Evolutoids of the Mixed-Type Curves

The evolutoid of a regular curve in the Lorentz-Minkowski plane ℝ 1 2 is the envelope of the lines between tangents and normals of the curve. It is regarded as the generalized caustic (evolute) of the curve. The evolutoid of a mixed-type curve has not been considered since the definition of the evolutoid at lightlike point can not be given naturally. In this paper, we devote ourselves to consider the evolutoids of the regular mixed-type curves in ℝ 1 2 . As the angle of lightlike vector and nonlightlike vector can not be defined, we introduce the evolutoids of the nonlightlike regular curves in ℝ 1 2 and give the conception of the σ -transform first. On this basis, we define the evolutoids of the regular mixed-type curves by using a lightcone frame. Then, we study when does the evolutoid of a mixed-type curve have singular points and discuss the relationship of the type of the points of the mixed-type curve and the type of the points of its evolutoid.

Novel Analytical Solution and Type-Curves for Lost-Circulation Diagnostics of Drilling Mud in Fractured Formation

Loss of circulation is a major problem that often causes interruption to drilling operations, and reduction in efficiency. This problem often occurs when the drilled wellbore encounters a high permeable formation such as faults or fractures, leading to total or partial leakage of the drilling fluids. In this work, we present a novel semi-analytical solution and type-curves that offer a quick and accurate diagnostic tool to assess the lost-circulation of Herschel-Bulkley fluids in fractured media. Based on the pressure and mud loss trends, the tool can estimate the effective fracture conductivity, the cumulative mud-loss volume, and the leakage period. The behavior of lost-circulation into fractured formation can be assessed using analytical methods that can be deployed to perform flow diagnostics, such as the rate of fluid leakage and the associated fracture hydraulic properties. In this study, we develop a new semi-analytical method to quantify the leakage of drilling fluid flow into fractures. The developed model is applicable for non-Newtonian fluids with exhibiting yield-power-law, including shear thickening and thinning, and Bingham plastic fluids. We propose new dimensionless groups and generate novel dual type-curves, which circumvent the non-uniqueness issues in trend matching of type-curves. We use numerical simulations based on finite-elements to verify the accuracy of the proposed solution, and compare it with existing analytical solutions from the literature. Based on the proposed semi-analytical solution, we propose new dimensionless groups and generate type-curves to describe the dimensionless mud-loss volume versus the dimensionless time. To address the non-uniqueness matching issue, we propose, for the first time, complimentary derivative-based type-curves. Both type-curve sets are used in a dual trend matching, which significantly reduced the non-uniqueness issue that is typically encountered in type-curves. We use data for lost circulation from a field case to show the applicability of the proposed method. We apply the semi-analytical solver, combined with Monte-Carlo simulations, to perform a sensitivity study to assess the uncertainty of various fluid and subsurface parameters, including the hydraulic property of the fracture and the probabilistic prediction of the rate of mud leakage into the formation. The proposed approach is based on a novel semi-analytical solution and type-curves to model the flow behavior of Herschel-Bulkley fluids into fractured reservoirs, which can be used as a quick diagnostic tool to evaluate lost-circulation in drilling operations.

A New Method to Identify and Quantify Hydraulic Communication between Isolated Reservoir Systems Using Pressure-Transient Data

