the operation of the offset wells during the pressure transient test. For a fieldwide situation in which the offset wells are left on during the pressure transient test, radial flow might be achieved, in which case the formation flow capacity calculated from the semilog plot should not be corrected. If radial flow is not achieved either due to interference from offset wells or the test not being run long enough, the data can be type curve matched to determine formation flow capacity.
Russell and Truitti and later Raghavan, et al. have shown that the formation flow capacity of a vertically fractured well in the center of a square closed system could not be calculated correctly by conventional semilog analysis of pressure buildup data. This is because if the fracture pressure buildup data. This is because if the fracture is long enough, boundary effects can be detected at the well and radial flow may not be achieved. Conventional semilog analysis assumes that radial flow is achieved. Instead, these authors proposed correction factors for the semilog-calculated formation flow capacity. Raghavan and Hadinoto found that a formation flow capacity correction factor was also required for pressure buildup or falloff data of a vertically fractured well in the center of a square constant pressure boundary system.
In this paper, the principle of superposition is applied to multiple well homogeneous reservoirs in which the well of interest is vertically fractured. The effect of the offset wells rather than a fixed boundary on shut-in pressure of the well of interest is examined.
Dimensionless Pressure for a Vertically Fractured Well
This memorandum considers only uniform-flux and infinite-conductivity fractures. Closed form analytical expressions for dimensionless pressure for drawdown at a single well in a homogeneous infinite reservoir exist for the two types of fractures: