Interpretation models and charts of production profiles in horizontal wells

Stratified flow is common for the gravity segregation and flow regimes are very complex because of borehole inclination, therefore, all the conventional production logging tools cannot be effectively applied in horizontal wells, thus significantly increasing the difficulties in log interpretation. In this paper, firstly, the overseas progress in updated integration tools for horizontal wells and production profile interpretation methods has been discussed in brief. Secondly, by means of theory study and experimental simulations, we have obtained the production profile interpretation model and experimental interpretation charts, which have been calibrated by the improved downhole technology and optimization methods. Finally, we have interpreted X-well with the production profile interpretation software designed by us, and it proves that the methods are useful for the production profile interpretation in horizontal wells.     

A STRATIGRAPHIC CASE HISTORY USING THREE-DIMENSIONAL SEISMIC DATA IN THE GULF OF THAILAND *

A three-dimensional marine seismic survey was conducted in the Gulf of Thailand to aid in the development of a gas field indicated by three wildcat wells. The results and interpretation reported previously demonstrated improved fault resolution and better structural definition. Five successful appraisal wells have now been drilled, and these show that most of the sands have limited extent. Widespread character changes in the seismic data also support stratigraphic variations in many of the sands. Several new methods of 3D stratigraphic interpretation have been developed while investigating the depositional history of this area. Anomalous seismic amplitudes, tied to sands penetrated by wells and mapped from Seiscrop^TM horizontal sections in time and depth, have indicated the distribution of bars and channels. Horizon Seiscrop sections, each sliced through a single bed, have been used to delineate these depositional features directly. G-LOG^TM sections, displaying seismic logs derived by rigorous wave equation inversion, confirm the existence of these features. Sands greater than 10 m thick have proved mappable.     

UNSTEADY MOVEMENT OF FRESH WATER IN THICK UNCONFINED SALINE AQUIFERS

Abstract

Fresh-water lenses are formed in unconfined saline aquifers in response to deep percolation from rainfall, artificial recharge, and seepage from irrigation waters and/or in response to injecting fresh water through vertical or horizontal wells. An approximate differential equation is derived in terms of the depth of the fresh-salt water interface below the initial position of the saline-water table. This equation is analogous to that of the ground-water motion in two dimensions. The wealth of knowledge available from solving the latter equation is used to obtain approximate expressions for the movement of the fresh-salt water interface in several flow systems wherein this interface does not reach the bottom of the aquifer. These approximate solutions as well as others for related quantities of interest may afford useful tools for rationally planning the extraction of usable waters from such flow systems.     

A method for evaluating horizontal well pumping tests

Predicting the future performance of horizontal wells under varying pumping conditions requires estimates of basic aquifer parameters, notably transmissivity and storativity. For vertical wells, there are well-established methods for estimating these parameters, typically based on either the recovery from induced head changes in a well or from the head response in observation wells to pumping in a test well. Comparable aquifer parameter estimation methods for horizontal wells have not been presented in the ground water literature. Formation parameter estimation methods based on measurements of pressure in horizontal wells have been presented in the petroleum industry literature, but these methods have limited applicability for ground water evaluation and are based on pressure measurements in only the horizontal well borehole, rather than in observation wells. This paper presents a simple and versatile method by which pumping test procedures developed for vertical wells can be applied to horizontal well pumping tests. The method presented here uses the principle of superposition to represent the horizontal well as a series of partially penetrating vertical wells. This concept is used to estimate a distance from an observation well at which a vertical well that has the same total pumping rate as the horizontal well will produce the same drawdown as the horizontal well. This equivalent distance may then be associated with an observation well for use in pumping test algorithms and type curves developed for vertical wells. The method is shown to produce good results for confined aquifers and unconfined aquifers in the absence of delayed yield response. For unconfined aquifers, the presence of delayed yield response increases the method error.     

