This article focuses on interpretation of well test data from wells completed in naturally fractured reservoirs. Because of the presence of two distinct types of porous media, the assumption of homogeneous behavior is no longer valid in naturally fractured reservoirs. This article discusses two naturally fractured reservoir models, the physics governing fluid flow in these reservoirs and semilog and type curve analysis techniques for well tests in these reservoirs. Naturally fractured reservoirs are characterized by the presence of two distinct types of porous media: matrix and fracture. Because of the different fluid storage and conductivity characteristics of the matrix and fractures, these reservoirs often are called dual-porosity reservoirs.

Summary This paper presents new analytical and semianalytical solutions derived from a coupled transient-wellbore/reservoir thermal model to investigate the information content of transient-temperature measurement made within the vertical wellbore across from the producing horizon or at a gauge depth above it during drawdown and buildup tests. The solutions consider flow of a slightly compressible, single-phase fluid in a homogeneous infinite-acting reservoir system with skin modeled as a composite zone adjacent to the wellbore and account for the Joule-Thomson (J-T) heating/cooling, adiabatic-fluid expansion, conduction and convection effects both in the wellbore and reservoir. They are developed depending on the assumption that the effects of temperature changes on wellbore and reservoir-pressure-transient data can be neglected so that the mass-, momentum-, and energy-balance equations in the wellbore and reservoir can be decoupled. The semianalytical solution for predicting sandface temperatures is verified by use of a general-purpose thermal simulator. Wellbore temperatures at a certain gauge depth are evaluated through the analytical steady-state and transient-wellbore-temperature equations coupled with a semianalytical reservoir-temperature model accounting for conservation of momentum in the wellbore. Results show that drawdown- and buildup-sandface-temperature data may exhibit two semilog straight lines: one at early times reflecting the effects of adiabatic-fluid expansion in the skin zone near the wellbore, and the other, the late-time semilog straight line, reflecting the J-T effects and exhibiting the nonskin-zone properties. However, the wellbore-temperature measurements made at locations above the producing horizon may not exhibit these semilog straight lines because they are strongly dependent upon distance above the producing horizon, geothermal gradient, and radial-heat losses from the wellbore fluid to the formation on the way to gauge. It is found that the skin-zone properties are very difficult to be estimated from drawdown- and buildup-wellbore temperatures unless the gauge location is not far from the producing zone. Specifically, we found that buildup-wellbore temperature is mostly dominated by wellbore-heat losses compared with drawdown-wellbore-temperature data, and hence may not be useful to estimate the formation properties, including skin-zone properties.

Summary This paper presents new semilog-straight-line and temperature-derivative methods for interpreting and analyzing sandface-temperature transient data from constant-rate drawdown and buildup tests conducted in infinite-acting reservoirs containing slightly compressible fluid of constant compressibility and viscosity. The procedures are dependent on the analytical solutions accounting for Joule-Thomson (J-T) heating/cooling, adiabatic-fluid expansion, and conduction and convection effects. The development of the analytical solutions is dependent on the fact that the effects of temperature changes on pressure-transient data can be neglected so that the pressure-diffusivity and thermal-energy-balance equations can be decoupled. The analytical solutions are verified by and are found in excellent agreement with the solutions of a commercial nonisothermal reservoir simulator. It is shown that drawdown and buildup sandface-temperature data may exhibit three infinite-acting radial-flow (IARF) periods (represented by semilog equations): one at early times reflecting the adiabatic expansion/compression effects, another at intermediate times reflecting the J-T expansion in the skin zone if skin exists, and the third at late times reflecting J-T expansion effects in the nonskin zone. Performing semilog analyses by use of these IARF regimes gives estimates of permeability of skin and nonskin zones as well as the radius of the skin zone, assuming that the J-T coefficient of the fluid and the viscosity are known. Parameters such as skin-zone permeability and radius are not readily accessible from conventional pressure-transient analysis (PTA) from which only the skin factor and nonskin-zone permeability can be obtained. The applicability of the proposed analysis procedure is demonstrated by considering synthetic and field-test data. The results indicate that the analysis procedure provides reliable estimates of skin-zone and nonskin-zone permeability and skin-zone radius from drawdown or buildup temperature data jointly with pressure data.

