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Introduction The first hydraulic fracturing treatment was pumped in 1947 on a gas well operated by Pan American Petroleum Corp. in the Hugoton field. Kelpper Well No. 1, located in Grant County, Kansas, was a low-productivity well, even though it had been acidized. The well was chosen for the first hydraulic fracture stimulation treatment so that hydraulic fracturing could be compared directly with acidizing. Since that first treatment in 1947, hydraulic fracturing has become a common treatment for stimulating the productivity of oil and gas wells. Hydraulic fracturing is the process of pumping a fluid into a wellbore at an injection rate that is too great for the formation to accept in a radial flow pattern. As the resistance to flow in the formation increases, the pressure in the wellbore increases to a value that exceeds the breakdown pressure of the formation open to the wellbore. Once the formation "breaks down," a fracture is formed, and the injected fluid begins moving down the fracture. In most formations, a single, vertical fracture is created that propagates in two directions from the wellbore. These fracture "wings" are 180 apart and normally are assumed to be identical in shape and size at any point in time; however, in actual cases, the fracture wing dimensions may not be identical. In naturally fractured or cleated formations, it is possible that multiple fractures can be created and propagated during a hydraulic fracture treatment. Fluid that does not contain any propping agent (called the "pad") is injected to create a fracture that grows up, out, and down, and creates a fracture that is wide enough to accept a propping agent. The purpose of the propping agent is to prop open the fracture once the pumping operation ceases, the pressure in the fracture decreases, and the fracture closes.
Since its introduction almost 50 years ago, hydraulic fracturing has been the prime engineering tool for improving well productivity, either bypassing near wellbore damage or actually stimulating performance. Historically (and in many instances erroneously) the emphasis for propped fracturing was on fracture penetration or length, culminating in massive treatments for tight gas sands using several million pounds of proppant with design 1/2 lengths in excess of 1500 feet (460 m). More recently, the importance of fracture conductivity has become appreciated. This has led to exciting "new" applications of propped fractures in better quality reservoirs as illustrated by North Sea wells, stimulations in Prudhoe Bay, and "frac-pack" operations in the Gulf of Mexico and Indonesia.
While better understanding and new technologies are being used today, the actual application of fracturing to higher permeability formations is not new. During early development of fracturing, nearly all applications were for moderate to high permeability zones (since low permeability rock was of little interest at oil prices of $3/BBL).
While tremendously successful at increasing PI, these early high permeability treatments were doing little more than bypassing damage. More recent development of improved, artificial proppant, cleaner fluid systems, and new technologies have changed this, making it possible to truly alter reservoir flow and stimulate production from moderate to high permeability reservoirs. The primary new tool in the engineers arsenal is the development of "tip screenout" fracturing. While higher permeability formations provide the "new" applications, the actual philosophy shift for fracturing occurred with the massive, tight gas stimulations. while outwardly a traditional, straight forward, application of fracturing to poor quality reservoirs, in actual fact these treatments represented the first engineering attempts to alter reservoir flow in the horizontal plane.
Since no other single expenditure has a greater impact on a tight reservoir's profitability than a hydraulic fracture profitability than a hydraulic fracture treatment, optimal job size selection is imperative. However, the actual reservoir deliverability improvement is usually quite different from the forecasted results. Poor fracturing results are primarily attributed to poor reservoir characterization and reduction of the in-situ fracture conductivity Over the laboratory estimates. To estimate in-situ fracture conductivity, and subsequently enhance the fracturing job design, a historical correlation between job size and wellbore improvement was established. This correlation was based on the post-fracture evaluation of 70 wells in the post-fracture evaluation of 70 wells in the Arkoma basin.
Matching our data with McGuire and Sikora's solution, the retained fracture conductivity ranged from 20% to 50% of laboratory estimates depending on the aggressiveness of proppant placement. The influence of a different thickness in propped height and net pay height was factored into the optimal job sizing process. When modified for this process. When modified for this difference, the PKN modeled FCD was consistent with our field observation for low FCD treatments. A field estimate of the optimal job size was also developed from the historical correlation using a marginal benefit and marginal cost model. Ease of application and historical accuracy are the two major strengths of this approach.
Greater cost effectiveness was achieved when these design considerations were incorporated into the field practice in the Arkoma basin. Since this study surveyed the diverse reservoirs and depositional environments within the Pennsylvanian age, we feel the approach Pennsylvanian age, we feel the approach will be applicable in similar areas.
The Arkoma basin, located in eastern Oklahoma and western Arkansas Fig.1), is one of the most prolific gas producing areas in the United States. producing areas in the United States. The basin extends for approximately 260 miles (418 km) in an east-west direction, and is 20 to 50 miles (32 to 81 km) wide from north to south. This long, arcuate trough is bounded on the south by the Ouachita overthrust belt, and on the north by the Ozark uplift. The stress associated with the Ouachita orogeny and the uplift of the Ozark dome resulted in extreme folding and faulting, which created a series of long, narrow, east-west trending anticlines and synclines.