Estimation of water velocities in boreholes using a new passive flowmeter

Abstract

Preferential flow pathways in a fractured aquifer may yield abrupt reductions of the water velocity in a well. We propose a new device for measuring low (5–13 cm d^-1) velocities in wells originating from fractures at different depths. The presented flowmeter has been applied in a well in the Bari (southern Italy) fractured aquifer. In the same well, the horizontal flowmeter velocity (9.6 cm d^-1) at 0.5 m depth was compared with velocity (8 cm d^-1) derived from a field tracer test, providing a value 16.5% higher. Moreover, the flowmeter measurements at 1.5 m depth gave a horizontal velocity of 7.2 cm d^-1, which is 11% less than water flow velocity estimated from the field test. The new flowmeter implements the tracer point-dilution method in a plastic (PVC) pipe by causing the water flow to pass through an artificial filter. Laboratory calibration tests have confirmed the good performance of the proposed flowmeter technique, even for water flow up to 300 cm d^-1. The flowmeter was sensitive to 0.1 cm d^-1, with a detection limit of 1.5 cm d^-1, i.e. half the measurable flow velocity of existing flowmeters in wells.

Editor D. Koutsoyiannis; Associate editor S. Grimaldi     

Predicting Collector Well Yields with MODFLOW

Groundwater flow models are commonly used to design new wells and wellfields. As the spatial scale of the problem is large and much local‐scale detail is not needed, modelers often utilize two‐dimensional (2D) or quasi three‐dimensional models based on the Dupuit‐Forchheimer assumption. Dupuit models offer a robust set of tools for simulating regional groundwater flow including interactions with surface waters, the potential for well interference, and varying aquifer properties and recharge rates. However, given an assumed operating water level or drawdown at a well screen, Dupuit models systematically overpredict well yields. For design purposes, this discrepancy is unacceptable, and a method for predicting accurate well yields is needed. While published methods exist for vertical wells, little guidance is available for predicting yields in horizontal screens or collector wells. In plan view, a horizontal screen has a linear geometry, and will likely extend over several neighboring cells that may not align with rows or columns in a numerical model. Furthermore, the model must account for the effects of converging three‐dimensional (3D) flow to the well screens and hydraulic interference among the well screens; these all depend on the design of a specific well. This paper presents a new method for simulating the yield of angled or horizontal well screens in numerical groundwater flow models, specifically using the USGS code MODFLOW. The new method is compared to a detailed, 3D analytic element model of a collector well in a field of uniform flow.     

MAPPING AND INTERPRETATION OF FIELD PHENOMENA FOR GROUNDWATER RECONNAISSANCE IN A PRAIRIE ENVIRONMENT,ALBERTA, CANADA

ABSTRACT

Theoretically, a small drainage basin may be divided into equal areas of downward flow and upward flow of groundwater. In regions where surface water does not obscure the phenomena produced by groundwater, these areas can be differentiated by mapping springs, seepages, groundwater levels, flowing wells, chemical quality of water, natural vegetation, salt precipitates, quality of crops, soap holes, and moist and dry depressions.

Mapping and interpretation of field phenomena have been carried out in a section of the Ghostpine Creek valley in a Prairie environment. The relief is gently rolling, the geology is simple, and the climate is cold, humid, and continental. The area of the “north flow-systems” is apportioned as follows: 26 per cent underlain by downward flow; 42 per cent underlain by a mid-line area; and 32 per cent underlain by upward flow.

Noting that groundwater flow is nearly parallel to the water table in the vicinity of the mid-line these results comply with the above-mentioned theory of groundwater flow distribution in small drainage basins. Thus, the method is suggested for: 1. A reconnaissance study of the groundwater regime in certain areas, and 2. Specific problems related to groundwater in a Prairie environment, such as: finding suitable locations for dug-out type water supplies, estimating prospects for slough-draining and irrigation, and explanation of the development of certain soil types. For such purposes, the method appears to be competitive with test drilling.     

