The post-treatment performance of hydraulically fractured wells has been a recurring theme in the petroleum literature, covering the spectrum of understanding the physics of flow to the optimization of design. Optimization itself has taken different hues meaning comprehensive economic, or just the reduction of execution costs, or the maximization of the production or injection rates. Irrespective of the ultimate criterion, the magnitude of the reservoir permeability has been central to the fracture morphology. Long fractures are warranted for low-permeability reservoirs; wide but short fractures are indicated for high-permeability formations. For a given reservoir of known permeability and dimensions the mass of proppant injected to the pay describes a unique and constant proppant number for which a maximum well productivity index can be achieved at the optimum dimensionless fracture conductivity. The proppant number and the optimum dimensionless fracture conductivity determine exclusively the optimum fracture dimensions. However, damaged hydraulic fracture performance deviates substantially from that of undamaged fractures. Two types of damage are considered, fracture face, often caused by fluid leakoff into the reservoir and choke fracture, which is caused by proppant flow-back, over-displacement or polymer damage. These damages, described by skin effects cause a departure, at times substantial, from the indicated undamaged optimum fracture geometry. In this work, the performance of a fractured well is calculated using a direct boundary element method. The method calculates the dimensionless productivity index and the model allows for the presence of the two different skin effects. The fracture face skin effect was found to have a significant detrimental effect on the dimensionless productivity index, especially for high-permeability reservoirs. The effect of the choke skin was found to be potentially also very detrimental, but less complex to account for, because it can be represented as an apparent reduction to the proppant number. Introduction This work is intended to calculate and optimize the performance of hydraulically fractured wells that are burdened by two types of flow impediments: fracture face damage and damage at the connection between the fracture and a well. The latter has been referred to as a choke. Fracture face damage can be actual damage to the reservoir permeability from fracturing fluid and polymer leakoff or it can be caused by the reduction in relative permeability changes because of a phase change. Valkó and Economides16 have proposed a means to calculate the pseudosteady-state productivity index of a fractured well and then by relating the productivity index with the dimensionless fracture conductivity to optimize fractured well performance. That work followed a considerable body of literature that has postulated for years, that the increase in the fractured well productivity (compared to the unfractured state) depends on both reservoir and fracture characteristics. In 1960, McGuire and Sikora9 studied the effect of vertical fractures on well productivity and showed how this well productivity depends on the fracture penetration and conductivity. Prats et al.11 and Cinco-Ley and Samaniego3,4 are credited with the introduction of dimensionless groups of variables to describe the performance of a fractured well. Since then, The concept of the dimensionless fracture conductivity has been used as the dominant indicator of the relative improvement in fluid flow that is provided by the fracture compared to the alternative, i.e., no fracture.

For a given reservoir of known permeability and dimensions, the proppant mass injected to the pay determines a unique proppant number. Unique to each proppant number, there exists an optimum dimensionless fracture conductivity that exclusively determines the optimum fracture dimensions. 1 Impairments affecting flow perpendicular to the fracture surface are accounted for as fracture-face-skin effect. On the other hand, flow impairment caused by a reduction of the fracture conductivity near the wellbore is called choked fracture skin. Both effects have a large influence on the productivity of a fractured well. In this work, the performance of a fractured well is calculated with a direct boundary element method. This method provides the dimensionless productivity index, and the model allows for the presence of each of the two different skin effects. The fracture face skin was found to have a significant detrimental effect on the dimensionless productivity index, even changing the character of its dependence on the dimensionless fracture conductivity. The effect of the choke skin also was found to be potentially detrimental but less complex to account for because it can be represented as an apparent reduction in the proppant number.

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In this paper we describe the possibility and benefits of incorporating the stability analysis of the proppant pack during the design stage of hydraulic fracturing treatments. After the well is treated and cleaned up, the flowback of proppant from a fracture-treated formation is highly undesirable for several reasons, including possible damage to the wellhead and flowlines, operational complications, and last but not least, decrease in well-productivity. The issue has been studied on an empirical basis and the most important factors have been determined. Nevertheless, qualitative models suggested so far seem to work only under limited conditions and currently there is no clear methodology for predicting the occurrence of proppant flowback while designing the treatment. In this work we review previously suggested prediction methods and analyze the proppant flowback patterns experienced in 24 South-Texas tight-gas completions. As a result of the study we conclude that the predictive power of the available models is not satisfactory and the implications for "proppant stability control agents" are not based on convincing evidence. A new semi-mechanistic model is proposed that shows reasonable agreement with both laboratory and field data. A methodology is suggested to incorporate the proppant flowback prediction at the fracture design stage. The suggested methodology is based on the concept of "minimum necessary departure from optimality to satisfy technical constraints", in this case the constraint being to keep the likelihood of proppant flowback under a certain threshold. Introduction Since the late 1940's, there have been more than a million fracturing treatments performed in the United States1. In a regular fracturing operation, some flowback of proppant occurs right after the treatment is completed. This stage is referred as the "clean up" phase and is unavoidable since under-displaced proppant will remain in the wellbore after the operation. In this stage, personnel and equipment are usually still in place and any produced solids can be easily handled. In contrast, flowback during the production phase of a fractured well can undermine the potential benefits of the stimulation treatment and represent operational complications. Along this paper we will refer to this latter situation as "proppant flowback". The problems associated with proppant flowback are the following:Local loss of fracture conductivity, which generates a reduction in the potential benefits of a hydraulic fracturing treatment.Damage to the equipment. (Consisting in abrasion to valves, tubing, surface pipelines and other equipment). The first and most obvious approach in dealing with this problem consisted in applying operational rules of thumb. The most common of these techniques focused on maintaining the production rates below a critical value that was determined as critical to initiate the flowback of proppant in a specific well. The evolution of forced closure technique, that is closing the fracture rapidly in order to trap the proppant grains in a "uniform distribution" generating a more stable fracture has been proven usually necessary but not sufficient. It has been reported2 that these methods do not work all the time, partly because their justification ignores the actual mechanisms that create instability in the proppant pack. Numerous flowback control additives have been offered by various service companies3. Unfortunately, there is lack of evidence that they work under conditions of high formation closure stresses. The use of resin coating in particular, has been reported unsufficient in some cases4. On the other hand, some experimental studies5 have helped deliniate the mechanisms behind proppant flowback. However, the available predicting models rely on empirical correlations6,7,8 and may be less reliable as the application conditions deviate from the conditions of laboratory experiments on which the correlations are based. The goal of this work is to summarize available information and improve the predictive power of the models.

Palm methyl ester (PME) is a renewable biofuel that is produced by the transesterifica tion o f palm oil and is a popular alternative fuel used in the transportation sector, partic ularly in Asia. The objective of this investigation was to study the combustion characteristics of flames of prevaporized number 2 diesel and PME in a laminar flame environment at initial equivalence ratios of 2, 3, and 7 and to isolate the factors attribut able to chemical structure of the fuel. The equivalence ratio was changed by altering the fuel flow rate, while maintaining the air flow rate constant. The global CO emission index of the PME flames was significantly lower than that of the diesel flames; however, the global NO emission index was comparable. The radiative fraction of heat release and the soot volume fraction were lower for the PME flames compared to those in the diesel flames. The peak temperatures were comparable in both flames at an equivalence ratio of 2, but at higher equivalence ratios, the peak temperatures in the PME flames were higher. The measurements highlight the differences in the combustion properties of biofuels and petroleum fuels and the coupling effects o f equivalence ratio.