Most of gas production from the basin is associated with anticlinal or fault-trap structures where sufficient effective porosity was developed. Currently more porosity was developed. Currently more than 30 gas producing horizons have been discovered which range in age from early Pennsylvanian to the Cambrian-Ordovician. Pennsylvanian to the Cambrian-Ordovician. Since the Pre-Pennsylvanian formations (Boone, Penters, Hunton, and Arbuckle) are typically treated with acid fracturing, our emphasis was placed on the hydraulic fracturing treatments of the Atokan and Morrowan sandstone series of the Pennsylvanian age.
A three-dimensional reservoir simulation study indicates that propped fracture height in excess of the productive thickness of the reservoir can add to well productivity. The effect of excess propped fracture height is more evident when fracture conductivity is relatively low compared to formation conductivity. The simulations indicated that in cases where dimensionless fracture conductivity (cd, as defined by Cinco et al,' is less than ten, any excess fracture height will increase well productivity. The magnitude of the productivity increase is a function of the dimensionless fracture conductivity and excess height.
A series of type curves is presented that compares the transient pressure behavior of hydraulically fractured wells where the propped fracture extends uniformly above and below the reservoir to the same wells where there is no excess fracture height. In addition, a comparison of the pseudo steady-state productivity increase that would be expected for a hydraulically fractured well is presented for wells with and without excess propped fracture height.
Selected cases are presented to illustrate the economic impact of excess propped fracture height and how it may affect proppant selection.
The ability to achieve adequate fracture conductivity is an essential part of fracture design. Many authors 2 have investigated the effect of fracture length and conductivity on post-fracture well productivity for vertically fracture reservoirs. The initial studies assumed pseudo steady-state or steady-state flow in the reservoir and fracture height equal to the reservoir thickness. Later, work by Tinsley et a investigated the relationship between fracture height and well productivity for cases where the fracture height was equal to or less than the reservoir thickness. All of these early works employed the use of two-dimensional mathematical or physical analog models to predict post-fracture well productivity.
The transient pressure behavior of vertically fractured wells was investigated by Cinco et al 1 using a mathematical model and by Agarwal et al using a two-dimensional reservoir simulator. As with earlier investigations, Cinco et all and Agarwal et al assumed that fracture height was equal to reservoir thickness. These authors presented type curves based on dimensionless variables to aid in evaluating well test data and production histories from hydraulically fractured reservoirs.
The earlier works of McGuire and Sikora and Tinsley et ap and the more recent publications of Cinco et all and Agarwal et al present relationships between fracture conductivity, reservoir permeability-thickness product, fracture length and post-fracture well productivity. Generally, the literature indicates that for a given reservoir and fracture length, there is an optimum fracture conductivity. Exceeding this optimum fracture conductivity will provide a negligible increase in production. However, if the optimum fracture conductivity is not attainable due to physical limitations of fracturing fluids, equipment, proppants, etc., any increase in fracture conductivity will increase well productivity.
The assumption that propped fracture height is equal to or less than the reservoir thickness predominates the literature available that evaluates post-fracture well performance. Currently, the majority of fracture modeling is based on constant height formulations. More recent developments in three-dimensional fracture modeling indicate that hydraulic fractures, in many cases, are not limited to the reservoir thickness. A number of research projects are currently aimed at quantifying fracture geometry and post-fracture well performance, which includes the Department of Energy's (DOE) Multiwell Experiment (MWX).
Summary A new model is developed that calculates the productivity of a hydraulically fractured well, including the effect of fracture-face damage caused by fluid leakoff. Results of the new model are compared with three previous models (McGuire and Sikora 1960; Prats 1961; Binder and Raymond 1967). The existing models assume either elliptical or radial flow around the well, with permeability varying azimuthally. Significant differences in the calculated well productivity indicate that earlier assumptions made regarding the flow geometry can lead to significant overestimates of well productivity index (PI). Agreement with the analytical solution of Prats (1961) is achieved for finite-conductivity fractures and no fracture damage. It is shown that the use of either McGuire's model (McGuire and Sikora 1960) or Raymond's model (Binder and Raymond 1967) to estimate improvement in well PI in fractured wells can lead to a significant overestimation of the well PI. The new model provides a useful tool to quickly calculate the productivity of wells that have both a finite-conductivity fracture and damage in the invaded zone. The simple and discrete nature of the model makes it ideal for implementation in spreadsheets and to connect to fracture-performance models. Cleanup of the damage in the invaded zone depends on the capillary properties of the formation and the drawdown pressure applied across the damaged zone during production. If capillary forces are small and drawdown pressure is high, the water will be recovered, resulting in negligible damage. It is found that the invaded zone will cause significant damage when the permeability of the damaged zone is reduced by more than 90%. For low-permeability, depleted formations where water recovery is poor, the fracturing fluid should be energized with a gas component so that the relative permeability damage to gas inflow can be minimized.