Varying Production Rates Research Articles

Modeling, optimization and control of a ceramic tunnel kiln for consistent product quality under changing production demands

This study presents a detailed physics-based model focusing on an industrial tunnel kiln under feedback control. Initially, an empirical sintering model is integrated into the kiln model to accurately predict the product outlet density, a quality-defining parameter reflecting firing process efficacy. Afterwards, the initial steady-state burner valve positions are determined using industrial temperature data. Subsequently, the interactions between gas temperatures and burner valve positions are quantified through the investigation of the Relative Gain Array. A systematic derivation of optimal set-points for different production rates is then carried out, aiming at minimizing energy consumption while meeting end-product quality specifications. The PID controllers are tuned using a dynamic optimization approach, which involves the minimization of integral criteria. Finally, a case study is conducted to evaluate the efficacy of the optimal set-points under varying production rates. The results demonstrate exceptional system response, thus indicating that firing curves should adapt to production rates for consistently producing quality products.

Techno-Economic Analysis of Interesterification for Biodiesel Production

Interesterification is an alternative reaction for the production of fatty acid alkyl esters from triglycerides, a pathway that avoids unwanted byproduct formation. In this work, the technical and economic feasibility of soybean oil interesterification for biodiesel production on a commercial scale is assessed. The interesterification kinetics of triolein (model soybean oil) and methyl acetate using ferric sulfate as a heterogeneous acid catalyst are experimentally determined, and the results are used to parameterize a kinetic model. Process simulations are developed using Aspen Plus V11 for acid and alkaline heterogeneously catalyzed interesterification plants at varying production rates and methyl acetate-to-oil molar ratios (MAOMRs). At all production capacities and MAOMRs tested, the acid-catalyzed processes are found to have more favorable process energy consumption and profitability metrics compared to the alkaline-catalyzed processes. The most economically promising design operates at a production capacity of 30,000 metric tons/yr and an MAOMR of 10:1 with a net present value of $34 million after 20 years and a biodiesel breakeven price of $0.78/kg. This case has a process energy demand of 35,000 MJ/h, resulting in a process energy ratio of 0.25. This work indicates that interesterification shows commercial viability and is a promising alternative to transesterification for biodiesel production.

ISO 13909 compliant contractual payment station coal sampling plant: process design and equipment selection for chemical, physical and moisture sampling

The paper discusses the process design and mass balance highlights to illustrate the ISO 13909 compliance of a 4-year-running contractual payment station sampling plant. The plant is used to sample -60mm coal supply to a coal fired power station infrastructure belonging to the South African National Power Utility. Payment parameters are proximate analysis (Calorific Value, Ash-, Sulphur content), physical (size and abrasion index) and moisture content. Over and above ergonomic physical samples and timeous moisture samples, the plant also delivers the crushed chemical sample in triplicate for buyer-, seller- and referee analysis. The lot period was defined as 24 hours production while the system compliance was designed around mass-based sampling. Production varies over a wide range of throughout tonnages from 800-3600 ton/h as dictated by complex boiler and silo operational requirements. The plant required a unique operational philosophy to adapt the number of primary increments (and corresponding time interval) per sublot size to the varying production rates which over a fix lot period results in varying lot size. Furthermore, a contractual grade, calibrated, 6-idler belt scale is used to measure the instantaneous conveyor load which in turn controls the cutter speed via a programmable logic controller (PLC) prompted variable speed drive (VSD) setpoint to sample fixed increment mass to represent fixed production mass interval. The primary belt end crosscut sampler boasts a unique articulated joint design sample chute to fit down the high sample tract; eliminating the delineation errors associated with the previous competitor design.

Modeling Ground Firefighting Resource Activities to Manage Risk Given Uncertain Weather

Wildland firefighting requires managers to make decisions in complex decision environments that hold many uncertainties; these decisions need to be adapted dynamically over time as fire behavior evolves. Models used in firefighting decisions should also have the capability to adapt to changing conditions. In this paper, detailed line construction constraints are presented for use with a stochastic mixed integer fire growth and behavior program. These constraints allow suppression actions to interact dynamically with stochastic predicted fire behavior and account for many of the detailed line construction considerations. Such considerations include spatial restrictions for fire crew travel and operations. Crew safety is also addressed; crews must keep a variable safety buffer between themselves and the fire. Fireline quality issues are accounted for by comparing control line capacity with fireline intensity to determine when a fireline will hold. The model assumes crews may work at varying production rates throughout their shifts, providing flexibility to fit work assignments with the predicted fire behavior. Nonanticipativity is enforced to ensure solutions are feasible for all modeled weather scenarios. Test cases demonstrate the model’s utility and capability on a raster landscape.

