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Subsurface environments host diverse microorganisms in fluid-filled fractures; however, little is known about how geological and hydrological processes shape the subterranean biosphere. Here, we sampled three flowing boreholes weekly for 10 mo in a 1478-m-deep fractured rock aquifer to study the role of fracture activity (defined as seismically or aseismically induced fracture aperture change) and advection on fluid-associated microbial community composition. We found that despite a largely stable deep-subsurface fluid microbiome, drastic community-level shifts occurred after events signifying physical changes in the permeable fracture network. The community-level shifts include the emergence of microbial families from undetected to over 50% relative abundance, as well as the replacement of the community in one borehole by the earlier community from a different borehole. Null-model analysis indicates that the observed spatial and temporal community turnover was primarily driven by stochastic processes (as opposed to deterministic processes). We, therefore, conclude that the observed community-level shifts resulted from the physical transport of distinct microbial communities from other fracture(s) that outpaced environmental selection. Given that geological activity is a major cause of fracture activity and that geological activity is ubiquitous across space and time on Earth, our findings suggest that advection induced by geological activity is a general mechanism shaping the microbial biogeography and diversity in deep-subsurface habitats across the globe.

Recent experience in applying recurrent neural networks (RNNs) to interpreting Permannt Downhole Gauge (PDG) records has highlighted the potential utility of machine learning algorithms to learn reservoir behavior from data. The power of the RNN resides in its ability to retain information in a form of memory of previous patterns and information contained in the previous behavior of phenomena being modeled. This memory plays a role of informing the decision at the present time by using what happened in the past. This property suggests RNNs as a suitable choice to model sequences of reservoir information, even when the reservoir modeler is faced with incomplete knowledge of the underlying physical system. Convolutional Neural Networks (CNNs) are another variant of machine learning algorithms that have shown promise in sequence modeling domains, such as audio synthesis and machine translation. In this study, RNN and CNN were applied to tasks that traditionally would be modeled by a reservoir simulator. This was achieved by formulating the relationship between physical quantities of interest from subsurface reservoirs as a sequence mapping problem. In addition, the performance of a CNN layer as compared to RNN was evaluated systematically to investigate their capabilities in a variety of tasks of interest to the reservoir engineer. Preliminary results suggest that CNNs, with specific design modifications, are as capable as RNNs in modeling sequences of information and as reliable when making inferences to cases that has not been seen by the algorithm during training. Design details and reasons pertaining to the way these two seemingly different architectures process information, and handle memory are also discussed.

Nano- and microparticles are expected to have several functionalities, and the ability to control size and shape is an advantage of using nano-/microparticles. This study investigated a possibility that the sizes of nano-/microparticle can be used to extract new information on structures in a fractured medium. Flow experiments were conducted to observe the particle transport in a micromodel on which a single fracture and rock matrix (grain and pore space) was fabricated on a silicon wafer. Water and nano-/microparticles were injected into the micromodel, and the droplets were collected at the outlet. Tunable Resistive Pulse Sensing (TRPS) was used to measure the frequency distributions of particle diameters from each droplet at each time. The result shows that the larger particles were observed only at early time, while the smaller particles were detected at early time and also at late time. This indicates that the larger particles flow in a fracture quickly, while smaller particles migrate through both fracture and matrix over a wider range of time. Particles with different sizes transport through fractured media differently depending on the fracture structures. The tracer response of nano- and microparticles may be useful to evaluate the fracture structures and the flow properties for different flow pathways.

Knowledge of well connectivity in a reservoir is crucial, especially for early-stage field development and water injection management. However, traditional interference tests can often take several weeks or even longer depending on the distance between wells and the hydraulic diffusivity of the reservoir. Therefore, instead of physically shutting in production wells, we can take advantage of deep learning methods to perform virtual interference tests. In this study, we first used the historical field data to train the deep learning model, a modified Long- and Short-term Time-series network (LSTNet). This model combines the Convolution Neural Network (CNN) to extract short-term local dependency patterns, the Recurrent Neural Network (RNN) to discover long-term patterns for time series trends, and a traditional autoregressive model to alleviate the scale insensitive problem. To address the time-lag issue in signal propagation, we employed a skip-recurrent structure that extends the existing RNN structure by connecting a current state with a previous state when the flow rate signal from an adjacent well starts to impact the observation well. In addition, we found that wells connected to the same manifold usually have similar liquid production patterns, which can lead to false causation of subsurface pressure communication. Thus we enhanced the model performance by using external feature differences to remove the surface connection in the data, thereby reducing input similarity. This enhancement can also amplify the weak signal and thus distinguish input signals. To examine the deep learning model, we used the datasets generated from Norne Field with two different geological settings: sealing and nonsealing cases. The production wells are placed at two sides of the fault to test the false-negative prediction. With these improvements and with parameter tuning, the modified LSTNet model could successfully indicate the well connectivity for the nonsealing cases and reveal the sealing structures in the sealing cases based on the historical data. The deep learning method we employed in this work can predict well pressure without using hand-crafted features, which are usually formed based on flow patterns and geological settings. Thus, this method should be applicable to general cases and more intuitive. Furthermore, this virtual interference test with a deep learning framework can avoid production loss.

Author(s): Fu, P; Schoenball, M; Ajo-Franklin, JB; Chai, C; Maceira, M; Morris, JP; Wu, H; Knox, H; Schwering, PC; White, MD; Burghardt, JA; Strickland, CE; Johnson, TC; Vermeul, VR; Sprinkle, P; Roberts, B; Ulrich, C; Guglielmi, Y; Cook, PJ; Dobson, PF; Wood, T; Frash, LP; Huang, L; Ingraham, MD; Pope, JS; Smith, MM; Neupane, G; Doe, TW; Roggenthen, WM; Horne, R; Singh, A; Zoback, MD; Wang, H; Condon, K; Ghassemi, A; Chen, H; McClure, MW; Vandine, G; Blankenship, D; Kneafsey, TJ | Abstract: The final version of the above article was posted prematurely on 16 July 2021, owing to a technical error. The final, corrected version of record will be made fully available at a later date.

