Hydraulic fracture geometry (i.e., critical results of length and proppant placement) is driven by four major in situ parameters: Fracture Height (H), Modulus (E), Fluid Loss (C), and "Apparent" Fracture Toughness (KI c-app ). In many (even most) cases, "Height" is the most important of these parameters – due to the need for some height confinement to achieve long fractures, or the need for height growth to insure good pay coverage. Due to this importance, industry research effort and most field measuring techniques concentrate on "Height." In particular, the growing use of seismic imaging is offering a tool to measure height growth away from the wellbore. Results from such diagnostics have often shown, as one expects, that in situ stress variations control height. However, results have also shown situations where this is apparently not the case. This paper examines another in situ parameter, "Layered Modulus," which also affects height. In addition, by controlling the "local" width of a fracture, layered modulus (i.e., layered formations with different layers having significantly different modulus) can have a critical effect on final proppant placement. The importance of layered modulus in directly controlling fracture height is illustrated in this paper, and this is compared with published solutions. In general, it is found that, just as concluded in the past, modulus contrast is probably not an important parameter in terms of direct control of fracture height. The greater importance lies in the effects on local fracture width. These local width changes can have a significant influence on controlling proppant placement – and this can be critical for low net pressure cases such as "water fracs" or fracturing in "soft" formations. It is also noted that layered modulus significantly impacts the average width of a fracture, and thus impacts the critical material balance aspects of fracture modeling if not properly accounted for. Finally, some of the theoretical solution problems created by "Layered Modulus" formations for fracture modeling are discussed and compared. This is done by comparing with 3–D Finite Element (static) solutions, and shows how some common industry "approximations" for layered modulus give incorrect results. Based on this, examples with a fracture propagation model using a finite element-generated stiffness matrix are used to define types of cases where a simple "average" modulus is acceptable, versus cases where more complex calculations are needed. Introduction Six major variables control hydraulic fracturing, fracture geometry, proppant placement, etc. Two of these are the "controllable" variables of fluid viscosity, µ, and pump rate, Q. The remaining four variables are "natural" variables and include:Height. Fracture height (or more generally fracture geometry) is possibly the most important unknown for fracture design and post-frac production success. Generally, it is recognized that in situ stress differences (the in situ stress profile) is the major controlling factor for this behavior. [1] At a minimum, in situ stress differences control the maximum fracture height, i.e., if the net pressure is not available to grow through high stress shale layers, then fracture height must be contained. The importance of fracture height/geometry is clear, and there are many research efforts and technical publications addressing this issue. [1–6]Fluid Loss. Fluid loss is typically characterized for hydraulic fracturing by a fluid loss coefficient, C, which characterizes linear flow fluid loss out of the fracture. This gives the familiar C/ (t-t) form of fluid loss behavior. Again, this variable has been exhaustively discussed in the literature including wall building characteristics of specific fluid systems, effects of natural fractures, behavior of fluid loss additives, etc. [7–16]

The success of conventional fracturing (using non-reactive fluids to carry proppant) and acid fracturing is dependant on both the creation of effective fracture conductivity and fracture penetration (fracture half-length). With acid fracturing, nonuniform acid-etching (or differential etching) of the fracture face creates lasting conductivity as long as stable points of support (asperities) exist along the etched fracture length. These hold the channels open and connected to the wellbore following fracture mechanical closure. However, both field experience and laboratory work have shown that even fairly competent carbonates soften and creep under closure stresses after contact with acid, thus, potentially resulting in poor retention of acid-etched fracture conductivity. Preservation of fracture conductivity becomes even more challenging in case of high effective closure pressure. Furthermore, acid fracture conductivity is dependant on surface etching patterns, which are determined by uneven permeability and mineralogy distributions. Therefore, a very clean, homogeneous isotropic carbonate may not be a good candidate for acid fracturing since a fairly uniformly etched fracture might close completely at bottomhole producing pressures. Also, carbonate formations with more than approximately 30 percent insoluble components are generally not good candidates because overall acid-etched fracture conductivity may be impaired due to low solubility and also the release of insoluble materials may tend to plug any conductive etched patterns created by the acid. The effective length of the acid-etched fracture is limited by the distance the acid can travel along the fracture and adequately etch the fracture faces before becoming spent. When acid fracturing, the etched length, not the hydraulic length, is considered the effective fracture length. Effective acid penetration will most often be shorter than any proppant placement (due to often high and increasing leak-off rates with time, and high reaction rates, especially at elevated temperatures). An indeed rare, but in theory, powerful well stimulation technique is the combination of acid fracturing (i.e., creation of a hydraulic fracture using reactive acid fluid) with proppant (CAPF) to provide permanent conductivity. Unless proppant is squeezed into the acid fracture before the end of the job, the conductivity of an acid fracture is vulnerably retained pending the stability of asperities all along the height/length of the fracture. Thus, the desire to include proppant in fracture acidizing treatments is conspicuous (but not limited to) "clean" carbonates (exhibiting uniform mineralogy and permeability), carbonates at high effective stress conditions, "soft" carbonates of any permeability (excluding high porosity chalks), low temperature dolomites (with low reaction rates) and together with organic acids where small and vulnerable etched-fracture widths are prevalent. Also, intuitively, effective fracture half-length may be extended if acid (or non-reactive fluids) can transport proppant beyond the etched penetration length "all the way" to the hydraulic tip of the fracture or even extend the hydraulic length for typical short acid fractures. A methodology proposed by Dowell more than three decades ago "Maximum Conductivity Stimulation" (MCS) is probably the first discussion of the idea of combining acid with proppant fracturing. However, the idea did not establish roots in the oil and gas industry for reasons discussed in this paper. Clearly, one missing ingredient was the lack of today's state of- the-art modeling tools for determining suitable applications and procedures. This paper presents and uses a recently developed planar 3D, gridded, FEM (finite element method) multi-layer (with varying percent of limestone/dolomite including non-reactive layers) acid fracturing model. This model fully couples rock mechanics (fracture width and propagation), matrix and natural fracture fluid loss (and effects of acid and non-acid gel fluid stages to increase and reduce fluid loss, respectively), acid reaction/acid diffusion, fluid flow, and proppant/acid transport into a single solution. Such a capability is unique at this time, and, in general, only a 3D gridded model is capable of such simulations due to the complex interactions. Case histories are examined in this paper as possible targets for CAPF. The extraordinary simulation results from modeling of this combined process and its impact on well productivity are discussed.

