Optimum Fractures in High-Permeability Formations

Abstract

Summary This paper describes an analytical model that (1) designs the pumping schedule of tip-screen-out (TSO) (frac-pack) fractures for high- and low-permeability formations, (2) estimates the reservoir production, and (3) determines the optimum propped length using the net present value concept. Sensitivity studies show the influence of the proppant permeability to propped fracture width. Sensitivity runs also show the influence of drainage area (and formation permeability) to optimum fracture length. A field example demonstrates the benefits of an appropriate fracture design. Introduction The frac-packing of moderate to high-permeability formations has increased dramatically over the last five years. The early jobs had limited success because of the lack of experience in the fracturing of high-permeability formations. The difficulty comes from the unconsolidated nature of those reservoirs. The fracture propagation (or lack off) after the onset of TSO was not well understood. Formation property data (Young's modulus, Poisson's ratio, in-situ stresses, etc.) were scarce due to the difficulty of extracting core samples to test in the laboratory. Currently, long strides are being taken to better understand the fracturing behavior.1–4 The reservoir properties are becoming more characterized by laboratory measurements.5–9 From a production point of view, the need to frac-pack a high-permeability reservoir is frequently questioned. The question is, can there be justifiable production gain by frac-packing a high-permeability reservoir? In response to this, numerous papers*** and field data10–15 show that in addition to production increase, there are other issues that make fracturing more beneficial:smaller pressure drop,lower flowing velocity,lesser volume of produced fines, andlonger sustained production. Another question is, what propped length and width should the fracture have? Although there are several papers related to fracture production,16–20 in general, this paper specifically addresses that question for frac-packs. It describes a model that optimizes the design (propped area and width) of TSO fractures. A field example is presented to illustrate the importance of appropriate fracture design. Description of the Model The model described in this paper performs three tasks:designs the proppant schedule for a given propped length and propped width,estimates the fracture production using the Fetkovich-Arps21,22 constant pressure-type curves, anddetermines the optimum fracture length using the net present value (NPV) concept. All the equations and their implementations are described, at length, in Appendices A and B. Optimum Design Example The NPV for six fractures with lengths increasing from 20 to 70 ft is calculated using the data listed in Table 1. The proppant concentration is selected to be 6 lbm/ft2. The calculations proceed as follows. The pumping schedule generator provides slurry-proppant schedules for six fracture half-lengths (20 to 70 ft). Fig. 1 shows the pad volume, slurry volume, and proppant ramping for the six frac-packs. The completion cost relative to the gravel-pack cost is depicted in Fig. 2. The production decline obtained from the Fetkovich-Arps-type curves is illustrated in Fig. 3. The estimated production is about 2,000 BOPD for the frac-packs and 1,200 BOPD for the gravel-pack for a drawdown pressure of 300 psi. There is no significant production gain with increase in fracture length. At last, Fig. 4 shows the NPV plot for the six fracture lengths. The estimated optimum fracture half-length (for 15 U.S.$/bbl oil price) is 30 ft for this particular example. Payout Time Fig. 5 shows the payout times for the frac-pack (with optimum length) and gravel-pack completions. The payout times are given by the intercept of the revenue plot with the horizontal axis. The revenue is defined as the difference between the cumulative production multiplied by hydrocarbon price minus the completion cost. Fig. 5 shows that the payout time is, generally, small (eight and nine production days for the gravel-pack and frac-pack, respectively). Fig. 5 shows also that the long-time revenue for the fracture is greater than the gravel-pack revenue. For this example, the frac-pack revenue is about 31% greater at the end of 100 production days. Three-Dimensional NPV Fig. 6 shows a three-dimensional NPV plot for the same data used in the previous example. However, in addition to propped length, the propped concentration (or width) is also optimized. The greater convexity of the plot in the direction of the length indicates that the NPV is more sensitive to propped length than to propped width. Fig. 6 indicates an optimum fracture length of 30 ft and an optimum propped concentration of 6 lbm/ft2 for this particular example. Sensitivity Analysis Fig. 7 shows the sensitivity of fracture width to proppant permeability. Fig. 7 indicates that for a given fracture length and formation permeability (xf=30 ft and k=100 md for this example) there is an optimum propped width. The optimum propped width decreases as the proppant permeability increases. Fig. 8 displays the sensitivity of drainage area, and formation permeability to propped fracture length. Fig. 8 says that the optimum propped length increases with increase in drainage radius, and the optimum length increases with decrease in formation permeability. Minimum Proppant Concentration As a rule of thumb, proppant concentrations of 6 to 10 lbm/ft2 are used in the poorly consolidated sands of the Gulf of Mexico. High concentrations are necessary to overcome proppant invasion and proppant embedment. Early fracturing attempts were unsuccessful when smaller (less than 2 lbm/ft2) concentrations were used. Laboratory data by Stimlab (Fig. 9) show that depending on the Young's modulus of the rock, the proppant lost to embedment for typical high-permeability sands can vary from 0.5 to 6 lbm/ft2. Therefore, we recommend limiting the minimum proppant concentration to 6 lbm/ft2.