Summary Permanent downhole gauges (PDGs) provide a continuous record of pressure, temperature, and, sometimes, flow rate during well production. The continuous record provides rich information about the reservoir and makes PDG data a valuable source for reservoir analysis (e.g., pressure-rate deconvolution for reservoir-model identification). It has been shown in previous work that the convolution-kernel (CK) -based data-mining approach is a promising tool to interpret flow-rate and pressure data from PDGs. The CK method denoises and deconvolves the pressure signal successfully without an explicit-breakpoint detection. However, the bottlenecks of computational efficiency and the incomplete recovery of reservoir behaviors limit the application of the method to interpret real-PDG data. In this paper, three different machine-learning techniques were applied to flow-rate/pressure interpretation. We formulated the machine-learning techniques into a linear regression (LR) on parameters that connect the nonlinear flow-rate features with pressure targets. Such a formulation leads to a closed-form solution, which speeds up the computation dramatically. The machine-learning algorithms that were formulated using LR were shown to have the same learning quality as the CK method, and they outperformed it with much less computational effort. Next, the kernel method was applied to address the issue of the incomplete recovery of reservoir behaviors, because it efficiently expanded the dimension of the feature space without an explicit representation of the features, but it led to overfitting. Finally, kernel ridge regression (KRR) used the expanded features given by the kernel function to capture the more detailed reservoir behaviors, while controlling the prediction error using ridge regression (RR). It was shown that KRR recovers the full reservoir behaviors successfully (e.g., wellbore-storage effect, skin effect, infinite-acting radial flow, and boundary effect). Some potential uses of temperature data from PDGs are also discussed in this paper. Machine learning was shown to be able to model the temperature and pressure data recorded by PDGs, even if the actual physical model is complex. This originates from the fact that, by using features as an approximation of model characteristics, machine learning does not require a perfect knowledge of the physical model. The modeling of pressure using temperature data was extended to two promising applications: pressure-history reconstruction using temperature data, and the cointerpretation of temperature and pressure data when flow-rate data are not available.

Tidal analysis provides a cost-effective way of estimating aquifer properties. Tidal response models that link aquifer properties with tidal signal characteristics, such as phase and amplitude, hav...

The maximum expected earthquake magnitude is an important parameter in seismic hazard and risk analysis because of its strong influence on ground motion. In the context of injection-induced seismicity, the processes that control how large an earthquake will grow may be influenced by operational factors under engineering control as well as natural tectonic factors. Determining the relative influence of these effects on maximum magnitude will impact the design and implementation of induced seismicity management strategies. In this work, we apply a numerical model that considers the coupled interactions of fluid flow in faulted porous media and quasidynamic elasticity to investigate the earthquake nucleation, rupture, and arrest processes for cases of induced seismicity. We find that under certain conditions, earthquake ruptures are confined to a pressurized region along the fault with a length-scale that is set by injection operations. However, earthquakes are sometimes able to propagate as sustained ruptures outside of the zone that experienced a pressure perturbation. We propose a faulting criterion that depends primarily on the state of stress and the earthquake stress drop to characterize the transition between pressure-constrained and runaway rupture behavior.

Financial risk due to geological uncertainty is a major barrier for geothermal development. Production from a geothermal well depends on the unknown location of subsurface geological structures, such as faults that contain hydrothermal fluids. Traditionally, geoscientists collect many different datasets, interpret the datasets manually, and create a single model estimating faults' locations. This method, however, does not provide information about the uncertainty regarding the location of faults and often does not fully respect all observed datasets. Previous researchers investigated the use of stochastic inversion schemes for addressing geological uncertainty, but often at the expense of geologic realism. In this paper, we present algorithms and open-source code to stochastically invert five typical datasets for creating geologically realistic structural models. Using a case study with real data from the Patua Geothermal Field, we show that these inversion algorithms are successful in finding an ensemble of structural models that are geologically realistic and match the observed data sufficiently. Geoscientists can use this ensemble of models to optimize reservoir management decisions given structural uncertainty.

Mechanisms for the delayed triggering between the Mw 4.8 foreshock and Mw 5.6 main shock of the 2011 earthquake sequence near Prague, Oklahoma, USA were investigated using a coupled fluid flow and fault mechanics numerical model. Because the stress orientations, stress magnitudes, fault geometry, and earthquake source mechanisms at the Prague site have been well-characterized by previous studies, this particular earthquake sequence offered an opportunity to explore the range of physical processes and in-situ fault properties that might be consistent with the 20 hour delayed triggering effect observed at the site. Our numerical experiments suggest that an initial undrained response resulting from elastic stress transfer from the foreshock followed by transient fluid flow along the fault may have contributed to the earthquake nucleation process. The results of the numerical experiments were used to constrain fault compliance and fault transmissivity for the fault that hosted the Mw 5.6 event. Relatively compliant behavior in response to changes in normal stress, corresponding to Skempton pore pressure coefficients near 1, was consistent with the field observations. Fault transmissivity was estimated to range from 10−18 to 10−15 m3. This study has implications for understanding hydraulic properties, frictional properties, and faulting behavior of basement faults in Oklahoma that are large enough to host damaging earthquakes.

Characterizing the fractures is an important task to improve the understanding and utilization of hydraulic fracturing. As an approach to augment and improve on the existing methods, time-lapse electric potential measurements could be used to characterize subsurface features. In this study we investigated the characterization of fracture length and fracture density by using time-lapse electric potential data. A new borehole ERT (electric resistivity tomography) method designed specifically for hydraulic fracture characterization is proposed to better capture reservoir dynamics during hydraulic fracturing. This method uses high resolution electric potential data by implementing electrodes in or near boreholes and monitor electric potential distribution near the horizontal fracture zone. The time-lapse electric potential data generated by this tool were simulated and subsequently used to analyze fracture characteristics. Inverse analysis was then performed on the electric potential data to estimate fracture length and fracture density. Last, we performed sensitivity analysis to examine the robustness of the estimates in nonideal environments. The results of this work show that time-lapse electric potential data are capable of capturing flow dynamics during the fracturing process. Using the proposed borehole ERT method we successfully estimated the true fracture length and true fracture density of a constructed fracture model. We were able to determine the best locations in the constructed reservoir to place the electrodes, and through sensitivity analysis we found the maximum noise level of the electric potential data that can still allow the proposed method to make robust fracture length and fracture density estimates. Our proposed method offers a new approach to make robust estimates of fracture length and fracture density. Electric potential data have been used mostly for well logging in the past. This study demonstrates a novel way of using electric potential data in unconventional development and opens possibilities for more applications such as production monitoring.

Fault zones affect the flow paths of fluids in groundwater aquifers and geological reservoirs. Fault-related fracture damage decreases to background levels with increasing distance from the fault core according to a power law. This study investigated mass transport in such a fault-related structure using nonlocal models. A column flow experiment is conducted to create a permeability distribution that varies with distance from a main conduit. The experimental tracer response curve is preasymptotic and implies subdiffusive transport, which is slower than the normal Fickian diffusion. If the surrounding area is a finite domain, an upper truncated behavior in tracer response (i.e., exponential decline at late times) is observed. The tempered anomalous diffusion (TAD) model captures the transition from subdiffusive to Fickian transport, which is characterized by a smooth transition from power-law to an exponential decline in the late-time breakthrough curves. This article is protected by copyright. All rights reserved.