Abstract This paper presents new semilog-straight line and temperature-derivative methods (similar to pressure-derivative method commonly used in pressure transient analysis) for interpreting and analyzing temperature transient data from constant-rate drawdown and buildup tests conducted in infinite-acting reservoirs containing slightly compressible fluid of constant compressibility and viscosity. The procedures are based on the analytical solutions accounting for Joule-Thomson (J-T) heating/cooling, adiabatic fluid expansion, conduction and convection effects. The development of the analytical solutions is based on the fact that the effects of temperature changes on pressure transient data can be neglected so that the pressure diffusivity and thermal energy balance equations can be decoupled. The analytical solutions are verified by and are found in excellent agreement with the solutions of a commercial non-isothermal reservoir simulator. It is shown that drawdown and buildup sandface temperature data may exhibit three infinite-acting radial flow (IARF) periods (represented by semilog equations); one at early times reflecting the adiabatic expansion/compression effects, second at intermediate times reflecting the J-T expansion in the skin zone if skin exists, and the third one at late times reflecting J-T expansion effects in the nonskin zone. Performing semilog analyses based on these IARF regimes gives estimates of permeability of skin and nonskin zones as well as radius of the skin zone assuming that the J-T coefficient of the fluid and viscosity is known. Parameters such as skin zone permeability and radius are not readily accessible from conventional pressure transient analysis from which only the skin factor and non-skin zone permeability can be obtained. The applicability of the proposed analysis procedure is demonstrated by considering synthetic and field test data. The results indicate that the analysis procedure provides reliable estimates of skin zone and non-skin zone permeabilities and skin zone radius from drawdown or buildup temperature data jointly with pressure data.

Abstract Thermal well testing of steam injection wells offers an inexpensive quick method to estimate flow capacity and swept volume in thermal recovery processes. Pressure falloff tests are commonly used for this purpose. Estimation of steam zone properties and swept volume from falloff test data in this study is based on the theory assuming a composite reservoir with two regions of highly contrasting fluid mobilities and the interface as an impermeable boundary. Consequently, the swept zone acts as a bounded reservoir for a short duration, during which the pressure response is characterized by pseudo steady state behavior. The purpose of this study is to evaluate the applicability and accuracy of thermal well test analysis method and effects of different parameters on results. Pressure falloff testing is simulated using a numerical thermal simulator. The generated pressure falloff data are then analyzed to calculate swept volume and reservoir parameters. Different gridblock models are considered. Viscosity of Athabasca heavy crude sample was measured in the lab using a rotational viscometer up to 300°C. Bitumen sample molar mass was measured by cryoscopy. Density at standard conditions was measured by a density measuring cell. These data were used as input for numerical simulation purposes. Results of this work show that the swept volume, swept zone permeability and skin factor can reasonably be estimated from pressure falloff tests. The effects of gravity, dip, permeability anisotropy and irregular shapes of swept zones are studied. It can be seen that these factors do not greatly affect the estimated results. Results of 3D models show that the estimation of permeability and steam swept volume depends on the vertical positions where pressure data are measured. It is also found that real gas analysis does not substantially improve the calculation accuracy and the pressure analysis technique suffices for all practical purposes.

Abstract Heavy oil reservoirs constitute a huge proportion of total world oil reserves. Among different thermal recovery methods, steam injection is the most widely used method in this type of reservoirs. Monitoring of swept volume over time is very important for evaluation of a thermal project. Thermal well testing offers an inexpensive method to estimate flow capacity and swept volume in thermal recovery processes. Pressure falloff tests are usually used for this purpose. Estimation of steam zone properties and swept volume from falloff test data in this study is based on the theory developed by Eggenschwiler et al. (1980), assuming a composite reservoir with two regions of highly contrasting fluid mobilities and the interface as an impermeable boundary. Consequently, the swept zone acts as a closed reservoir for a short duration, during which the pressure response is characterized by pseudo steady state behavior. The purpose of this work is to investigate the feasibility of thermal well test analysis and effects of different parameters. Pressure falloff testing is simulated using a numerical thermal simulator. The generated pressure falloff data are then analyzed to calculate swept volume and reservoir parameters. Different gridblock models are designed. Results of this study show that the swept volume, swept zone permeability and skin factor can be reasonably estimated from pressure falloff tests. The effects of gravity, dip, permeability anisotropy and irregular shapes of swept zones are investigated. It is found that these factors do not affect the estimated results significantly. Results of 3D models show that the estimation of flow capacity and steam swept volume depends on the vertical positions where pressure data are measured (i.e. the location of pressure gauges). This finding should be considered in thermal well test interpretation.

Summary This paper presents a semianalytical model for transient flow into multiple vertical wells producing from a porous medium containing randomly distributed discrete fractures. Both vertical openhole wells and hydraulically fractured vertical wells are considered. The semianalytical model simulates pressure and pressure-derivative characteristics of wells and flow distribution along and through both the natural and the hydraulic fractures. The study shows that single or multiple isolated natural fractures yield negative pseudoskin factors in vertical wells near isolated fractures. The negative pseudoskin factor is a function of fracture conductivity, density, length, distance from the wellbore, and azimuth. Using the model, we demonstrate that the shape of the pressure derivative is related to fracture distribution. The results of this study indicate that the conventional double-porosity analysis to predict the storativity ratio of a naturally fractured system is not reliable. Also, the displacement between two semilog straight lines is not necessarily a good indicator of the storativity ratio. Introduction The main objective in this study is to develop a semianalytical model to simulate the flow inside a homogenous porous medium containing randomly distributed and unconnected fractures. Once such a model is available, the effect of isolated fractures on the pressure-transient behavior of producing wells may be investigated. In the current literature, only a few analytical studies focus on the effect of stochastically distributed natural fractures on well performance. To the best of our knowledge, the literature lacks a model to simulate the transient flow toward a system of vertical open holes and hydraulically fractured wells producing from a porous medium dissected by randomly distributed but disjointed natural fractures. This study offers such a model.