Enhancing Recombinant Protein Yields in the E. coli Periplasm by Combining Signal Peptide and Production Rate Screening.

Proteins that contain disulfide bonds mainly mature in the oxidative environment of the eukaryotic endoplasmic reticulum or the periplasm of Gram-negative bacteria. In E. coli, disulfide bond containing recombinant proteins are often targeted to the periplasm by an N-terminal signal peptide that is removed once it passes through the Sec-translocon in the cytoplasmic membrane. Despite their conserved targeting function, signal peptides can impact recombinant protein production yields in the periplasm, as can the production rate. Here, we present a combined screen involving different signal peptides and varying production rates that enabled the identification of more optimal conditions for periplasmic production of recombinant proteins with disulfide bonds. The data was generated from two targets, a single chain antibody fragment (BL1) and human growth hormone (hGH), with four different signal peptides and a titratable rhamnose promoter-based system that enables the tuning of protein production rates. Across the screen conditions, the yields for both targets significantly varied, and the optimal signal peptide and rhamnose concentration differed for each protein. Under the optimal conditions, the periplasmic BL1 and hGH were properly folded and active. Our study underpins the importance of combinatorial screening approaches for addressing the requirements associated with the production of a recombinant protein in the periplasm.

A Semianalytical Model for Evaluating the Performance of a Refractured Vertical Well With an Orthogonal Refracture

SummaryProduction from a fractured vertical well will lead to a redistribution of the stress field in formations. If the induced stress changes are sufficiently large to overcome the effect of the initial horizontal-stress deviator, the direction of the minimum horizontal stress can be turned into the direction of the maximum horizontal stress within an elliptical region around the initial fracture, resulting in a stress-reversal region near the wellbore. In such cases, a refracturing treatment can create a refracture that propagates orthogonally to the initial fracture because of the stress reversal. As such, the high-pressure area of the formation can be stimulated by the refracture, and the productivity of the refractured well can be improved. In this work, we develop a semianalytical model to evaluate the performance of a refractured vertical well with an orthogonal refracture. To simulate the well performance throughout the entire production period, we divide the well production into three stages: the first stage, when the well is producing oil with the initial fracture; the second stage, when the well is shut down for the refracturing treatment; and the third stage, when the well is producing oil with both the initial fracture and the refracture. In addition, by discretizing the initial fracture and the refracture into small segments, the conductivity of the fractures can be taken into account, and the geometry of the fracture system can be captured. We use the Green-function method to analytically simulate the reservoir flow and use the finite-difference method to numerically simulate the fracture flow; therefore, a semianalytical model can be constructed by coupling the reservoir-flow equations with the fracture-flow equations. This proposed model is applied to different wellbore and reservoir conditions. The calculated results show that this proposed model is versatile because it can simulate various wellbore constraints, including the conditions of constant bottomhole pressure (BHP), varying BHP, constant production rate, and varying production rate. The permeability anisotropy of the reservoir system, as well as the nonuniform conductivity distribution along the fracture, can also be incorporated into this proposed model. In addition, we demonstrate that this proposed model can be used to simulate other types of refractured vertical wells with minor modifications.

Design of single mixed refrigerant natural gas liquefaction process considering load variation

This study presents a comprehensive design approach to determine optimal equipment size and operating conditions while considering process load variation. We applied the suggested approach to PRICO® Single Mixed Refrigerant (SMR) process to take account of the feed gas load reduction owing to depletion of natural gas fields. The suggested approach differs from a traditional one in that it performs design and optimization with several steady-state operation regimes depending on the load variation. The economics of each design approach is evaluated by the economic assessment model that reflects the annual profit under the varying production rate according to the actual production profiles of the gas field wells, Maui and Kapuni in New Zealand. The proposed design approach makes a loss in the compressor equipment cost. However, it reduces the operation cost over a wide range of operations, leading to the overall improvement of economics in a gas well along its lifetime production. This study also conducts a quantitative analysis between the load capacity that a single train must bear and the key economic variables through a case study on two-train operation. This provides insight into the economics and operability of the process depending on the number of trains.