Evidence for extreme variations in the permeability of laterite from a detailed analysis of well behaviour in Nigeria

Laterite soils are widespread in tropical Africa and have a large impact on the hydrology of the areas they cover. The permeability of laterite helps determine the partitioning of runoff and interflow and regulates groundwater recharge to underlying bedrock. Groundwater within laterite also forms a widespread source of drinking water, typically from unimproved hang‐dug‐wells. Despite its importance, there is little published information on laterite aquifer properties. In this study, data from a 6 m deep well in Nigeria have been analysed to characterise the hydraulic conductivity of the laterite from repeated pumping tests. Transmissivity measurements from 40 tests spread out across a hydrological year varied from 0.1 to 1000 m²/d. Further interpretation of the data demonstrate a strong non‐linear decrease in horizontal hydraulic conductivity with depth, characterised by an upper horizon of extreme permeability (400 m/d), and a much lower permeability profile beneath (<0.1 m/d). These data are substantiated with observations from other wells throughout the area. This non‐linear permeability structure has several implications: the upper laterite can facilitate rapid lateral throughflow in the wet season, enabling contaminants to be transported significant distances (up to 1 km); natural groundwater levels are restricted to a narrow range for much of the year; and, in the dry season, the lower permeability of the deeper laterite restricts the amount of water which can be abstracted from shallow wells, leading to well failure. The work highlights the need for a wider study to better understand laterite soils and the role they play in regional hydrology. © 2013 Natural Environment Research Council. Hydrological Processes published by John Wiley & Sons Ltd.     

Recent advances in modeling of well hydraulics

Well hydraulics is a discipline to understand the process of flow to the well in an aquifer which is regarded as a source of groundwater. A variety of analytical and numerical models have been developed over the last few decades to provide a framework for understanding and quantifying the flow behavior in aquifer systems. In this review, we first briefly introduce the background of the theory of well hydraulics and the concepts, methodologies, and applications of analytical, semi-analytical, numerical and approximate methods in solving the well-hydraulic problems. We then address the subjects of current interests such as the incorporation of effects of finite well radius, wellbore storage, well partial penetration, and the presence of skin into various practical problems of groundwater flow. Furthermore, we also summarize recent developments of flow modeling such as the flow in aquifers with horizontal wells or collector wells, the capture zone delineation, and the non-Darcian flow in porous media and fractured formations. Finally, we present a comprehensive review on the numerical calculations for five well functions frequently appearing in well-hydraulic literature and suggest some topics in groundwater flow for future research.     

Geostatistics applied to cross-well reflection seismic for imaging carbonate aquifers

Cross-well seismic reflection data, acquired from a carbonate aquifer at Port Mayaca test site near the eastern boundary of Lake Okeechobee in Martin County, Florida, are used to delineate flow units in the region intercepted by two wells. The interwell impedance determined by inversion from the seismic reflection data allows us to visualize the major boundaries between the hydraulic units. The hydraulic (flow) unit properties are based on the integration of well logs and the carbonate structure, which consists of isolated vuggy carbonate units and interconnected vug systems within the carbonate matrix. The vuggy and matrix porosity logs based on Formation Micro-Imager (FMI) data provide information about highly permeable conduits at well locations. The integration of the inverted impedance and well logs using geostatistics helps us to assess the resolution of the cross-well seismic method for detecting conduits and to determine whether these conduits are continuous or discontinuous between wells. A productive water zone of the aquifer outlined by the well logs was selected for analysis and interpretation. The ELAN (Elemental Log Analysis) porosity from two wells was selected as primary data and the reflection seismic-based impedance as secondary data. The direct and cross variograms along the vertical wells capture nested structures associated with periodic carbonate units, which correspond to connected flow units between the wells. Alternatively, the horizontal variogram of impedance (secondary data) provides scale lengths that correspond to irregular boundary shapes of flow units. The ELAN porosity image obtained by cokriging exhibits three similar flow units at different depths. These units are thin conduits developed in the first well and, at about the middle of the interwell separation region, these conduits connect to thicker flow units that are intercepted by the second well. In addition, a high impedance zone (low porosity) at a depth of about 275 m, after being converted to ELAN porosity, is characterized as a more confined low porosity structure. This continuous zone corresponds to a permeability barrier in the carbonate aquifer that separates the three connected conduits observed in the cokriging image. In the zones above and below this permeability barrier, the water production is very high, which agrees with water well observations at the Port Mayaca aquifer.     

