Thesis (Ph. D.)--Civil and Environmental Engineering, Georgia Institute of Technology, 2005. / Puzrin, Alexander M., Committee Member ; Rix, Glenn J., Committee Member ; Mayne, Paul W., Committee Member ; Lowell, Robert P., Committee Member ; Germanovich, Leonid, Committee Chair ; Xu, Wenyue, Committee Member ; Van Dyke, Peter, Committee Member. Vita. Includes bibliographical references.

Acid fracturing stimulation is one of the preferred methods to improve well productivity in carbonate reservoirs. Acid is injected into the fractured zone after a starter fracture is created in the near wellbore area by viscous fluid (pad). This results in propagation of a two-wing crack away from the perforations with simultaneous dissolution etching of the created surfaces. If the created etched surface is non-uniform, then after the treatment ends and the fracture face closes, a high conductivity path may remain in the formation, connected to the well. The important factors controlling the effectiveness of acid fracturing are the etched-fracture penetration and conductivity. In this research, I use the distributed volumetric sources (DVS) method to calculate gas production from a well stimulated by acid fracturing. The novel concept realized in this research is that, during the production process, the conductivity of the acid created fracture changes. I use the Nierode - Kruk correlation to describe this effect as a function of effective closure stress that in turn is determined from the flowing bottomhole pressure and minimum horizontal stress. By combining the well productivity calculation from the DVS method taking into account varying fracture conductivity with gas material balance, I obtain an improved model of gas production. The model is then used to not only forecast production from acid fractured wells but also to evaluate the known production history of such wells. Based on the concepts discussed above, I have developed a program called "Gas Acid" which is useful to optimize acid fracturing treatments and also suitable to infer created fracture parameters from known production history. The "Gas Acid" program has been validated with data from two Saudi Aramco gas wells. It was found that the production forecast obtained from the "Gas Acid" program matches the actual production history with reasonable accuracy and the remaining discrepancy could be resolved by taking into account refinement of the material balance. The refinement became necessary, because the "Gas Acid" program was developed for dry gas but the reservoir fluids in the field examples were classified as retrograde gas and wet gas. When accounting for the additional mass of gas "hidden" in the produced condensate, the match of forecast and actual data was improved considerably.

A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy. Johannesburg, 2015. / The propagation of hydraulic fractures with tortuosity is investigated. Tortuosity is the complicated fracture geometry that results from asperities at the fluid-rock interface and, if present, from contact regions. A tortuous hydraulic fracture can either be open without contact regions or partially open with contact regions. We replace the tortuous hydraulic fracture by a two-dimensional symmetric model fracture that accounts for tortuosity. A modified Reynolds flow law is used to model the tortuosity in the flow due to surface roughness at the fracture walls. In order to close the model, the linear and hyperbolic crack laws which describe the presence of contact regions in a partially open fracture are used. The Perkins-Kern-Nordgren approximation in which the normal stress at the crack walls is proportional to the half-width of the symmetric model fracture is used. A Lie point symmetry analysis of the resulting governing partial differential equations with their corresponding boundary conditions is applied in order to derive group invariant solutions for the half-width, volume and length of the fracture. For the linear hydraulic fracture, three exact analytical solutions are derived. The operating conditions of two of the exact analytical solutions are identified by two conservation laws. The exact analytical solutions describe fractures propagating with constant speed, with constant volume and with fluid extracted at the fracture entry. The latter solution is the limiting solution of fluid extraction solutions. During the fluid extraction process, fluid flows in two directions, one towards the fracture entry and the other towards the fracture tip. It is found that for fluid injection the width averaged fluid velocity increases approximately linearly along the length of the fracture. This leads to the derivation of approximate analytical solutions for fluid injection working conditions. Numerical solutions for fluid injection and extraction are computed. The hyperbolic hydraulic fracture is found to admit only one working condition of fluid injected at the fracture entry at a constant pressure. The solution is obtained numerically. Approximate analytical solutions that agree well with numerical results are derived. The constant pressure solutions of the linear and hyperbolic hydraulic fracture are compared. While the hyperbolic hydraulic fracture model is generally considered to be a more realistic model of a partially open fracture, it does not give information about fluid extraction. The linear hydraulic fracture model gives various solutions for di erent working conditions at the fracture entry including fluid extraction.