Summary Hydraulic fracturing is a widely applied well-stimulation technique. Recently, the application of multiple hydraulic fractures along horizontal wells has made possible the exploitation of unconventional reservoirs, such as shale gas and shale oil. However, the process of horizontal-well fracturing is uncertain and it is not fully understood yet. There exist many questions about the number and position of created fractures and whether the fracture stays contained within the main reservoir thickness. This work presents the modeling and analysis of temperature data during and after the creation of multiple fractures along a horizontal well. Our model accounts for fracture growth and closure, the well effects, and interaction between multiple fractures. The interference between multiple fractures growing simultaneously and the presence of reservoir-permeability heterogeneity were investigated. Capabilities and limitations of information carried by temperature data are presented through different geometry analyses. A special consideration of fracture growth out of zone was addressed. For this case, it was considered that one of the hydraulic fractures activates a pre-existing fault and interconnects the reservoir with other zones hundreds of feet away. Our work shows the advantage of the use of continuous-distributed-temperature data in comparison with the traditional single-point-pressure analysis. The local characteristic of temperature allows us to identify not only which of the created hydraulic fractures has interconnected the main reservoir with a different zone, but also the location of this zone. We also account for the effect of the interconnection on the growth of the other hydraulic fractures along the horizontal wellbore. The simultaneous multiple fracture growth shows that falloff-distributed-temperature data can predict the number of created fractures. More than that, in the presence of heterogeneity, the interaction between the contained fractures can be captured by the temperature analysis. Different from the pressure analysis, distributed-temperature data can differentiate between heterogeneity locations along the wellbore. Throughout this study, we present a series of examples in which the temperature can provide information that would not be obtained from the traditional pressure analysis.

One of the key issues to a successful EGS (Enhanced or engineered Geothermal System) is the creation of a great density of fractures. The detection and characterization of the created fractures is crucial in evaluating the geothermal energy resources in such EGS projects as well as in reservoirs for CO 2 sequestration and storage. Methods to evaluate the fractures after stimulations are few, and limited in application. To this end, an approach to detecting and evaluating the fractures using resistivity data measured at different frequencies was developed in this study. The effects of fractures on resistivity measurements at different frequencies have been investigated as a function of water saturation in rocks with different porosity, permeability and lithology. Different rocks (Berea sandstone, and greywacke from The Geysers geothermal reservoir) were used in this study. The permeability of the samples ranged from 0.5 to over 1000 md for the matrix. The frequency ranged from 100 to 100,000 Hz. It was found that the effect of frequency on resistivity is different in rocks with and without fractures, especially in the range of low water saturation. The validity of the Archie equation depends on the existence of fractures, the frequency, and the range of water saturation. The relationship between resistivity and water saturation did not follow the Archie equation at low water saturation in some rocks with fractures. Models for characterizing different types of rocks with specific fracture patterns have been established using the resistivity data measured at different frequencies and different water saturations.

The enthalpy of two-phase geothermal fluids is typically monitored at the surface to understand the performance of a geothermal field. Surface enthalpy, however, cannot reflect real reservoir conditions downhole because of the heat loss along the wellbore. In addition, with only the surface enthalpy, the energy contributions from separate feed zones cannot be evaluated individually. A technique for determining downhole enthalpy in two-phase geothermal wells using surface inputs and chloride concentrations was developed in this study, including analytical models, experimental work and numerical studies, so that the downhole flowing enthalpy, the energy contribution from each feed zone and the heat loss along the wellbore can be evaluated. Chloride always stays in the liquid phase and becomes more concentrated as the geothermal fluid ascends to the surface and boils, and the change in chloride concentration along the wellbore can be utilized to calculate the change in the flowing steam fraction and the enthalpy. Analytical models to implement this idea were established for geothermal wells with a single feed zone or multiple feed zones, and the calculation procedures are elaborated with detailed flow diagrams and examples. The analytical models involve mass balance, energy balance and an assumption that the chloride concentration in the liquid from the feed zone is determinable. Inputs to the analytical model include two-phase mass flow rates and enthalpy at the surface and chloride concentrations at the surface and in the downhole. Temperature or pressure measurements are utilized to apply the energy balance in the model for multiple feed zones. Experiments were conducted to test the feasibility of an accurate determination of chloride concentration in two-phase fluids and validate the assumption in the analytical model. Chloride concentration distribution in the mixing area at the inlet of the feed zone was determined and visualized in the experiments. At the same time, similar mixing processes were visualized by a numerical simulation using ANSYS Fluent, and results from the numerical simulation are consistent with those from the experiments. Therefore, both the experiments and the simulation support the assumption in the analytical model that chloride concentration in the liquid from the feed zone can be determined accurately. It is demonstrated that the proposed method provides a fast and cost-effective way to determine the downhole two-phase flowing enthalpy in geothermal wells with multiple feed zones and estimate flow rates and energy contribution from each individual feed zone.

We reviewed published results from six projects where hydraulic stimulation was performed in granitic rock. At each project, fractures in the formation were well-oriented to slip at the injection pressures used during stimulation. In all but one case, thousands of cubic meters of water were injected, and in every case, flow rates on the order of tens of liters per second were used. Despite these similarities, there was a large variation in the severity of induced seismicity that occurred in response to injection. At the three projects where induced seismicity was significant, observations at the wellbore showed evidence of well-developed brittle fault zones. At the three projects where induced seismicity was less significant, observations at the wellbore indicated only crack-like features and did not suggest significant fault development. These results suggest that assessments of the degree of fault development at the wellbore may be useful for predicting induced seismicity hazard. We cannot rule out that the differences were caused by variations in frictional properties that were unrelated to the degree of fault development (and it is possible that there is a relationship between these two parameters). The projects with more significant seismicity tended to be deeper, and if this is a meaningful correlation, it is unclear whether depth influenced seismic hazard through the degree of fault development, frictional properties, or some other variable. The results of this paper are not conclusive, but they suggest that there may be significant opportunity for future research on identifying geological conditions that increase induced seismicity hazard.

