Analysis of Experimental Data for Flow Thorough Fractures using Geostatistics DICMAN ALFRED Dr. ERWIN PUTRA Dr. DAVID SCHECHTER

Fracture model W = 2b Cubic law of fractures From the experiments knowing pressure drop and flow rate, the aperture b can be calculated.

Actual core surface

Actual fracture surface 2b e Louis (1974) proposed that when e/D < 0.033, then f = 1 e/D >0.033, then f = ( (e/D)^1.5) e/D is defined relative roughness, where D is the hydraulic diameter = 2*2b Modified cubic law

Work by researchers, such as Neuzil and Tracy (1981), Brown (1987), Tsang and Tsang (1987), Tsang et al. (1988) and Moreno et al. (1988), have shown that the flow through a fracture follows preferred paths or flow channels due to the variation in fracture aperture. Previous Research Detailed measurements of fracture apertures have been obtained by joint surface profiling (Bandis et al. 1981, Brown and Scholz 1985, Gentier 1986), low melting point metal injection (Pyrak-Nole et al. 1987, Gale 1987), and resin casting technique (Hakami 1988, Gentier et al. 1989). BUT THEY ARE EXPENSIVE AND THE DATA MAY NOT BE A TRUE REPRESENTATIVE OF THE FRACTURE. Tsang (1990) chose a statistical description of a fracture with variable apertures by means of three parameters, performed numerical flow and transport experiments with them with particular emphasis of correlate the fracture geometry parameters. But concluded that the correspondence between observations and the hydrological properties is STILL AMBIGUOUS.

Our Approach Experimental data-DP,K,Q,K avg Expermental data analysis b,K f Q f, Q m Fracture surface generated randomly through geostatistics Simulation model with varying permeability distribution Study the effect of variance and friction factor on flow Simulate and match the pressure drop from experimental data Multiphase flow Upscaling to outcrop studies Include the friction factor to derive fracture permeabilty

Probability Density Function for Log Normal Distribution Ifis the mean andis the variance To standardize this, Similar to the normal distribution

How do we apply this to our research ??????

Variogram : summarises the relationship between the variance of the difference between measurements and the distance of the corresponding points from each other. Kriging : uses the information from a variogram to find an optimal set of weights that are used in estimating a surface at unsampled locations. Variogram and Kriging

Lag distance Co- variance Sill : describes where the variogram develops a flat region, i.e. where the variance no longer increases. Range : the distance between locations beyond which observations appear independent i.e. the variance no longer increases. Nugget variance : when the variogram appears not to go through the origin.

Kriging We can use the variogram to estimate values at points other than where measurements were taken. This process is termed kriging.

Variance 1800 Variance 2320 Variance 2200 What is the effect of changing variance on permeability ????

So lets get started !!!!

cc/min10 cc/min15 cc/min Pressure Drop Experimental Data Flow through fracture

Core56 var 200 Core40 var 100 Core20 var 30 VARIOGRAM MODELING

CORE 56.4 VAR 200

CORE 40 VAR 100

CORE 20 VAR 30

PERMEABILITY DISTRIBUTION CORE 56.4 VAR 200

PERMEABILITY DISTRIBUTION CORE 40 VAR 100

PERMEABILITY DISTRIBUTION CORE 20 VAR 30

The volume of the core is maintained constant Grid definition 31*15*15

RESULTS Sensitivity studies Pressure Drop match Rate comparisons between theoretical and simulated flow Permeability comparison Variance vs Overburden pressure Comparison between cubic law and modified cubic law

Future Considerations Extending it to outcrop studies Modeling 2-phase flow.