Most available data from shale production zones tends to point towards the presence of complex hydraulic fracture networks, especially in the Barnett and Marcellus formations. Representing these complex hydraulic fracture networks in reservoir simulators while incorporating the geo-mechanical parameters and fracture apertures is a challenge. In our work we developed a fracture to production simulation workflow using complex hydraulic fracture propagation model and a commercial reservoir simulator. The workflow was applied and validated using geological, stimulation and production data from the Marcellus shale. For validation, we used published data from a 5200 ft. long horizontal well drilled in the lower Marcellus. There were 14 fracturing stages with micro-seismic data and an available production history of 9 months. Complex hydraulic fractures simulations provided the fracture network geometry and aperture distributions as the output, which were up-scaled to grid block porosity and permeability values and imported into a reservoir model for production simulation and history match. The approach of using large grid blocks with conductivity adjustment to represent hydraulic fractures in a reservoir simulator which has been employed in this workflow was validated by comparing with published numerical and analytical solutions. Our results for history match were found to be in reasonable agreement with published results. The incorporation of apertures, complexity and geo-mechanics into reservoir models through this workflow reduces uncertainty in reservoir simulation of shale plays and leads to more realistic production forecasting. The workflow was utilized to study the effect of fracture conductivity damage on production. Homogenous and heterogeneous damage cases were considered. Capillary pressures, determined using empirical relationships and experimental data, were studied using the fracture to production workflow. Assuming homogenous instead of heterogeneous permeability damage in reservoir simulations was shown to have a significant impact on production forecasting, overestimating production by 70% or more over the course of two years. Capillary pressure however was less significant and ignoring capillary pressure in damaged hydraulic fractures led to only 3% difference in production in even the most damaged cases. / text

Growing global energy demand has prompted the exploitation of non-conventional resources such as Coal Bed Methane (CBM) and conventional resources such as gas-condensate reservoirs. Exploitation of these resources primarily depends on stimulation by hydraulic fracturing. Traditional hydraulic fracturing practices, however, are in many ways inadequate in addressing difficulties associated with these non-conventional and conventional resources. For example, complex in-situ stress distribution, large material property contrasts and unique production mechanism complicate the implementation of hydraulic fracture treatments in CBM and gas-condensate reservoirs respectively. An integrated approach to optimise hydraulic fracture treatments in reservoirs under complex conditions is developed in this thesis. The optimisation methodology integrates a fracture geometry model which predicts fracture geometry for a given set of treatment parameters, a production model which estimates reservoir productivity after stimulation and an economic model which calculates net present value. A stochastic optimisation algorithm combining features of evolutionary computations is used to search for the optimum design. Numerical techniques such as finite element analysis, iterative semi-analytical methods and evolutionary computation are also used. The following are the major contributions of this thesis: 1. A three-dimensional hydraulic fracture geometry model which accounts for poroelastic effects, in-situ stress and rock material properties, has been developed to provide a more realistic description of the hydraulic fracture geometry. This served as a tool to visualise hydraulic fracture propagation for a given in-situ stress distribution, rock material properties and treatment parameters. Furthermore, by accounting for poroelastic effects, it is possible to identify the causes of exceptionally high treatment pressures. 2. An innovative production model was formulated in this thesis to quantify the well deliverability due to hydraulic fracturing. The production model has been used for a range of production scenarios for CBM and gas-condensate reservoirs such as: multiple wells at arbitrary locations and various well types (stimulated and unstimulated wells). 3. The optimisation methodology presented in this work provides a platform for operators to assess risks and gains associated with different field development scenarios. The added feature of sub-optimal NPV contouring provided flexibility to calibrate the treatment design in real-time. The strength of the optimisation methodology lies in the flexibility to: (1) impose design constraints, (2) optimise multiple variables and (3) simulate multiple objectives.

The conductivity created in acid fracturing is a competition between two phenomena: etching of the rock surface and weakening of the rock. This study presents experimental results of acid fracturing conductivity experiments with polymer gelled acid, while varying contact time and rock type. The experiments were conducted in a laboratory facility properly scaled from field to laboratory conditions to account for the hydrodynamic effects that take place in the field. The rocks of study were Indiana limestone, San Andres dolomite and Texas Cream chalk. Our results illustrate that acid fracturing conductivity is governed by the etching pattern of the rock surface and influenced by the hardness of the rock. If channels are created, the fracture is more likely to retain conductivity after closure. The hardness of the rock is the dominating factor to determine the conductivity response when no channeling is present. Among the rocks tested, Texas Cream chalk had the lowest hardness measurement before and after acidizing and the fracture closed at a much lower stress compared with limestone and dolomite. Dolomite had the highest conductivity under all closure stresses even without a channeling pattern. Additionally, it was observed that a higher reduction in rock strength at the contact points for dolomite yielded lower conductivity after closure. The effects of hardness variation on conductivity are higher in dolomite than in limestone and chalk. It is apparent that longer contact times do not always provide higher conductivity after closure.