Cost-optimal design of a batch electrodialysis system for domestic desalination of brackish groundwater

This study presents the pareto-optimal design of a domestic point-of-use batch electrodialysis (ED) system. Specifically, the optimal geometry, flow-rates, and applied voltage for total cost minimization were explored for varying production rate (9–15 L/h) and product concentration (100–300 mg/L) requirements, while feed concentration and recovery ratio were maintained at 2000 mg/L and 90%, respectively. Capital cost dominated over energetic cost; hence, optimal designs maximized current density. Capital cost was significantly higher for 100 mg/L systems, than 200 and 300 mg/L: $141 vs. $93 and $79, at 12±0.5 L/h of production. Pumps were an important consideration, contributing up to 46% of the total cost. Large membrane length-to-width aspect ratios (3.5:1 to 6:1) and thin channels (0.30–0.33 mm) promoted high current densities, and 11–21 cm/s velocities optimized mass transfer against pressure drop. Optimal voltages were 0.9–1.3 V/cell-pair at 9 L/h, and decreased at higher rates. Lastly, higher production was obtained primarily by increasing cell-pair area rather than number of cell-pairs (36–46). It was additionally observed that active area increased linearly with feed concentration (1500–2500 mg/L), while recovery (60–90%) minimally affected design. This work also suggests that voltage control during the batch process, and less expensive pumps, can further reduce cost.

The sorption-corrected multiwell deconvolution method to identify shale gas reservoir containing sorption gas

In the analysis of the pressure data acquired from a shale gas reservoir, the rate-normalized pressure (RNP) method has been widely used in the shale gas industry due to its simplicity. However, for sharply varying production rate and shut-in of a well, and for pressure-interfered data at a well, the RNP method gives erroneous results in evaluation of the reservoir characteristics. Meanwhile, the deconvolution method can overcome the limit of the RNP method for sharply varying data. However, because the deconvolution method is only applicable to a linear relationship in the pressure-rate data, it is not possible to analyze the pressure data acquired from adsorbed gas-contained shale gas reservoir. This data shows a nonlinear relationship because of the compressibility of desorbed gas which is a strong function of pressure.In this study, we newly proposed the sorption-corrected multiwell deconvolution method for correctly identifying the shale gas reservoir containing the adsorbed gas. This method was suggested to analyze not only sharply varying production rate but also pressure-interfered data acquired from the multiwell. With the use of this method, we evaluated and compared the effective permeability and the estimated ultimate recovery (EUR) of shale reservoir with RNP method that is currently applied in shale gas industry. From the results, it was concluded that the sorption-corrected multiwell deconvolution method was found to be an excellent methodology comparing to RNP method for analyzing pressure-interfered shale gas production data containing the adsorbed gas.

Referential Choices and Specific Language Impairment: Sensitivity to Contrast Levels and Grammatical Role

Speakers’ referential choices differ in the degree of explicitness, ranging from very explicit expressions (such as lexical NPs, e.g., the boy) to less explicit expressions (such as pronouns, e.g., he, and null elements). We examine the referential choices of children with Specific Language Impairment (SLI), in order to differentiate between the linguistic and pragmatic abilities involved in the selection of appropriate referring expressions. Existing findings on referential choices by children with SLI are currently inconsistent and have mainly been reported based on narratives. We used an elicited production task to manipulate the referent’s accessibility by means of two factors: (a) contexts that instantiate different levels of contrast (one vs. two contrasts) and (b) the grammatical role of the expression (subject vs. object). We show that children with SLI and typically developing controls produce more explicit expressions for increased contrast levels and for objects than for subjects. Although children with SLI modify the explicitness of their referring expressions according to the accessibility of referents as typically developing children do, we also find varying production rates between the groups. We discuss how these differences in production rates surface as a consequence of language impairment, although the explicitness of referential choices remains otherwise largely unaffected.