A new analytical workflow that uses pressure-transient data to characterize connectivity between two originally non-communicating reservoir zones is presented. With this technique, hydraulic communication is clearly identified and corresponding fluid crossflow rates accurately quantified. It is applicable to a wide range of communication mechanisms, including inactive commingled-completion wells, conductive fractures and faults, in addition to behind-casing completion problems. The impact of interference is also captured by handling an unlimited number of wells and communicating media. The solution uses pressure-transient data effectively to diagnose communication and estimate the amount of transported fluids. The new formulation is a general formulation for handling an unlimited number of producing wells and communicating media, which helps analyze pressure responses under the influence of interference. The reservoir system under consideration is assumed to be two-dimensional with two initially-isolated reservoir zones, intersected by an arbitrary number of wells, part of which are active producers while others can be penetrating wells with commingled completion, in addition to other communicating media. The well test duration is assumed long enough for the pressure-transient data to be affected by fluid communication. To demonstrate the applicability of the new model, a synthetic case study is presented to diagnose a fluid-communication mechanism. The system under consideration consists of two isolated reservoirs and two wells: a single producer completed in the top reservoir in which pressure responses are measured, and an offset well connecting both reservoirs through a fluid communication mechanism. Using the model, type-curves have been utilized to diagnose the hydraulic communication in the offset well. The connectivity of the communication channel in the offset well is also estimated by matching the pressure-transient responses of the model with the measured data. The rate of crossflow between the two reservoirs is also quantified as a function of time. It is observed from the log-log plot that higher connectivity values of the cement sheath causes a steeper merging ramp in the transition region, following a period dominated by the producing reservoir. Although the rate of crossflow depends on the magnitude of the connectivity, it is observed that there is an upper limit controlled by the rock and fluid properties of the individual reservoirs. In addition, the pressure regime at the location of the offset well plays an important role in the rate of crossflow. This study presents a novel analytical approach to detect communication from pressure-transient data, and to quantify the magnitude of crossflow rates between reservoir zones. The formulation captures the influence of interference between wells caused by production. While complementing diagnostic information from other sources to confirm fluid movement from isolated zones, the method also quantifies the connectivity of the communicating media, and the amount of crossflow rates as a continuous function of time.

Annual Work Plan Execution Performance Using an Automated Production Forecast Tool

Shaya Consortium ramped up its production from 60 KBOPD to almost 85 KBOPD as a result of an agile execution of its Field Development Plan, made of infill drilling, workover interventions, and full-field expansion of waterflooding. This combined activity made the planning process very complex and dynamic due to the high volume of operations and scenario evaluation. Additionally, the consortium was requested to provide a weekly production forecast to its major stakeholders highlighting all deviations from the original execution plan and remedial activities to come back on track. The proposed application tool has simplified and automated the forecasting processes using short-term updates of the executed activities from field reports, current well status, planned workover interventions, and new wells drilling schedule. Any deviation of the Annual Work Plan due to schedule variance or well performance is automatically adjusted by the tool, creating a new forecast to End-Of-Year or Quarter even Weekly, thus, reflecting the impact on the estimated recoverable volumes. The tool pulls information from different sources and consolidates them in a single unified environment, not only for forecasting but also as a visualization and analysis tool. Furthermore, it has several modules to facilitate the control of official type curves, scenario profiles for the Annual Work Plan, and it is fully linked to key corporate applications. This paper presents the development of a production forecasting tool that introduced a new way of working within the Shaya Production Team by improving activity scheduling and overcome underperforming new wells, keeping the operations team informed to facilitate the production management.

Semi-analytical model of multiple fractured horizontal well across a discontinuity in a linear composite reservoir

Many geologic settings can be treated as linear composite (LC) reservoirs, where linear discontinuities divide the formation into multiple zones with different properties. Although there have been many studies on pressure behavior of production wells in an LC reservoir, most of the studies focus on vertical wells. The modeling of multiple fractured horizontal (MFH) wells in an LC reservoir remains limited. The goal of the present work is to propose a general semi-analytical model of an MFH well situated anywhere in a two-zone LC reservoir. This model can take into account the situation where the horizontal well intersects with the discontinuity and hydraulic fractures are distributed in both the two zones. According to the point-source function method, the semi-analytical solution for an MFH well in LC reservoirs is derived by using superposition principle, fracture discrete scheme and numerical inversion algorithm of Laplace transformation. Type curves of MFH wells far away from a discontinuity and across a discontinuity in an LC reservoir are drawn and analysed, respectively. Furthermore, the effects of some parameters on pressure behavior and rate response of an MFH well across a discontinuity are studied. This research finds that the pressure behavior and rate response of an MFH well across a discontinuity are significantly affected by the well location, properties of hydraulic fractures and formation properties.