Summary The classical concept of hydraulic fracturing is that a single, planar, opening mode fracture propagates through the formation. In recent years, there has been a growing consensus that natural fractures play an important role during stimulation in many settings. There is not universal agreement on the mechanisms by which natural fractures affect stimulation, and these mechanisms may vary depending on formation properties. One potentially important mechanism is shear stimulation, in which increased fluid pressure induces slip and permeability enhancement on pre-existing fractures. We propose a tendency-for-shear-stimulation (TSS) test as a direct, relatively unambiguous method for determining the degree to which shear stimulation contributes to stimulation in a formation. In a TSS test, fluid injection is performed while maintaining the bottomhole fluid pressure slightly less than the minimum principal stress. Under these conditions, shear stimulation is the only possible mechanism for permeability enhancement (except, perhaps, thermally induced tensile fracturing). A TSS test is different from a conventional procedure because injection is performed at a specified pressure (rather than a specified rate). With injection at a specified rate, fluid pressure may exceed the minimum principal stress, and it may cause tensile fractures to propagate through the formation. If this occurs, it will be ambiguous whether stimulation was because of shear stimulation or tensile fracturing. Maintaining pressure less than the minimum principal stress ensures that the effect of shear stimulation can be isolated. Low-rate injectivity tests could be performed before and after the TSS test to estimate formation permeability. An increase in formation permeability would indicate that shear stimulation has occurred. The flow-rate transient during injection may also be interpreted to identify shear stimulation. Numerical simulations of shear stimulation were performed with a discrete-fracture-network (DFN) simulator that couples fluid flow with the stresses induced by fracture deformation. These simulations were used to qualitatively investigate how shear stimulation and fracture connectivity affect the results of a TSS test. Two specific field projects are discussed as examples of a TSS test, the Enhanced Geothermal Systems (EGS) projects at Desert Peak, Nevada, and Soultz-sous-Forêts, France.

Relative permeability is one of the key parameters governing fluid flow through porous media. Determination of relative permeability is traditionally conducted in the laboratory using either recombined reservoir oil or laboratory oil at simulated reservoir conditions, or simply at laboratory conditions. This is because it is expensive to sample representative uncontaminated reservoir fluids and extremely difficult to cut reservoir cores without altering their surface properties. Restoring rock properties to their original reservoir conditions has been a technical challenge to the industry. Upscaling laboratory special core-analysis data to reservoir scale is also a concern. Consequently, the industry has been researching new methods to extract relative permeability in situ , including the utilization of specially designed permanent downhole electric resistivity array, pressure and flow rate measurements. In this study, a different approach was taken. A semi-analytical model, developed to infer relative permeability from resistivity, was verified using experimental and field data. Relative permeability and resistivity were measured simultaneously in the laboratory. The results demonstrated that relative permeability derived from measured resistivity was close to the measured relative permeability. Relative permeability calculated from resistivity logs in two wells was compared to measured relative permeability with encouraging results.

An inverse modeling approach was developed to characterize fracture connectivity in geothermal reservoirs using an injection of a conductive fluid and time-lapse electric potential measurements. Discrete fracture networks with sparsely connected fractures were modeled and a flow simulator was used to solve electric fields as a conductive tracer flows through the fracture networks. The electric potential difference between well pairs drops progressively in time as the conductive fluid fills interconnected fractures along paths from the injector toward the producer. Therefore, the fractional connected area of reservoirs could be estimated using inverse modeling to match the response to other fracture networks by comparing time histories of the electric potential. This method was compared to estimating fractional connected area using tracer return curves alone and the study showed that locations of connected areas were estimated better using the electric potential approach. A sensitivity analysis was performed to study the effect of fractional connected area on time-lapse electric potential and tracer return data. The study verified the advantages of using electric potential measurements instead of only the tracer return curves.

We describe a numerical investigation of seismicity induced by injection into a single isolated fracture. Injection into a single isolated fracture is a simple analog for shear stimulation in enhanced geothermal systems (EGS) during which water is injected into fractured, low permeability rock, triggering slip on preexisting large scale fracture zones. A model was developed and used that couples (1) fluid flow, (2) rate and state friction, and (3) mechanical stress interaction between fracture elements. Based on the results of this model, we propose a mechanism to describe the process by which the stimulated region grows during shear stimulation, which we refer to as the sequential stimulation (SS) mechanism. If the SS mechanism is realistic, it would undermine assumptions that are made for the estimation of the minimum principal stress and unstimulated hydraulic diffusivity. We investigated the effect of injection pressure on induced seismicity. For injection at constant pressure, there was not a significant dependence of maximum event magnitude on injection pressure, but there were more relatively large events for higher injection pressure. Decreasing injection pressure over time significantly reduced the maximum event magnitude. Significant seismicity occurred after shut-in, which was consistent with observations from EGS stimulations. Production of fluid from the well immediately after injection inhibited shut-in seismic events. The results of the model in this study were found to be broadly consistent with results from prior work using a simpler treatment of friction that we refer to as static/dynamic. We investigated the effect of shear-induced pore volume dilation and the rate and state characteristic length scale, [Formula: see text]. Shear-induced pore dilation resulted in a larger number of lower magnitude events. A larger value of [Formula: see text] caused slip to occur aseismically.

Summary With recent advances in permanent downhole technology, well-test analysts now have to deal with enormous amounts of data. Using these data requires the development of efficient algorithms that are able to extract the relevant information from the data at minimal cost. We present a multiresolution wavelet approach to estimate the spatial distribution of reservoir parameters, by performing the nonlinear least-squares regression in the wavelet domains of both time and space. Wavelet transforms have the ability to reveal important events in time signals or spatial images. Thus, we transformed both the model space and the time-series pressure data into spatial wavelet and time wavelet domains, respectively, and used a thresholding to select a subset of wavelet coefficients from each of the transformed domains. These subsets were used subsequently in nonlinear regression to estimate the appropriate description of reservoir parameters. The appropriate subset is not only smaller; the problem is also reduced to the consideration of only the important components of the measured data and only the part of the reservoir description that depends on them. As a test of the approach, we first applied the model to well-test problems involving 1D (radially composite) reservoir systems. The inverse problem was solved to estimate the distributed permeability values by performing the nonlinear least-squares regression in the wavelet domains (time and space). Results obtained were compared with those obtained from the conventional nonlinear-regression approach, using all the pressure-time data and the full set of spatial reservoir parameters. The time/space wavelet approach proved to be efficient. By reducing the dimensions of the model and data spaces, the approach eliminates redundancy in the reservoir description and in the data set. Significantly, the approach reveals the true number of reservoir parameters that can be appropriately estimated from a given data set and also reveals which components of the full data set are active in constraining the reservoir model. Thus, the approach provides a good means to integrate different data properly while avoiding the inclusion of irrelevant data during nonlinear regression.