Moving Horizon Scheduling of an Air Separation Unit under Fast-Changing Energy Prices

Maximizing the benefits of time-of-use pricing for industrial electricity consumers requires varying production rates, such that energy use is shifted from peak price periods to off-peak times during the day. Assuming that excess capacity and product storage are available, production of energy intensive processes can be increased at off-peak times beyond nominal rates, and the stored product can be used at peak times when the production rate is lowered. Under these rapidly changing circumstances, scheduling calculations must take into consideration explicitly the dynamic model of the process, often rendering the scheduling problem intractable in practical amounts of time. To address this challenge, we introduce a class of scheduling-relevant low-order process models, which capture the closed-loop input-output behavior of a plant. We use these models to close the scheduling loop, whereby the scheduling problem is formulated over a moving horizon with feedback. We apply the theoretical concepts to an industrial-scale air separation unit model, demonstrating that variable production rate operation with product storage has the potential for significant operating cost savings while abiding by product quality and safety constraints.

Assessing divergent SST behavior during the last 21 ka derived from alkenones andG. ruber-Mg/Ca in the equatorial Pacific

Equatorial Pacific SST reconstructions derived from Mg/Ca ratios in planktonic foraminifera Globigerinoides ruber and from alkenone-producing coccolithophorids record different trends throughout the Holocene and the last deglaciation. We set forth the hypothesis that their diverging behavior may be related to different seasonal sensitivities which result from the annually varying production rates of alkenone-producing coccolithophorids and of G. ruber. Using a series of transient paleoclimate model simulations forced with the time-varying forcing history over the last 21 ka, a good qualitative agreement is found between simulated boreal winter temperatures and alkenone-SST reconstructions as well as between simulated boreal summer temperatures and reconstructed Mg/Ca-based SST variations. Pronounced features in the reconstructions that can be readily explained by the conjectured seasonal biases include the mismatch in middle-to-late Holocene temperature trends and the different onsets of deglacial climate change in the eastern equatorial Pacific. The analysis presented here further suggests that through combinations of Mg/Ca and alkenone SST reconstructions information can be gained on annual mean temperature changes and the amplitude of the seasonal cycle in SST. Our study concludes by discussing potential weaknesses of the proposed model-derived seasonal bias interpretation of tropical Pacific SST proxies in terms of present-day core-top data, sediment trap studies, and satellite-based observations of chlorophyll.

High-resolution anatomy of a grainstone package in Khuff Sequence KS4, Oman Mountains, Sultanate of Oman

ABSTRACTThis study is part of a large-scale outcrop analog study on Middle Permian to Lower Triassic Khuff-equivalent strata in the Oman Mountains, Al Jabal al-Akhdar, Sultanate of Oman. The Khuff outcrop equivalent can be divided into six sequences (Khuff sequences KS6 to KS1, from base to top). The main focus of this study is the description of the internal anatomy of the shoal grainstone bodies in the lower part of Sequence KS4 (“lower KS4”). High-resolution sedimentological logging of three outcrop sections in wadis Sahtan, Bani Awf and Mistal yielded eight lithofacies types that were grouped into five facies associations. Lower KS4 strata were mainly deposited within a “shoal complex” of an epeiric carbonate ramp, resulting in a thick pile of up to 70 m of grainstones that, on first sight, appear relatively homogeneous. However, detailed facies and microfacies analysis revealed their heterogeneous architecture on various scales: (1) Minor changes in depositional environments directly affected the type of carbonate grains (ooids versus peloids/cortoids versus bioclasts), leading potentially to highly variable pore systems (moldic versus interparticle versus intraparticle). (2) Vertically, detailed sequence-stratigraphic analysis revealed a higher-order of cyclicity (“mini-cycles”) on a decimeter- to meter-scale. Four mini-cycle types were recognized. (3) Laterally, facies changes, the amalgamation of grainstone beds and mini-cycle pinch-outs were observed in 2-D correlations on a scale of a few kilometers. These different types of heterogeneities may contribute to varying production rates commonly observed in the subsurface KS4 reservoir.

Sustainability strategies in an EPQ model with price‐ and quality‐sensitive demand

PurposeThe purpose of this paper is to present a mathematical model that illustrates the trade‐offs between sustainability, demand, costs, and profit in a supply chain with a single supplier and a single manufacturer.Design/methodology/approachIt is assumed that a single product is produced and sold on a market where demand is sensitive to price and quality. Sustainability is treated as a quality attribute and is measured in terms of the levels of scrap and emissions generated in the supply chain. It is assumed that the emissions and scrap can be controlled by varying production rates or by investing in production processes. The impact of cooperative and non‐cooperative behaviour between the supplier and the manufacturer is explored. Numerical studies are used to illustrate the behaviour of the model.FindingsThe analysis shows that the supplier and the manufacturer can attract additional customers by controlling scrap and emissions. The behaviour of the supplier and the manufacturer are dictated by the decision criteria, such as changes in the level of sustainability, used by customers to evaluate the product. It is shown that the profit of the system is higher and that the level of quality is lower in the case of cooperation than in the case of non‐cooperation.Research limitations/implicationsSeveral areas for future work are highlighted. The study of alternative demand functions, linking sustainability to a monetary component, including additional players, and incorporating additional sustainability indicators all offer possibilities for extending the model.Originality/valueThere is an identified need for analytical models that consider sustainability in the supply chain. The results are especially important for companies operating in markets where customers perceive the sustainability of a product as a quality criterion.