Estimation of the inland extending length of the freshwater–saltwater interface in coastal unconfined aquifers

ABSTRACT

The inland extending length of the freshwater–saltwater interface toe is useful in studies of seawater intrusion in coastal areas. The submarine fresh groundwater discharge in coastal zones is affected not only by hydraulic conductivity and hydraulic gradient of the aquifer, but also by the position of the interface. Two observation wells at different distances from the coast are required to calculate the fresh groundwater flow rate in coastal unconfined aquifers. By considering that the submarine groundwater discharge is equal to the groundwater flow rate, the length of the interface toe extending inland can be estimated when the groundwater flow is at a steady-flow state. Aquifers with horizontal and sloping confined beds and without/with unique surface vertical infiltration are considered. Examples used to illustrate the application of these methods indicate that the inland extending lengths of the interface toe in aquifers with vertical surface infiltration are much shorter than those in aquifers without vertical surface infiltration, and the length of the interface in aquifers with a horizontal confining lower bed are smaller than those in aquifers with a confining lower bed sloping towards the sea. The extent of the interface on the northwestern coast near the city of Beihai in southern Guangxi, China, on 18 January 2013 was estimated as 471–478 m.

Editor M.C. Acreman Associate editor not assigned     

The role of science in setting water resource use limits: case studies from New Zealand

Abstract

Water resource use limits ensure protection of environmental values and define the availability and reliability of water supply for out-of-channel use. We examined how three types of scientific tools (environmental flow setting methods, hydrological analyses for setting total allocations and spatial frameworks) have been used to define limits across jurisdictional regions comprising multiple catchments in New Zealand. We found that recently developed minimum flow and total allocation setting tools are widely used. Spatial frameworks are increasingly used to discriminate and account for variation in environmental characteristics, thereby increasing the specificity of water resource use limits. The uptake of scientific tools has enabled improvements in the clarity of water management objectives and the transparency of limits defined by regional water management plans. We argue that more integrated use of scientific tools could improve the clarity and transparency of regional limits by explicitly demonstrating the trade-off between out-of-channel use and protection of environmental values.

Editor D. Koutsoyiannis; Guest editor M. Acreman

Citation Snelder, T.H., Rouse, H.L., Franklin, P.A., Booker, D.J., Norton, N., and Diettrich, J., 2014. The role of science in setting water resource use limits: case studies from New Zealand. Hydrological Sciences Journal, 59 (3–4), 844–859.     

Flow of reinjected water and transmissibility distribution estimated by a tracer test in Otake Geothermal Reservoir, Japan

In order to estimate the distribution of pressure and transmissibility in the Otake Geothermal Reservoir, in which flow can be assumed to be two-dimensional and horizontal, well-head pressure and flow rates measured at both production and reinjection wells, and the time required for a tracer to arrive at certain production wells from one of the reinjection wells were analyzed. Analysis of these data was performed by means of an equation which was obtained by combining the Darcy and the continuity equations, in which the transmissibility and two components of the flow remain unknown. Estimation of pressure and transmissibility distributions and flow patterns within the reservoir was possible by numerical solution of this equation using the finite-difference method and by assuming suitable boundary conditions.     

Study on the simulation of acoustic logging measurements in horizontal and deviated wells

