A New Model for a Fractured Well in a Radial, Composite Reservoir

Abstract

Summary. A flow problem was identified by using a pressure-derivative technique to analyze several hundred pressure-derivative technique to analyze several hundred pressure-falloff tests from the Big Horn basin. To handle the pressure-falloff tests from the Big Horn basin. To handle the problem, a new analytic model was developed to allow direct problem, a new analytic model was developed to allow direct analysis of fractured wells with either finite conductivity or uniform flux in a radial, composite reservoir. In this paper, we demonstrate that this simple model further explains the buildup-pressure behavior of a fractured well producing below dewpoint pressure in a gas-condensate reservoir. Introduction Several hundred pressure-falloff tests were conducted to evaluate injection-well completion efficiency before beginning a polymerflood in the Big Horn basin. A pressure-falloff test was run on each injector to determine injection performance after perforating more holes in the injection intervals. A work over program was designed to create a short. wide fracture to minimize shear degradation of the polymer as it passed from the wellbore into the formation. The Permian Phosphoria (locally called the Embar)and Pennsylvanian Tensleep reservoirs are two common producing zones that have been operated in the Big Horn basin since the 1920's.This paper focuses on pressure-falloff tests performed on the Embarformation, which is characterized by layers of fossili ferous limestone, sandy limestone, dolomitic limestone, and dolomite. From pressure-falloff test analysis of the Embar formation alone, the pressure behavior was classified as follows:homogeneous, fractured well, or composite reservoir. Using the pressure-derivative technique, we also found that more than 20 pressure-derivative technique, we also found that more than 20 tests exhibited fractured-well behavior at early times and composite-reservoir behavior at late times. To analyze this fourth category of pressure behavior, a new analytic model was developed to allow direct analysis of a fractured well in a composite reservoir. The model is an extension of Cinco-Ley and Meng's work. Their model incorporates a finite-conductivity, vertically fractured well into the solution for the pressure behavior ininfinite-homogeneous or infinite, double-porosity systems. The new model links the fractured well with the solution for either abounded. radial reservoir or a radial. composite reservoir and also allows double porosity. The solution for the bounded reservoir appears in Ozkan and Raghavan's work. Two field examples from the Big Horn basin were analyzed to demonstrate the application of the new model. The composite-reservoir behavior observed in the Big Horn basin is not caused by fluid banks because the field has been under continuous water injection for many years. In addition, most wells are producing greater than 95 % water, implying that water breakthrough has producing greater than 95 % water, implying that water breakthrough has occurred . Instead, composite behavior is the result of a reduced-permeability region induced by plugging natural fractures near the wellbore with debris or corrosion products carried by the injection water, Another application of the new model was discovered during analysis of pressure-buildup data acquired on a fractured wellproducing from a low-permeability gas-condensate reservoir. A producing from a low-permeability gas-condensate reservoir. A sequence of pressure buildups demonstrated a dynamic process of changing reservoir behavior from homogeneous to composite. This behavior was interpreted as a reduced-mobility zone near the wellbore formed by liquid dropout. The liquid dropout region resulting from production below the dewpoint pressure was treated in this new way as one region in a composite reservoir. Typical Behavior of Pressure-Falloff Tests In the Big Horn Basin Homogeneous, fractured-well. and composite-reservoir pressure-falloff tests each illustrate reservoir behavior patterns pressure-falloff tests each illustrate reservoir behavior patterns observed in the Embar formation. All pressure-falloff tests were run by setting a plug on the seating nipple downhole to minimize wellbore storage effects. Homogeneous Behavior-Case 1. Fig. 1 is a log-log graph of the pressure difference. p = p - p, and its derivative. p pressure difference. p = p- p, and its derivative. p . Here, the derivative is given by d(p)/d ln(t). The pressure-derivative technique has been applied extensively to pressure-derivative technique has been applied extensively to diagnose pressure-transient behavior. The derivative curve in Fig. 1 exhibits a horizontal stabilization, beginning at 0.25hours, that reflects the infinite-acting radial flow period. Ref,6 presents both semilog and type-curve analyses for the first three cases. Fractured-Well Behavior-Case 2. A 48-hour pressure-falloff test was conducted on this well after many years of continuous water injection. The pressure difference and its derivative are plotted on log-log coordinates(Fig. 2). The pressure-derivative curve has a half-slope at early times, which characterizes fractured-wellbehavior, and a horizontal line later, which reflects pseudoradial flow. The deviation from horizontal stabilization suggests better permeability away from the wellbore. permeability away from the wellbore. Composite-Reservoir Behavior-Case 3. Fig. 3 is a log-log graph of p and its pressure derivative, p', vs. falloff time. The pressure derivative exhibits composite-reservoir behavior. The pressure derivative exhibits composite-reservoir behavior. The derivative curve in Fig. 3 has two horizontal stabilized periods(t less than 0.2 hours and greater than 6 hours) that characterize infinite-acting radial flow in the altered region(reduced permeability)and in the unaltered region, respectively. Composite-reservoir behavior is the most common pressure behavior observed on pressure-falloff tests conducted on the Embar formation. A New Behavior: A Fractured Well In a Composite Reservoir-Case 4 Analysis of a sequence of pressure-falloff tests on one of the BigHorn basin wells was particularly interesting. Fig. 4 shows the log-log graph of the prefracture pressure-falloff test, The pressure-derivative curve has two horizontal stabilized periods for t greater than 2 hours. Fig. 5 represents the response plotted on semilog coordinates. The first semilog straight line represents the reduced permeability (82 md) in the near-wellbore zone. The second semilog straight line reflects the unaltered permeability, (965md) of the formation. By use of the pressure-integral method, Fig. 6 shows a match of the field data on the composite-reservoir type curve with a mobility ratio of 0.087 and a distance to the radial discontinuity of 115 ft. The calculated skin from the first semilog straight line of Fig. 5 is -2.8. Subsequently, the well was fractured, and Fig. 7 shows the postfracture pressure-falloff test as a log-log graph of p and its postfracture pressure-falloff test as a log-log graph of p and its derivative. The early-time data, up to 0.25 hours, are dominated by a half-slope, which represents the fracture linear flow, The late-time pressure derivative exhibits a horizontal stabilization beginning at 4 hours, characterizing infinite-acting radial flow in the unaltered region. A straight-line slope through the late-time data on a semilog graph (Fig. 8) of the pressure response yields a 967-md permeability to water. We observe, on the basis of the prefracture test, that the reservoir exhibited composite-system behavior. SPEFE P. 225

