Heat flow and geothermal potential of Kansas

Temperature, thermal-conductivity measurements, and heat-flow values are presented for four holes in Kansas originally drilled for cooperative water-resources investigations by the Kansas Geological Survey and the U.S. Geological Survey. These holes cut most of the sedimentary section and were cased and allowed to reach temperature equilibrium. Several types of geophysical logs were run for these holes. Temperature data from an additional five wells also are presented. Temperature gradients in the sedimentary section vary over a large range (over 4:1), and significantly different temperatures occur at the same depth in different portions of the state. Temperatures as high as 34°C (93°F) occur at a depth of 500 m (1,650 ft) in the south-central portion of the state but are 28°C (82°F) or lower at that depth in other parts of the state. In addition to cuttings measurements, thermal conductivities were estimated from geophysical well-log parameters; useful results suggest more use of the technique in the future. With these results, geophysical well logs can be used to predict temperatures as a function of depth in areas for which no temperatures are available if heat flow is assumed. The extreme variation in gradients observed in the holes occurs because of the large contrast in thermal-conductivity values. Shale thermal-conductivity values appear to have been overestimated in the past; Paleozoic shales in Kansas have thermal-conductivity values of approximately 1.18 ± 0.03 Wm-1K-1. Conversely, evaporite and dolomite units have thermal conductivities of over 4 Wm-1K-1. In spite of the large variations of gradient, the heat-flow values throughout the holes do not vary more than 10%, and any water-flow effects which might be present from the lateral motion on any of the aquifers are less than 10%. The best estimates for heat flow in the four holes come from carbonate units below the base of the Pennsylvanian and range in value from 48 mWm-2 to 62 mWm-2. Two of the holes were drilled to the basement, and correlation of the heat flow with basement radioactivity suggests that the heat-flow/heat-production line postulated for the midcontinent by Roy, Blackwell, and Birch (1968) applies to these data. Because of the low thermal conductivity of the shales, the radiogenic-pluton concept should apply to the midcontinent. Thus, if very radioactive plutons can be identified, much higher temperatures may occur in the sedimentary section than have been thought possible in the past. However, the past overestimation of the shale-conductivity values suggests that some previous high heat-flow values in the midcontinent probably are not correct, and the high gradients are due instead to normal heat flow and very low thermal-conductivity values. In spite of the presence of-low thermal-conductivity values in the midcontinent region, significant use could be made of geothermal energy in Kansas for space heating, thermal assistance, and heat-pump applications because the temperatures in the sedimentary section in much of Kansas are in excess of 40°C (104°F)

Heat flow and geothermal potential of Kansas

Temperature, thermal-conductivity measurements, and heat-flow values are presented for four holes in Kansas originally drilled for cooperative water-resources investigations by the Kansas Geological Survey and the U.S. Geological Survey. These holes cut most of the sedimentary section and were cased and allowed to reach temperature equilibrium. Several types of geophysical logs were run for these holes. Temperature data from an additional five wells also are presented. Temperature gradients in the sedimentary section vary over a large range (over 4:1), and significantly different temperatures occur at the same depth in different portions of the state. Temperatures as high as 34°C (93°F) occur at a depth of 500 m (1,650 ft) in the south-central portion of the state but are 28°C (82°F) or lower at that depth in other parts of the state. In addition to cuttings measurements, thermal conductivities were estimated from geophysical well-log parameters; useful results suggest more use of the technique in the future. With these results, geophysical well logs can be used to predict temperatures as a function of depth in areas for which no temperatures are available if heat flow is assumed. The extreme variation in gradients observed in the holes occurs because of the large contrast in thermal-conductivity values. Shale thermal-conductivity values appear to have been overestimated in the past; Paleozoic shales in Kansas have thermal-conductivity values of approximately 1.18 ± 0.03 Wm-1K-1. Conversely, evaporite and dolomite units have thermal conductivities of over 4 Wm-1K-1. In spite of the large variations of gradient, the heat-flow values throughout the holes do not vary more than 10%, and any water-flow effects which might be present from the lateral motion on any of the aquifers are less than 10%. The best estimates for heat flow in the four holes come from carbonate units below the base of the Pennsylvanian and range in value from 48 mWm-2 to 62 mWm-2. Two of the holes were drilled to the basement, and correlation of the heat flow with basement radioactivity suggests that the heat-flow/heat-production line postulated for the midcontinent by Roy, Blackwell, and Birch (1968) applies to these data. Because of the low thermal conductivity of the shales, the radiogenic-pluton concept should apply to the midcontinent. Thus, if very radioactive plutons can be identified, much higher temperatures may occur in the sedimentary section than have been thought possible in the past. However, the past overestimation of the shale-conductivity values suggests that some previous high heat-flow values in the midcontinent probably are not correct, and the high gradients are due instead to normal heat flow and very low thermal-conductivity values. In spite of the presence of-low thermal-conductivity values in the midcontinent region, significant use could be made of geothermal energy in Kansas for space heating, thermal assistance, and heat-pump applications because the temperatures in the sedimentary section in much of Kansas are in excess of 40°C (104°F)

