Adaptability of Power Law Exponential Decline Model for Hydraulically Fractured Unconventional Reservoirs during and After Linear Flow

Reserve estimation of unconventional formations is a new challenge to reservoir engineers due to the geological uncertainty and complex flow patterns evolving in the multi-fractured horizontal wells (MFHWs). Some predicting models have been presented and widely used in MFHWs exhibiting a long-term linear flow, such as stretched-exponential production-decline (SEPD), power law exponential decline (PLE) and Duong’s model. Plenty of successful field applications of these models seem to have demonstrated their availability and correctness especially in the transient linear flow period. Due to the limitation of reservoir boundaries or size of stimulated volume, any fractured tight reservoir will eventually exhibit a boundary-dominated-flow (BDF). The models above which show “goodness of fit” in linear flow may not be used or will cause great error when used to predict production in BDF period. This paper compared the newly developed PLE model with the traditional Arps’ hyperbolic decline model in terms of production historic match, decline rate and decline exponent during and after linear flow. The analysis result demonstrated that PLE model actually cannot match production decline characteristics as previously thought when only linear flow appears and it is a model which should be used in the transition period rather than linear flow period as applied in the past few years. The wrong usage of the model will cause great error to reserve estimation. The modified steps to predict production in different flow pattern are given in this work. The outcome of this work should help the industry to forecast production and ultimate reserve more accurately in tight oil and shale gas reservoirs.

Costs of accuracy determined by a maximal growth rate constraint

The present study is best understood as an extension and critique of two schools of thought. The first is that of Malloe and his students, among whom we number ourselves. It is to Maaloe that we are indebted for the idea that logarithmically growing bacteria assemble and use tibosomes in amounts that are optimally adjusted to yield the maximal growth rates supported by different media. Her, we begin our analysis by applying this optimization priciple to all the components of a logarithmically growing system. Our objective is to use the growth optimization constraint as a tool to explore the physiological limits on the accuracy of gene expression. This brings us to our second source of inspiration, which is Orgel's (1963) conception of a problem that Ninio (1982) has referred to as the ‘great error loop’.

GELATINASE AND THE GATES-GILMAN-COWGILL METHOD OF PEPSIN ESTIMATION

The Gates photographic film method for pepsin estimation as developed by Gilman and Cowgill measures an activity corresponding to that determined by the hemoglobin method of Anson and Mirsky rather than that resulting from the use of the gelatin viscosity technique. Therefore, the presence of gelatinase is not a source of great error in the gelatin film procedure.

Importance of Temperature and Humidity Control in Rubber Testing. II—Resistance to Abrasion

This study shows that in determining resistance to abrasion the temperature of the room or cabinet should be controlled within ± 1 ° C. in order to avoid significant errors in the results from this source. Below are shown the percentage differences per degree Centigrade obtained with each of the stocks. It must be remembered that this probably holds only over the range of temperatures studied and might change rapidly outside of this range. As the temperature changes from 15 ° C. to 35 ° C., the resistance to abrasion changes per degree Centigrade in the following manner: In the light of the present investigation there will be no great error in results caused by differences in relative humidity either with the raw or vulcanized stock. Where laboratories are equipped to condition raw and vulcanized stock for stress-strain tests, it appears that it would be advisable also to condition samples for determining resistance to abrasion. It would at least tend to produce more nearly uniform results by eliminating possible sources of small errors. As the relative humidity during exposure of raw stock increases from 10 per cent to 100 per cent, the resistance to abrasion per 1 per cent relative humidity changes roughly in the following manner: As these variations are small compared with the experimental error, it is evident that if the relative humidity does not vary over too wide a range its effect may be neglected. The temperature of storing the cured samples while maintaining a constant relative humidity has a negligible effect as in the case of relative humidity. As the temperature increases the resistance to abrasion per degree changes in the following manner: