Analysis of Hydraulic Fracture Closure in Laboratory Experiments

Abstract

Summary Conventional models of hydraulic fracture closure make assumptions about the fracture geometry and rock mechanical behavior. In this paper we present the results of scaled laboratory experiments. We show that deviations from conventional assumptions influence leak-off volumes, mechanical behavior, and pressure decline significantly. We discuss mechanisms that lead to these deviations from assumptions during fracture closure. Introduction Analysis of the pressure decline during closure of mini-hydraulic fractures is used in field practice to infer the leak-off coefficient and least in-situ stress, needed for determining net pressure. These are important parameters for the design of a propped hydraulic fracture. A routinely used method in the industry for analyzing the pressure decline is the use of the so-called G -plot,1 which was introduced by Nolte (see, e.g., Ref. 2). This model is based on certain assumptions, among which are linear elastic rock behavior and constant fracture area after shut-in. Nolte recognized that this last assumption is in practice not always met,3,4 and he introduced diagnostic methods to detect deviations from ideal behavior. He proposed the "3/4 rule" to identify the transition from extension to recession. In scaled laboratory experiments both radius growth after shut-in and radius recession were reported in materials with, respectively, low and higher permeability.5 In this paper we present the results of scaled laboratory experiments concerning fracture closure. While in field cases the pressure is usually the only source of information, in our experiments we obtain extensive information by measuring pressure, width, radius, and volume of the fracture, using advanced acoustic monitoring techniques.6,7 This enables us to identify the processes that occur during fracture closure independently from the measured pressure decline. The objective of this paper is first to validate the conventional modeling assumptions in our experiments, and second to investigate how possible deviations from ideal behavior can influence the leak-off rate and mechanical behavior of the fracture, and subsequently pressure decline and closure times. Possible deviations we want to address are radius changes after shut-in, surface roughness of the fracture, and plastic rock deformation. Experimental Setup and Method Scaling. We performed scaled model experiments of hydraulic fracture propagation and closure. The experiments are scaled in terms of energy rates associated with fluid flow, fracture opening, and rock separation.8 Leak-off is scaled by the fracture efficiency. In order to have sufficient time for measurements during fracture propagation, the time scale for the propagation phase is about 103 seconds. The fracture radius is approximately 0.10 m. These practical conditions require a relatively high fluid viscosity and low separation energy of the rock material. There are various length scales involved in hydraulic fracturing, which can be used for scaling up our experimental fracture size to field scale. Depending on the processes that take place, a length scale must be chosen. In our experiments, it is probably best to obtain a length scale from the fracture toughness or to use the length scale for the tip region obtained by an asymptotic solution for the stress field near the hydraulic fracture tip.9 This solution takes into account the sharp pressure drop near the tip and neglects fracture toughness. Experimental Setup. Fig. 1 shows a schematic view of the experimental setup used for the hydraulic fracturing experiments. Cubic blocks of 0.30 m size are loaded in a true triaxial machine to simulate in-situ stress states; no pore pressure can be applied. We used 0.1 mm thin Teflon sheets greased with vaseline to reduce friction between the block and the loading platens. Six linear variable differential transformers (LVDTs) measure the block deformation. The hydraulic fracture is oriented transversely to the wellbore wall, which was sealed with a 0.5-mm-thick glue layer. A 3-mm-deep notch was sawn in the wellbore wall to control the fracture location. The confining stress ? c perpendicular to the plane of the fracture is always smaller than both stresses ?h directed parallel with the fracture plane, which have equal values. The deviation of the stress inside the block from the expected value is smaller than 10% in the region of interest. During fracture propagation, a high-pressure pump injects fluid into the wellbore, at whose end a dead string is mounted where the wellbore pressure is measured. An LVDT, mounted with clamps in the wellbore, measures the fracture width with a measuring error of approximately 10%. The block extension during propagation is a measure for the fracture volume. The fracturing fluid we use is silicon oil which behaves approximately Newtonian at the shear rates of interest. Fig. 1 shows a schematic view of the ultrasonic measurements. During fracture propagation, two diffractions are measured, which we interpret as coming from the fluid front and fracture tip position.7 From the travel time of these diffractions and the material velocities we can construct the ray path, and calculate the fracture radius and a measure of the size of the nonpenetrated zone. In experiments on plaster with nonpenetrated zone sizes of 1 to 2 cm, this measure of the nonpenetrated zone size agreed well with the size of the dry zone measured after opening of the block (as is visible in Fig. 2). When the fracture stops growing, the diffraction disappears. Then, the ultrasonic shear-wave transmissions gave us the radius over which the fracture was open. These measurements have an accuracy of approximately ±1 cm. The Young's modulus is determined during loading of the block in the true triaxial machine. We determined the leak-off coefficient independently in a triaxial cell. In these leak-off experiments, we used the same fluid as was injected in the hydraulic fracturing experiments. Cylindrical cores (with 40 mm diam and 80 mm length) were hydrostatically pressurized, and at one of the axial rock faces fluid pressure was applied. The opposite face was connected to free air. The fluid pressure at the axial face of the core was kept constant, while the flow rate into the core was measured. In another type of leak-off experiment, the pressurization history of a fracture face was imitated. At one axial face of the core fluid pressure was applied for about the propagation time of the hydraulic fracture, after which the pump was stopped and the pressure dropped. From the pressure drop rate the leak-off rate can be calculated using the system compressibility. By making the decompression volume small, a similar initial pressure decline rate as in the hydraulic fracturing experiments was achieved.