Summary Permanent downhole gauges (PDGs) provide a continuous source of downhole pressure, temperature, and sometimes flow-rate data. Until recently, the measured temperature data have been largely ignored, although a close observation of the temperature measurements reveals a response to changes in flow rate and pressure. This suggests that the temperature measurements may be a useful source of reservoir information. In this study, reservoir temperature-transient models were developed for single- and multiphase-fluid flows, as functions of formation parameters, fluid properties, and changes in flow rate and pressure. The pressure fields in oil- and gas-bearing formations are usually transient, and this gives rise to pressure/temperature effects appearing as temperature change. The magnitudes of these effects depend on the properties of the formation, flow geometry, time, and other factors and result in a reservoir temperature distribution that is changing in both space and time. In this study, these thermometric effects were modeled as convective, conductive, and transient phenomena with consideration for time and space dependencies. This mechanistic model included the Joule-Thomson effects resulting from fluid compressibility and viscous dissipation in the reservoir during fluid flow. Because of the nature of the models, the semianalytical solution technique known as operator splitting was used to solve them, and the solutions were compared to synthetic and real temperature data. In addition, by matching the models to different temperature-transient histories obtained from PDGs, reservoir parameters such as average porosity, near-well permeabilities, saturation, and some thermal properties of the fluid and formation could be estimated. A key target of this work was to show that temperature measurements, often ignored, can be used to estimate reservoir parameters, as a complement to other more-conventional techniques.

Summary Current downhole measuring technologies have provided a means of acquiring downhole measurements of pressure, temperature, and sometimes flow-rate data. Jointly interpreting all three measurements provides a way to overcome data limitations that are associated with interpreting only two measurements—pressure and flow-rate data—as is currently done in pressure-transient analysis. This work shows how temperature measurements can be used to improve estimations in situations where lack of sufficient pressure or flow-rate data makes parameter estimation difficult or impossible. The model that describes the temperature distribution in the reservoir lends itself to quasilinear approximations. This makes the model a candidate for Bayesian inversion. The model that describes the pressure distribution for a multirate flow system is also linear and a candidate for Bayesian inversion. These two conditions were exploited in this work to present a way to cointerpret pressure and temperature signals from a reservoir. Specifically, the Bayesian methods were applied to the deconvolution of both pressure and temperature measurements. The deconvolution of the temperature measurements yielded a vector that is linearly related to the average flow-rate from the reservoir and, hence, could be used for flow-rate estimation, especially in situations in which flow-rate measurements are unavailable or unreliable. This flow rate was shown to be sufficient for a first estimation of the pressure kernel in the pressure-deconvolution problem. When the appropriate regularization parameters are chosen, the Bayesian methods can be used to suppress fluctuations and noise in measurements while maintaining sufficient resolution of the estimates. This is the point of the application of the method to data denoising. In addition, because Bayesian statistics represent a state of knowledge, it is easier to incorporate certain information, such as breakpoints, that may help improve the structure of the estimates. The methods also lend themselves to formulations that make possible the estimation of initial properties, such as initial pressures.

Summary In this study, we show significant improvements over conventional pressure-transient analysis on the basis of nonlinear regression by using total least squares (TLS), which minimizes errors in both pressure and time simultaneously. To our knowledge, TLS has not been applied to pressure-transient analysis before in this sense. TLS regression is not an easy problem to solve mathematically, especially for nonlinear pressure-transient-model functions. In this work, we compare four different versions of TLS. We formulate a robust approximation of the TLS solution, which can handle a variety of tests and reservoir models yet does not compromise the performance of the analysis. We show that our technique reduces ambiguity in the estimation of parameters to a large extent, especially in the presence of noise in time. Using our TLS algorithm, we obtain much narrower confidence intervals on the parameter estimates of a variety of real data sets, compared to the conventional least squares (LS) approach. For synthetic data sets, we observe that the TLS estimates are often closer to the true values than estimates made with LS, especially for poorly determined problems. When the deviation is in pressure only, TLS and LS results are comparable. However, in the presence of deviations in time in addition to pressure, the performance of TLS algorithms is substantially better. We, therefore, expect that our technique will provide more accurate estimation of reservoir parameters, allowing for better forecasting of reservoir performance.

Is there any method to study the feasibility of water injection into naturally fractured geothermal reservoirs before implementing liquid injection? How can we identify the difference of water injectability between different reservoirs? Spontaneous water imbibition tests in rocks from The Geysers and in Berea sandstone have been designed to answer these questions. The maximum water saturation and the maximum imbibition rate by spontaneous water imbibition were used to evaluate the feasibility and the ability of water injection into geothermal reservoirs. Reservoirs with high imbibition rates and high maximum water saturation are good candidates for water injection. If there is no imbibition of water into the rocks at all, then the reservoir is not suitable for water injection. The relationships between imbibition rate and time for The Geysers rocks have been measured under countercurrent and cocurrent imbibition conditions, respectively. The measured maximum water saturation by the spontaneous water imbibition in The Geysers rock was about 87.9%, which was greater than that in Berea although the imbibition rate was lower. Experimental results and the continuing practice of water injection in the field showed that The Geysers geothermal reservoir may be appropriate for water injection.

Capillary pressure curves of six low porosity and low permeability core samples from The Geysers geothermal field were measured using the mercury-intrusion approach to characterize the heterogeneity of rock. One high permeability Berea sandstone core sample was analyzed similarly, for comparison. The maximum pressure of mercury intruded into the rock was about 200 MPa to reach the extremely small pores. Experimental data showed that the capillary pressure curves of The Geysers rock are very different from that of the Berea sandstone. It was found that the frequently used capillary pressure models could not be used to represent the data from The Geysers rock samples. This might be because of the fractures in the rock. To this end, a fractal technique was proposed to model the features of the capillary pressure curves and to characterize the difference in heterogeneity between The Geysers rock and Berea sandstone. The results demonstrated that the rock from The Geysers geothermal field was fractal over a scaling range of about five orders of magnitude. The values of the fractal dimension of all the core samples (six from The Geysers and one Berea sandstone) calculated using the proposed approach were in the range from 2 to 3. The results showed that The Geysers rock with a high density of fractures had a greater fractal dimension than Berea sandstone which is almost without fractures. This shows that The Geysers rock has greater heterogeneity, as expected.

The wettability in gas–liquid–rock systems, including geothermal (steam–water–rock) systems, is central to defining the relative permeability and capillary pressure, which govern the forecasts of future production and reinjection performance. Since the frequently used Amott and USBM approaches are appropriate only for specific liquid–liquid–rock systems, we developed a model to evaluate the wettability in gas–liquid–rock systems. The method can be applied to determine the wettability at specific wetting-phase saturation if the capillary pressure and relative permeability at this fluid saturation are known. The proposed model can also be used in liquid–liquid–rock systems. The validity of the technique was tested qualitatively and quantitatively using experimental data from different rock–fluid systems. The calculated wettability indices in gas–liquid–rock systems were higher than in liquid–liquid–rock systems, as expected. Results also show that the wettability index calculated using the new method may or may not be independent of fluid saturation in the cases studied. In addition, the wettability index in drainage was seen to be greater than that in imbibition, a wettability difference that is particularly important in steam–water–rock (geothermal) systems because of the impact on reinjection.

