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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]

Summary Hydraulic fracturing has historically been a prime engineering tool for improving well producing rates, either by circumventing near-well damage or by stimulating well performance. This paper describes a somewhat new fracturing application where increasing rate was not the primary goal. In this case, the goal for fracturing was modification of the flow profile to allow a more uniform vertical production profile and thereby maximize sand-free rates over the perforated section of the reservoir. In best cases for such applications, this technique allows perforating of "weak" rock to be skipped, reduces risks of sand production, and allows greater wellbore drawdown through perforated intervals in more competent reservoir rock. This allows better long-term productivity and improved recovery and total project economics. In short, it was hoped that propped fractures would improve reservoir management of the Etive/ Rannoch formations in the Gullfaks field. Introduction The Gullfaks field, in the central part of the East Shetland basin in the northern North Sea, is operated by Statoil. The field was developed with three platforms and started production in Dec. 1986. Of more than 116 planned wells, 81 wells (including 6 subsea satellite wells) have been drilled. The field currently can produce about 600,000 BOPD, and estimated production life of the field is 20 years. The main drive mechanism is water injection. Predicted ultimate oil production from the field is 1,590 million bbl. About 465 million bbl was produced by Nov. 1993. Forecasted ultimate production represents 46% field recovery. Oil is produced from three major sandstone units: the Brent group, the Cook formation, and the Statfjord formation. The Etive/Rannoch formations of the Lower Brent group contain about 33% of mapped HCPV for the field. The reservoirs are overpressured, with an initial reservoir pressure of 4,495 psi at datum depth (6,070 ft below mean sea level) and 158°F. The shallow, highly porous sands are generally poorly consolidated. The oil is undersaturated, with a saturation pressure of about 3,550 psi, depending on formation depth and location.