THE SOURCES OF HCN AND CH3OH AND THE ROTATIONAL TEMPERATURE IN COMET 103P/HARTLEY 2 FROM TIME-RESOLVED MILLIMETER SPECTROSCOPY

One of the least understood properties of comets is the compositional structure of their nuclei, which can either be homogeneous or heterogeneous. The nucleus structure can be conveniently studied at millimeter wavelengths, using velocity-resolved spectral time series of the emission lines, obtained simultaneously for multiple molecules as the body rotates. Using this technique, we investigated the sources of CH3OH and HCN in comet 103P/Hartley 2, the target of NASA's EPOXI mission, which had an exceptionally favorable apparition in late 2010. Our monitoring with the IRAM 30 m telescope shows short-term variability of the spectral lines caused by nucleus rotation. The varying production rates generate changes in brightness by a factor of 4 for HCN and by a factor of 2 for CH3OH, and they are remarkably well correlated in time. With the addition of the velocity information from the line profiles, we identify the main sources of outgassing: two jets, oppositely directed in a radial sense, and icy grains, injected into the coma primarily through one of the jets. The mixing ratio of CH3OH and HCN is dramatically different in the two jets, which evidently shows large-scale chemical heterogeneity of the nucleus. We propose a network of identities linking the two jets with morphological features reported elsewhere, and postulate that the chemical heterogeneity may result from thermal evolution. The model-dependent average production rates are 3.5x10**26 molec/s for CH3OH and 1.25x10**25 molec/s for HCN, and their ratio of 28 is rather high but not abnormal. The rotational temperature from CH3OH varied strongly, presumably due to nucleus rotation, with the average value being 47 K.

Distribution of tetraether lipids in the 25-ka sedimentary record of Lake Challa: extracting reliable TEX86 and MBT/CBT palaeotemperatures from an equatorial African lake

The distribution of isoprenoid and branched glycerol dialkyl glycerol tetraether (GDGT) lipids was studied in the sedimentary record of Lake Challa, a permanently stratified, partly anoxic crater lake on the southeastern slope of Mt. Kilimanjaro (Kenya/Tanzania), to examine if the GDGTs could be used to reconstruct past variation in regional temperature. The study material comprised 230 samples from a continuous sediment sequence spanning the last 25 ka with excellent age control based on high-resolution AMS 14C dating. The distribution of GDGTs showed large variation through time. In some time intervals (i.e., from 20.4 to 15.9 ka BP and during the Younger Dryas, 12.9–11.7 ka BP) crenarchaeol was the most abundant GDGT, whereas at other times (i.e., during the Early Holocene) branched GDGTs and GDGT-0 were the major GDGT constituents. In some intervals of the sequence the relative abundance of GDGT-0 and GDGT-2 was too high to be derived exclusively from lacustrine Thaumarchaeota, suggesting a sizable contribution from methanogens and other archaea. This severely complicated application of TEX86 palaeothermometry in this lake, and limited reliable reconstruction of lake water temperature to the time interval 25–13 ka BP, i.e. the Last Glacial Maximum and the period of post-glacial warming. The TEX86-inferred timing of this warming is similar to that recorded previously in two of the large African rift lakes, while its magnitude is slightly or much higher than that recorded at these other sites, depending on which lake-based TEX86 calibration is used. Application of calibration models based on distributions of branched GDGTs developed for lakes inferred temperatures of 15–18 °C for the Last Glacial Maximum and 19–22 °C for the Holocene. However, the MBT/CBT palaeothermometer reconstructs temperatures as low as 12 °C for a Lateglacial period centred on 15 ka BP. Variation in down-core values of the BIT index are mainly determined by the varying production rate of crenarchaeol relative to in-situ produced branched GDGTs. The apparent relationship of the BIT index with climatic moisture balance can be explained either by the direct influence of lake level and wind strength on nutrient recycling, or by influx of soil nutrients promoting aquatic productivity and nitrification. This study shows that GDGTs can aid in obtaining climatic information from lake records but that the obtained data should be interpreted with care.

