A MATHEMATICAL MODEL FOR TRANSIENT FREE SURFACE FLOW IN NONHOMOGENEOUS OR ANISOTROPIC POROUS MEDIA

ABSTRACT A mathematical model was developed to solve a steady free surface flow problem and a rapid drawdown problem in a two-dimensional porous medium. The same problem was also solved by an analogue device and excellent agreement was found to exist between the two solutions. This paper contains the formulation of the numerical problem from first principles and a discussion of measures that had to be taken in order to assure numerical stability and proper convergence of the solution. Although the scope of this study was limited to a two-dimensional flow case, the elements of simulation discussed are general in nature and applicable to three-dimensional problems. It was demonstrated that numerical solution can be obtained for the position of the free surface at given time intervals, for the piezometric head distribution within the flow field and for flow quantities across given boundaries. In addition, the mathematical model will permit consideration of nonhomogeneous or anisotropic characteristics of the porous medium, without difficulty. It is concluded that mathematical models, incorporating some or all of the techniques discussed in this paper, in conjunction with some analogue control device, can be very efficient and reliable tools for solving complex porous flow problems, including those which, so far, have eluded comprehensive analysis, due to physical and/or cost limitation.     

A COMPARISON OF SOME DYNAMIC,LINEAR AND POLICY ITERATION METHODS FOR RESERVOIR OPERATION1

Within the past few years, a number of papers have been published in which stochastic mathematical programming models, incorporating first order Markov chains, have been used to derive alternative sequential operating policies for a multiple purpose reservoir. This paper attempts to review and compare three such mathematical modeling and solution techniques, namely dynamic programming, policy iteration, and linear programming. It is assumed that the flows into the reservoir are serially correlated stochastic quantities. The design parameters are assumed fixed, i.e., the reservoir capacity and the storage and release targets, if any, are predetermined. The models are discrete since the continuous variables of time, volume, and flow are approximated by discrete units. The problem is to derive an optimal operating policy. Such a policy defines the reservoir release as a function of the current storage volume and inflow. The form of the solution and some of the advantages, limitations and computational efficiencies of each of the models and their algorithms are compared using a simplified numerical example.     

RESEARCH: Optimizing the Mix of Strategies for Control of Vehicular Emissions

/ A number of strategies for the control of vehicular emissions are being considered by the Philippine government to address Metropolitan Manila's air quality problem. An analytical tool is needed for optimizing criteria pollutant reductions given the budgetary constraints. The simplest approach is to take costs and pollutant removals to be linear with each strategy's scale of activity, and this is readily solved as a linear programming problem. Another approach is to use a dynamic system of weights which shift with progressive improvements in pollutant emissions. The two approaches yield somewhat different results, suggesting the sensitivity of the solution to the assumed weights. The study also illustrates the importance of a sound methodology for evaluating priorities given to different air quality goals. One such methodology may involve a polling of expert panels and the public to gain insight into the relative importance given to competing emissions reduction goals. An informal polling of resource agency staff was conducted and discussed in this paper. The authors take the position that proper planning involves tracing intermediate steps to the final outcome and not just focusing on the latter.KEY WORDS: Vehicular emissions; Urban air quality; Emissions control; Optimization; Manila; Environmental systems analysis     

NONSTEADY FLOW TO A WELL WITH TIME DEPENDENT DRAWDOWN1

Confined flow toward a single well of finite radius in an extensive aquifer of uniform transmissibility is studied under the assumption of time-dependent drawdown. Three particular cases are considered: (a) linear drawdown (including constant drawdown); (b) exponential drawdown; (c) periodic (sinusoidal) drawdown. The differential equation governing unsteady axial symmetric flow toward a single well in a confined aquifer is solved for the three different situations by the use of the Laplace transform method. The resulting expressions are integrated by adapting a modified Gemant scheme. General computer programs have been developed and operated for several combinations of characteristics. The results are plotted to show the effect of time dependent drawdown on the variation of the well discharge and the piezometric head distribution.     