The primary objective of hydraulic fracturing is to create a propped fracture with sufficient conductivity and length to optimize well performance. In permeable reservoirs, the design objective is to achieve a Dimensionless Fracture Capacity, CfD, of at least 2. In lower permeability applications, additional conductivity is required (CfD > 10) to allow effective fracture fluid cleanup and optimized well performance. In some tight formation gas applications, conventional cross-linked gel fracture stimulations are not creating the desired fracture dimensions. The potential reasons for the shorter than desired effective fracture lengths are numerous with the most likely being reservoir heterogeneity, excessive fracture height growth, and poor fracture fluid cleanup. In recent years, there has been much discussion regarding the causes for, or reasons that the dimensions of the hydraulic fracture are shorter than desired. These include: relative permeability effects, fracture fluid cleanup, multi-phase flow, and non-Darcy flow. The former causes and reasons have been investigated in some detail; however, little data has been published regarding the effects of non-Darcy flow on fracture conductivity and effective fracture length. Some in the industry have suggested that tight gas well performance is hindered significantly by non-Darcy flow effects. This view, though potentially correct, is supported by little actual data in the literature. Further, to mitigate this effect, tip screen-out fracturing techniques and larger fracture stimulation designs often utilizing much more expensive ceramic proppants have been recommended and executed even in very low permeability applications. These methods may not be effective in tight gas applications but they surely are more expensive, potentially eroding the economic benefits of fracturing these low deliverability applications. In addition, little actual well performance data has been presented to justify the importance of non-Darcy flow in fractures with much of the justification coming from the use of semi-analytical calculations and spreadsheets. This paper will document an investigation of non-Darcy flow to hydraulically fractured oil and gas well performance. The investigation will utilize both a three dimensional single-phase numeric finite difference simulator and actual well performance to investigate the importance of non-Darcy flow to hydraulically fractured oil and gas wells. This paper will demonstrate the following:The importance or lack of importance of non-Darcy flow on hydraulically fractured oil and gas well performance,Compare and contrast actual well performance of off-setting wells where sand and ceramics were utilized in East Texas, Trinidad, and North Sea applications,Develop treatment guidelines and fracture design objectives to limit/mitigate the effects of non-Darcy flow across a broad spectrum of fracturing applications. Introduction The industry has been aware of the potential for non-Darcy flow in propped fracture for many years - since the pioneering work by Cooke.1 Since that work, much additional technology has been added, and that history has been well covered and will not be reviewed here (except as appropriate below). The primary problem was that the importance of this behavior was, at best, difficult to prove or quantify. The "problem" was that fracturing was traditionally (at least in the 70's and 80's when this idea was broached) applied to low permeability formations. The traditional, "definitive" test for non-Darcy effects (multi-rate drawdown) was difficult to apply operationally to such wells, and, again, at best, difficult to interpret as normal fractured well transient flow tends to mask non-Darcy effects. More recently, several papers have dealt with new analysis approaches that may make analysis for these effects more definitive in the future, but that is outside the realm of this work. Because of this "problem", the bulk of the literature has dealt with theoretical (analytical and numerical and semi-numerical) studies and extensive laboratory testing. However, very few papers have examined well test data over a range of conditions to compare the magnitude of the non-Darcy effects with these predictions.

Many shale plays are being successfully developed throughout North America. Numerous studies have attempted to focus on the possible success mechanisms for these unconventional formations. The focus of these studies tends to fall into two distinct camps, (1) complexity and (2) the rock. It is the intent of this paper to show, however, that these two mechanisms are not distinct and independent and that they are in fact very interrelated. This paper looks at two main issues: laboratory investigation of the stress sensitivity of un-propped fractures for several active unconventional formations, and Discrete Natural Fracture (DFN) simulation of the effect of this on post-frac production.

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