DOI: 10.18419/darus-2816
title: Pressure and volumetric flux measurements intended to scale relative permeability under steady state, co-flow conditions, in a PDMS micromodel

description: The current repository contains raw data collected during a systematic laboratory study, examining the flow rate dependency of steady-state, co-injection of two-immiscible fluids within a microfluidic pore network model. The study is presented in the paper by Karadimitriou et al., 2023. The two fluids were the wetting phase (WP), FluorinertTM, FC770, and the non-wetting phase (NWP), deionized water mixed with ink. The two fluids were co-injected through a Poly-Di-Methyl-Siloxane (PDMS) micromodel.&lt;br&gt;
The objective of the study was to validate, as a proof of concept, the theoretically developed, generic, relative permeability scaling model taking into account the flow rate dependency. Also to verify the capability of detecting various invariant characteristic properties of the two-fluid and pore network system, such as the locus of flow conditions of equal relative permeabilities, the locus of critical flow conditions, and the intrinsic dynamic capillary pressure (IDCP) curve. Applications-wise, the degree of consistency between flow rate ratio and mobility ratio values, the IDCP curve, the locus of critical flow conditions, and the locus of equal relative permeabilities, as well as some associated invariant characteristic values, can be used for assessing the extent of end effects and for characterizing the flow as capillary- or viscous-dominated.&lt;br&gt;&lt;br&gt;

 &lt;b&gt;Main data &lt;/b&gt;&lt;br&gt;
Raw datasets acquired during the laboratory study, organized in 12 log files, each pertaining to a complete cycle of flow rate ratio scanning under constant volumetric flux of the WP or, equivalently, to constant capillary number value of the WP. In particular, 12 files with the generic name FC770_/A/_/B/.tar.gz, Table I, where /A/ and /B/ parameters indicate the Ca values and the corresponding WP volumetric fluxes examined per constant-Ca experiment (Table I) as follows.
Each of the 12 data files contains measured values of the volumetric fluxes of the WP, qw, and the NWP, qn, as well as the corresponding pressures, P&lt;sub&gt;w&lt;/sub&gt; and P&lt;sub&gt;n&lt;/sub&gt;, at the inlet ports of the microfluidic network.&lt;br&gt;&lt;br&gt;

 &lt;b&gt;Procedure followed for each constant–Ca experiment &lt;/b&gt;&lt;br&gt;
The term “experiment” pertains to a complete cycle of co-injecting the two phases at constant WP volumetric flux but with successive increases of the NWP flux. For every experiment, a fixed capillary number value, Ca&lt;sub&gt;i&lt;/sub&gt;, i = 1,…,12, is maintained, whereas the flow rate ratio takes successive values, rj, spanning across a domain between 0.1 and 10. The domain of flow conditions in the entire set of experiments is depicted in Karadimitriou et al., 2023, Figure 2.&lt;br&gt;
The typical cycle in every experiment comprises the following interventions:&lt;br&gt;
&lt;ul&gt;
&lt;li&gt; The micromodel is initially saturated with the WP. Then, both phases are injected into the microfluidic pore network.&lt;/li&gt;
&lt;li&gt; The WP is injected at a fixed volumetric flux to maintain a constant value of the capillary number, Ca, during the entire cycle of the experiment.&lt;/li&gt;
&lt;li&gt; The volumetric flux of the NWP starts at approximately one-tenth of the WP flux, and it is increased in successive steps (about 9 to 12) to 10 times larger; the result is approximately three orders of magnitude in successive increments. Initial co-injection is considered as primary drainage type. Successive co-injections at increasing steps of constant volumetric flux of the NWP are considered as secondary drainage type. In particular, there are two particular experiments that need to be referenced:&lt;/li&gt;
&lt;ul&gt;
&lt;li&gt; Experiment with Ca=3.83×10&lt;sup&gt;–5&lt;/sup&gt;, was run two times to check repeatability.&lt;/li&gt;
&lt;li&gt; Experiment with Ca=4.79×10&lt;sup&gt;-5&lt;/sup&gt;, whereby the flux of the NWP was increased r&lt;sub&gt;j&lt;/sub&gt; ∈ {0.2, 1.0, 2.0, 10.0} and then decreased, r&lt;sub&gt;j&lt;/sub&gt; ∈ {10.0, 8.0, 5.0, 0.8, 0.2}, and the co-injection type evolved from drainage to imbibition.&lt;/li&gt;
&lt;/ul&gt;
&lt;li&gt; After each step-up of the NWP flux, an adequate period of time is allowed for the interstitial flow to reach a steady state.&lt;/li&gt;
&lt;li&gt; As soon as the time-averaged pressure values showed signs of stabilization for both phases (kinetic stabilization), the entire microfluidic network was visually inspected in order to cross-check that the interstitial flow was also stabilized, or any fluctuations showed some kind of sustainable, short-cycle periodicity.&lt;/li&gt; 
&lt;li&gt; Following the establishment of steady-state conditions in the interstitial flow, the volumetric flux of the non-wetting phase was stepwise increased.&lt;/li&gt;
&lt;li&gt; After successive repeats with progressive stepwise increments of the volumetric flux of the NWP, the latter would have reached values ~10 times the value of the WP, corresponding to a flow rate ratio value, r = 10. Then, the experiment for that particular constant-Ca value stops.&lt;/li&gt;
&lt;li&gt; The system was then reconfigured to accommodate the next set of steady-state two-phase flows at a different constant-Ca value (constant WP flux, qw value). A new experiment pertaining to a new Ca value, repeating a new cycle as described above, is deployed.&lt;/li&gt;
&lt;/ul&gt;
Details on technical aspects of the materials (equipment, fluids, pore network) and the deployment of the experiments can be found in the paper by Karadimitriou et al. (2023)
description: CETONI QMixElements, v20190108