Well Test Analysis in Gas-Condensate Reservoirs

“…There are relatively few publications dealing with well testing in gas condensate reservoirs 1,10,11,15,17,19,21 . Published interpretations are performed mainly on build-up data, because drawdown data are usually affected by flow rate fluctuations, and in the particular case of gas condensate wells, by noise due to condensate unloading in the wellbore.…”

“…Published interpretations are performed mainly on build-up data, because drawdown data are usually affected by flow rate fluctuations, and in the particular case of gas condensate wells, by noise due to condensate unloading in the wellbore. Analyses use pressure 1,12,17 , single-phase pseudo-pressure 11,12,21 or twophase pseudo-pressures 10,12,19 . The latter, which require good experimental measurements of relative permeability curves (rare for gas condensate systems) yield homogeneous looking derivatives and give access to the mechanical skin only.…”

“…Consequently, many laboratory 5,6,11,12,33 theoretical 1,2,4,9-14 and field investigations 10, [15][16][17][18][19][20][21][22][23] have been conducted over the last forty years to try to understand condensate reservoir flow behavior. It has been found that, when reservoir pressure around a well drops below the dew point pressure, retrograde condensation occurs and three regions are created with different liquid saturations 14,24,25 .…”

Interpretation of pressure tests in hydraulically fractured wells in bi-zonal gas reservoirs

“…For fractured wells in a composite reservoir, Chu and Shank (1993) presented a mathematical model for both finite-conductivity or uniform-flux vertically fractured wells within a composite reservoir. Chen and Raghavan (1995) developed a model for a fractured well producing in a composite reservoir.…”

From Straight Lines to Deconvolution: The Evolution of the State of the Art in Well Test Analysis

“…• Understand and recognize heterogeneous reservoir behaviors, such as double permeability (Bourdet 1985;Joseph et al 1986) and composite (Chu and Shank 1993).…”