Although steam–water capillary pressure is of central importance in geothermal reservoir engineering, it is nevertheless still poorly understood because of the difficulties involved in making direct measurements. To this end, we have conducted some experimental and theoretical studies. Unique methods have been developed to measure capillary pressures in order to overcome the complications in laboratory procedures associated with mass transfer as temperature and pressure changes. Both steam–water and air–water capillary pressures were measured and compared. Significant differences were found; in the cases studied, the steam–water capillary pressures were smaller. The drainage capillary pressure was greater than the imbibition capillary pressure, as was expected. Using experimental data, an empirical model was derived to calculate steam-water capillary pressure directly. Also developed was a generalized capillary pressure model based on fractal modeling of a porous medium; it encompasses the frequently used Brooks–Corey model (Brooks, R.H., Corey, A.T., 1964. Hydraulic Properties of Porous Media. Colorado State University, Hydro paper No. 3, Fort Collins, CO, USA, 24 pp.) as well as others. Recent studies on the topic are summarized and reviewed.

Summary Phase transformation affects multiphase flow in geothermal and gas/condensate reservoirs owing to the same substance occurring in different phases. These effects change the phase behavior and the flow characteristics. The goals of this research were to compare the flow behavior and relative permeability differences between two-phase flow with and without phase-transformation effects in smooth-walled and rough-walled fractures. During this research, an experimental apparatus was built to capture the unstable nature of the two-phase flow in fractures and to display the flow structures in real time. Two-phase-flow experiments with phase-transformation effects (steam/water flow) and without phase-transformation effects (nitrogen/water flow) were conducted. The porous-medium approach was used to calculate two-phase relative permeabilities. From the results in this study, steam/water relative permeabilities are different from nitrogen/water relative permeabilities. The enhanced steam-phase relative permeability is caused by the effects of phase transformation. This shows consistency with some earlier studies in porous media. The nitrogen/water relative permeability is described most appropriately by using the viscous coupling model. However, steam/water flow in the rough-walled fracture, which is coupled with strong phase-transformation effects, seems to be represented better by Brooks-Corey relative permeability functions for fractured media (λ→∞). The results from this study suggest that relative permeabilities accounting for phase-transformation effects must be used in simulations of geothermal and solution-gas reservoirs to represent two-phase interactions adequately.

Summary It has been a challenge to understand why recovery by spontaneous imbibition could both increase and decrease with initial water saturation. To this end, mathematical models were developed with porosity, permeability, viscosity, relative permeability, capillary pressure, and initial water saturation included. These equations foresee that recovery and imbibition rate can increase, remain unchanged, or decrease with an increase in initial water saturation, depending on rock properties, the quantity of residual gas saturation, the range of initial water saturation, and the units used in the definitions of gas recovery and imbibition rate. The theoretical predictions were verified experimentally by conducting spontaneous water imbibition at five different initial water saturations, ranging from 0 to approximately 50%. The effects of initial water saturation on residual saturation, relative permeability, capillary pressure, imbibition rate, and recovery in gas/water/rock systems by cocurrent spontaneous imbibition were investigated both theoretically and experimentally. Water-phase relative permeabilities and capillary pressures were calculated with the experimental data of spontaneous imbibition. Experimental results in different rocks were compared.

Summary Scaling the experimental data of spontaneous imbibition without serious limitations has been difficult. To this end, a general approach was developed to scale the experimental data of spontaneous imbibition for most systems (gas/liquid/rock and oil/water/ rock systems) in both cocurrent and countercurrent cases. We defined a dimensionless time with almost all the parameters considered. These include porosity, permeability, size, shape, boundary conditions, wetting- and nonwetting-phase relative permeabilities, interfacial tension (IFT), wettability, and gravity. The definition of the dimensionless time was not empirical; instead, it was based on theoretical analysis of the fluid-flow mechanisms that govern spontaneous imbibition. The general scaling method was confirmed against the experimental data from spontaneous water imbibition conducted at different IFTs in oil-saturated rocks with different sizes and permeabilities. A general analytical solution to the relationship between recovery and imbibition time for linear spontaneous imbibition was derived. The analytical solution predicts a linear correlation between the imbibition rate and the reciprocal of the recovery by spontaneous imbibition in most fluid/ fluid/rock systems.

Summary This paper focuses on an automated way to generate multiple history-matched reservoir models with the inclusion of both geological uncertainty and varying levels of trust in the production data, using wavelet methods. As opposed to previously developed automated history-matching algorithms, this methodology not only ensures geological consistency in the final models but also includes uncertainty in the production data. A data distribution, such as a permeability field, can be (reversibly) transformed into wavelet space in which it is fully described by a set of wavelet coefficients. It was found that different subsets of the collection of wavelet coefficients can be constrained separately to (a) the production history and (b) the geological constraints. This means that the history match need be performed only once, after which multiple realizations can be generated by adjusting only the second subset of coefficients. The ability to include both geological and production-data uncertainty into the reservoir model automatically is of great consequence to reservoir modeling and, hence, to reservoir management, risk analysis, and making key economic decisions. A more complete and realistic reservoir model will lead to better reservoir production and development decisions. Introduction Reservoir modeling is an important step in forecasting the performance of a reservoir, forming the basis for reservoir management, risk analysis, and making key economic decisions. A history match, however, is not a sufficient condition for a reservoir to make better predictions for future production. The model should at least conform to all the available data and the geologist's prior conception of the reservoir. Thus, the purpose of reservoir modeling is to use all available sources of information to develop such a reservoir model. This model then can be used to forecast future performance and optimize reservoir-management decisions. It is essential to integrate all the different sources of data to provide the most complete reservoir model or models (Landa and Horne 1997; Landa 1997; Wang 2001). Our model certainty is always limited by the data available to us. As such, it is never possible to infer or develop a reservoir model with full certainty. However, the optimal use of all consistent data available will yield reservoir models that are less and less uncertain. Herein lies the significance of methodologies that can realistically and efficiently integrate different sources of reservoir information. Reservoir data are, generally speaking, divided into two categories: production data (e.g., pressure and water-cut histories from wells) and all other sources of data (e.g., core samples, seismic, and well logs). This second category of data depends on reservoir properties like porosity and permeability in a relatively direct way. Core samples can be used to provide porosity and permeability measurements at specific locations (well locations); semivariograms (Deutsch and Journel 1998; Isaaks and Srivastava 1989) obtained from outcrops, for example, act as spatial statistics information, and seismic surveys may provide 3D impedance distributions that can be inverted and used as "soft-conditioning data" at the corresponding locations. These different sources of data can be combined together with different approaches (e.g., Bayesian probability techniques) to give a single set of probabilities.