Summary This paper provides a quick method to determine subsidence, compaction, and in-situ stress induced by pore-pressure change. The method is useful for a reservoir whose Young's modulus is less than 20% or greater than 150% of the Young's modulus of the surrounding formation (where the conventional uniaxial strain assumption may not hold). In this work, a parameter study was conducted to find groups of parameters controlling the in-situ stress, subsidence, and compaction. These parameter groups were used to analyze the numerical calculation results generated by a three-dimensional (3D), general, nonlinear, finite-element model (FEM). The procedure and a set of figures showing how to calculate the in-situ stress, subsidence, and compaction induced by pore-pressure changes are provided. Example problems are also included to prevent confusion on sign convention and units. This work showed that Geertsma's results, which are based on no modulus contrast between cap and reservoir rocks, should be extended to simulate more closely "real" reservoirs, which generally have distinct property differences between the cap and reservoir rocks. Highly porous and high-pressure North Sea reservoirs and tight sand formations surrounded by soft shale often fall into this category. The application is intended for sand-production control, casing buckling problems, design of hydraulic fracturing jobs, subsidence, and estimation of PV and formation damage resulting from permeability reduction during hydrocarbon production. Introduction The in-situ stress induced by pore-pressure change usually has been calculated on the assumption that a rock deforms uniaxially without inducing strain along the horizontal direction. The amount of subsidence was calculated by Geertsma, with the strain nuclei method. These calculations assume that a reservoir is thin, that its depth is reasonably great, and that its rigidity is close to that of the confining formation. However, statistics of field measurements has shown that many hydrocarbon reservoirs are thick or shallow or have elastic moduli that are significantly different from those of confining formations. For example, North Sea reservoirs often have static Young's moduli that are orders of magnitude smaller than those of the surrounding rocks before they are compacted because of hydrocarbon production, although the dynamic Young's modulus calculated from sonic logs may give only three to six times modulus contrast. Some tight formations in the U.S. also have rock several times more rigid than surrounding shale. When a hydraulic fracture, a sand-control process. a subsidence-control operation, or an evaluation of formation damage resulting from permeability reduction is conducted in such a reservoir, accurate information on the in-situ stress, reservoir compaction, or subsidence induced by pore-pressure changes helps in designing such operations. This work does not use or develop new mathematical techniques, but emphasizes two important issues. First, the common practice in the oil industry is to calculate PV compressibility, reservoir compaction, and in-situ stress change on the basis of reservoir-rock property data. However, this work emphasizes that some reservoirs also require the caprock property data to evaluate these quantities. Second, a quick method to evaluate PV compressibility, reservoir compaction, in-situ stress change, and subsidence has not been published previously. Although techniques to calculate these values are available, they require long times to run sophisticated simulation models. The purpose of this work is to provide a method for quick estimation of in-situ stress, compaction, and subsidence for a reservoir having simple geometry. A quick estimation of these values is often sufficient during the reservoir development stage because accurate reservoir descriptions are not available. Such a crude estimation is essential because the decisions on downhole and surface facility designs are made during the early stages of reservoir development. After more accurate reservoir descriptions are collected, however, we recommend that the 3D FEM be used for this work to get a better evaluation. The model can handle various complex problems, such as multilayer problems with heterogeneous rock properties, inclined reservoirs, irregular reservoirs, nonuniform pore pressure, nonlinear properties of rock, hysteresis effect of cyclic loading, and nonuniform reservoir pressure. Assumptions and Calculation Methods The in-situ stress is decomposed into two parts-original in-situ stress and-in-situ stress induced by pore-pressure change. ................................ (1a) and ............................ (1b) where K is the stress-ratio coefficient affected by rock grain shape, grain-size distribution, sedimentation process, present Poisson's ratio, tectonic force, temperature, and pore pressure. Delta sigma and delta sigma are in-situ stress components induced by pore-pressure change. If the pore-pressure change occurs over several years, we can reasonably assume that rock deforms elastically during the period. In addition, if the pore-pressure change is reasonably small and the state of stress is not far from hydrostatic-i.e., a small deviatoric stress-then a linear elastic deformation is a good approximation. Hence, a linear elastic deformation is assumed in this work for the calculation of delta sigma and delta sigma induced by the pore-pressure change. A disk-shaped reservoir is assumed for the present calculation as shown in Fig. 1. Although the moduli of the reservoir and the surrounding formation may vary within each formation, uniform moduli are assumed within both structures, respectively. The reservoir is located at depth D below the surface and its radius and height are r and h, respectively. More complex reservoir geometries require that data be entered directly into the 3D FEM used for the present calculations. Fig. 2 shows the finite-element meshes used for this work. The upper surface is free from a traction force, and the bottom surface is fixed to the rigid base rock. Infinite elements were used for the outer boundary. The hatched section is the reservoir and has elastic moduli different from those of surrounding formations. The pore pressure of the reservoir section is reduced to calculate the deformations and stress change of the reservoir and surrounding formations. Test runs were conducted for a well with and without a casing cemented to the borehole. JPT P. 9^