UNCONFINED FLOW THROUGH JOINTED ROCK1

The two-dimensional, steady-state, unconfined flow of a homogeneous fluid through jointed rock is studied for both laminar and turbulent conditions by use of a method which is based on previously developed theoretical and experimental flow relationships. However, only the independent unknowns are selected in order to reduce the complexity of the problem and render it more readily tractable. The intact rock is assumed to be impermeable, and two intersecting systems of plane, parallel joints are used in the mathematical model, taking into account the surface roughness of the joints. The mathematical solution of the resulting nonlinear (due to turbulent flow in some joints) system of equations is obtained by use of a rapidly converging iterative procedure, wherein each iteration takes special advantage of the banded nature of the associated matrix. For the particular case where a free surface exists, the general flow equations are not satisfied, because some of the joints in the vicinity of the free surface do not flow full; therefore, new equations must be established to handle this condition. Once the development of the mathematical model is accomplished, several cases involving different geometric characteristics (width, orientation, and roughness of joints) are solved for a rectangular domain, and graphs are given to illustrate the influence of the various parameters on the manifested flow behavior.     

A multiobjective optimization framework for multicontaminant industrial water network design

The optimal design of multicontaminant industrial water networks according to several objectives is carried out in this paper. The general formulation of the water allocation problem (WAP) is given as a set of nonlinear equations with binary variables representing the presence of interconnections in the network. For optimization purposes, three antagonist objectives are considered: F(1), the freshwater flow-rate at the network entrance, F(2), the water flow-rate at inlet of regeneration units, and F(3), the number of interconnections in the network. The multiobjective problem is solved via a lexicographic strategy, where a mixed-integer nonlinear programming (MINLP) procedure is used at each step. The approach is illustrated by a numerical example taken from the literature involving five processes, one regeneration unit and three contaminants. The set of potential network solutions is provided in the form of a Pareto front. Finally, the strategy for choosing the best network solution among those given by Pareto fronts is presented. This Multiple Criteria Decision Making (MCDM) problem is tackled by means of two approaches: a classical TOPSIS analysis is first implemented and then an innovative strategy based on the global equivalent cost (GEC) in freshwater that turns out to be more efficient for choosing a good network according to a practical point of view.     

A water network optimization using MATLAB—A case study

The methodology of mass and energy integration is widely applied for reduction of water consumption, which belongs to the area of mass integration, and is also energy integration problem if water is considered an energy source (cooling water and steam). This work presents a study of water-consumption reduction through optimization of the process superstructure. A petroleum refinery water network was analyzed and a solution is proposed to minimize the costs of fresh water and wastewater treatment. Three processes which use water, with three contaminants, were monitored and three potential treatment units are proposed. The procedure was based on relaxation of a non-convex non-linear programming problem into a mixed integer linear programming (MILP). The MILP model was further simplified using heuristic rules and solved by using MATLAB.     

POLITICAL RESOLUTION OF ENVIRONMENTAL CONFLICTS1

ABSTRACT Many water resources management problems ultimately require a political decision in order to formulate a course of action to follow. Metagame analysis is a nonquantitative technique that can model the decision-making process and is used in this article to arrive at a politically feasible solution to a typical water pollution problem. The output from the linear programming formulation of the problem is used as input to the “political” metagame analysis. This allows a solution to the pollution conflict that is not only physically and economically feasible according to the linear programming analysis, but politically feasible as well.     

Solar Assisted Small-Scale Biomass District Heating System in the Northern Part of Sweden

Abstract

This article presents a case study of a projected solar assisted biomass district heating system in the north of Sweden. It is generally known that a biomass district heating system combined with solar heat brings many important benefits. The most common system solution is to install a heat store and a large solar collector field near the heating central. No plant of this type is however in operation in the northern part of Sweden. The main reason for this is that the solar irradiation at these latitudes is very low when the demand for heat is high. Solar heat could however be useful during summer in order to generate hot tap water. One problem is that the heat losses, calculated as percentage of the delivered heat, become very large during these months. This article presents the idea of allowing the connected households to generate their own hot tap water using solar collectors and heat stores installed in each house. The district heating network can therefore be closed in summer, which eliminates the heat losses outside the heating period. A case study of a projected plant has been carried out and it is shown that it is possible to reduce the heat losses by 20% compared to a conventional system. This idea also provides many other important technical and economic benefits.     