Summary Well-placement decisions made during the early stages of exploration and development activities have the capability to improve later placement decisions by providing more information (greater certainty). Therefore, recovery and efficient use of information may add value beyond the amount of oil recovered. This study proposes an approach that emphasizes the value of time-dependent information to achieve better decisions in terms of reduced uncertainty and increased probable net present value (NPV). Unlike previous approaches, well-placement optimization is coupled with recursive probabilistic history-matching steps through the use of the pseudohistory concept. The pseudohistory is defined as the probable (future) response of the reservoir that is generated by a probabilistic forecasting model. To test the results of the proposed approach, an example reservoir was investigated with multiple realizations, all of which match the same production history. The results of this study showed that subsequent well-placement decisions can be improved when probabilistic production profiles obtained from the wells, as they are drilled, are incorporated in the optimization scheme.

Capillary pressure curves of The Geysers rocks have unique features because of their microfractures. The frequently used Brooks–Corey (1964) model does not match these capillary pressure curves. It would be useful to represent these curves mathematically, to provide a model for use in reservoir performance calculations. A general model developed from fractal modeling of a porous medium was applied and found to match the capillary pressure curves of The Geysers rocks satisfactorily. Capillary pressures were measured using a mercury intrusion technique. The values of fractal dimension, which is a representation of rock heterogeneity, were inferred from the match of the general capillary pressure model to the experimental data. The results demonstrate that the heterogeneity of The Geysers rocks can be determined quantitatively using the values of fractal dimension.

Summary Decline-curve-analysis models are used frequently but still have many limitations. Approaches of decline-curve analysis used for naturally fractured reservoirs developed by waterflooding have been few. To this end, a decline-analysis model derived on the basis of fluid-flow mechanisms was proposed and used to analyze the oil-production data from naturally fractured reservoirs developed by waterflooding. Relative permeability and capillary pressure were included in this model. The model reveals a linear relationship between the oil-production rate and the reciprocal of the oil recovery or the accumulated oil production. We applied the model to the oil-production data from different types of reservoirs and found a linear relationship between the production rate and the reciprocal of the oil recovery as foreseen by the model, especially at the late period of production. The values of maximum oil recovery for the example reservoirs were evaluated with the parameters determined from the linear relationship. An analytical oil-recovery model was also proposed. The results showed that the analytical model could match the oil-production data satisfactorily. We also demonstrated that the frequently used nonlinear type curves could be transformed to linear relationships in a log-log plot. This may facilitate the production-decline analysis. Finally, the analytical model was compared with conventional models.

SummaryIt is well documented that history matching is a problem with possibly nonunique solutions. In the past few years, several automated or semiautomated history-matching algorithms have been proposed. Depending on the algorithm used, it is possible that the final estimated reservoir-property distribution that allows for a good history match may not be geologically realistic. Therefore, there is a need to include other constraints to generate multiple, geologically realistic history-matched realizations. These constraints might, for example, include the variogram, a training image, the distribution of net-to-gross, pore volume, or other geostatistical information about the reservoir. This inclusion is particularly useful because it introduces uncertainty information in the reservoir description when we have limited history from existing wells in the field and intend to drill infill wells or implement a secondary-recovery process.The algorithm proposed in this paper uses multiresolution wavelet analysis to integrate history data with the geostatistical information contained in the variogram proposed for the reservoir. Wavelets allow the representation and manipulation of property distributions at various resolutions at the same time. Using wavelets, information from different sources such as production history and seismic surveys (that would be at different resolutions) can be incorporated directly at the appropriate resolution level. In the first step, we fix the wavelet coefficients sensitive to the history-match data. This has the effect of fixing the field history without fixing individual gridblock properties. In the second step, the remaining free wavelet coefficients are modified to integrate variogram information into the reservoir description. Generating multiple realizations of only the second set of wavelets coefficients results in multiple history-matched, variogram-constrained descriptions of the reservoir. The computational investment is very modest because the history match is done only once.In a number of example cases, different areal Gaussian fields with varying amounts of available production-history data were studied to test the algorithm. It was found that the wavelet coefficients constraining the history can be decoupled from those constraining the variogram. The implication of this observation is that the history data and variogram can be integrated sequentially into the reservoir model—that is, after the initial history match, new information can be added to the model without disturbing the original match to yield multiple history-matched and geostatistically constrained realizations.

Summary Gas slippage in single-phase gas flow (the Klinkenberg effect) has been investigated extensively. Few papers, however, have been published on the gas slippage in gas/liquid two-phase flow. The gas relative permeabilities at water saturations close to the residual value have been found to be significantly greater than 1 in both nitrogen/water and steam/water flow through rocks. These values became less than 1 after the calculation was calibrated by taking the two-phase gas slip effect into consideration. The gas relative permeabilities have been measured at different mean pore pressures, and the values of two-phase gas slip factors have been computed at different water saturations. The effects of temperature on both nitrogen and steam slip factors also have been studied and compared. These data have then been used to conduct a calibration to obtain intrinsic gas relative permeabilities that do not vary with the test pressures. It has been found from the present work that neglecting the two-phase gas slip effect may overestimate gas relative permeabilities. It is the intrinsic gas relative permeabilities instead of those measured at low test pressures that should be used in numerical simulation or other reservoir-engineering calculations.

Summary A method was developed to scale the experimental data of spontaneous water imbibition (cocurrent) for gas/water/rock systems. In this method, a dimensionless time was defined with the effects of relative permeability, wettability, and gravity included. The definition was not empirical but based on a theoretical derivation. Using this dimensionless time, experimental data from spontaneous water imbibition in different rocks with different size, porosity, permeability, initial water saturation, interfacial tension, and wettability might be scaled. The scaling model proposed in this study for gas/water/rock systems was verified experimentally for different rocks (Berea, chalk, and graywacke from The Geysers) with significantly different properties; it was also verified experimentally at different initial water saturations in the same rock. The scaling results from this study demonstrated that the cocurrent spontaneous water imbibition in gas/water/rock systems could be scaled and predicted.