The conventional acoustic logging interpretation method, which is based on vertical wells that penetrate isotropic formations, is not suitable for horizontal and deviated wells penetrating anisotropic formations. This unsuitability is because during horizontal and deviated well drilling, cuttings will splash on the well wall or fall into the borehole bottom and form a thin bed of cuttings. In addition, the high velocity layers at different depths and intrinsic anisotropy may affect acoustic logging measurements. In this study, we examine how these factors affect the acoustic wave slowness measured in horizontal and deviated wells that are surrounded by an anisotropic medium using numerical simulation. We use the staggered-grid finite difference method in time domain (FDTD) combined with hybrid-PML. First, we acquire the acoustic slowness using a simulated array logging system, and then, we analyze how various factors affect acoustic slowness measurements and the differences between the effects of these factors. The factors considered are high-velocity layers, thin beds of cuttings, dipping angle, formation thickness, and anisotropy. The simulation results show that these factors affect acoustic wave slowness measurements differently. We observe that when the wavelength is much smaller than the distance between the borehole wall and high velocity layer, the true slowness of the formation could be acquired. When the wavelengths are of the same order (i.e., in the near-field scenarios), the geometrical acoustics theory is no longer applicable. Furthermore, when a thin bed of cuttings exists at the bottom of the borehole, Fermat's principle is still applicable, and true slowness can be acquired. In anisotropic formations, the measured slowness changes with increments in the dipping angle. Finally, for a measurement system with specific spacing, the slowness of a thin target layer can be acquired when the distance covered by the logging tool is sufficiently long. Based on systematical simulations with different dipping angles and anisotropy in homogenous TI media, slowness estimation charts are established to quantitatively determine the slowness at any dipping angle and for any value of the anisotropic ratio. Synthetic examples with different acoustic logging tools and different elastic parameters demonstrate that the acoustic slowness estimation method can be conveniently applied to horizontal and deviated wells in TI formations with high accuracy.     

Geothermal gradients and heat flow in the Beaufort-Mackenzie Basin,Arctic Canada

Thermal gradients have been calculated and heat flow estimates made for 34 petroleum exploration wells along four regional profiles crossing the Mesozoic-Cenozoic Beaufort-Mackenzie Basin of northern Canada. The geothermal gradients vary from 22 mKm^–1 to 44 mKm^–1. Four sets of possible thermal conductivity values were used to calculate a range of heat flow values for each well. Generally low heat flow is observed in wells within the deeper portions of the basin and higher heat flow values occur in wells along the Aklavik Arch Complex which forms the southeastern margin of the basin.The contribution to heat flow by heat generation below the Mesozoic-Cenozoic basin fill sediments has been considered. The heat flow contribution from sub-Mesozoic sedimentary strata and underlying basement is highest along the basin-bounding Aklavik Arch Complex. The decrease in heat flow from below the basin fill sediments toward the basin depocenter may be related to basinward crustal thinning and corresponding reductions in intra-crustal radiogenic heat production.     

COMPARISON OF CORE ANALYSIS AND DRAWDOWN-TEST RESULTS FROM A WATER-BEARING UPPER PENNSYLVANIAN SANDSTONE OF CENTRAL OKLAHOMA / Comparaison de l'analyse d'échantillons et des résultats de rabattements pour une couche perméable de grès du Pensylvanien Supérieur dans l'Oklahoma Central

Abstract

Drawdown-test data from a brine-saturated consolidated sandstone reservoir in central Oklahoma show that permeability can be determined accurately from laboratory measurement of small core samples. Such confirmation is significant because permeability values determined by core analyses are frequently considered not representative, at least quantitatively, of reservoir conditions. Yet such analyses are often the only way to obtain the permeability value necessary to predict the performance of a reservoir.

The field value for permeability was computed by applying the Theis typecurve solution of the non-equilibrium formula to drawdown data from 64 wells in an 8-acre area surrounding a single discharging well. The laboratory value was based on complete cores from 39 of these wells. For objective analysis, the gross reservoir thickness was defined as that entire interval in which flow was confiined, regardless of the permeability of the included rock strata. This thickness was measured directly from the cores. Each plug was saturated with reservoir water and permeability was measured with a constant-head discharging apparatus.

Both laboratory and drawdown-test methods show the reservoir to have a permeability of about 0.4 darcy and a mean transmissibility (permeability x thickness) of about 3.4 darcy-ft.     