SOLUTION OF A WATER RESOURCES PROBLEM WITH ECONOMIES OF SCALE BY LINEAR PROGRAMMING1

ABSTRACT Both because of its effectiveness and ease in use, linear programming has become progressively popular in water resources planning problems. Yet, the assumptions of linear construction costs can be misleading. Diseconomies of scale in construction can be handled by successive approximations to the cost function but problems with economies of scale yield paradoxical results when piecewise approximations are used. If significant economies of scale exist in only one facility, the solution to problems of this nature can be found using normal linear programming codes by successively adjusting the unit construction cost on that single facility to iteratively work toward the true optimal solution.     

USING REFERENCE SITES AND SIMPLE LINEAR REGRESSION TO ESTIMATE LONG‐TERM WATER LEVELS IN COASTAL PLAIN FORESTS1

ABSTRACT: The ability of regulators, resource managers, and consultants to assess accurately wetland hydrology is crucial when identifying and delineating wetlands. In this study, simple linear regression and long‐term (ten year) New Jersey Pinelands stream gaging and pitch pine lowland water‐level data sets were used to estimate long‐term hydroperiods at lowland test sites with short‐term (two year) records. Separate regression equations were developed for each test site using reference site data and stream gaging data, and two sets of equations for selected test sites were produced using two different short‐term periods of record. Test sites had long‐term records ranging from four to ten years, allowing validation of the regression models. Measured and predicted test site growing season water levels were similar regardless of which short‐term period of record was used. The results based on the stream gaging site data were similar, although the difference between measured and estimated growing season water levels was greater when this approach was used. Excellent agreement was found between measured and estimated frequencies of near‐surface saturation at test sites for each growing season month, and these relationships improved when cumulative, seasonal frequencies were considered. The reference wetland approach used in this study may have its greatest value in regions with both high development pressures and problem wetlands and may provide an effective way of resolving costly wetland delineation disputes.     

IMPROVED RIVER BASIN UTILIZATION THROUGH SYSTEMS ANALYSIS1

ABSTRACT. Theoretical and practical results are summarized for a study to determine optimal water resource allocation in a proposed water conservancy district. The area of this district, which covers several river basins, contains a large number of existing and proposed facilities such as reservoirs and diversions. The operation of all of these facilities was to be determined along with the sizing of the proposed facilities in order to optimize given objective functions. Related efforts in optimal river basin utilization were surveyed, and linear programming was selected as an expedient optimization technique. The problem is formulated by identifying time stages which together constitute a repetitive cycle such as a year. With these stages, it is possible to associate operational and capacity variables with network components, which are branches and nodes. Objective functions are assembled for the component variables. Constraint equations are written in terms of the variables to reflect network nodal continuity, capacity restrictions, and adjudications such as water rights. A numerical example is considered in which the existing and proposed facilities are aggregated to produce a small, tractable number of facilities. This paper examines the example results and suggests future improvements for models of this type.     

EFFECT OF CATCHMENT SIZE ON PHOSPHORUS EXPORT1

ABSTRACT: We tested the common assumption, made when expressing phosphorus export on an areal basis, that this export is a linear function of catchment area and found it wanting. The data show that in agricultural catchments, TP (total phosphorus) export varies as the 0.77 power of drainage basin area, resulting in a reduction in phosphorus delivery per unit area with increasing catchment size. Following further division of catchments according to agricultural practice, we found that this spatial scale effect is restricted to row crops and pastures. We present simple statistical models to allow a comparison of TP export from catchments of different size. Such models are not needed for nonrow crops, mixed agricultural and forested catchments, where TP export is a linear function of catchment size.     

MATHEMATICAL ANALYSIS OF ARTIFICIAL RECHARGE FROM BASINS1

ABSTRACT: One of the most common methods of artificial recharge to the ground water is from basins. In this paper, seven analytical solutions that describe artificial recharge from basins are presented. Most of these solutions are derived by directly solving the general partial differential equation for ground water flow. The solutions differ in that they use different boundary conditions, basin shapes, and consider the nonlinearity of the artificial recharge problem differently. Use of each analytical solution is demonstrated in this paper by application to an example problem. A comparison of each analytical solution presented in this paper was made to give suggestions on their use, their ease of implementation, and their relative agreement. Although no attempt is made in the paper to conclude which analytical solution is best for all problems, some general conclusions can be stated on the applicability of the various analytical solutions. Of the analytical solutions presented in this paper, Glovers and Hantush's solutions for rectangular recharge basins are highly recommended. Baumanns solution for a circular basin also gave fairly reliable results and is very easy to evaluate numerically.     