Summary Determining the best location for new wells is a complex problem that depends on reservoir and fluid properties, well and surface-equipment specifications, and economic criteria. Numerical simulation is often the most appropriate tool to evaluate the feasibility of well configurations. However, because the data used to establish numerical models have uncertainty, so do the model forecasts. The uncertainties in the model reflect themselves in the uncertainties of the outcomes of well-configuration decisions. We never possess the true and deterministic information about the reservoir, but we may have geostatistical realizations of the truth constructed from the information available. An approach that can translate the uncertainty in the data to uncertainty in the well-placement decision in terms of monetary value was developed in this study. The uncertainties associated with well placement were addressed within the utility-theory framework using numerical simulation as the evaluation tool. The methodology was evaluated by use of the Production forecasting with UNcertainty Quantification (PUNQ)-S3 model, which is a standard test case that was based on a real field. Experiments were carried out on 23 history-matched realizations, and a truth case was also available. The results were verified by comparison to exhaustive simulations. Utility theory not only offered the framework to quantify the influence of uncertainties in the reservoir description in terms of monetary value, but it also provided the tools to quantify the otherwise arbitrary notion of the risk attitude of the decision maker. A hybrid genetic algorithm (HGA) was used for optimization. In addition, a computationally cheaper alternative was also investigated. The well-placement problem was formulated as the optimization of a random function. The genetic algorithm (GA) was used as the optimization tool. Each time a well configuration was to be evaluated, a different realization of the reservoir properties was selected randomly from the set of realizations, all of which honored the geologic and dynamic data available from the reservoir. Numerical simulation was then carried out with this randomly selected realization to calculate the objective function value. This approach has the potential to incorporate the risk attitudes of the decision maker and was observed to be approximate but computationally feasible.

Summary Technological achievements in the area of well testing, such as permanent downhole gauges, demand automated techniques to cope with the large amounts of data acquired. In such an application, the need to interpret large quantities of data with little human intervention suggests the desirability of automated model recognition. Also, in some cases, the characteristic behavior of the pressure or its derivative curves for specific models may be hidden behind noise, or human bias may lead to the selection of an invalid or inappropriate model. This paper demonstrates an approach based on a genetic algorithm (GA) that is able to select the most probable reservoir model from among a set of candidate models, consistent with a given set of pressure-transient data. The type of reservoir model to be used is defined as a variable and is estimated together with the other unknown model parameters (permeability, skin, etc.). Several reservoir models are used simultaneously in the regression process. GA populations consist of individuals that represent parameters for different models. As the GA iterates, individuals that belong to the most likely reservoir model dominate the population, while less likely models become extinct. Because different models may require different numbers of parameters, the solution vectors have varying lengths. The GA is able to cope with such solution vectors of differing size. Information exchange (GA crossover operator) is allowed only between parameters that are physically related. Alternatively, we illustrate the use of the GA as a preprocessor for conventional gradient-based algorithms such as Levenberg-Marquardt.1 When combined with the GA, the dependency of such conventional algorithms on the initial guess is reduced, and the overall regression performance is improved. For automated interpretations in which the model is already known, this method allows us to eliminate the initial guess-determination step. Tests on real and synthetic pressure-transient data indicated that the proposed method was able to select the correct reservoir model. The method revealed hidden implications of the pressure transient that may otherwise have been overlooked because of noise. As a preprocessor for more conventional nonlinear regression approaches, applying the GA to a number of noisy pressure-transient tests demonstrated that the method is robust and efficient.

Summary Long-term data from permanent gauges have the potential to provide more information about a reservoir than data from traditional pressure-transient tests that last for a relatively small duration. Besides reducing ambiguity and uncertainties in the interpretation, long-term data also provide an insight on how reservoir properties may change as the reservoir is produced. This study developed a multistep procedure for the processing and interpretation of long-term pressure data. The procedure was tested with several sets of simulated and actual field data. It was found to be an effective approach for the analysis of long-term pressure data from permanent gauges.

Production from the gas-condensate window of the liquid-rich shale plays in the US such as Barnett, Marcellus and Eagle Ford, has increased during the past few years. However, there is still a lack of understanding of the flow behavior of gas-condensate in liquid-rich shales when the flowing bottom-hole pressure falls below the dew-point pressure. Condensate dropout below the dew-point pressure leads to variation in the composition of vapor and liquid hydrocarbons. The phase behavior prediction is further complicated by the nanometer-sized pores of the shale formations where fluid-rock interaction could be different than in conventional reservoirs. This work investigated the compositional variation of gas-condensate during flow through Marcellus shale in laboratory coreflooding experiments. During the experiments, a gas-condensate mixture was injected into the core and during the flow, gas samples were collected through ports spaced along the core holder. Then, the gas samples were characterized using gas chromatography for compositional analysis. The results were compared to equivalent experiments in Berea sandstone. The gas-condensate sample used in the coreflooding experiment was collected from the Marcellus liquid-rich region and the experiments were conducted at reservoir pressure and temperature. Prior to conducting the experiments, the permeability of the Marcellus shale core and the Berea sandstone core were characterized using the pressure pulse decay technique and the Darcy flow technique; respectively. Results from this study showed that the gas composition varies along the direction of flow during depletion. The change in gas composition is due to the combination of condensate dropout and relative permeability effects. However, the magnitude of variation in the gas composition across the Marcellus shale core was less than that in the Berea sandstone core. This is an indication that the amount of condensate dropout varies between shale and sandstone for the same fluid system and at similar flowing conditions. Hence, the phase behavior is affected by the additional fluid-rock interaction expected for the shale due to flow through nanometer-sized pores.

Reservoir chloride concentration and injection rate data are used to examine injector-producer connectivity in two reservoirs, Dixie Valley, Nevada and Palinpinon-I, Philippines. General trends of chloride and injection rate with time are isolated from their respective short-term variations using the wavelet transformation approach. Multiple regression techniques are then used to correlate the isolated short-term variations in chloride with corresponding short-term fluctuations in injection rates and subsequently to quantify the degree of connectivity between injectors and producers. Communication between specific injector-producer pairs, as implied by analysis of data from Palinpinon-I, was also verified by comparison with tracer test data and qualitative field observations. Results of analysis of data from Dixie Valley demonstrate that multilinear modeling is not suitable for analyzing data sets that lack sufficient time variability. In contrast, adequate time variability is observed in data from Palinpinon-I, and qualitative field observations and tracer test data agreed best with the results of regression on changes in chloride concentration over four-month periods (wavelet detail level 3). Improvements in the analysis could result from increased data collection frequency of both chloride and injection rate as well as accounting for the nonlinearity of chloride with injection rate.

The modeling of a geothermal reservoir requires an in-depth understanding of the heat transfer process that causes the fluid flowing within a fracture to boil as heat is transferred to the fluid from the surrounding rock. One of the key parameters that describes this process is the boiling heat transfer coefficient. In this work, experiments were performed and a model based on the experiments was developed in order to quantify the heat transfer coefficient. In the process, it was also determined that flow in fractures may be described using linear relative permeability functions.

Summary In this paper we present a method to integrate well test, production, shut-in pressure, log, core, and geological data to obtain a reservoir description for the Pagerungan field, offshore Indonesia. The method computes spatial distributions of permeability and porosity and generates a pressure response for comparison to field data. This technique produced a good match with well-test data from three wells and seven shut-in pressures. The permeability and porosity distributions also provide a reasonable explanation of the observed effects of a nearby aquifer on individual wells. As a final step, the method is compared to an alternate technique (object modeling) that models the reservoir as a two-dimensional channel.