This dissertation is composed of three parts of major contributions: In Chapter II, we developed a new conceptual model and derived a new semi-analytical model for flow to a horizontal well beneath a water reservoir. Instead of treating the leakage from aquitard as a source term inside the aquifer which is called Hantush’s assumption (1964), we linked flows in aquitard and aquifer by the idea of continuity of flux and drawdown. The result in this chapter is compared with that of Zhan and Park in 2003 which Hantush’s assumption is adopted at various hydraulic and well configurations. It shows that Hantush’s assumption becomes inaccurate in regions where vertical velocity components are significant. In Chapter III, we deal with the interaction of an aquifer with two parallel surface water bodies such as two streams or canals. In this chapter, new closed-form analytical and semi-analytical solutions are acquired for the pumping induced dynamic interaction between two streams and ground water for two different cases. In the first case, the sediment layers separating the streams from the aquifer ground water do not exist. In the second case, the two low permeable layers are considered. The effect of aquitard and water right competition is addressed in this chapter. This model can be used for interpreting and deriving hydrologic parameters of aquitard and aquifer when pumping occurs between two channels. It can also be used to predict stream depletion which is essential for water management and ecology conservation. In Chapter IV, we investigated the three dimensional upconing due to a finite-length of horizontal well and its critical conditions. The results are compared with those of vertical wells. The critical condition which includes the critical rise and the critical time at a certain pumping rate depends on the well length, the initial interface location, the well location, and the pumping rate. Our results show that horizontal well might be a better tool for coastal groundwater resources development. In real field applications, installing long wells as shallow as possible is always desirable for sustaining long periods of pumping with significant rates.

This dissertation is composed of three parts of major contributions: In Chapter II, we developed a new conceptual model and derived a new semi-analytical model for flow to a horizontal well beneath a water reservoir. Instead of treating the leakage from aquitard as a source term inside the aquifer which is called Hantush’s assumption (1964), we linked flows in aquitard and aquifer by the idea of continuity of flux and drawdown. The result in this chapter is compared with that of Zhan and Park in 2003 which Hantush’s assumption is adopted at various hydraulic and well configurations. It shows that Hantush’s assumption becomes inaccurate in regions where vertical velocity components are significant. In Chapter III, we deal with the interaction of an aquifer with two parallel surface water bodies such as two streams or canals. In this chapter, new closed-form analytical and semi-analytical solutions are acquired for the pumping induced dynamic interaction between two streams and ground water for two different cases. In the first case, the sediment layers separating the streams from the aquifer ground water do not exist. In the second case, the two low permeable layers are considered. The effect of aquitard and water right competition is addressed in this chapter. This model can be used for interpreting and deriving hydrologic parameters of aquitard and aquifer when pumping occurs between two channels. It can also be used to predict stream depletion which is essential for water management and ecology conservation. In Chapter IV, we investigated the three dimensional upconing due to a finite-length of horizontal well and its critical conditions. The results are compared with those of vertical wells. The critical condition which includes the critical rise and the critical time at a certain pumping rate depends on the well length, the initial interface location, the well location, and the pumping rate. Our results show that horizontal well might be a better tool for coastal groundwater resources development. In real field applications, installing long wells as shallow as possible is always desirable for sustaining long periods of pumping with significant rates.

Hydrocarbon use has been increasing and will continue to increase for the foreseeable future in even the most pessimistic energy scenarios. Over the past few decades, natural gas has become the major player and revenue source for many countries and multinationals. Its presence and power share will continue to grow in the world energy mix. Much of the current gas reserves are found in gas condensate reservoirs. When these reservoirs are allowed to deplete, the pressure drops below the dew point pressure and a liquid condensate will begin to form in the wellbore or near wellbore formation, possibly affecting production. A field optimization includes determining the number of wells, type (vertical, horizontal, multilateral, etc.), trajectory and location of wells. Optimum well placement has been studied extensively for oil reservoirs. However, well placement in gas condensate reservoirs has received little attention when compared to oil. In most cases involving a homogeneous gas reservoir, the optimum well location could be determined as the center of the reservoir, but when considering the complexity of a heterogeneous reservoir with initial compositional variation, the well placement dilemma does not produce such a simple result. In this research, a horizontal well placement problem is optimized by using a modified Genetic Algorithm. The algorithm presented has been modified specifically for gas condensate reservoirs. Unlike oil reservoirs, the cumulative production in gas reservoirs does not vary significantly (although the variation is not economically negligible) and there are possibly more local optimums. Therefore the possibility of finding better production scenarios in subsequent optimization steps is not much higher than the worse case scenarios, which delays finding the best production plan. The second modification is developed in order to find optimum well location in a reservoir with geological uncertainties. In this modification, for the first time, the probability of success of optimum production is defined by the user. These modifications magnify the small variations and produce a faster convergence while also giving the user the option to input the probability of success when compared to a Standard Genetic Algorithm.