INTERPRETATION OF THE GRAVITY ANOMALY OVER A CAUSATIVE BODY WITH CIRCULAR SYMMETRY*

The interpretation of the gravity anomaly on a horizontal plane over a causative body having circular symmetry about a vertical axis is considered from a rather unconventional approach. As the analytical expression for the gravity effect of a circular body assumes a closed form only on the axis of symmetry, the interpretation in this approach is carried out with the anomaly profile along the axis—which leads to simpler and faster computation. A numerical method is developed for computation of the anomaly profile along the vertical axis from the horizontal radial profile of the symmetric anomaly by upward continuation. Provision is also made for an end correction when the radial profile has only a limited extension. Some simple geometrical shapes are assumed for the causative body. Its parameters are then determined from least squares fitting of its gravity effects to the observed (upward continued) vertical profile (i) by the steepest descent method and (ii) by the Newton-Raphson method. Some applications of these methods are demonstrated.     

Modeling Flow into Horizontal Wells in a Dupuit-Forchheimer Model

Horizontal wells or radial collector wells are used in shallow aquifers to enhance water withdrawal rates. Groundwater flow patterns near these wells are three-dimensional (3D), but difficult to represent in a 3D numerical model because of the high degree of grid refinement needed. However, for the purpose of designing water withdrawal systems, it is sufficient to obtain the correct production rate of these wells for a given drawdown. We developed a Cauchy boundary condition along a horizontal well in a Dupuit-Forchheimer model. Such a steady-state 2D model is not only useful for predicting groundwater withdrawal rates but also for capture zone delineation in the context of source water protection. A comparison of our Dupuit-Forchheimer model for a radial collector well with a 3D model yields a nearly exact production rate. Particular attention is given to horizontal wells that extend underneath a river. A comparison of our approach with a 3D solution for this case yields satisfactory results, at least for moderate-to-large river bottom resistances.     

A Finite Layer Formulation for Groundwater Flow to Horizontal Wells

A finite layer approach for the general problem of three‐dimensional (3D) flow to horizontal wells in multilayered aquifer systems is presented, in which the unconfined flow can be taken into account. The flow is approximated by an integration of the standard finite element method in vertical direction and the analytical techniques in the other spatial directions. Because only the vertical discretization is involved, the horizontal wells can be completely contained in one specific nodal plane without discretization. Moreover, due to the analytical eigenfunctions introduced in the formulation, the weighted residual equations can be decoupled, and the formulas for the global matrices and flow vector corresponding to horizontal wells can be obtained explicitly. Consequently, the bandwidth of the global matrices and computational cost rising from 3D analysis can be significantly reduced. Two comparisons to the existing solutions are made to verify the validity of the formulation, including transient flow to horizontal wells in confined and unconfined aquifers. Furthermore, an additional numerical application to horizontal wells in three‐layered systems is presented to demonstrate the applicability of the present method in modeling flow in more complex aquifer systems.     

Heat flow in the Ozark Plateau, Arkansas and Missouri: relationship to groundwater flow

Heat flow values were calculated from direct measurements of temperature and thermal conductivity at thirteen sites in the Arkansas-Missouri Ozark Plateau region. These thirteen values are augmented by 101 estimates of heat flow, based on thermal conductivity measurements and temperature gradients extrapolated from bottom-hole temperatures. The regional heat flow profile ranges from 9 mW m⁻² to over 80 mW m⁻², but at least two distinct thermal regimes have been identified. Seven new heat flow determinations are combined with three previously published values for the St. Francois Mountains (SFM), a Precambrian exposure of granitic and rhyolitic basement rocks, average 47 mW m⁻². Radioactive heat production of 76 samples of the exposed rocks in the SFM averages 2.4 μW m⁻² and a typical continental basement contribution of 14 mW m⁻² is implied. Conversely, the sedimentary rock sequence of the plateau is characterized by an anomalously low heat flow, averaging approximately 27 mW m⁻². Groundwater transmissivity values that are based on data from 153 wells in deep regional aquifers demonstrate an inverse relationship to the observed heat flow patterns. The areas of high transmissivity that correspond to areas of low total heat flux suggest that the non-conservative vertical heat flow within the Ozark sedimentary sequence can be attributed to the effects of groundwater flow.