Summary This paper presents a practical method to estimate the storativity ratio of a dual-permeability layered reservoir with crossflow from pressure-transient data. The method uses an analytical formula for the storativity ratio in terms of the separation between the two semilog straight lines on the pressure vs. log-time plot, similar to the method used for dual-porosity systems. Knowing the storativity ratio from a well test allows individual-layer properties to be estimated if the layer flow rates are available from production logs. Demonstrations of the method to estimate the storativity ratio and individual-layer properties are presented by examples. Comparison of the results with those obtained from the existing techniques is also provided to highlight the accuracy of the proposed technique. Introduction Depletion characteristics of commingled multilayer reservoirs are determined by the characteristics of interlayer-fluid transfer, which is dictated by the properties of the individual layers. In such systems, to obtain the individual layer properties from pressure-transient tests, two parameters are required: the storativity ratio, ?, defined as the ratio of the storativity of the layer with higher flow capacity to the total system storativity, and the transmissivity ratio, ?, which is the ratio of the higher of the layer flow capacities to the total system flow capacity. If the layer skin factors are equal, the transmissivity ratio is equal to the ratio of the flow rate of the layer with higher flow capacity to the total flow rate and may be obtained from production logs. The storativity ratio, on the other hand, needs to be determined from the pressure-transient data or by independent means. In the literature, dual-porosity and dual-permeability system definitions are usually associated with naturally- fractured and layered systems, respectively. In principle, dual-porosity systems constitute a subset (a limiting case) of the dual-permeability systems and, as such, possess many characteristics that resemble those of dual-permeability systems (Bourdet 1985). For dual-porosity systems, such as naturally fractured reservoirs, ? may be determined from the vertical separation,dp, between the two parallel straight lines on the pressure vs. log-time plot (Pollard 1959; Warren and Root 1963). However, for dual-permeability systems, as in layered reservoirs with crossflow, the separation between the two parallel semilog straight lines is not only a function of ? but also a function of ?. Therefore, the objective of this study is to obtain a practical relation for the storativity ratio of layered systems with crossflow in terms of the separation between the two semilog straight lines on pressure vs. log-time plot and the transmissivity ratio. We demonstrate that having an initial estimate of ? is crucial for the estimation of the other layer properties from straight-line or regression-analysis techniques.

Abstract The storage capacity ratio (w) measures the flow capacitance of the secondary porosity and the interporosity flow parameter (l) is related to the heterogeneity scale of the system. Currently, both parameters l and w are obtained from well test data by using the conventional semilog analysis, type-curve matching or the TDS Technique. Warren and Root showed how the parameter w can be obtained from semilog plots. However, no accurate equation is proposed in the literature for calculating fracture porosity. This paper presents an equation for the estimation of the l parameter using semilog plots. A new equation for calculating the interporosity flow parameter, the storage capacity ratio and fracture porosity from the coordinates of the minimum point of the trough on the pressure derivative is presented. The influence of the wellbore storage on the trough was investigated and a new equation was derived to correct the coordinates of the minimum point. The equations are applicable to both pressure buildup and pressure drawdown tests. The interpretation of these pressure tests follows closely, the classification of naturally fractured reservoirs into four types, as suggested by Nelson. The paper also discusses new procedures for interpreting pressure transient tests for three common cases: the pressure test is too short to observe the early-time radial flow straight line and only the first straight line is observed, the pressure test is long enough to observe the late-time radial flow straight line, but the first straight line is not observed due to inner boundary effects, such as wellbore storage and formation damage, and Neither straight line is observed for the same reasons, but the trough on the pressure derivative is well defined. Analytical equations are derived in all three cases for calculating permeability, skin, storage capacity ratio and interporosity flow coefficient, without using type curve matching. In naturally fractured reservoirs, the matrix pore volume, therefore the matrix porosity, is reduced as a result of large reservoir pressure drop due to oil production. This large pressure drop causes the fracture pore volume, therefore fracture porosity, to increase. This behavior is observed particularly in reservoir where matrix porosity is much greater than fracture porosity. Fractures in reservoirs are more vertically than horizontally oriented, and the stress axis on the formation is also essentially vertical. Using these principles, a new method is introduced for calculating fracture porosity from the storage capacity ratio, without assuming the total matrix compressibility is equal to the total fracture compressibility. Several numerical examples are presented for illustration purposes. Introduction Nelson1 identifies four types of naturally fractured reservoirs; based on the extent the fractures have altered the reservoir matrix porosity and permeability. In Type 1 reservoirs, fractures provide the essential reservoir storage capacity and permeability. Typical Type-1 naturally fractured reservoirs are the Amal field in Libya, the LaPaz and Mara fields in Venezuela, and pre-Cambrian basement reservoirs in Eastern China. All these fields contain high fracture density. In Type 2 naturally fractured reservoirs, fractures provide the essential permeability, and the matrix provides the essential porosity, such as in the Monterey fields of California, the Spraberry reservoirs of West Texas, and Agha Jari and Haft Kel oil fields of Iran. In Type 3 naturally fractured reservoirs, the matrix has an already good primary permeability. The fractures add to the reservoir permeability and can result in considerable high flow rates, such as in Kirkuk field of Iraq, Gachsaran field of Iran, and Dukhan field of Qatar. Nelson includes Hassi Messaoud (HMD) in this list. While indeed there are several low-permeability zones in HMD that are fissured; in most zones however the evidence of fissures is not clear or unproven. In Type 4 naturally fractured reservoirs, the fractures are filled with minerals and provide no additional porosity or permeability. These types of fractures create significant reservoir anisotropy, and tend to form barriers to fluid flow and partition formations into relatively small blocks.