SPE and IADC Members Abstract A successful reinjection of oil-wet drill cuttings has been performed on the Norwegian Gullfaks Field. The reinjection was carried out in the annulus between two casing strings through a wear-protected wellhead. An effective way of grinding cuttings and mixing slurry by use of a new patent pending method known as SMACCC - Statoil Method for Autogenous Crushing and Classifying of Cuttings has been developed. The paper discusses reservoir aspects and presents simulated fracture geometries as a result of rock mechanical and slurry in-put property data. Further, the paper describes a 1000 hour wear test, involved equipment, and gives a derived formula describing wear from sand slurries on internal wellhead components. Introduction The basic background to the cuttings reinjection project wasStatoil's environmental policy to cause the least possible pollution of the environment, andthe company's policy to develop technologies and concepts meeting low crude prices. The increasing demand for highly deviated and longer wells currently necessitates the use of oil-based mud, which is neither permitted to be discharged into the sea nor to be burned. With newly realized environmental concerns, about disposal problems for drill cuttings and drilling solids residue for oil based mud systems, several new disposal methods are currently being considered and investigated by the oil industry. Since 1988, Statoil has reduced the use of oil-based mud by about 95% on the Gullfaks Field. The project of reinjecting cuttings, waste mud and oily waste water from drilling was a following-up project to virtually eliminate the discharge of oily waste from Statoil's drilling and production platforms. As of November 1st 1992, a total of 6500 Sm (40880 BBL) of waste drilling fluids and cuttings have been reinjected into shallow formations on the Gullfaks Field. Reinjection of cuttings by use of the new crushing and mixing system is now planned on several Statoil platforms in the North Sea. This paper discusses simulated reservoir and rock mechanical data together with fluid/slurry properties in conjunction with down-holedisposal operations describes a 1000-hour combined wellhead and centrifugal pump sand erosion test. An equation relating erosion to velocity and sand concentration is given. describes the size and capacity of the new SMACCC system, including an improved and wear-resistant centrifugal pump presents actual field test data and performance analyses for offshore disposal operations RESERVOIR MODELLING AND SIMULATION RESULTS General Considerations Subsurface injection is a world wide common method of waste disposal, and many injection wells have been operating for years with massive volumes of material being injected. The major difference between such "normal" disposal operations and disposal of drilling cuttings and impure mud is the high percentage of solids to be injected, with the corresponding requirement for injection above fracture closure pressure - e.g. it will be necessary to open and probably extend hydraulic fractures and/or open and extend existing natural fractures. P. 773^

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.

The paper describes a systematic study of the effect of the turbulence on productivity (or injectivity) of fractured wells. It extends significantly beyond previous work, and shows its limitations. A new correlation has been developed, based on over 2,000 high-accuracy numerical solutions for vertically fractured well for a simple geometry. The base correlation was developed for fully penetrating fracture and it is applicable to liquid and high-pressure gas systems. The general correlation for fully penetrating fracture is a function of the two dimensionless parameters and two other parameters, which can be chosen as fracture conductivity and permeability. Additional results are provided for the effect of partial perforations on a fully penetrating fracture. As a limiting case, this scenario can represent also transversely fractured horizontal well. The final correlation therefore involves 5 variables. The results show that the conventional notion that turbulence is important only in high rate gas wells is often false. Turbulence effect on productivity or injectivity can be significant for liquid flow in high permeability formations, with limited perforations and especially in transversely fractured horizontal wells. Introduction Non-Darcy (turbulence) effects have been traditionally studied primarily for gas wells. The work of Guppy1,2 showed that the effect of turbulence can be expresses as an "apparent conductivity" and a solution was obtained which correlates the ratio of the apparent to true conductivity with dimensionless rate QD and dimensionless fracture conductivity CfD. More recently, turbulence has been shown to reduce productivity in high-rate oil wells. Smith et al.3 have shown that for typical "indirect" fracture completions in the Cook formation of the Gullfaks field, that turbulence can reduce well productivity index (PI) by up to 40%. Approximate analytical method, as well as numerical simulation, was used to obtain those results. Settari et al.4 have applied similar modeling techniques to the investigation of productivity of gas condensate wells. Their results also indicated reduction of PI of 30–40% due to turbulence, both in single phase, and multiphase flow conditions. Stark et al.5,6 conducted a numerical study of turbulence in gas wells. The study introduced the concept of a "neutral skin" whereby the negative skin due to fracturing would negate the positive skin from turbulence such that the well PI would be equal to that of an unfractured well without turbulence. The work showed that in many cases fracturing could not even restore the well to the neutral skin. These studies indicate that evaluating the effect of turbulence is important in many more situations than previously thought. Similar results would be expected in high-rate water injection wells, which have been converted from fractured producers. The paper describes a systematic study of the effect of the turbulence on productivity (or injectivity) of fractured wells. It extends significantly beyond the previous works, and shows the limitations of the Guppy correlation. The study was performed in two parts. In the first part, the correlations for a fully penetrating fracture were developed. In the second part, the effect of partial perforation was studied and added to the correlation. Additional work is ongoing to verify the applicability for parameters, which have not been varied in this work.