Recent Developments in Multiscale and Multiphase Modelling of the Hydraulic Fracturing Process

“…However, the fractures tend to close after a hydraulic fracturing operation and thus suitable proppants have to be selected, blend in a certain ratio with the fracturing fluid, fill the fractures, and keep them open after fluid injection [2]. Therefore estimation of the residual openings [46,104,105] or the permeability of the fracture openings [106], which are filled with proppants, as well as the optimisation of the used proppants [107] is of great significance for EGR/EOR applications. A number of studies have focused on the transport of suspended proppant particles within the fracture and the interaction between the formation and the proppant.…”

“…Furthermore, factors such as measurements of the minimum in situ stress and permeability are significant for the design of hydraulic fractures, which affect several engineering applications, and therefore extended research has been conducted relating the changes in the rock permeability with in situ stresses [111][112][113][114][115] as well as the influence of the in situ stresses to the fracturing pattern (propagation and closure) on pressure sensitive materials [104]. It is significant to observe how individual studies, such as the aforementioned or others related to the influence of stress and deformation on the propagation of hydraulic fractures [116][117][118], become part of the bigger picture of hydraulic fracturing and can be connected with more recent studies focusing on the use and stability of the proppants in the fractures (as previously discussed). Recently more engineering applications have emerged where the fracking procedure is the dominant part.…”

Application of New Fall-Off Test Interpretation Methodology to Fractured Water Injection Wells Offshore Sakhalin

“…A number of possible explanations has been proposed, such as a nonuniform post-shut-in pressure profile, fracture surface roughness, plastic deformation around the fracture tip, and poroelasticity 10 . Within the framework of the current fall-off test analysis model, post shut-in length recession is based qualitatively on the results of Refs.…”

“…Within the framework of the current fall-off test analysis model, post shut-in length recession is based qualitatively on the results of Refs. 9,10 . These results are captured phenomenologically as…”

A computationally efficient approach to modeling contact problems and fracture closure using superposition method

“…This is especially the case for large scale subsurface fractures, such as those generated by hydraulic fracturing. Van Dam et al (2000) presented scaled laboratory experiments on hydraulic fracture closure behavior. Their work shows that the roughness of the fracture surfaces appears as a characteristic pattern of radial grooves and it is influenced by the externally applied stress.…”