Some new characterizations of a space curve due to a modified frame N⃗,C⃗,W⃗$\left\{ \overrightarrow {N},\; \overrightarrow {C},\; \overrightarrow {W}\right\}$ in Euclidean 3-space

In our paper, we computed some new characterizations due to an alternative modified frame N ⃗ , C ⃗ , W ⃗ $\left\{ \overrightarrow {N}, \overrightarrow {C}, \overrightarrow {W}\right\}$ in Euclidean 3-space and we get general differential equation characterizations of a space curve due to the vectors N ⃗ , C ⃗ , W ⃗ $ \overrightarrow {N}, \overrightarrow {C}, \overrightarrow {W}$ . Furthermore, we investigated some differential equations characterizations of the harmonic and harmonic 1-type curves.

Pedal Curves of the Mixed-Type Curves in the Lorentz-Minkowski Plane

In this paper, we consider the pedal curves of the mixed-type curves in the Lorentz–Minkowski plane R12. The pedal curve is always given by the pseudo-orthogonal projection of a fixed point on the tangent lines of the base curve. For a mixed-type curve, the pedal curve at lightlike points cannot always be defined. Herein, we investigate when the pedal curves of a mixed-type curve can be defined and define the pedal curves of the mixed-type curve using the lightcone frame. Then, we consider when the pedal curves of the mixed-type curve have singular points. We also investigate the relationship of the type of the points on the pedal curves and the type of the points on the base curve.

1-TYPE AND HARMONIC 1-TYPE TIMELIKE CURVES IN SEMI-EUCLIDEAN SPACE 42

In the present study we consider 1-type, biharmonic, weak biharmonic and harmonic 1-type curves in semi-Euclidean space 42R according to the timelike Frenet frame. We give some characterizations and classifications of these type curves.

Study on Mechanical Characteristics of Composite Alkali-activated Materials-stabilized Gold Tailings Under Direct Shear

In this study, the traditional industrial waste residue and some alkaline activators were mixed to prepare a new composite alkali-activated materials (CAAMs), which was used to stabilize gold mine tailings (GMTs). Due to emissions of greenhouse gases and solid dust, alkali-activated materials have been widely used to replace Portland cement to solidify geotechnical materials to enhance their mechanical properties. Different admixture of CAAMs (i.e., 0, 3, 5, 8% ) and gold mine tailings were prepared, and the samples were cured in saturated water and under no air conditions. In order to investigate the mechanical characteristics of CAAMs-stabilized GMTs, laboratory direct shear tests were carried out on samples after curing them for 3, 7, 14 and 28 days, respectively. The test results showed that as the curing periods increased, the brittleness of the samples increased, and the stress-displacement curves for all the cured specimens changed from plateau-type to peak-type curves. The curing periods and the content of CAAMs are both beneficial for enhancing the shear strength of CAAMs-stabilized GMTs samples, but the increase rate decreased as the vertical confining pressure increased. Furthermore, the influence of CAAMs content on shear strength increment was larger than that of curing periods. An exponential growth model could be well used to describe the change of shear strength with the curing periods at different vertical stresses.

Rate Transient Analysis of Heterogeneous Unconventional Gas Reservoir Using a Fractional Decline Model

In this study, an extended version of the fractional decline model is analytically developed for gas flow in fracture reservoir using the anomalous diffusion equation incorporated with the fractional calculus and equation of state. The model can represent the heterogeneity of complex fracture networks and can further be used to interpret reservoir properties by performing type-curve matching of flow rate and cumulative production from multi-fractured horizontal wells in unconventional reservoirs. To address the limitations of conventional planar fracture idealization, the hydraulic fractures in this present study are integrated with the fracture network, and the fractional diffusivity is solved for a horizontal wellbore. Upon establishing and solving the governing equation in the Laplace domain, the solutions are converted back to the real-time and space domain by performing numerical Laplace inversion. A set of distinctive type curves is generated on the basis of an infinite conductivity horizontal well model, considering early and middle times, in order to capture the heterogeneity of the fractal network in the reservoir model. Application of this new model is demonstrated through type-curve matching of two synthetic cases of simulation data obtained from commercial software; the cases cover orthogonal evenly and unevenly distributed networks. Results from these examples show an acceptable match between the fractional decline model and synthetic data and, hence, showcase the applicability of this model to capture the transient flow in heterogeneous fractured reservoirs.