Advanced linear scheduling program with varying production rates for pipeline construction projects

Abstract Linear scheduling is known to have superior schedule management capabilities specifically in linear construction projects such as oil and gas pipeline projects which typically involve repetitive-work activities with the same crew and equipment throughout a project. This promising scheduling method, however, has not been actively used in practice historically, probably due to the aggressive marketing and the domination of Critical Path Method (CPM) in the U.S. market. This study discusses on developing an automated alignment based linear scheduling program for applying temporal and spatial changes in production rates. An actual 750 mile natural gas liquids pipeline project starting in Wyoming and terminating in Kansas is used to develop a production rate regression model and validate the program successfully. This newly developed program can provide a project team with the ability to better understand how changes in the project plan and schedule will impact production rates for the project.

Annual distribution of allergenic fungal spores in atmospheric particulate matter in the Eastern Mediterranean; a comparative study between ergosterol and quantitative PCR analysis

Abstract. Airborne fungal spores are an important fraction of atmospheric particulate matter and are major causative agents of allergenic and infectious diseases. Predicting the variability and species of allergy-causing fungal spores requires detailed and reliable methods for identification and quantification. There are diverse methods for their detection in the atmosphere and in the indoor environments; yet, it is important to optimize suitable methods for characterization of fungal spores in atmospheric samples. In this study we sampled and characterized total and specific airborne fungal spores from PM10 samples collected in Rehovot, Israel over an entire year. The total fungal spore concentrations vary throughout the year although the species variability was nearly the same. Seasonal equivalent spore concentrations analyzed by real-time quantitative-PCR-based methods were fall > winter > spring > summer. Reported concentrations based on ergosterol analysis for the same samples were and fall > spring > winter > summer. Correlation between the two analytical methods was found only for the spring season. These poor associations may be due to the per-spore ergosterol variations that arise from both varying production rates, as well as molecular degradation of ergosterol. While conversion of genome copies to spore concentration is not yet straightforward, the potential for improving this conversion and the ability of qPCR to identify groups of fungi or specific species makes this method preferable for environmental spore quantification. Identifying tools for establishing the relation between the presence of species and the actual ability to induce allergies is still needed in order to predict the effect on human health.

Not-So-Quicksilver

Environmental Science In aquatic or subsurface environments, sulfate-reducing bacteria mediate the transformation of inorganic divalent mercury into highly toxic, bio-available methylmercury (MeHg), but it is unclear how this reaction depends on the phase of the Hg(II). Zhang et al. examined the degree to which sulfate-reducing bacteria methylated three forms of Hg(II), representing different size fractions and different states of aging: dissolved Hg(II) ions, 3- to 4-nm-diameter HgS nanoparticles, and >500-nm HgS particles. The bacteria methylated dissolved Hg(II) fastest, but there were also significant differences between nanoparticles and larger particles of HgS that were attributed to size-dependent crystallinity differences and not simply the amount of reactive surface area. Furthermore, aging HgS nanoparticles—which transformed them into larger HgS particles over time—resulted in less MeHg formation as well, suggesting that methylation is related to the intermediate Hg(II) phases present and the crystal growth kinetics. These observations may help explain the varying production rates of MeHg in the environment. Environ. Sci. Technol. 10.1021/es203181m (2011).

Linear Scheduling Model with Varying Production Rates

Activity production rates drive the development and accuracy of linear schedules. The nature of linear projects dictates an assortment of variables that affect each activity’s production rate. The purpose of this research was to expand the capabilities of linear scheduling to account for variance in production rates when and where the variance occurs and to enhance the visual capabilities of linear scheduling. This new linear scheduling model, a linear scheduling model with varying production rates (LSMVPR), has two objectives. The first is to outline a framework to apply changes in production rates when and where they occur along the horizontal alignment of the project. The second objective is to illustrate the difficulty or ease of construction through the time-location chart. This research showed that the changes in production rates because of time and location can be modeled for use in predicting future construction projects. Using the concept of working windows, LSMVPR allows the scheduler to develop...