Abstract This paper presents an analytical study of transient flow into multiple vertical wells producing from a porous media containing randomly distributed discrete fractures. The model may be used to analyze the production and well test data from tight gas sands and Austin chalk type reservoirs. Both vertical openholes and hydraulically fractured vertical wells are considered. Wells and fractures are randomly distributed. The model dynamically couples the multiple fracture flow models with an analytical reservoir flow model. The analytical model simulates pressure and pressure derivative characteristics of wells and flow distribution along and through both the natural and hydraulic fractures. The study shows that single or multiple isolated fractures yield negative pseudoskin factors in vertical wells near isolated fractures. The negative pseudoskin factor in un-stimulated wells has also been observed in field tests. The negative pseudoskin factor is a function of fracture conductivity, fracture density, length, distance from the wellbore, and azimuth. Using the model, we demonstrate that the shape of pressure derivative is related to fracture distribution. However, the wellbore pressure derivative response is controlled by the fractures in the near wellbore region. The result of this study indicate that the conventional analysis, based on the double porosity model such as the Warren and Root model, to predict the storativity ratio of a naturally fractured system is not reliable. Also, the displacement between two semilog straight lines is not necessarily a good indicator of the storativity ratio. Introduction Naturally fractured reservoirs may be classified as extremely heterogeneous porous media. Modeling the fluid flow in naturally fractured reservoirs has been one of the most challenging topics in the petroleum industry throughout years. There are many naturally fractured reservoirs all around the world. A significant part of the known hydrocarbon reserves are in naturally fractured porous rocks. Therefore, building realistic models representing naturally fractured reservoirs are of vital importance to maximize hydrocarbon recovery from such reservoirs. The main focus of this study is to develop an analytical model to simulate the flow inside a homogenous porous media containing randomly distributed and unconnected fractures. Once such a model is available, the effect of isolated fractures on the pressure transient behavior of producing wells may be investigated. In the current literature, only a few analytical studies focus on the effect of stochastically distributed natural fractures on well performance. To the best of our knowledge, the literature lacks a model to simulate the transient flow towards a system of vertical openholes and hydraulically fractured wells producing from a porous media dissected by randomly distributed but disjointed natural fractures. This study offers such a model to investigate the effect of multiple isolated fractures on wellbore pressure. Literature Review The model presented in this study could be used to simulate the flow behavior in an infinite reservoir that contains naturally fractures, hydraulically fractured wells, and vertical openholes. Therefore, a summary of the current literature on each subject is presented. The literature review is divided into five different sections; multiple vertical well models, dual porosity models, hydraulic fracture models, single isolated natural fracture model, and discreet fracture network models. Multiple Vertical Well Models. The available literature on this subject is too extensive; hence, we just refer to only a few studies. Several researchers have presented flow models for multiple vertical wells producing from a common reservoir. The researchers have investigated the pressure response and inflow performance of a multiple well system in infinite and finite homogenous formations.1–7 The interference between wells in closed and infinite reservoirs have also been examined. Most of the publications concentrate on the calculation of the productivity of a multi-well system, the drainage area for each well, and the analysis of transient pressure data.3–7 Rodriguez and Cinco-Ley 1 presented a two-dimensional analytical solution for multiple vertical wells producing from closed-boundary reservoirs. Their model predicts the production performance of multiple wells producing at constant bottomhole pressure.