A Priori Bounds on the Euclidean Traveling Salesman

It is proved that there are constants $c_{1}$, $c_{2}$, and $c_{3}$ such that for any set S of n points in the unit square and for any minimum-length tour T of S the sum of squares of the edge lengths of T is bounded by $c_{1} \log n$. (2) the number of edges having length t or greater in T is at most $c_{2}/t^{2}$, and (3) the sum of edge lengths of any subset E of T is bounded by $c_{3}|E|^{1/2}$. The second and third bounds are independent of the number of points in S, as well as their locations. Extensions to dimensions $d \u3e 2$ are also sketched. The presence of the logarithmic term in (1) is engaging because such a term is not needed in the case of the minimum spanning tree and several analogous problems, and, furthermore, we know that there always exists some tour of S (which perhaps does not have minimal length) for which the sum of squared edges is bounded independently of n

Worst-Case Growth Rates of Some Classical Problems of Combinatorial Optimization

A method is presented for determining the asymptotic worst-case behavior of quantities like the length of the minimal spanning tree or the length of an optimal traveling salesman tour of $n$ points in the unit $d$-cube. In each of these classical problems, the worst-case lengths are proved to have the exact asymptotic growth rate of $\beta _n^{{{(d - 1)} / d}}$, where $\beta$ is a positive constant depending on the problem and the dimension. These results complement known results on the growth rates for the analogous quantities under probabilistic assumptions on the points, but the results given here are free of any probabilistic hypotheses

Equidistribution of Point Sets for the Traveling Salesman and Related Problems

Given a set S of n points in the unit square [0, 1)2, an optimal traveling salesman tour of S is a tour of S that is of minimum length. A worst-case point set for the Traveling Salesman Problem in the unit square is a point set S(n) whose optimal traveling salesman tour achieves the maximum possible length among all point sets S C [0, 1)2, where JSI = n. An open problem is to determine the structure of S(n). We show that for any rectangle R contained in [0, 1 F, the number of points in S(n) n R is asymptotic to n times the area of R. One corollary of this result is an 0( n log n) approximation algorithm for the worst-case Euclidean TSP. Analogous results are proved for the minimum spanning tree, minimum-weight matching, and rectilinear Steiner minimum tree. These equidistribution theorems are the first results concerning the structure of worst-case point sets like S(n)

Researchers explore Arctic freshwater\u27s role in ocean circulation

A critical, but insufficiently understood, component of global change is the influence of Arctic freshwater input on water mass exchange between the Arctic Ocean and Atlantic and Pacific Oceans. Four of the Earth\u27s 10 largest river systems, the Mackenzie, Ob,Yenisei, and Lena, contribute water to the Arctic shore (Figure 1) from a vast watershed that drains continental interiors. This river discharge flows into the world\u27s largest contiguous continental shelf and supplies over 50% (1823 km3 ) of the riverine input to the Arctic Ocean

Lithologic Influences on Groundwater Recharge through Incised Glacial Till from Profile to Regional Scales: Evidence from Glaciated Eastern Nebraska

[1] Variability in sediment hydraulic properties associated with landscape depositional and erosional features can influence groundwater recharge processes by affecting soil-water storage and transmission. This study considers recharge to aquifers underlying river-incised glaciated terrain where the distribution of clay-rich till is largely intact in upland locations but has been removed by alluvial erosion in stream valleys. In a stream-dissected glacial region in eastern Nebraska (Great Plains region of the United States), recharge estimates were developed for nested profile, aquifer, and regional scales using unsaturated zone profile measurements (matric potentials, Cl− and 3H), groundwater tracers (CFC-12 and SF6), and a remote sensing-assisted water balance model. Results show a consistent influence of till lithology on recharge rates across nested spatial scales despite substantial uncertainty in all recharge estimation methods, suggesting that minimal diffuse recharge occurs through upland glacial till lithology whereas diffuse recharge occurs in river valleys where till is locally absent. Diffuse recharge is estimated to account for a maximum of 61% of total recharge based on comparison of diffuse recharge estimated from the unsaturated zone (0–43 mm yr−1) and total recharge estimated from groundwater tracers (median 58 mm yr−1) and water balance modeling (median 56 mm yr−1). The results underscore the importance of lithologic controls on the distributions of both recharge rates and mechanisms

Do Financial Incentives Help Low-Performing Schools Attract and Keep Academically Talented Teachers? Evidence from California

This study capitalizes on a natural experiment that occurred in California between 2000 and 2002. In those years, the state offered a competitively allocated $20,000 incentive called the Governor's Teaching Fellowship (GTF) aimed at attracting academically talented, novice teachers to low-performing schools and retaining them in those schools for at least four years. Taking advantage of data on the career histories of 27,106 individuals who pursued California teaching licenses between 1998 and 2003, we use an instrumental variables strategy to estimate the unbiased impact of the GTF on the decisions of recipients to begin working in low-performing schools within two years after licensure program enrollment. We estimate that GTF recipients would have been less likely to teach in low-performing schools than observably similar counterparts had the GTF not existed, but that acquiring a GTF increased their probability of doing so by 28 percentage points. Examining retention patterns, we find that 75 percent of both GTF recipients and non-recipients who began working in low-performing schools remained in such schools for at least four years.