In situ measurement of soil moisture and pore-water pressures in an ‘incipient’ landslide: Lake Tutira,New Zealand

The immediate cost of shallow regolith landslides in New Zealand has been estimated to exceed US$33M annually. Since the majority of these landslides occur during prolonged wet conditions, or intense rainstorms, moisture conditions are a critical control. The nature, dynamics, and character of soil moisture conditions, and the piezometric response to rainfall, have been recorded within an ‘incipient’ landslide for more than 5 years. The study site, on pastoral hill country within the Lake Tutira catchment in northern Hawkes Bay, is typical of large areas of New Zealand episodically affected by extensive landsliding. Detailed continuous measurements show that both the soil moisture and piezometric response within the regolith are highly storm- and site-specific. The development of positive pore pressures is infrequent; they form only during intense rainstorms, and persist for a short time. The hydraulic response of the soil is primarily a function of storm characteristics, but this response can be modified by antecedent moisture conditions, topographic position, and heterogeneity of soil properties.     

环境治理中府际合作的逻辑

公共事务的积累只是为制度化解决提供了必要性,当政者维护政权的根本利益需要决定了公共事务处理的优先序列。客观问题的属性和解决的迫切程度只有在政府最高层统治集团认为维系权力存续的手段具备充分的支撑条件时,才会愿意在正式制度上进行调整,为解决问题提供制度供给。新中国成立后很长一段时间内,我国环境问题并不突出,中央政府根据社会主要矛盾需要制定了以发展经济为重心的制度体系。这种制度结构使地方政府和辖区企业形成了利益共容关系。为适应竞争的需要,地方政府庇护辖区企业环境行为,机会主义地执行环境管理制度,使环境问题积累成为影响安全价值的显著因素。在国内外政治压力下,中央政府最终做出了战略调整,地方政府在中央政府制度调控下,自发地合作治理环境问题。     

AN APPLICATION OF NETWORK THEORY TO WATER MANAGEMENT IN POULTRY PROCESSING1

ABSTRACT This paper summarizes a study employing a systems approach for analyzing one class of modifications within a poultry processing plant. The modifications considered were changes in water-flow arrangements and process characteristics to reduce water intake of the plant and waste-treatment costs. The object of the study was to develop a technique or techniques by which a combination of proposed modifications could be chosen to minimize water flow through the plant. Existing and proposed flows were represented as a network, and linear programming was used to solve the minimum-flow problem for the network. Application of the technique was made to an existing, typical plant in Durham, N.C. Results of the application showed fresh water intake could be reduced by 45% to 51%, and furthermore that annual returns of 62% to 494% could be obtained on investment in the optimum modification sets, as fresh water costs varying from 10 cents to $1.00 per 1000 gal. Types of modifications of a poultry processing plant are classified by types, and the relative importance and effectiveness of each type are discussed.     

A quality approach to environmental communication

Too often in the past, public relations professionals were consulted only when there was a problem—or a crisis—that needed explaining. The author provides a model for a process-oriented approach to environmental communication that focuses on building and sustaining positive public relationships over time. The key is dialogue with critical publics as well as links with other important actors in the environmental drama that can help position you as part of the solution, not the problem.     

Optimization of a monitoring network for sulfur dioxide

In this study, we develop and apply a methodology to reduce an existing monitoring network to find an optimal configuration of a smaller network. We use a criterion based on locally weighted regression with two different weight functions. The methodology is applied to the Dutch national SO2 network and offers the possibility to include different politically relevant options in the model by weight criteria. Because full enumeration of all monitoring networks is impossible, a combinatorial search algorithm is applied to find a (sub)optimal solution. If different (optimal) monitoring networks result from different criteria, then the best can be selected.