Ranney radial collector wells consist of an array of horizontal lateral wells arranged radially around and connected to the base of a vertical well. They offer numerous advantages over traditional vertical wells with application in both the petroleum industry and hydrologic sciences. This study improved the understanding of the interaction of collector wells and the aquifers/reservoirs they tap by numerically modeling flux exchanges between a collector well and a river in an unconfined aquifer with regional background flow. Modeling demonstrated that flux along each horizontal lateral increased with distance from the vertical well stem following a third order polynomial function. Ultimately these models demonstrated that in the collector well/aquifer/river system, the pumping rate of the collector well was the dominant factor in controlling flux between the river and aquifer under various conditions. This study can be used to project the maximum allowable pumping rate without causing an initially gaining river to become a losing river.

Ranney radial collector wells consist of an array of horizontal lateral wells arranged radially around and connected to the base of a vertical well. They offer numerous advantages over traditional vertical wells with application in both the petroleum industry and hydrologic sciences. This study improved the understanding of the interaction of collector wells and the aquifers/reservoirs they tap by numerically modeling flux exchanges between a collector well and a river in an unconfined aquifer with regional background flow. Modeling demonstrated that flux along each horizontal lateral increased with distance from the vertical well stem following a third order polynomial function. Ultimately these models demonstrated that in the collector well/aquifer/river system, the pumping rate of the collector well was the dominant factor in controlling flux between the river and aquifer under various conditions. This study can be used to project the maximum allowable pumping rate without causing an initially gaining river to become a losing river.

This thesis presents new productivity and well testing formulae of horizontal wells. Taking a horizontal well as a uniform line source, this thesis finds velocity potential formula and the productivity formulae for a horizontal well in an ellipsoid of revolution drainage volume by solving analytically the involved three-dimensional partial differential equations. These formulae can account for the advantages of horizontal wells, and they are more accurate than other formulae which are based on two-dimensional hypotheses. This thesis also presents new well testing formulae of horizontal wells in a single porosity system and a double porosity system. Compared with the formulae published in the literature, our formulae, which do not use the sum of infinite series, are more reasonable and easy to be used in well testing analysis. / Master of Science

Horizontal wells are drilled to achieve improved reservoir coverage, high production rates, and to overcome water coning problems, etc. Many of these wells often produce at rates much below the expected production rates. Low productivity of horizontal wells is attributed to various factors such as drilling induced formation damage, high completion skins, and variable formation properties along the length of the wellbore as in the case of heterogeneous carbonate reservoirs. Matrix acidizing is used to overcome the formation damage by injecting the acid into the carbonate rock to improve well performance. Designing the matrix acidizing treatments for horizontal wells is a challenging task because of the complex process. The estimation of acid distribution along wellbore is required to analyze that the zones needing stimulation are receiving enough acid. It is even more important in cases where the reservoir properties are varying along the length of the wellbore. A model is developed in this study to simulate the placement of injected acid in a long horizontal well and to predict the subsequent effect of the acid in creating wormholes, overcoming damage effects, and stimulating productivity. The model tracks the interface between the acid and the completion fluid in the wellbore, models transient flow in the reservoir during acid injection, considers frictional effects in the tubulars, and predicts the depth of penetration of acid as a function of the acid volume and injection rate at all locations along the completion. A computer program is developed implementing the developed model. The program is used to simulate hypothetical examples of acid placement in a long horizontal section. A real field example of using the model to history match actual treatment data from a North Sea chalk well is demonstrated. The model will help to optimize acid stimulation in horizontal wells.