Hydraulic Fracturing stimulation technology is used to increase the amount of oil and gas produced from low permeability reservoirs. The primary objective of the process is to increase the conductivity of the reservoir by the creation of fractures deep into the formation, changing the flow pattern from radial to linear flow. The dynamic conductivity test was used for this research to evaluate the effect of closure stress, temperature, proppant concentration, and flow back rates on fracture conductivity. The objective of performing a dynamic conductivity test is to be able to mimic actual field conditions by pumping fracturing fluid/proppant slurry fluid into a conductivity cell, and applying closure stress afterwards. In addition, a factorial design was implemented in order to determine the main effect of each of the investigated factors and to minimize the number of experimental runs. Due to the stochastic nature of the dynamic conductivity test, each experiment was repeated several times to evaluate the consistency of the results. Experimental results indicate that the increase in closure stress has a detrimental effect on fracture conductivity. This effect can be attributed to the reduction in fracture width as closure stress was increased. Moreover, the formation of channels at low proppant concentration plays a significant role in determining the final conductivity of a fracture. The presence of these channels created an additional flow path for nitrogen, resulting in a significant increase in the conductivity of the fracture. In addition, experiments performed at high temperatures and stresses exhibited a reduction in fracture conductivity. The formation of a polymer cake due to unbroken gel dried up at high temperatures further impeded the propped conductivity. The effect of nitrogen rate was observed to be inversely proportional to fracture conductivity. The significant reduction in fracture conductivity could possibly be due to the effect of polymer dehydration at higher flow rates and temperatures. However, there is no certainty from experimental results that this conductivity reduction is an effect that occurs in real fractures or whether it is an effect that is only significant in laboratory conditions.

Success of acid fracturing treatment depends greatly on the created conductivity under closure stress. In order to have sufficient conductivity, the fracture face must be non-uniformly etched while the fracture strength maintained to withstand the closure stress. While there have been several experimental studies conducted on acid fracturing, most of these have not scaled experiments to field conditions and did not account for the effect of rock weakening and etching pattern. Hence, acid fracture conductivity predictions based on the above works have not been able to match actual results. In order to develop a more appropriate and accurate prediction of acid fracturing treatment outcome, a laboratory facility was developed that is properly scaled to field conditions and enables analysis of etching pattern and rock strength. A systematic experimental study that covered a variety of formations, acid types, and acid contact times was conducted. An acid fracture conductivity correlation was developed based on etched volume, etched pattern, and fracture strength under closure stress. Results suggested that there is an optimal time of acid exposure resulting in maximum fracture conductivity. There were large differences in the conductivity created with the different acid systems tested due to different etching patterns and degree of rock strength weakening. There was an optimal acid system depending on formation type, contact time and overburden stress. The acid fracture conductivities measured did not agree with the predictions of the Nierode-Kruk correlation. The newly developed correlation predicts conductivity much closer as it includes the effect of rock strength and surface etching pattern on resulting conductivity.

The conductivity created in acid fracturing is a competition between two phenomena: etching of the rock surface and weakening of the rock. This study presents experimental results of acid fracturing conductivity experiments with polymer gelled acid, while varying contact time and rock type. The experiments were conducted in a laboratory facility properly scaled from field to laboratory conditions to account for the hydrodynamic effects that take place in the field. The rocks of study were Indiana limestone, San Andres dolomite and Texas Cream chalk. Our results illustrate that acid fracturing conductivity is governed by the etching pattern of the rock surface and influenced by the hardness of the rock. If channels are created, the fracture is more likely to retain conductivity after closure. The hardness of the rock is the dominating factor to determine the conductivity response when no channeling is present. Among the rocks tested, Texas Cream chalk had the lowest hardness measurement before and after acidizing and the fracture closed at a much lower stress compared with limestone and dolomite. Dolomite had the highest conductivity under all closure stresses even without a channeling pattern. Additionally, it was observed that a higher reduction in rock strength at the contact points for dolomite yielded lower conductivity after closure. The effects of hardness variation on conductivity are higher in dolomite than in limestone and chalk. It is apparent that longer contact times do not always provide higher conductivity after closure.

This thesis presents and develops efficient and effective methodologies for optimal hydraulic fracture design and fracture performance evaluation. These methods incorporate algorithms that simultaneously optimize all of the treatment parameters while accounting for required constraints. Damage effects, such as closure stress, gel damage and non-Darcy flow, are also considered in the optimal design and evaluation algorithms. Two user-friendly program modules, which are active server page (ASP) based, were developed to implement the utility of the methodologies. Case analysis was executed to demonstrate the workflow of the two modules. Finally, to validate the results from the two modules, results were compared to those from a 3D simulation program. The main contributions of this work are: An optimal fracture design methodology called unified fracture design (UFD) is presented and damage effects are considered in the optimal design calculation. As a by-product of UFD, a fracture evaluation methodology is proposed to conduct well stimulation performance evaluation. The approach is based on calculating and comparing the actual dimensionless productivity index of fractured wells with the benchmark which has been developed for optimized production. To implement the fracture design and evaluation methods, two web ASP based user interfaces were developed; one is called Frac Design (Screening), and the other is Frac Evaluation. Both modules are built to hold the following features. o Friendly web ASP based user interface o Minimum user input o Proppant type and mesh size selection o Damage effects consideration options o Convenient on-line help.