Horizontal wells are drilled to achieve improved reservoir coverage, high production rates, and to overcome water coning problems, etc. Many of these wells often produce at rates much below the expected production rates. Low productivity of horizontal wells is attributed to various factors such as drilling induced formation damage, high completion skins, and variable formation properties along the length of the wellbore as in the case of heterogeneous carbonate reservoirs. Matrix acidizing is used to overcome the formation damage by injecting the acid into the carbonate rock to improve well performance. Designing the matrix acidizing treatments for horizontal wells is a challenging task because of the complex process. The estimation of acid distribution along wellbore is required to analyze that the zones needing stimulation are receiving enough acid. It is even more important in cases where the reservoir properties are varying along the length of the wellbore. A model is developed in this study to simulate the placement of injected acid in a long horizontal well and to predict the subsequent effect of the acid in creating wormholes, overcoming damage effects, and stimulating productivity. The model tracks the interface between the acid and the completion fluid in the wellbore, models transient flow in the reservoir during acid injection, considers frictional effects in the tubulars, and predicts the depth of penetration of acid as a function of the acid volume and injection rate at all locations along the completion. A computer program is developed implementing the developed model. The program is used to simulate hypothetical examples of acid placement in a long horizontal section. A real field example of using the model to history match actual treatment data from a North Sea chalk well is demonstrated. The model will help to optimize acid stimulation in horizontal wells.

Multiple transverse fracturing along a horizontal well is a relatively new technology that is designed to increase well productivity by increasing the contact between the reservoir and the wellbore. For multiple transverse fractures, the performance of the well system is determined by three aspects: the inflow from the reservoir to the fracture, the flow from the fracture to the wellbore, and the inflow from the reservoir to the horizontal wellbore. These three aspects influence each other and combined, influence the wellbore outflow. In this study, we develop a model to effectively formulate the inter-relationships of a multi-fracture system. This model includes a reservoir model and a wellbore model. The reservoir model is established to calculate both independent and inter-fracture productivity index to quantify the contribution from all fractures on pressure drop of each fracture, by using the source functions to solve the single-phase gas reservoir flow model. The wellbore model is used to calculate the pressure distribution along the wellbore and the relationship of pressure between neighboring fractures, based on the basic pressure drop model derived from the mechanical energy balance. A set of equations with exactly the same number of fractures will be formed to model the system by integrating the two models. Because the equations are nonlinear, iteration method is used to solve them. With our integrated reservoir and wellbore model, we conduct a field study to find the best strategy to develop the field by hydraulic fracturing. The influence of reservoir size, horizontal and vertical permeability, well placement, and fracture orientation, type (longitudinal and transverse), number and distribution are completely examined in this study. For any specific field, a rigorous step-by-step procedure is proposed to optimize the field.

This work of well performance modeling is focused on solving problems of transient and pseudo-steady state fluid flow in a rectilinear closed boundaries reservoir. This model has been applied to predict and to optimize gas production from a horizontal well intercepted by multiple transverse fractures in a bounded reservoir, and it also provides well-testing solutions. The well performance model is designed to provide enhanced efficiency with the same reliability for pressure transient analysis, and well performance prediction, especially in complex well fracture configuration. The principle is to simplify the calculation of the pressure response to an instantaneous withdraw, which happens in other fractures, within a shorter computational time. This pressure response is substituted with the interaction between the two whole fractures. This method is validated through comparison to results of rigorous Distributed Volumetric Sources (DVS) method in simple symmetric fracture configuration, and to results of field production data for complex well/fracture configuration of a tight gas reservoir. The results show a good agreement in both ways. This model indicates the capability to handle the situations, such as: various well drainages, asymmetry of the fracture wings, and curved horizontal well. The advantage of this well performance model is to provide faster processing - reducing the computational time as the number of fractures increase. Also, this approach is able to be applied as an optimization and screening tool to obtain the best fracture configurations for reservoir development of economically marginal fields, in terms of the number and dimensions of fractures per well, also with external economic and operational constraints.